AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

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AP Board 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న1.
1, -1, – 3, ……. A.P. యొక్క సామాన్య భేదంను రాయండి.
జవాబు :
సామాన్య భేదం d = a2 – a1 = 1 – 1 = -2

ప్రశ్న2.
0.6, 1.9, 3.2, ……… అంకశ్రేణి సామాన్యభేదంను కనుగొనండి.
జవాబు :
d = 1.9 – 0.6 = 1.3

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న3.
14, 11, 8, …. అంకశ్రేణిలో మొదటి ఋణ పదమును తెల్పండి.
జవాబు :
ఇచ్చిన అంకశ్రేణిని పొడిగించగా
14, 11, 8, 5, 2 – 1,…….
∴ మొదటి ఋణపదం = -1

ప్రశ్న4.
ఒక గుణ శ్రేణి నందు n వ పదం arn-1 అయిన r సూచించునది ………
A) సామాన్య భేదం
B) సామాన్య నిష్పత్తి
C) మొదటి పదం
D) వ్యాసార్ధం
జవాబు :
B

ప్రశ్న5.
ఒక A.P. లో n వ పదం an = 3 + 2n అయిన సామాన్య భేదం ఎంత ?
జవాబు :
an = 3 + 2n,
∴ a1 = 3+ 2 = 5,
a1 = 3 + 2(2) = 7
సామాన్య భేదం d = a2 – a1 = 7 – 5 = 2.
(Note: nవ పదంలో n గుణకమే సామాన్య భేదం అవుతుంది. ∴ d = 2)

ప్రశ్న6.
ఒక అంకశ్రేణి x – y,x, x + y, ….. యొక్క సామాన్య భేదంను కనుగొనుము.
జవాబు :
d = x – (x – y) = x – x + y =y.

ప్రశ్న7.
2a-b, 4a – 3b, 6a-5bశ్రేణి యందు సామాన్య భేదంను గణించండి.
జవాబు :
d = (4a – 3b) – (2a – b)
= 4a – 3b – 2a + b = 2a – 26

ప్రశ్న8.
ఒక గుణ శ్రేణి నందు మొదటి పదం 20 మరియు 4వ పదం 540 అయిన సామాన్య నిష్పత్తిని కనుగొనుము.
జవాబు :
గుణశ్రేణిలో a = 20,
4 వ పదం a4 = ar3 = 540,
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 1
∴ r = 3

ప్రశ్న9.
అంకశ్రేఢి యొక్క ‘n’ పదాల మొత్తంనకు సూత్రాన్ని తెల్పండి.
జవాబు :
Sn = \(\frac{n}{2}\)[22 + (n – 1)d] (లేదా)
Sn = \(\frac{1}{2}\)[a + l]

ప్రశ్న10.
ఒక అంకశ్రేణి నందు 3వ పదం 5, 7వ పదం 9 అయిన ఆ శ్రేఢి సామాన్య భేదం ఎంత ?
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 2
Short cut :
a7 – a3 ⇒ 4d = 9 – 5 = 4
∴ d = 1

ప్రశ్న11.
√2 సామాన్య నిష్పత్తి గల గుణశ్రేణినొక దానిని రాయండి.
జవాబు :
1, √2, 2, 2√2, ……….

ప్రశ్న12.
ఒక అంకశ్రేణిలో a25 – a12 =- 52 అయిన దాని సామాన్య భేదమును కనుగొనుము.
జవాబు :
a25 – a12 = (a + 24d) – (a + 11d) =-52
⇒ 240 – 11d = – 52
⇒ 13d = – 52
∴ d = \(\frac{-52}{13}\) = -4

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న13.
log 2 + log 4 + log 8 + log 16 + ….. శ్రేణిలోని పది పదముల మొత్తము
A) 45 log 2
B) 90 log 2
C) 10 log 2
D) 55 log 2
జవాబు :
log 2 + log 4 + log 8 + log 16 +… 10 పదాలు.
log 21 + log 22 + log 23 + log 24 + ….. + log 210
= log 2 + 2 log 2 + 3 log 2 + 4 log 2 + ……. + 10 log 2
= [1 + 2 + 3 + 4 + ……. + 10] log 2
= 55 log 2
(లేదా)
log (21 × 22 × 23 × …….. 210)
= log 21+ 2 + 3 + …… + 10
= log255 = 55 log 2

ప్రశ్న14.
24, 21, 18, ….. అంకశ్రేణిలో ఋణపదము అయ్యే మొదటి పదము ఏది ?
జవాబు :
ఇచ్చిన అంకశ్రేడిని కొనసాగించగా
24, 21, 18, 15, 12, 9, 6, 3, 0, – 3, ……
మొదటి ఋణ పదం a10 = -3

ప్రశ్న15.
మొదటి 100 సహజ సంఖ్యల మొత్తంను కనుగొనుము.
A) 4050
B)4500
C) 5500
D) 5050
జవాబు :
D మొదటి n సహజ సంఖ్యల మొత్తం = \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
n = 100, మొదటి 100 సహజ సంఖ్యల మొత్తం
\(\frac{100 \times 101}{2}\) = 50 × 101 = 5050

ప్రశ్న16.
a, b, cలు గుణశ్రేణిలో ఉంటే be a, Cలలో తెల్పండి.
జవాబు :
a, b, c లు A.P. లో ఉంటే b – a = c – b
⇒ 2b = a + c ⇒ b = \(\frac{a+c}{2}\)

ప్రశ్న17.
గుణశ్రేణి 3, .3√3 , 9, ……… లో ఎన్నవ పదం 243 అగును ?
జవాబు :
3, 3√3, 9, …………
a = 3, r = \(\frac{a_{2}}{a_{1}}=\frac{3 \sqrt{3}}{3}\) = √3, an = 243
a 3 G.P లో an = a.rn-1 = 243
3(√3)n-1 = 243
= (√3)n-1 = \(\frac{243}{3}\) = 81
⇒ 3n-1/2 = 34 ⇒ \(\frac{\mathrm{n}-1}{2}\) = 4 ⇒ n – 1 = 8
∴ n = 9
9వ పదం 243 అవుతుంది.
(లేదా)
ఇచ్చిన G.P పొడిగించగా
3, 3√3, 9, 9√3, 27, 27√3, 81, 81√3, 243, ……
9వ పదం 243 అవుతుంది.

ప్రశ్న18.
x, x + 2, x + 6 లు గుణశ్రేణిలో మూడు వరుస పదాలైన ‘X’ విలువను కనుగొనుము.
జవాబు :
x, x + 2, x + 6 లు G.Pలో మూడు వరుస పదాలు అయిన
\(\frac{a_{2}}{a_{1}}=\frac{a_{3}}{a_{2}} \Rightarrow \frac{x+2}{x}=\frac{x+6}{x+2}\)
(x + 2)2 = x(x + 6)
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 3
⇒ 4 = 6x – 4x ⇒ 4 = 2x ⇒ x = \(\frac{4}{2}\) = 2

ప్రశ్న19.
ఒక అంకశ్రేణిలో మొదటి రెండు పదాలు వరుసగా -3 మరియు 4 అయితే 21 వ పదంను కనుగొనుము.
జవాబు :
మొదటి పదం a1 = a = -3,
రెండవ పదం a2 = 4
∴ d = a2 – a1 = 4 – (- 3) = 7.
21వ పదం an = a + 20 d
=-3 + 20 (7) = 137

ప్రశ్న20.
ఒక అంకశ్రేణిలో a18 – a14 = 32 అయితే సామాన్య భేదం ఎంత ?
జవాబు :
a18 – a14 = 32 ⇒ 4d = 32
d = \(\frac{32}{4}\) = 8

ప్రశ్న21.
ఒక అంకశ్రేణిలో a = 1, an = 20 మరియు Sn = 399 అయిన n విలువను కనుగొనుము.
జవాబు :
a = 1, an = 1 = 20, Sn = 399
Sn = \(\frac{n}{2}\) [a + l] = 399
⇒ \(\frac{n}{2}\)[1 + 20] = 399
⇒ n(21) = 399 × 2
⇒ \(\frac{399 \times 2}{21}\) = 19 × 2 = 38

ప్రశ్న22.
\(\frac{1}{3}, \frac{1}{9}, \frac{1}{27}\) ……. అనే గుణశ్రేణిలో వన్నవ పదం \(\frac{1}{2187}\) అవుతుంది ?
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 4
(లేదా)
\(\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \frac{1}{81}, \frac{1}{243}, \frac{1}{729}, \frac{1}{2187}\) (గుణశ్రేణిని పోడిగించగా)
∴ 7వ పదం 3787 అవుతుంది.

ప్రశ్న23.
4, a, 9 గుణశ్రేణిలో ఉంటే a విలువ ఎంత ?
జవాబు :
4, a, 9 లు G. P. లో ఉంటే \(\frac{a_{2}}{a_{1}}=\frac{a_{3}}{a_{2}}\)
⇒ \(\frac{a}{4}=\frac{9}{a}\) ⇒ a2 = 9 × 4 = 36
∴ a = \(\sqrt{36}\) = ± 6.

ప్రశ్న24.
\(\sqrt{3}, \sqrt{12}, \sqrt{27}\) అంకశ్రేఢిలోని తరువాత పదంను రాయండి.
జవాబు :
\(\sqrt{3}, \sqrt{12}, \sqrt{27}=\sqrt{3}, \sqrt{4 \times 3}, \sqrt{9 \times 3}\)
= \(\sqrt{3}, 2 \sqrt{3}, 3 \sqrt{3}\)
∴ తరువాత పదం 4√3 = \(\sqrt{48}\)

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న25.
అంకశ్రేణి యొక్క పదాంతరము ‘2’ అయిన a10 – a5 విలువ ఎంత?
జవాబు :
d = 2, ∴ a10 – a5 = 5d = 5(2) = 10

ప్రశ్న26.
గుణశేరిలోని 5వ పదము 32 మరియు 7వ పదము 128. అయిన గుణశ్రేఢి సామాన్య నిష్పత్తిని కనుగొనుము.
జవాబు :
G.P లో a5 = ar4 = 32; a7 = ar6 = 128
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 5
r2 = 4 ⇒ r = 4 = ± 2

ప్రశ్న27.
log2 2, log2 4, log2 8 అంకశ్రేణి యొక్క సామాన్య భేదము 1 అని చూపండి.
జవాబు :
log2 2 = 1,
log2 4 = log2 22 = 2 log2 2 = 2
∴ a1 = 1, a2 = 2
∴ సామాన్య భేదం a2 – a1 = 2 – 1 = 1

ప్రశ్న28.
క్రింది సంఖ్యల జాబితాలో అంకశ్రేణి ఏది ?
A) 1, 3, 6, 10, 15, ………
B) 100, 80, 60, 40, …….
C) 2, 4, 8, 16, ……
D) 3, 3, 4, 4, 5, 5, …….
జవాబు :
B) 100, 80, 60, 40, …….

ప్రశ్న29.
క్రింది సంఖ్యల జాబితాలో అంకశ్రేణి కానిది ఏది ?
A) 1, 2, 3, 4, ……..
B) 3, 3, 3, 3, ……..
C) 6, 3, 0, – 3, ……
D) 6, 4, 1, – 3, ……..
జవాబు :
D) 6, 4, 1, – 3, ……..

ప్రశ్న30.
అంకశ్రేణికి ఉదాహరణను రాయండి.
జవాబు :
3, 6, 9, 12, ………….

ప్రశ్న31.
అంకశ్రేణికి చెందిన క్రింది ఏది అసత్యం ?
A) జాబితాలోని రెండు వరుస సంఖ్యల మధ్య గల భేదం స్థిరము.
B) పరిమిత అంకశ్రేణికి చివరి పదము ఉంటుంది.
C) జాబితాలోని రెండు వరుస సంఖ్యల నిష్పత్తి స్థిరము.
D) అపరిమిత అంకశ్రేణికి చివరి పదం ఉండదు.
జవాబు :
C) జాబితాలోని రెండు వరుస సంఖ్యల నిష్పత్తి స్థిరము.

ప్రశ్న32.
5, 2, -1, – 4, ……. శ్రేణిలో k + 1 వ పదము 5 – 3k అయిన kవ పదంను కనుగొనుము.
జవాబు :
5, 2, -1, – 4, ……. అంకశ్రేఢి (A.P.)లో కలవు. .
a = 5, d = 2-5 = -3
ak+1 = 5 – 3k అయిన
ak = ak+1 + (- 3) = 5 – 3k – 3
kవ పదము ak = 2 – 3k.

ప్రశ్న33.
ఒక అంకశ్రేణిలో a25 – a20 = 60 అయిన a15 – a10 విలువ ఎంత ?
జవాబు :
a25 – a20 = 60 ⇒ 5d = 60 …… (1)
ఇప్పుడు a15 – a10 = 5d = 60 [(1) నుండి]
(లేదా)
a25 – a20 = a15 – a10 = 60

ప్రశ్న34.
4, 10, 16, 22, ….. ఇంకశ్రేణిలో 10వ పదము ఎంత?
జవాబు :
ఇచ్చిన A.P. : 4, 10, 16, 22, ……
a = 4, d = 10 – 4 = 6,
a10 = a + 9d = 4 + 54 = 58
(లేదా)
ఇచ్చిన A.P. ని పొడిగించగా
4, 10, 16, 22, 28, 34, 40, 46, 52, 58
∴ 10వ పదము = 58

ప్రశ్న35.
క్రింది వానిని జతపరచడంలో సరైన సమాధానాన్ని ఎన్నుకొనుము..

i) అంకశ్రేణిలో 1వ పదము a) arn-1
ii) అంకశ్రేణిలో n పదాల మొత్తం b) \(\frac{n}{2}\)[2a+(n – 1)d]
iii)గుణ శ్రేణిలో 1వ పదము c) a + (n – 1)d

A) i-a, ii-b, iii-c
B) i-c, ii-b, iii-a
C) i-c, ii-a, iii- b
D ) i-b, ii-a, iii-c
జవాబు :
B) i-c, ii-b, iii-a

ప్రశ్న36.
\(\frac{1}{4}, \frac{-1}{4}, \frac{-3}{4}, \frac{-5}{4}\) ……. అంకశ్రేణి యొక్క సామాన్య భేదంను కనుగొనుము.
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 6

ప్రశ్న37.
ఒక అంకశ్రేణి మొదటి పదం a = 4, పదాంతరం d =-3 అయిన ఆ శ్రేఢి 4వ పదమును రాయండి.
జవాబు :
a = 4, d = -3.
4వ పదం aa = a + 3d ,
= 4 + 3(- 3) = 4 – 9 = -5

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న38.
ఇచ్చిన పటంలో x విలువ ఎంత ?
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 7
జవాబు :
\(\frac{1}{2}\)

ప్రశ్న39.
2, \(\frac{5}{2}\), 3, \(\frac{7}{2}\), 4, ………… A.P. లో తరువాత పదంను కనుగొనుము.
జవాబు :
2, 1, 3, . , ……. తరువాత పదం
∴ a = 2, d = \(\frac{5}{2}\) – 2 = \(\frac{1}{2}\)
∴ a6 = a + 5d
= 2 + 5(½) = 2 + \(\frac{5}{2}\) = \(\frac{9}{2}\)
(లేదా)
ఆ శ్రేఢ 2, 2½, 3, 3½, 4, 4½
కావలసిన పదం = 4½ = \(\frac{9}{2}\)

ప్రశ్న40.
3, 3 + √2, 3 + 2√2, 3 + 3√2, ……….. A.P. యొక్క సామాన్య భేదంను కనుగొనుము.
జవాబు :
సామాన్య భేదం d = a2 – a2
= (3 + √2) – 3 = √2

ప్రశ్న41.
5, 1, -3, -1, ….. ఒక అంకశ్రేణిని ఏర్పరుస్తాయి అని చూపుము.
జవాబు :
ఇచ్చిన A.P. : 5, 1, – 3, – 7, – 11, – 15,
– 19, – 23, – 27, – 31
(లేదా)
a = 5, d = a2 – a1 = 1 – 5 = -4,
a10 = a + 9d = ?
a10 = 5 + 9(-4) = 5 – 36 = -31.

ప్రశ్న42.
√2, √8, \(\sqrt{18}, \sqrt{32}\), ….. అంకశ్రేణి లో తరువాత పదంను రాయండి.
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 8

ప్రశ్న43.
21, 18, 15, …… శ్రేణిలో – 81 ఎన్నవ పదము ?
జవాబు :
a = 21, d = 18 – 21 = -3, an = -81,
n = ?
an = a + (n – 1)d = – 81
⇒ 21 + (n – 1) (- 3) = – 81
⇒ (n – 1) (- 3) = – 81 – 21 = – 102
⇒ n – 1 = \(\frac{-102}{-3}\) = 34
∴ n = 34 + 1 = 35

ప్రశ్న44.
21, 18, 15, …… A.P. లో సున్న ఎన్నవ పదం అవుతుంది ?
జవాబు :
21, 18, 15, 12, 9, 6, 3, 0, …… (ఇచ్చిన A.P. ని పొడిగించగా).
∴ 8వ పదం సున్న అవుతుంది.
(లేదా)
an = a + (n – 1)d = 0
⇒ 21 + (n – 1) (- 3) = 0
⇒ (n – 1) (- 3) = – 21
⇒ n – 1 = \(\frac{-21}{-3}\) = -21
∴ n = 7 + 1 = 8

ప్రశ్న45.
loga a, loga a4, loga a7, loga a10 ………. ఒక
A) గుణశ్రేఢి
B) అంకశ్రేఢి
C) హరాత్మక శ్రేఢి
D) ఏదీకాదు
జవాబు :
B) అంకశ్రేఢి

loga a, 4 loga a, 7 loga a, 10 loga a గా ఇచ్చిన A.P. ని రాయవచ్చును.
a2 – a1 – 4 loga – log a = 3 log a
a3 – a2 = 7 log a – 4 log a = 3 log a
a4 – a3 = 10 log a – 7 log a = 3 log a
∴ సామాన్య భేదం సమానం. కావున అంకశ్రేణి.
(లేదా)
దత్తాంశము loga a, loga a4, loga a7, loga a10… a2 – a1 = logaa4 – log a
= log \(\frac{a^{4}}{a}\) = log a3

a3 – a2 = loga a7 – loga a4
= log \(\frac{a^{7}}{a^{4}}\) = log a3

a4 – a3 = logaa10 – logaa7
= log \(\frac{a^{10}}{a^{7}}\) = log a3
∴ సామాన్య భేదం సమానం. కావున అంకశ్రే.

ప్రశ్న46.
మొదటి 10 సహజ సంఖ్యల మొత్తం ఎంత ?
జవాబు :
\(\frac{10 \times 11}{2}\) = 55

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న47.
1, 8, 4, 16, 2 సంఖ్యలను r = \(\frac{1}{2}\) అయ్యే విధంగా గుణ శ్రేణిలో అమర్చుము.
జవాబు :
1, 8, 4, 16, 2 లను r = \(\frac{1}{2}\) అయ్యే విధంగా గుణ శ్రేణిలో అమర్చగా
16, 8, 4, 2, 1 (∵ r< 1 కాబట్టి GP అవరోహణ’ క్రమంలో ఉంటుంది.)

ప్రశ్న48.
మొదటి పదం 3.5, పదాంతరము సున్న (0) గా గల అంకశ్రేఢి 108వ పదము ఎంత ?
జవాబు :
a = 3.5, d = 0
∴ a108 = a + 107d = 3.5 + 0 = 3.5

ప్రశ్న49.
ఒక A.P. లో a1 = 2 మరియు a3 = 18 అయిన a2 విలువ ఎంత ?
జవాబు :
a1 = 2, a + 2d = 18 = 2 + 2d = 18
⇒ 2d = 16 ⇒ d = 8
a2 = a + d = 2 + 8 = 10
(లేదా)
a2 = \(\frac{a_{1}+a_{3}}{2}=\frac{2+18}{2}\) = 10

ప్రశ్న50.
3, 8, 13, 18, …., 78 శ్రేణిలోని పదాల సంఖ్యను కనుగొనుము.
జవాబు :
3, 8, 13, 18, …., 78
a = 3, 4 = 5, a = 78, n = ?
an = a + (n – 1)d = 78
⇒ 3 + (n – 1) 5 = 78
⇒ (n – 1) 5 = 75 ⇒ n – 1 = 15
∴ n = 16.

ప్రశ్న51.
(x + 2), 2x, (2x + 2) లు అంకశ్రేణిలో 3 వరుస పదాలైతే x విలువను కనుగొనుము.
జవాబు :
x + 2, 25, 2x + 2 లు A.P. లో కలవు.
(2x) – (x + 2) = (2x + 2) – 2x
x – 2 = 2 ⇒ x = 4

ప్రశ్న52.
క్రింధి వానిలో ఏవి అంకశ్రేణిలో గల లంబకోణ త్రిభుజ భుజాలు అవుతాయి ?
A) 6, 8, 10
B) 3, 5, 7
C) 2, 4, 6
D) పైవన్నీ
జవాబు :
A) 6, 8, 10

ప్రశ్న53.
7, 13, 19, ……. అంకశ్రేణిలో 10వ పదమును కనుగొనుము.
జవాబు :
a = 7, d = 13 – 7 = 6, a10 = ?
10వ పదం = a + 9d
= 7 + 9(6) = 7 + 54 = 61
(లేదా)
ఇచ్చిన A.P. ని 10 పదాల వరకు పొడిగించగా, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61
10వ పదం a10 = 61

ప్రశ్న54.
– 11, -7, – 3, 1, ….. జాబితా ఒక అంకశ్రేఢి అని నిరూపించండి.
జవాబు :
– 11, -1, -3, 1, 5, …..
a2 – a1 = (-7) – (-11) = 4
a3 – a2 = (-3) – (-7) = 4
a4 – a3 = 1 – (- 3) = 4
సామాన్య భేదం అన్ని సందర్భాలలో సమానం.
∴ అంకశ్రేఢి అవుతుంది.

ప్రశ్న55.
25, 20, 15, ….. శ్రేణిలో ఎన్నవ పదం మొదటి ఋణ సంఖ్య అవుతుంది ?
జవాబు :
25, 20, 15, …… లో మొదటి ఋణ పదం = ?
a = 25, d = 20 – 25 =-5, an < 0
a + (n – 1)d < 0
⇒ 25 + (n-1) (-5) < 0
⇒ (n – 1) (-5) < – 25 ⇒ n – 1 > \(\frac{-25}{-5}\) = 5
⇒ n – 1 > 5 = n > 6.
కావున 7వ పదం మొదటి ఋణసంఖ్య అవుతుంది.
(లేదా)
ఇచ్చిన A.P. : 25, 20, 15, 10, 5, 0, – 5
మొదటి ఋణ సంఖ్య 7వ పదము.

ప్రశ్న56.
ఒక అంకశ్రేణి యొక్క n వ పదం an = 2n + 3 అయిన 12వ పదంను కనుగొనుము.
జవాబు :
an = 2n + 3 ⇒ a12 = 2(12) + 3 = 27

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న57.
ఒక అంకశ్రేణి యొక్క nవ పదము 7 – 2n అయిన ఆ అంకశ్రేఢి సామాన్య భేదంను తెల్పండి.
జవాబు :
a = 7 – 2n
∴ a1 = 7 – 2(1) = 5
a2 = 7 – 2(2) = 3
d = a2 – a1 = 3 – 5 = – 2.
(లేదా)
an = 7 – 2n of n గుణకం = d = – 2

ప్రశ్న58.
x, y, z లు అంకశ్రేణిలో ఉంటే క్రింది ఏది సత్యం ?
A) y = \(\frac{x+z}{2}\)
B) 2y = x + z
C) y – x = z – y
D) పైవన్నీ
జవాబు :
D) పైవన్నీ

ప్రశ్న59.
24, 21, 18, …. అంకశ్రేణి యొక్క S4 = S13 =78 అయిన ఆ శ్రేఢి యొక్క 5వ పదం నుండి 13వ పదం వరకు గల పదాల మొత్తం ఎంత ?
జవాబు :
0,

S13 = S4 + S(5 నుండి 13 వరకు),
⇒ S13 – S4 = S(5 నుండి 13 వరకు) (∵S13 = S4)
0 = S(5 నుండి 13 వరకు)

ప్రశ్న60.
క్రింది వానిలో అంకశ్రేఢి యొక్క ఏది సత్యం ?
A) an = S + Sn-1
B) an = a + (n – 1) d
C) Sn = n(2a + (n – 1) d]
D) పైవన్నీ
జవాబు :
B) an = a + (n – 1) d

ప్రశ్న61.
ఒక అంకశ్రేణి 17వ పదం, 10వ పదంకన్నా 21 ఎక్కువ అయిన సామాన్యభేదం ఎంత ?
జవాబు :
a17 = a17 + 21 ⇒ a17 – a10 = 21
⇒ 7d = 21 =d = 3

ప్రశ్న62.
1 మరియు 250ల మధ్య గల 4 యొక్క గుణిజాల సంఖ్య ఎంత ?
జవాబు :
1, 250 మధ్యగల 4 యొక్క గుణిజాలు
4, 8, 12, …….., 248
a = 4, d = 8 – 4 = 4, a = 248, n = ?
an = a + (n – 1)d = 248
⇒ 4 + (n – 1) 4 = 248
⇒ (n – 1) 4 = 244
n – 1 = \(\frac{244}{4}\) = 61
n = 61 + 1 = 62
1, 250 మధ్యగల 4 యొక్క గుణిజాల సంఖ్య = 62
(లేదా )
1, 250 మధ్యగల గుణిజాలు … (4, 8, 12, 16, 20, ………, 248)
= (4 × 1, 4 × 2, 4 × 3, ….., 4 × 62)
∴ 1, 250 మధ్యగల 4 యొక్క గుణిజాల సంఖ్య = 62

ప్రశ్న63.
ఒక అంకశ్రేఢ a2 = 6 మరియు a7 = – 4 అయిన an = 0 అయ్యేట్లు n విలువను కనుగొనుము.
జవాబు :
a7 – a2 = 5d = (- 4) – (6) = – 10
d = = =-2
a = a1 = 6 – (-2) = 8, d = -2
an = 0, n = ?
an = a + (n – 1)d = 0
= 8 + (n – 1) (-2) = 0
= (n – 1) (-2) = -8
= n – 1 = \(\frac{-8}{-2}\) = 4
n = 4 + 1 = 5.
(లేదా)
d = -2
ఆ శ్రేఢి a1, a2, a3, a4, a5, a6, a7
8, 6, 4, 2, 0, -2, -4
∴ n – 5

ప్రశ్న64.
– 11, – 8, – 5, ……. 49 అంకశ్రేణిలో చివరి 2. నుండి 4వ పదమును రాయండి.
జవాబు :
– 11, – 8, – 5, ……, 49 అంకశ్రేణిలో చివరి నుండి 4వ పదము = 40.
ఆ శ్రేఢి = -11, -8, -5,…… 40, 43, 46, 49

ప్రశ్న65.
a = -1.25, d = -0.25 అయిన a్మను లెక్కించండి.
జవాబు :
a. = – 1.25, d = 0.25
a = a + 3d
= (- 1.25) + 3(-0.25)
= 1.25 – 0.75 = -2,

ప్రశ్న66.
ప్రవచనం-1 : అంకశ్రేఢి యొక్క nవ పదం an = a.rn-1
ప్రవచనం-II : గుణశ్రేఢి యొక్క nవ పదం an = a + (n – 1) d
A) I సత్యం, II అసత్యం
B) I అసత్యం, II సత్యం
C) I మరియు II లు రెండూ సత్యం
D) I మరియు II లు రెండూ అసత్యం
జవాబు :
D) I మరియు II లు రెండూ అసత్యం

ప్రశ్న67.
2, 7, 12, ……. అంకశ్రేణిలో 10 పదాల మొత్తం ఎంత ?
జవాబు :
a = 2, d = 7 – 2 = 5, an = 10, Sn = ?
S = \(\frac{n}{2}\) [2a + (n – 1)d
= \(\frac{10}{2}\) [4 + 9(5)] = 5(49) = 245

ప్రశ్న68.
ఒక అంకశ్రేణిలో a = 7, a13 = 35 అయిన S13 = 273 అని చూపుము.
జవాబు :
a = 7, a13 = 1 = 35; S13 = ?, n = 13.
Sn = \(\frac{n}{2}\)[a + l]
= \(\frac{13}{2}\) [7+ 35] = 13 × 21 = 273

ప్రశ్న69.
– 37, – 33, – 29, ….. అంకశ్రేణిలో 12 పదాల మొత్తంను కనుగొనుము.
జవాబు :
a = – 37, d = – 33 – (-37) = 4, n = 12 1.
Sn = \(\frac{n}{2}\) [2a + (n – 1)d] .
= \(\frac{12}{2}\) [2(-37) + 11(4)]
= 6 (-74 + 44) = 6 (30) = – 180

ప్రశ్న70.
S = {x/x అనేది 2n + 3, n వ పదంగా గల అంకశ్రేణిలోని పదము, మరియు n < 6} అయిన S సమితిని రోస్టర్ రూపంలో రాయండి.
జవాబు :
an = 2n + 3
n = 1, a1 = 2(1) + 3 = 5,
a2 = 2(2) + 3 = 7,
a3 = 2(3) + 3 = 9,……..
S = {5, 7, 9, 11, 13, 15}

ప్రశ్న71.
ఒక త్రిభుజంలోని కోణాలు సామాన్య భేదం 10గా గల అంకశ్రేణిలో ఉంటే ఆ కోణాలను కనుగొనుము.
జవాబు :
మూడు కోణాలు a, a + d, a + 2d అనుకొనుము.
(∵అంకశ్రేఢిలో కలవు), d = 10 మూడు కోణాల మొత్తం .
a + a + d + a + 2d = 180°
3a + 3d = 1800
3a + 30 = 180° ( d = 10)
3a = 180 – 30 = 150°
a = 50°
∴ మూడు కోణాలు 50, 60, 70°.

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న72.
6 చే భాగింపబడే మొదటి 40 ధనపూర్ణ సంఖ్యల మొత్తంను లెక్కించండి.
జవాబు :
6 చే భాగింపబడే మొదటి 40 ధనపూర్ణ సంఖ్యలు
6, 12, 18, ……….., 40 పదాలు
a = 6, d = 12 – 6 = 6, an = 40, Sn = ?
Sn = \(\frac{n}{2}\) [2a + (n – 1)d]
= \(\frac{40}{2}\)[12 + 39 × 6]
= 20 × 246 = 4920
(లేదా)
(6 + 12 + 18 + ……. + 40 పదాలు )
= 6(1 + 2 + 3 + 4 + …. + 40]
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 9
= 3 × 40 × 41 = 4,920.

ప్రశ్న73.
అంకశ్రేణి n వ పదం an = 9 – 5n అయిన ఆ అంకశ్రేఢి మొదటి 15 పదాల మొత్తం ఎంత ?
జవాబు :
an = 9 – 5n
a1 = a = 9-5(1) = 4
a2 = 9-5(2) = -1
d = a2 – a1 = -1 – 4 = -5
n = 15, Sn = ?
Sn = \(\frac{n}{2}\) [2a + (n – 1)d]
= \(\frac{15}{2}\) [8 + 14 (-5)] = \(\frac{15}{2}\)(-62)
=- 465

ప్రశ్న74.
ఒక అంకశ్రేణిలో n పదాల మొత్తం 2n2 + 3n అయిన ఆ అంకశ్రేణి సామాన్యభేదం 4 అని చూపండి.
జవాబు :
Sn = 2n2 + 3n
S1 = a1 = 2(1)2 + 3(1) = 5
S2 = a1 + a2 = 2(2)2 + 3(2)
= 8 + 6 = 14
a2 = 14 – 5 = 9
∴ d = a2 – a1 = 9 – 5 = 4

ప్రశ్న75.
ఒక అంకశ్రేణి n పదాల మొత్తం 3n2 + 5n అయిన ఆ శ్రేఢి యొక్క 2 వ పదంను రాయండి.
జవాబు :
Sn = 3n2 + 5n
S1 = a1 = 3(1)2 + 5(1) = 8
S2 = a1 + a2 = 3(2)2 + 5(2) = 22
a2 = 22 – a1 = 22 – 8 = 14
(లేదా)
a2 = S2 -S1
= [3(2)2 + 5(2)] – [3(1)2 + 5(1)]
= 22 – 8 = 14

ప్రశ్న76.
a7 = 4, d = 2 మరియు S8 = – 8 అయిన ఆ శ్రేణిలో S9 = 0 అని చూపుము.
జవాబు :
a7 = 4, d = 2
a + 6d = 4 ⇒ a + 6(2) = 4
⇒ a + 12 = 4 .
⇒ a = -8
a = -8, d = 2 .

Sn = \(\frac{n}{2}\)[2a + (n – 1]d]
= \(\frac{9}{2}\)[2 (-8) + (9 – 1) (2)]
= \(\frac{9}{2}\)[- 16 + 16] = 0
∴ S9 = 0

ప్రశ్న77.
100 నుండి 200 వరకు గల బేసి సంఖ్యల మొత్తం ఎంత ?
జవాబు :
100, 200 మధ్యగల బేసి సంఖ్యలు
101, 103, 105, ….., 199
a = 101, d = 2, an = 199, n = ?, Sn = ?
an = a + (n – 1)d = 199
⇒ 101 + (n – 1) (2) = 199
⇒ (n – 1) (2) = 199 – 101 = 98
⇒ n – 1 = \(\frac{98}{2}\) = 49
∴ n = 49 + 1 = 50
S = \(\frac{n}{2}\) [2a + (n – 1)d]
= \(\frac{50}{2}\) [202 + 49 × 2]
= 25 × 300 = 7500
(లేదా)
100 నుండి 200 వరకు గల బేసి సంఖ్యల మొత్తం ‘= (1 నుండి 200 వరకు గల బేసి సంఖ్యల మొత్తం)
– (1 నుండి 100 వరకు గల బేసి సంఖ్యల మొత్తం)
= (100)2 – (50)2 = 10000 – 2500 = 7500

ప్రశ్న78.
మొదటి n బేసి సంఖ్యల మొత్తాన్ని కనుగొనుము.
జవాబు :
1, 3, 5, …, n పదాలు , a = 1, d = 2
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 10

ప్రశ్న79.
క్రింది వానిలో గుణశ్రేఢి ఏది ?
A) 6, 12, 24, ….
B) 1, 4, 9, 16, ……
C) 0, 3, 9, 27, …
D) పైవన్నీ
జవాబు :
A) 6, 12, 24, ….

ప్రశ్న80.
ఒక గుణ శ్రేఢి మొదటి పదం ar2 మరియు సామాన్య. నిష్పత్తి r అయిన ఆ శ్రేఢి 5వ పదంను రాయండి.
జవాబు :
మొదటి పదం a = a1 = ar,
సామాన్య భేదం = r
a2 = ar3r.r = ar3
a3 = ar4,
a4 = ar5
∴ a5 = ar6
(లేదా)
an = ar2, r = r, n = 5
∴ an = arn-1
= as = ar2(r)5-1 = ar2r4
a5 = ar6

ప్రశ్న81.
\(\frac{1}{16}, \frac{1}{64}, \frac{1}{256}\) ….. గుణశ్రేణి సామాన్య నిష్పత్తి ఎంత ?
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 11

ప్రశ్న82.
క్రింది వానిలో సామాన్య నిష్పత్తి 3 గా గల గుణ శ్రేణి ఏది ?
A) 1, 3, 9, 27, ….
B) 5, 15, 45, 135,
C) 2, 6, 18, 54, ..
D) పైవన్నీ
జవాబు :
D) పైవన్నీ

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న83.
x, \(\frac{4 x}{3}, \frac{5 x}{3}, 2 x, \frac{7 x}{3}\) …….. అంకశ్రేణిలో 7వ పదమును కనుగొనుము.
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 12

ప్రశ్న84.
మొదటి పదం a = 3, సామాన్యనిష్పత్తి r = 2 గా గల గుణశ్రేణిని రాయండి.
జవాబు :
a = 3, r = 2గా గల గుణశేథి 3, 6, 12, 24, …

ప్రశ్న85.
64, -32, 16, – 8, … గుణశ్రేఢి అని చూపుము.
జవాబు :
64, -32, 16, – 8, …….
\(\frac{a_{2}}{a_{1}}=\frac{-32}{64}=-\frac{1}{2}, \frac{a_{3}}{a_{2}}=\frac{16}{-32}=-\frac{1}{2}\)
\(\frac{a_{4}}{a_{3}}=\frac{-8}{16}=-\frac{1}{2}\)
∴ సామాన్య భేదం స్థిరము.
∴ ఇచ్చిన సంఖ్యలు గుణశ్రేణిలో కలవు.

ప్రశ్న86.
6 చే భాగింపబడే మొదటి 40 ధనపూర్ణ సంఖ్యల మొత్తము కనుగొనుము. ఈ సమస్యా సాధనా సోపాన క్రమంలో సరైన దానిని ఎన్నుకొనుము.
సోపానం (a) : Sn = A [2a + (n – 1)d] ,
సోపానం (b) : 6చే భాగింపబడే మొదటి 40 ధనపూర్ణ సంఖ్యలు 6, 12, 18, 24, ….., 40 పదాలు
సోపానం (c) : S40 = \(\frac{40}{2}\) [2(6)+ (40 -1)(6)] = 20 [12 + 234]
సోపానం (d) : a = 6, d = a2 – a1 = 6, n = 40
సోపానం (e) : S40 = 20 × 246 = 4920
A) b, e, c, a, d
B ) c, b, a, d, e
C) b, a, c, e, d
D) b, d, a, c, e
జవాబు :
D) b, d, a, c, e

ప్రశ్న87.
a = √5, r = \(\frac{1}{5}\) గా గల గుణశ్రేణి యొక్క 2వ పదంను రాయండి.
జవాబు :
a2, = ar = √5 × \(\frac{1}{5}=\frac{1}{\sqrt{5}}\)

ప్రశ్న88.
-2, 6, – 18, 54, ….. గుణ శ్రేణిలో తరువాతి పదం తెల్పండి.
జవాబు :
– 2, 6, – 18, 54 లో తరువాత పదం a5 = ?
a = – 2, r =-3
a5 = a.r4 = (-2) (- 3)4
=- 2 (81) = – 162

ప్రశ్న89.
x, 1, \(\frac{1}{x}\), … గుణశ్రేణిలో తరువాతి పదంను రాయండి.
జవాబు :
x, 1, \(\frac{1}{x}\)లు గుణశ్రేణిలో కలవు.
a = x, r = \(\frac{a_{2}}{a_{1}}=\frac{1}{x}\)
∴ తరువాత పదం = \(\frac{1}{x} \times \frac{1}{x}=\frac{1}{x^{2}}\)

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న90.
x, 4, 4x లు గుణశ్రేణిలో మూడు వరుస పదాలైతే x విలువను కనుగొనుము.
జవాబు :
x, 4, 4x లు గుణశ్రేణిలో 3 వరుస పదాలు
∴ \(\frac{4}{x}=\frac{4 x}{4} \Rightarrow \frac{4}{x}\)
⇒ 4 = x2 = x = √4 = +2

ప్రశ్న91.
అగ్గిపుల్లల సహాయంతో మోహన్ క్రింది ఆకారాలను తయారు చేశాడు. ప్రతి ఆకారానికి వాడిన అగ్గిపుల్లల సంఖ్య వరుసగా ఏ శ్రేణి అవుతుంది ?
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 13
జవాబు :
అంకశ్రేణి

ప్రశ్న92.
0.4, 0.04, 0.004, …… గుణశ్రేణి సామాన్య నిష్పత్తిని తెల్పండి.
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 14

ప్రశ్న93.
\(\frac{1}{\sqrt{2}}\), -2, \(\frac{8}{\sqrt{2}}\) …. గుణశ్రేణి తరువాత పదంను గుణశ్రేణి తరువాత పదంను కనుగొనుము.
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 15

ప్రశ్న94.
\(\frac{5}{2}, \frac{5}{4}, \frac{5}{8}\) …….. గుణ శ్రేణిలో nవ పదమును కనుగొనుము
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 16

ప్రశ్న95.
2, 8, 32, …….గుణ శ్రేణిలో ఎన్నవ పదం 512 అవుతుంది ?
జవాబు :
2, 8, 32, …….
a = 2, r = \(\frac{8}{2}\) = 4, an = 512, n = ?
an = arn-1 = 512
⇒ 2(4)n-1 = 512
⇒ 4n-1 = \(\frac{512}{2}\) = 256 = 44
∴n – 1 = 4 ⇒ n = 5
∴ 5వ పదం 512 అవుతుంది.
(లేదా)
ఇచ్చిన G.P. ని పొడిగించగా
2, 8, 32, 128, 512, ……
∴ 5వ పదం = 512

ప్రశ్న96.
ఒక గుణ శ్రేఢి 3వ పదం 36 మరియు 6వ పదం 972 అయిన ఆ గుణశ్రేఢి 4వ పదమును కనుగొనుము.
జవాబు :
a3 = ar2 = 36, a6 = ar5 = 972
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 17
నాల్గవ పదం a4 = a3, r = 36 × 3 = 108

ప్రశ్న97.
గుణశ్రేఢి యొక్క n వ పదం కనుగొను సూత్రాన్ని రాయండి.
జవాబు :
గుణ శ్రేఢిలో 1వ పదము an = a.rn-1

ప్రశ్న98.
2, – 6, 18, – 54, ….. గుణ శ్రేఢి n వ పదమును రాయండి.
జవాబు :
2 = 2, r = \(\frac{a_{2}}{a_{1}}=\frac{-6}{2}\) = – 3, an = ?
an = a.rn-1 = 2(- 3)n-1

ప్రశ్న99.
a1 = 9, r = \(\frac{1}{3}\) గా గల గుణశ్రేణిలో ఇలను కనుగొనుము.
జవాబు :
a1 = 9, r = \(\frac{1}{3}\)
a5 = ar4 = 9\(\left(\frac{1}{3}\right)^{4}\) = 9 × \(\frac{1}{81}=\frac{1}{9}\)

ప్రశ్న100.
ఒక గుణశ్రేణి యొక్క n వ పదం 3 \(\left(\frac{1}{2}\right)^{n-1}\). ఆ గుణశ్రేణి యొక్క సామాన్య నిష్పత్తి ఎంత ?
జవాబు :
\(\frac{1}{2}\)

ప్రశ్న101.
2, 2√2 , 4, …… గుణశ్రేణిలో ఎన్నవ పదం 64 అవుతుంది ?
జవాబు :
2, 2√2 , 4, ……….
a = 2, r = \(\frac{a_{2}}{a_{1}}=\frac{2 \sqrt{2}}{2}\) = √2 , an = 64.
an = arn-1 = 64
⇒ 2(√2)n-1 = 64 ⇒ (√2)n-1 = \(\frac{64}{2}\) = 32
⇒ 2\(\frac{\mathrm{n}-1}{2}\) = 25 ⇒ \(\frac{\mathrm{n}-1}{2}\) = 5
⇒ n – 1 = 10 ⇒ n = 11
(లేదా)
2, 2√2, 4, 4√2, 8, 8√2, 16, 16√2, 32, 32√2, 64 గా రాయవచ్చును.
∴ 11వ పదం 64 అవుతుంది.

ప్రశ్న102.
x – 1, x – 2, x – 3, ….. అంకశ్రేణిలో 10 పదాల మొత్తం ఎంత ?
జవాబు :
x – 1, x – 2, x – 3, ….. (x – 10) అంకశ్రేణిలో 10 పదాల మొత్తం
a = x – 1, d = (x – 2) – (x – 1) = – 1,
n= 10
Sn = \(\frac{n}{2}\) [a + l]
= \(\frac{10}{2}\) [(x-1) + (x – 10)]
S10 =5(2x – 11) = 10x – 55
(లేదా)
(x – 1) + (x – 2) + (x – 3) +…. + (x – 10)
= 10x – (1 + 2 + 3 + …. + 10)
= 10x – \(\frac{10 \times 11}{2}\) = 10x – 55

ప్రశ్న103.
a1 = – 12, r = \(\frac{1}{3}\) గా గల గుణశ్రేణిలో 6వ పదాన్ని కనుగొనుము.
జవాబు :
a6 = (- 12) \(\left(\frac{1}{3}\right)^{5}\)
= -12 × \(\frac{1}{3^{5}}=\frac{-4}{3^{4}}=\frac{-4}{81}\)

ప్రశ్న104.
2x, (x + 10), (3x + 2) లు అంకశ్రేణిలో ఉంటే x విలువ ………..
A) 6
B) 3
C) 5
D) 4
జవాబు :
A) 6

2x, (x + 10), (3x + 2) లు A.P లో కలవు.
∴ (x + 10) – (2x) = (3x + 2) – (x + 10)
x + 10 – 2x = 3x + 2 – x – 10.
⇒ 10 – x = 2x – 8
⇒ – x – 2x = – 8 – 10
⇒ – 3x = – 18 ⇒ x = \(\frac{-18}{-3}\) = 6.

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న105.
ప్రాచీన భారతీయ గణితశాస్త్రవేత్త ఆర్యభట్ట యొక్క ప్రసిద్ధ గ్రంథము …………
A) ఆర్యతర్కం
B) ఆర్యభట్టీయం
C) సిద్ధాంత శిరోమణి
D) కరణకుతూహలం
జవాబు :
B) ఆర్యభట్టీయం

ప్రశ్న106.
క్రింది వానిలో ఏది అసత్యం ?
A) అంకశ్రేణిలోని ప్రతి పదానికి ఒక స్థిర సంఖ్యను – కలుపగా వచ్చే ఫలిత జాబితా అంకశ్రేణి.
B) అంకశ్రేణిలోని ప్రతి పదము నుంచి ఒక స్థిరసంఖ్యను తీసివేయగా ఫలిత జాబితా అంకశ్రేణి.
C) అంకశ్రేణిలోని ప్రతి పదాన్ని ఒక స్థిర సంఖ్యతో గుణించగా వచ్చే ఫలిత జాబితా అంకశ్రేణి.
D) అంకశ్రేణిలోని ప్రతి పదాన్ని ఒక స్థిర సంఖ్యతో భాగించగా వచ్చే ఫలిత జాబితా ఒక గుణ శ్రేఢి.
జవాబు :
D) అంకశ్రేణిలోని ప్రతి పదాన్ని ఒక స్థిర సంఖ్యతో భాగించగా వచ్చే ఫలిత జాబితా ఒక గుణ శ్రేఢి.

ప్రశ్న107.
6, 2 – 2, – 6, …… అంకశ్రేణి సామాన్య భేదం ఎంత ?
జవాబు :
సామాన్య భేదం d = a2 – a1 = 2 – 6 = -4

ప్రశ్న108.
క్రింది వానిని జతపరుచుము :

i) మొదటి n సహజ సంఖ్యల మొత్తం a) \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
ii) మొదటి n బేసి సంఖ్యల మొత్తం b) n2
iii)మొదటి n సరి సంఖ్యల మొత్తం c) n(n + 1)

A) i-a, ii-b, iii-c
B) i-b, ii-c, iii-a
C) i-c, ii-a, iii-b
D) i-a, ii-c, iii-b
జవాబు :
A) i-a, ii-b, iii-c

ప్రశ్న109.
2x, 3x, 4x, ….. అంకశ్రేణిలో 10వ పదంను రాయండి.
జవాబు :
a = 2x, d = 3x – 2x = x
a10 = a + 9d = 2x + 9x = 11x
(లేదా)
ఇచ్చిన A.P. ని 10 పదాల వరకు రాయగా 2x, 3x, 4x, 5x, 6x, 7x, 8x, 9x, 10x, 11x
10వ పదము a10 = 11x

ప్రశ్న110.
ఒక టాక్సీ మొదటి కి.మీ. ప్రయాణానికి ₹ 20 ల చొప్పున, తరువాత ప్రతి కి.మీ.కు ₹8 ల చొప్పున చెల్లించవలసిన, 15 కి.మీ. ప్రయాణానికి అయ్యే సొమ్మును కనుగొనుము.
జవాబు :
ప్రతి కి.మీ.కి వరుసగా చెల్లించాల్సిన సొమ్ము
= 20, 28, 36, ……… A. P. లో కలదు.
a = 20, d = 8, a15 = ?
a15 = a + 14d.
= 20 + 14(8)
= 20 + 112 = ₹ 132

ప్రశ్న111.
√2, √8, √18 అంకశ్రేణిలో తరువాత పదం ఏది?
జవాబు :
ఇచ్చిన A.P. : √2, √8, √18 , ………
= \(\sqrt{1 \times 2}, \sqrt{4 \times 2}, \sqrt{9 \times 2}\), …….
= √2, 2√2, 3√2, ………..
∴ తరువాత పదం = 4√2 = \(\sqrt{16 \times 2}=\sqrt{32}\)

ప్రశ్న112.
√3, √12, √27 , ….. అంకశ్రేణిలో 5వ పదమును కనుగొనుము.
జవాబు :
√3, √12, √27 , …… A.P లో 5వ పదం.
\(\sqrt{3}, \sqrt{4 \times 3}, \sqrt{9 \times 3}\)….
= 13, 2/3, 3/3, ……..
5వ పదం 5/3 = \(\sqrt{25 \times 3}\) = \(\sqrt{75}\)

ప్రశ్న113.
ఒక గుణశ్రేణి యొక్క 1వ పదం an = 3(2)n-1 అయిన క్రింది వానిని జతపరుచుము.

i) మొదటి పదం a a) 2
ii) సామాన్య నిష్పత్తి b) 3
iii)రెండవ పదం a<sub>2</sub> c) 6
iv)నాల్గవ పదం a<sub>4</sub> d) 24

A) i-c, ii-b, iii-d, iv-a
B) i-b, ii-a, iii-c, iv-d
C) i-a, ii-c, iii-b, iv-d
D) i-c, ii-a, iii-b, iv-d
జవాబు :
B) i-b, ii-a, iii-c, iv-d

ప్రశ్న114.
log a, log b, log cలు అంకశ్రేణిలో ఉంటే క్రింది వానిలో ఏది నిజం ?
A) log b2 = log ac
B) b2 = ac
C) 2 log b = log ac
D) పైవన్నీ
జవాబు :
D) పైవన్నీ

ప్రశ్న115.
sin 0°, sin 30°, sin 90° విలువలు వరుసగా ఏ శ్రేడిని ఏర్పరుస్తాయి ?
జవాబు :
0, \(\frac{1}{2}\), 1 [:: sin 0° = 0, sin 30° = \(\frac{1}{2}\), sin 90° = 1]
అంకశ్రేణిని ఏర్పరుస్తాయి.

ప్రశ్న116.
a = 7, d = 3, n = 8 గా గల అంకశ్రేఢి యొక్క an+1 ను కనుగొనుము.
జవాబు :
an+1 = a8+1
= a9 = a + 8d = 7 + 8(3) = 31

ప్రశ్న117.
sin 30, sin 90°, cosec 30° విలువలు వరుసగా ఏ శ్రేణిని ఏర్పరుస్తాయి ?
జవాబు :
\(\frac{1}{2}\), 1, sin 30° = \(\frac{1}{2}\), sin 90° = 1, cosec 30° = 2]
గుణశ్రేణిని ఏర్పరుస్తాయి.

ప్రశ్న118.
a2 = 13, a4 = 3 గా గల అంకశ్రేణిలో ఇ, విలువ ఎంత ?
జవాబు :
a3 = \(\frac{a_{4}+a_{2}}{2}=\frac{3+13}{2}\) = 8
a1, a2, a3, a4, లు A.P.లో కలవు
= a1, 13, a3, 3
a3 – 13 = 3 – a3
⇒ 2a3 = 16 ⇒ a3 = \(\frac{16}{2}\) = 8

ప్రశ్న119.
“చతురస్రం / దీర్ఘచతురస్రంలోని నాలుగు కోణాల విలువలు వరుసగా ఒక గుణ శ్రేణిలో ఉంటాయి” అని రిషి అంటున్నారు. రిషి తెల్పిన ప్రవచనాన్ని సమర్ధించండి.
జవాబు :
చతురస్రం / దీర్ఘచతురస్రంలోని నాలుగు కోణాల ‘విలువలు వరుసగా 90, 90, 90, 90.
\(\frac{a_{2}}{a_{1}}=\frac{90}{90}\) = 1, \(\frac{a_{3}}{a_{2}}=\frac{90}{90}\) = 1, \(\frac{a_{4}}{a_{3}}=\frac{90}{90}\) = 1, \(\) = 1
సామాన్య భేదం అన్ని సందర్భాలలో సమానంగా కలదు. కావున చతురస్ర / దీర్ఘచతురస్ర కోణాలు గుణ శ్రేణిలో ఉంటాయి. కావున రిషి చెప్పిన ప్రవచనంతో ఏకీభవిస్తాను.

ప్రశ్న120.
ఒక అంకశ్రేణి సామాన్య భేదం – 3 మరియు 18వ పదం – 5 అయితే ఆ శ్రేఢి మొదటి పదం ఎంత ?
జవాబు :
d = 3, a18 ⇒ a + 17d = -5
⇒ a + 17(- 3) = . 5
⇒ a = – 5 + 51 = 46

ప్రశ్న121.
క్రింద ఇవ్వబడిన అసత్య ప్రవచనాన్ని సత్య ప్రవచనంగా మార్చి రాయండి.
ప్రవచనం : ఒక అంకశ్రేణిలో n పదాల మొత్తం
Sn = a + (n – 1]d
జవాబు :
ఒక అంకశ్రేణిలో n పదాల మొత్తం =
Sn = \(\frac{n}{2}\) [2a + (n – 1)d]
(లేదా)
Sn = \(\frac{n}{2}\)[a + l]

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న122.
1 నుంచి 100 వరకు గల అన్ని సహజ సంఖ్యల మొత్తాన్ని సూక్ష్మ పద్ధతిలో తెలిపిన గణితశాస్త్రజ్ఞుడు
A) యూలర్
B) ఆర్యభట్ట
C) గాస్
D) రామానుజం
జవాబు :
C) గాస్

ప్రశ్న123.
24, 21, 18, ……. అంకశ్రేణిలో మొదటి నాలుగు పదాల మొత్తం ఎంత ?
జవాబు :
a1 = 24, a2 = 21, a3 = 18,
d = 21 – 24 = -3
a4 = a + 3d = 24 – 9
a4 = 15
S4 = 24 + 21 + 18 + 15 = 78

ప్రశ్న124.
మొదటి n ధనపూర్ణ సంఖ్యల (సహజ సంఖ్యల) మొత్తమునకు సూత్రాన్ని రాయండి.
జవాబు :
\(\frac{n(n+1)}{2}\)

ప్రశ్న125.
an = 3 + 2n గా గల అంకశ్రేణిలో 5వ పదంను కనుగొనుము.
జవాబు :
an = 3 + 2n, a5 = 3 + 2(5) = 13

ప్రశ్న126.
వాక్యం X : a, b, c లు అంకశ్రేణిలో ఉంటే b = \(\frac{a+c}{2}\)
వాక్యం Y : a, b, c లు గుణశ్రేణిలో ఉంటే b2 = ac
A) X – సత్యం, Y – అసత్యం
B) X – సత్యం, Y – సత్యం
C) X – అసత్యం, Y – సత్యం
D) X – అసత్యం , Y – అసత్యం
జవాబు :
B) X – సత్యం , Y – సత్యం

ప్రశ్న127.
3n + 5 కు 1వ పదంగా గల అంకశ్రేణి సామాన్య భేదం ఎంత ?
జవాబు :
3

ప్రశ్న128.
ఒక అంకశ్రేణి n పదాల మొత్తం
Sn = \(\frac{n}{2}\) [2a + (n – 1)d]., సూత్ర పదాలను వాని వివరణకు జతపరుచుము.

i) a p) n పదాల మొత్తము
ii) d q) పదాల సంఖ్య
iii) Sn r) మొదటి పదం
iv) n s) సామాన్య భేదం

A) is, ii-p, iii-r, iv-q
B) i-r, ii-p, iii-q, iv-S
C) i-r, ii-s, iii-p, iv-q
D) is, ii-r, iii-p, iv-4
జవాబు :
C) i-r, ii-s, iii-p, iv-q

ప్రశ్న129.
1, 3, 5, 7, 9, ……. శ్రేణిలో మొదటి 20 పదాల మొత్తం …………….
A) 900
B) 100
C) 1600
D) 400
జవాబు :
D) 400

n = 20, Sn = n2 = 202 = 400
(∵ 1, 3, 5, ….. బేసి సంఖ్యలు)

ప్రశ్న130.
అంకశ్రేణి n పదాల మొత్తం Sn = n2 + 3n అయిన ఆ అంకశ్రేఢి n వ పదము …….
A) 2n
B) 2n – 2
C) 2n + 2
D) 2n – 1,
జవాబు :
Sn = n2 + 3n
an = Sn – Sn-1
= (n2 + 3n) – [[n – 1)2 + 3(n – 1)]
= (n2 + 3n) – [n2 – 2n + 1 + 3n – 3]
= n2 + 3n – (n2 + n – 2)
= n2 + 3n – n2 – n + 2
= 2n + 2
(లేదా)
Sn = n2 + 3n
a1 = S1 = (1)2 + 3(1) = 4
S2 = a1 + a2
= (2)2 + 3(2) = 4 + 6 = 10

∴ a2 = 10 – 4 = 6
d = a2 – a1 = 6 – 4 = 2
an = a + (n – 1)d
= 4 + (n – 1)2 = 2n + 2

ప్రశ్న131.
అంకశ్రేఢ nపదాల మొత్తం Sn = n2 + 5n అయిన ఆ అంకశ్రేఢి 7వ పదమును కనుగొనుము.
A) 16
B) 18
C) 20
D) 22
జవాబు :
B) 18

Sn = n2 + 5n, a7 = ?
a7 = S7 – S6
= [[7)2 + 5(7)] – [[6)2 + 5(6)]
= 84 – 66 = 18

ప్రశ్న132.
ఒక అంకశ్రేణిలో n పదాల మొత్తం Sn = an2 + 5n అయిన క్రింది వానిని జతపరుచుము.

i) మొదటి పదము a a) 450
ii) సామాన్య భేదం d b) 9
iii)10 పదాల మొత్తం S10 c) 17
iv) రెండవ పదము a2 d) 8.

A) i-c, ii-b, iii-d, iv-a.
B) i-b, ii-d, iii-a, iv-c
C) i-a, ii-b, iii-c, iv-d
D) i-d, ii-b, iii-c, iv-a
జవాబు :
B) i-b, ii-d, iii-a, iv-c

ప్రశ్న133.
వాక్యం X : అంకశ్రేణిలోని ప్రతి పదాన్ని స్థిర సంఖ్య (ఒకే సంఖ్య)తో గుణించగా ఏర్పడు సంఖ్యల జాబితా తిరిగి అంకశ్రేణి అవుతుంది.
వాక్యం Y : అంకశ్రేణిలోని ప్రతి పదాన్ని ఒక స్థిర సంఖ్యతో భాగించగా వచ్చు నూతన సంఖ్యల జాబితా తిరిగి అంకశ్రేఢి అవుతుంది.
A) X, Y లు రెండూ సత్యం
B) X, Y లు రెండూ అసత్యం
C) X – సత్యం, Y – అసత్యం
D) X – అసత్యం , Y – సత్యం
జవాబు :
C) X – సత్యం, Y – అసత్యం

ప్రశ్న134.
125, – 25, 5, ……. గుణశ్రేణి నాల్గవ పదమును రాయండి.
జవాబు :
a = 125, r = \(\frac{a_{2}}{a_{1}}=\frac{-25}{125}=\frac{-1}{5}\)
a4 = a3r = 5 × \(\frac{-1}{5}\) = -1

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న135.
ఒక గుణశ్రేణి మొదటి పదం \(\frac{1}{64}\), సామాన్య నిష్పత్తి 2 అయిన ఆ గుణ శ్రేఢి 9వ పదము ఎంత ?
జవాబు :
a = \(\frac{1}{64}\), r = 2,
a9 = ar8 = \(\frac{1}{64}\) × 28 = \(\frac{1}{2^{6}}\) × 28
= 22 = 4

ప్రశ్న136.
సామాన్య నిష్పత్తి 2గా గల ఒక గుణ శ్రేణిని రాయండి.
జవాబు :
r = 2 గా గల ఒక గుణశ్రేఢి 3, 6, 12, 24, …..

ప్రశ్న137.
3, -32, 33, ……….. గుణ శ్రేణిలో సామాన్య నిష్పత్తి ఎంత ?
జవాబు :
-3

ప్రశ్న138.
\(\frac{1}{3},-\frac{1}{6}, \frac{1}{12}\) గుణశ్రేణిలో తరువాత పదం ఏది ?
జవాబు :
\(\frac{1}{24}\)

ప్రశ్న139.
ఒక గుణశ్రేఢిలో 3వ పదం 24 మరియు 6వ పదం 192 అయిన ఆ గుణశ్రేణి సామాన్య నిష్పత్తి ఎంత ?
జవాబు :
G.P. లో a3 = ar2 = 24, a6 = ar5 = 192
\(\frac{a_{6}}{a_{3}}=\frac{a r^{5}}{a r^{2}}=\frac{192}{24}\) ⇒ r3 = 8 = 23
∴ r = 2

ప్రశ్న140.
2, 2√2, 4, ….. గుణశ్రేణిలో 6వ పదం ఏది ?
జవాబు :
2, 2√2, 4 ను 6 పదాల వరకు పొడిగించగా
2, 2√2, 4, 4√2, 8, 8√2.

ప్రశ్న141.
గుణశ్రేణి యొక్క క్రింది వానిని జతపరుచుము.
√3, √6, 2√3, 2√6, …………

i) మొదటి పదం a a) 4√3
ii) సామాన్య నిష్పత్తి r b) √3
iii)3వ పదము a3 c) 2√3
iv) 5వ పదము a5  d) √2

A) i-a, ii-c, iii-b, iv-d
B) i-b, ii-a, iii-d, iv-c
C) i-b, ii-d, iii-c, iv-a
D) i-b, ii-a, iii-c, iv-d
జవాబు :
C) i-b, ii-d, iii-c, iv-a

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న142.
√3, √6, 2√3, ……. గుణశ్రేణి సామాన్య నిష్పత్తి √2 అని చూపుము.
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 18

ప్రశ్న143.
1, \(-\frac{1}{3}, \frac{1}{9},-\frac{1}{27}\) ……. గుజశ్రేణిలో 6వ పదమును కనుగొనుము.
జవాబు :
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 19

ప్రశ్న144.
p) 1, \(\frac{1}{2}, \frac{1}{4}, \frac{1}{8}\) …………….
q) 1, 2, 4, 8, …….. అయితే
A) p-గుణ శ్రేణి, q-అంకశ్రేణి
B) p, q లు రెండూ అంకశ్రేఢులు
C) p, q లు రెండూ గుణ శ్రేఢులు
D) p-అంకశ్రేణి, q-గుణ శ్రేడి C
జవాబు :
C) p, q లు రెండూ గుణ శ్రేఢులు

ప్రశ్న145.
x, y, z లు గుణశ్రేణిలో ఉంటే,
i) y2 = xz
ii) 2 log y = log x + log z
A) i – మాత్రమే సత్యం
B) ii – మాత్రమే సత్యం
C) i మరియు ii సత్యం
D) i మరియు ii లు రెండూ అసత్యం
జవాబు :
C) i మరియు ii సత్యం

ప్రశ్న146.
3, 5, 7, 9, ……… 201 అంకశ్రేణిలో చివరి నుండి 5వ పదంను రాయండి.
జవాబు :
3, 5, 7, 9, ……., 201 అంకశ్రేణిలో చివరి నుండి 5వ పదం
ఇచ్చిన A.P ని చివరి నుండి రాయగా
201, 199, 197, 195, 193, ……., 9, 7, 5, 3
చివరి నుండి 5వ పదం 193.

ప్రశ్న147.
an = 3n + 7 అంకశ్రేణిలో మొదటి పదము ఏది?
జవాబు :
an = 3n +7
∴ a15 = 3(1) + 7 = 10.

ప్రశ్న148.
an = 3 + 4n అంకశ్రేణిలో 15వ పదం ఏది ?
జవాబు :
an = 3 + 4n
∴ a15 = 3 + 4(15) = 63.

ప్రశ్న149.
p(x) = (x + 1) (x – 2) (x – 5) ఘన బహుపది యొక్క శూన్యాలు ఏ శ్రేణిలో ఉంటాయి ?
జవాబు :
p(x) శూన్యాలు, -1, 2, 5 లు అంకశ్రేణిలో ఉంటాయి.

ప్రశ్న150.
A అనేది an = 2n గా గల అంకశ్రేణిలో మొదటి ‘నాలుగు పదాలుగా గల సమితి, B అనేది a = 2n-1గా గల గుణశ్రేఢిలో మొదటి నాలుగు పదాలుగా గల సమితి అయిన A ∩ B సమితిని కనుగొనుము.
A) {2, 4, 8}
B) {2, 4, 6, 8}
C) {1, 2, 4, 8}
D) {1, 2, 4, 6, 8}
జవాబు :
A) {2, 4, 8}

A = {2, 4, 6, 8}, B = {1, 2, 4, 8}
A ∩ B = {2, 4, 8}

ప్రశ్న151.
5\(\left(\frac{1}{3}\right)^{n-1}\) n వ పదంగా గల గుణశ్రేణిలో 4వ పదంను కనుగొనుము.
జవాబు :
an = 5\(\left(\frac{1}{3}\right)^{n-1}\)

ప్రశ్న152.
\(\frac{1}{16}, \frac{1}{8}, \frac{1}{4}\) ……. గుణశ్రేణిలో మొదటి పూర్ణసంఖ్య ఏది ?
జవాబు :
ఇచ్చిన G.P. = \(\frac{1}{16}, \frac{1}{8}, \frac{1}{4}, \frac{1}{2}\),1, 2, 3, ….. గా రాయవచ్చును.
∴ ఇచ్చిన G.P లో 1 మొదటి పూర్ణసంఖ్య అవుతుంది.

ప్రశ్న153.
A అనేది an = 2n గా గల అంకశ్రేణిలో మొదటి నాలుగు పదాలుగా గల సమితి, B అనేది an = 2n-1 గా గల గుణశ్రేణిలో మొదటి నాలుగు పదాలుగా గల సమితి అయిన A ∪ B ని కనుగొనుము.
జవాబు :
A ∪ B = {1, 2, 4, 6, 8}

ప్రశ్న154.
ఒక AP నందలి ప్రతీ పదాన్ని 3 చే గుణించినపుడు ఏర్పడిన అంకశ్రేణి నందు పదాంతరం ……….. రెట్లు పెరుగును.
జవాబు :
3

→ గమనిక : “ఒక ఆటో మొదటి కి.మీ. ప్రయాణానికి ₹30, ఆపై ప్రతి కి.మీ. ప్రయాణానికి ₹ 10 చొప్పున చెల్లించవలసి యున్నది”. పై సమాచారం ఆధారంగా 155-158 వరకు గల ప్రశ్నలకు సమాధానాలు రాయండి.

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న155.
ప్రతి కి.మీ. చెల్లించాల్సిన సొమ్ము జాబితా రాయండి.
జవాబు :
30, 40, 50, 60, 70, 80, ……

ప్రశ్న156.
ఏర్పడిన జాబితా ఏ శ్రేణిలో ఉంటుంది ?
జవాబు :
అంకశ్రేణి

ప్రశ్న157.
ఏర్పడిన జాబితాలో సామాన్య భేదం ఎంత ?
జవాబు :
d = a2 – a1 = 40 – 30 = 10

ప్రశ్న158.
ఆటోలో 3 కి.మీ. ప్రయాణించినచో చెల్లించాల్సిన సొమ్ము ఎంత ?
జవాబు :
3 కి.మీ. ప్రయాణానికి చెల్లించాల్సిన సొమ్ము
a3 = 50

ప్రశ్న159.
ఒక GP నందు 5వ పదం a5, 6వ పదం a్య అయిన (a5) (a6) విలువ క్రింది వానిలో దేనికి సమానం ?
A) a.a7
B) a(a11)
C) a(a10)
D) a(a12)
జవాబు :
C) a(a10)

a5 = art, a6 = ars
= a5.a6 = a2.r9 = a.ar9 = a.a10

ప్రశ్న160.
4, x, 9 లు GP లో ఉన్న x విలువ ఎంత ?
జవాబు :
4, x, 9 లు G.P లో ఉంటే \(\frac{x}{4}=\frac{9}{x}\) = x2 = 36
∴ x = \(\sqrt{36}\) = ± 6.

ప్రశ్న161.
AP నందు 8వ పదం 10, 18వ పదం 15 అయిన సామాన్య భేదంను కనుగొనుము.
జవాబు :
a8 = 10, a18 = 15,
a18 – a8 = 10d = 15 – 10 = 5
∴ d = \(\frac{5}{10}=\frac{1}{2}\)

ప్రశ్న162.
a, b ల మధ్య ‘n’ పదాలుండేటట్లు ఒక అంకశ్రేణి ఉంటే ఆ శ్రేణి సామాన్య భేదం
A) \(\frac{b-a}{n+1}\)
B) \(\frac{a+b}{n-1}\)
C) \(\frac{b-a}{n-1}\)
D) \(\frac{b+a}{n-1}\)
జవాబు :
A) \(\frac{b-a}{n+1}\)

ప్రశ్న163.
క్రిందివానిలో √3 సామాన్య నిష్పత్తిగా గల గుణశ్రేణి
A) 3, 9, 27, …..
B) √3, 3, 3√3, ….
C) 3, \(\frac{1}{3}, \frac{1}{9}\)
D) √3, 2√3, 3√3, ….
జవాబు :
B) √3, 3, 3√3, ….

→ గమనిక : “ఒక గుణశ్రేణి యొక్క 1వ పదం an = a.rn-1 పై సమాచారం ఆధారంగా 164-166 వరకు గల ప్రశ్నలకు సమాధానాలు రాయండి.

ప్రశ్న164.
పై సూత్రంలో ‘r’ దేనిని సూచిస్తుంది ?
జవాబు :
సామాన్య నిష్పత్తి

ప్రశ్న165.
a = 3, r = 3 అయిన 2, విలువ ఎంత ?
జవాబు :
a3 = 3(√3)3-1 = 3(√3)2 = 9

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న166.
n + 1వ పదం an+1 ను కనుగొనుము.
జవాబు :
an+1 = a(r)(n + 1) – 1 = arn

ప్రశ్న167.
5, 10, 20, 40,……….. గుణశ్రేణిలో 120 ఒక పదంగా ఉండదని చూపండి.
జవాబు :
ఇచ్చిన G.P లో a = 5, r = \(\frac{a_{2}}{a_{1}}=\frac{10}{5}\) = 2
a 5 ఇచ్చిన G.P ని పొడిగించగా 5, 10, 20, 40, 80, 160, 320, …..
కావున 120 ఇచ్చిన G.Pలో ఒక పదంగా ఉండదు.

ప్రశ్న168.
అంకశ్రేణిలో గల 6వ, 7వ, 8వ పదాల మొత్తం 678 అయిన 7వ పదం ఎంత ?
జవాబు :
a6 + a7 + a8 = (a + 5d) + (a + 6d) + (a + 7d) = 678
= 3a + 18d = 3(a + 6d) = 678
= 3 . a7 = 678
= a7 = \(\frac{678}{3}\) = 226.

ప్రశ్న169.
ఏదైనా శ్రేఢి (GP | AP) నందు S10 – S9 విలువ ఆ శ్రేఢి ఎన్నవ పదానికి సమానము ?
జవాబు :
10వ పదము.

ప్రశ్న170.
ఒక గుణ శ్రేణిలో an7 = (- 1)n. 2020 అయిన ఆ శ్రేణి సామాన్య నిష్పత్తిని కనుగొనుము.
జవాబు :
an = (-1)n 2020, :
a1 = – 2020, a2 = 2020
సామాన్య భేదం r = \(\frac{\mathrm{a}_{2}}{\mathrm{a}_{1}}=\frac{2020}{-2020}\) = -1

ప్రశ్న171.
34 × 38 × 312 ….. (16 పదాలు) లబ్దం
A) 3544
B) 364
C) 3456
D) 316
జవాబు :
A) 3544

34 × 38 × 312 ….. 16 పదాలు
= 34 + 8 + 12 …….. (16 పదాలు) ……. (1)
ఇపుడు 4 + 8 + 12 + ……. + 16
a = 4, d = 4, n = 16, Sn = ?
Sn = \(\frac{n}{2}\)[2a + (n – 1 d]
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 20
∴ లబ్దం = 3544

ప్రశ్న172.
(1 + 5) + (4 + 9) + (7 + 13) + ………….. (10 పదాలు) మొత్తం ఎంత ?
జవాబు :
(1 + 5) + (4 + 9) + (7 + 13) + …. 10 పదాల మొత్తం
= 6 + 13 + 20 + ……. 10 పదాలు A.P లో కలవు.
a = 6, d = 13 – 6 = 7, n = 10

Sn = \(\frac{n}{2}\) [2a + (in = 1)d]
= \(\frac{10}{2}\) [12 + 63] = 5(75) = 375

ప్రశ్న173.
x, y, 2 లు అంకశ్రేణిలో కలవు. y = 46 అయిన x + y + Z విలువ ఎంత ?
జవాబు :
x, y, 2 లు A.P లో ఉంటే
y – x = z – y = 2y = x + Z,
∴ x + y + 7 = 3y = 3 (46) = 138

ప్రశ్న174.
p, q, r లు AP లో కలవు. q = 40 అయిన p+ r విలువ ఎంత ?
జవాబు :
p, q, r లు A.P లో కలవు.
∴ 2q = p + r
∴ p + r = 2(40) = 80

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న175.
x, y, z లు GP లో గలవు. y = 14 అయిన xz విలువను కనుగొనుము.
జవాబు :
x, y, z లు G.P లో ఉంటే
\(\frac{y}{x}=\frac{z}{y}\) ⇒ y2= (14)2 = 196

ప్రశ్న176.
p, q, r లు GP లో గలవు. q = 12 అయిన pqr + 1 విలువ కనుగొనుము.
జవాబు :
p, q, r లు G.P లో ఉంటే q2 = pr
par = q = (12)3 = 1728
∴ pqr + 1 = 1729.

ప్రశ్న177.
3, 7, 9, 12, ….. ఒక అంకశ్రేణి. (సత్యం / అసత్యం )
జవాబు :
అసత్యం

ప్రశ్న178.
ఒక AP నందు మొదటి ‘n’ పదాల మొత్తం Sn = 4n2 + 5n అయిన మొదటి పదం ఎంత ?
జవాబు :
a1 = S1 = 4(1)2 + 5(1) = 9

ప్రశ్న179.
a మొదటి పదం, 1 చివరి పదంగా గల అంకశ్రేఢి n- పదాల మొత్తం Sn = \(\frac{n}{2}\)(a + l) (సత్యం / అసత్యం)
జవాబు :
సత్యం

ప్రశ్న180.
tan A, tan B, tan C లు G.P. లో ఉండిన cot A, cot B, cot C లు గుణశ్రేఢిలో ఉండును అని చూపుము.
జవాబు :
tan A, tan B, tan C లు G.P. లో కలవు.
⇒ \(\frac{\tan \mathrm{B}}{\tan \mathrm{A}}=\frac{\tan \mathrm{C}}{\tan \mathrm{B}}\)
⇒ tan B’ cot A = tan C . cot B.
⇒ \(\frac{\cot A}{\cot B}=\frac{\cot B}{\cot C}\) (‘: సామాన్య నిష్పత్తి సమానం)
∴ cot A, cot B, cot C లు G.P. లో కలవు.

ప్రశ్న181.
అపరిమిత అంకశ్రేణికి ఒక ఉదాహరణనిమ్ము.
జవాబు :
అపరిమిత అంకశ్రేణికి ఒక ఉదాహరణ : 1, 3, 5, 7, 9, ……….

ప్రశ్న182.
పరిమిత గుణశ్రేణికి ఒక ఉదాహరణనిమ్ము.
జవాబు :
పరిమిత గుణ శ్రేణికి ఒక ఉదాహరణ :
1, 3, 9, 27, ………..

ప్రశ్న183.
రెండు అంకశ్రేఢుల యొక్క ‘n’ వ పదాల నిష్పత్తి 2n + 3 : 4n + 5 అయిన ఆ రెండు శ్రేఢుల ’10’ వ పదాల యొక్క నిష్పత్తి ఎంత ?
జవాబు :
రెండు అంకశ్రేఢుల nవ పదాల నిష్పత్తి
\(\frac{a_{n}}{A_{n}}=\frac{2 n+3}{4 n+5}\)
∴ \(\frac{\mathrm{a}_{10}}{\mathrm{~A}_{10}}=\frac{2(10)+3}{4(10)+5}=\frac{23}{45}\)
10వ పదాల నిష్పత్తి = 23 : 45
(లేదా)
1వ శ్రేణిలో 10వ పదం
= an = 2n + 3 = 2(10) + 3 = 23
2వ శ్రేణిలో 10వ పదం
= an = 4n + 5 = 4(10) + 5 = 45
10వ పదాల నిష్పత్తి = 23:45

AP 10th Class Maths Bits 6th Lesson శ్రేఢులు

ప్రశ్న184.
cos2 60, cos- 45, cos2 30 లు అంకశ్రేణిలో కలవు అని చూపండి.
జవాబు :
cos2 60 = \(\left(\frac{1}{2}\right)^{2}=\frac{1}{4}\)
cos2 45 = \(\left(\frac{1}{\sqrt{2}}\right)^{2}=\frac{1}{2}\)
cos2 30 = \(\left(\frac{\sqrt{3}}{2}\right)^{2}=\frac{3}{4}\)
∴ cos2 60, cos2 45, cos2 30 విలువల జాబితా \(\)
a2 – a1 = \(\frac{1}{2}-\frac{1}{4}=\frac{1}{4}\)
a3 – a2 = \(\frac{3}{4}-\frac{1}{2}=\frac{1}{4}\)
సామాన్య భేదం సమానం కావున అంకశ్రేణిలో ఉంటాయి.

ప్రశ్న185.
35, 37, 39 లు గుణశ్రేణిలో కలవు. పై ప్రవచనాన్ని సమర్థించండి.
జవాబు :
\(\frac{a_{2}}{a_{1}}=\frac{3^{7}}{3^{5}}\) = 32
\(\frac{a_{3}}{a_{2}}=\frac{3^{9}}{3^{7}}\) = 32
సామాన్య నిష్పత్తి సమానము.
∴ కావున GPలో ఉంటాయి.

ప్రశ్న186.
1, 4, – 2, 10, 7 లు అంకశ్రేణిలో ఉండునట్లు అమర్చుము.
జవాబు :
1, 4, – 2, 10, 7 లను అంకశ్రేణిలో అమర్చగా
-2, 1, 4, 7, 10 (లేదా) 10, 7, 4, 1, -2

→ గమనిక : “2020 సంవత్సరం క్యాలెండర్ నవంబర్ నెలలో మొదటి ఆదివారం 1వ తేదీన వచ్చినది”.
పై సమాచారం ఆధారంగా 187-190 వరకు గల ప్రశ్నలకు సమాధానాలు రాయండి.

ప్రశ్న187.
నవంబర్ 2020 క్యాలెండర్ నందు ఆదివారము వచ్చు తేదీలను సూచించు సంఖ్యల జాబితా రాయండి.
జవాబు :
ఆదివారం వచ్చు తేదీల సంఖ్యల జాబితా
1, 8, 15, 22, 29.

ప్రశ్న188.
పై జాబితా ఏ శ్రేణి అవుతుంది ?
జవాబు :
పై జాబితా అంకశ్రేఢి అవుతుంది.

ప్రశ్న189.
పై జాబితా యొక్క సామాన్య భేదం ఎంత ?
జవాబు :
d = a2 – a1 = 8 – 1 = 7,

ప్రశ్న190.
పై జాబితాలో 30 ఒక పదం అవుతుందా ? కాదా ? .
జవాబు :
పై జాబితాలో 30 ఒక పదం కాదు.

ప్రశ్న191.
క్రింది పటంలో ఇవ్వబడిన త్రిభుజ భుజాల మధ్య బిందువులను కలుపుతూ ఏర్పడిన వరుస త్రిభుజాల చుట్టుకొలతలు ఏ రకమైన శ్రేణిని ఏర్పరుస్తాయి ?
AP 10th Class Maths Bits 6th Lesson శ్రేఢులు 21
జవాబు :
గుణశ్రేణి.

AP Board 9th Class Maths Solutions Chapter 2 బహుపదులు మరియు కారణాంక విభజన Ex 2.1

SCERT AP 9th Class Maths Solutions Chapter 2 బహుపదులు మరియు కారణాంక విభజన Ex 2.1 Textbook Exercise Questions and Answers.

AP State Syllabus 9th Class Maths Solutions 2nd Lesson బహుపదులు మరియు కారణాంక విభజన Exercise 2.1

ప్రశ్న1.
కింద ఇవ్వబడిన ప్రతి బహుపది యొక్క పరిమాణం కనుగొనండి.
i) x5 – x4 + 3
ii) x2 + x – 5
iii) 5
iv) 3x6 + 6y3 – 7
v) 4 – y2
vi) 5t – \(\sqrt{3}\)
సాధన.
i) x5 – x4 + 3 పరిమాణం – 5.
ii) x2 + x – 5 పరిమాణం – 2.
iii) 5 పరిమాణం – 0.
iv) 3x6 + 6y3 – 7 పరిమాణం – 6.
v) 4 – y2 పరిమాణం – 2.
vi) 5t – \(\sqrt{3}\) పరిమాణం – 1.

AP Board 9th Class Maths Solutions Chapter 2 బహుపదులు మరియు కారణాంక విభజన Ex 2.1

ప్రశ్న2.
కింది బహుపదులలో ఏక చరరాశితో కూడిన బహుపదులేవి? ఏవికావు ? సకారణంగా తెలపండి.
i) 3x2 – 2x + 5
సాధన.
ఇచ్చిన బహుపది ‘x’ అను ఏక చరరాశితో ఏర్పడినది.

ii) x2 + \(\sqrt{2}\)
సాధన.
ఇచ్చిన బహుపది ‘x’ అను ఏక చరరాశితో ఏర్పడినది.

iii) p2 – 3p + q
సాధన.
ఇచ్చిన బహుపది ఏక చరరాశితో ఏర్పడిన బహుపది కాదు. ఎందుకనగా దీనిలో p మరియు q అను చరరాశులు కలవు.

iv) y + \(\frac{2}{y}\)
సాధన.
ఇచ్చిన సమాసము బహుపది కాదు. ఎందుకనగా రెండవ పదము హారములో చరరాశిని కలిగి వున్నది.

v) 5\(\sqrt{x}\) + x\(\sqrt{5}\)
సాధన.
ఇచ్చిన సమాసము .బహుపది కాదు. ఎందుకనగా మొదటి పదపు చరరాశి పరిమాణం పూర్ణసంఖ్య కాదు కాబట్టి.

vi) x100 + y100
సాధన.
ఇచ్చిన సమాసము నందు రెండు చరరాశులు కలవు.
కావున ఇది ఏక చరరాశి బహుపది కాదు.

ప్రశ్న3.
కింది వానిలో x3 యొక్క గుణకాలను రాయండి.
i) x3 + x +1
సాధన.
x3 గుణకము 1.

ii) 2 – x3 + x2
సాధన.
x3 గుణకము – 1.

iii) \(\sqrt{2}\)x3 + 5
సాధన.
x3 గుణకము \(\sqrt{2}\).

iv) 2x3 + 5
సాధన.
x3 గుణకము 2.

v) \(\frac{\pi}{2} x^{3}+x\)
సాధన.
x3 గుణకము \(\frac{\pi}{2}\).

vi) –\(\frac {2}{3}\)x3
సాధన.
x3 గుణకము – \(\frac {1}{2}\)

vii) 2x2 + 5
x3 గుణకము ‘0’.

viii) 4
సాధన.
x3 గుణకము ‘0’.

AP Board 9th Class Maths Solutions Chapter 2 బహుపదులు మరియు కారణాంక విభజన Ex 2.1

ప్రశ్న4.
కింది బహుపదులను రేఖీయ, వర్గ మరియు ఘన బహుపదులుగా వర్గీకరించండి.
i) 5x2 + x – 7
సాధన.
దీని యొక్క పరిమాణం ‘2’ కావున ఇది వర్గ బహుపది.

ii) x – x3
సాధన.
దీని యొక్క పరిమాణం ‘3’ కావున ఇది ఘన బహుపది.

iii) x2 + x + 4
సాధన.
దీని యొక్క పరిమాణం ‘2’ కావున ఇది వర్గ బహుపది.

iv) x – 1
సాధన.
దీని యొక్క పరిమాణం ‘1’ కావున ఇది రేఖీయ బహుపది.

v) 3p
సాధన.
దీని యొక్క పరిమాణం ‘1’ కావున ఇది రేఖీయ బహుపది.

vi) πr2
సాధన.
దీని యొక్క పరిమాణం (2) కావున ఇది వర్గ బహుపది.

ప్రశ్న5.
కింది ప్రవచనాలు. సత్యమో, అసత్యమో తెల్పండి. సమాధానాలకు కారణాలు తెలపండి.
i) ద్విపదిలో కనీసం రెండు పదాలుంటాయి.
ii) ప్రతి బహుపది ఒక ద్విపది అవుతుంది.
iii) ద్విపది యొక్క పరిమాణం 3 కూడా కావచ్చు.
iv) శూన్య బహుపది యొక్క పరిమాణం సున్న.
v) x2 + 2xy + y2 బహుపది పరిమాణం 2.
vi) πr2
సాధన.
i) ద్విపదిలో కనీసం రెండు పదాలుంటాయి. – సత్యము
ii) ప్రతి బహుపది ఒక ద్విపది అవుతుంది. – అసత్యం
[∵ బహుపదిలో రెండు కంటే ఎక్కువ పదాలుంటాయి]
iii) ద్విపది యొక్క పరిమాణం 3 కూడా కావచ్చు. – అసత్యము
iv) శూన్య బహుపది యొక్క పరిమాణం సున్న. – అసత్యం
v) x2 + 2xy + y2 బహుపది పరిమాణం 2. – సత్యము
vi) πr2 అనేది ఒక ఏకపది. – సత్యం

AP Board 9th Class Maths Solutions Chapter 2 బహుపదులు మరియు కారణాంక విభజన Ex 2.1

ప్రశ్న6.
10 వ పరిమాణం కలిగిన ఒక ఏకపదికి, త్రిపదికి ఒక్కొక్క ఉదాహరణ ఇవ్వండి.
సాధన.
– 7x10 అను ఏకపది పరిమాణము 10.
3x2y8 + 7xy – 8 అను త్రిపది పరిమాణము 10.

AP 7th Class English Important Questions Unit 6 The Why – Why Girl

These AP 7th Class English Important Questions 6th Lesson The Why – Why Girl will help students prepare well for the exams.

AP Board 7th Class English Unit 6 Important Questions and Answers The Why – Why Girl

Reading Comprehension (Seen)

1. Read the following passage carefully.

“But why ?”
The question came from a small girl, about ten years old. She was chasing a large snake. I ran after her. grabbed her plait and held her back, shouting. “No, Moyna,
don’t!”

“Why shouldn’t I ?” she asked,
“It’s not a grass snake nor a rat snake, it’s a cobra, “I replied.
“Why shouldn’t I catch a cobra ?”
“Why should you ?”
“We eat snakes, you know,” Moyna said. “The head you chop off, the skin you sell, the meat you cook.”

“Yes, but don’t do it this time” I said.
“I will, 1 will.”
“No, child !”
“But why?”

I dragged Moyna back to the Samithi office, where I worked. Her mother, Khiri, was there, weaving a basket. The Samithi was a place where people could come to learn, to read and write, or simply sing and dance together. (The Why – Why Girl)
Now, answer the following questions.
1. What was Moyna running after?
Answer:
She is running after a cobra.

2. Who grabbed Moyna’s plait?
Answer:
The author / The speaker / The narrator

3. Where did the narrator work?
Answer:
At the Samithi office

4. Why do people come to the Samithi office?
Answer:
The Samithi was a place where people could come to learn to read and write, or simply sing and dance together.

5. Who was the mother of Moyna?
Answer:
Khiri

AP 7th Class English Important Questions Unit 6 The Why – Why Girl

2. Read the following passage carefully.

“Come,” I said to Moyna. “Come and rest for a little while.”
“Why?”
“Aren’t you tired?” I asked. Moyna shook her head vigorously.
“Who will bring the goats home and collect firewood, fetch water and lay traps for the birds?” came the questions, one after another.
“Moyna, don’t forget to thank the Babu for the rice he sent us,” said Khiri.

“Why should I? Moyna said. “Don’t I sweep the cowshed and do a thousand jobs for him? Does he ever thank me? Why should I?” saying this, Moyna ran off. Khiri sighed and shook her head. “Never seen a child like this. AH she keeps saying is ‘why’. No wonder the postman calls her why – why girl!” (The Why – Why Girl)
Now, answer the following questions.
1. Who will bring the Babu’s goats home?
Answer:
Moyna

2. Why does Moyna not like to take rest?
Answer:
Because she has much work to do.

3. Who gave the rice to Moyna’s family?
Answer:
Babu

4. Who did not thank Moyna?
Answer:
Babu

5. How was Moyna called?
The why-why Girl

3. Read the following passage carefully.

Moyna was a Shabar. The Shabars were a poor tribal group, and they owned no land. But nobody complained. Only Moyria’s questions went on and on.
“Why do I have to walk so far to the river to fetch water? Why do we live in a leaf hut? Why can’t we eat rice twice a day?” Moyna tended the goats of the village landlords or Babus, but she was neither humble nor grateful. She did her work and came home in the evening.

“Why should I eat their leftovers ?” She would ask,

“I will cook delicious meal with green leaves and rice and crabs and chilli powder and eat with my family.”

The Sabars did not usually send their daughters to work. But Moyna’s mother had a bad leg and so couldn’t walk properly. Her father had gone off to faraway Jamshedpur in search of work and her brother, Goro, went to the forest every day to collect fire-wood. (The Why-Why Girl)
Now, answer the following questions.
1. Who are the Sabars?
Answer:
The Sabars were a poor and landless tribal group.

2. What is the difference between Moyna and other Sabars?
Answer:
Other Sabars ftever complain but Moytla asks endless questions.

3. What is the problem with Moyna’s mother?
Answer:
She had a bad leg.

4. Why did Moyna!s father leave the village?
Answer:
For work

5. Who is Goro?
Answer:
Moyna’s brother

4. Read the following passage carefully.

One night she asked me, “Why do you read books before you go to sleep?”

“Because books have the answers to your whys!” I replied. And for once, Moyna was silent. She tidied the room, watered the flowering tree and fed fish to the mon-goose. Then she came up to me and said, “I will learn to read and find the answers to my questions.” When Moyna grazed the goats, she told the other children all that she had learned from me.

“Many stars are bigger than the sun. But they live far away so they look small. The sun is nearer, so it looks bigger. The fish do not speak like us. They have a fish lan-guage, which is silent. The earth is round, did you know that ?” (The Why – Why Girl)
Now, answer the following questions.
1. Why does the speaker read books?
Answer:
To know the answers to the questions.

2. What was Moyna’s wish?
Answer:
She wants to read and find the answers to her questions.

3. Who learnt all the things to Moyna?
Answer:
The narrator

4. Why do big starts appear smaller than the sun?
Answer:
Because they are far away.

5. What does the narrator do before she goes to sleep?
Answer:
She reads books.

AP 7th Class English Important Questions Unit 6 The Why – Why Girl

5. Read the following passage carefully.

“Who’s stopping you?”
“But there’s no class !”
“School is over for the day,” Malati pointed out.
“Why?”
“Because, Moyna, I take the class from 9 to 11 in the morning,” said Malati.

Moyna stamped her foot and said, “Why can’t you change the hours? I have to graze the goats in the morning. I. can come only after 11. If you don’t teach me, how will I learn? I will tell the old lady” – me! – “that none of us, goatherds and cowherds, can come if the hours are not changed.” Then she saw me and fled with her goat.

I went to Moyna’s house in the evening. Nestling close to the kitchen fire, Moyna was telling her little sister and elder brother, “You cut one tree and plant another two. You wash your hands before you eat, do you know why? You’ll get stomach pain if you don’t. You know nothing – do you know why? Because you don’t attend the classes at the Samithi.” Who do you think was the first girl to be admitted to the village primary school?
Moyna. (The Why – Why Girl)
Now, answer the following questions.
1. Who is Malati?
Answer:
The Samithi teacher

2. What should we do before we eat?
Answer:
We should wash our hands.

3. What should one do to know all the things?
Answer:
One should go to Samithi.

4. Who was the first student of the primary school?
Answer:
Moyna

5. Why can’t Moyna come to school in the morning?
Answer:
She has to graze the goats in the morning.

6. Read the following lines carefully.

If you can’t be a pine on the top of the hill, .
Be a scrub in the valley – but be The best little scrub by the side of the rill;
Be a bush if you can’t be a tree. (Be The Best of Whatever You Are)
Now, answer the following questions:
1. Where is the pine?
Answer:
On the top of the hill

2. Where is the scrub?
Answer:
In the valley

3. It is better to be ………………. if we can’t be a tree.
(a) a brush (b) a valley (c) a hill
Answer:
(a) a brush

4. What is the poet’s tone in these lines?
Answer:
Optimism

5. What figure of speech is used in the line ‘ If you can’t be a pine on the top of the hill, Be a scrub in the valley”?
Answer:
The figure of speech used in this line is antithesis. Antithesis is the figure of speech that conveys two opposite thoughts brought together. Pine is a tall tree while a scrub is comparatively very small.

7. Read the following lines carefully.

If you can’t be a bush be a bit of the grass,
And some highway happier make;

If you can’t be a muskie then just be a bass
But the liveliest bass in the lake! (Be The Best of Whatever You Are)
Now, answer the following questions.
1. How should we be if we can’t be a bush?
Answer:
We should be a bit of the grass.

2. Which makes the highway happier?
Answer:
Grass

3. Which word in these lines refer to ‘a big fish’?
Answer:
Muskie

4. Which is important?
(a) a bush
(b) a bit of grass
(c) both
Answer:
(c) both

5. What figure of speech is used in ‘And some highway happier make’?
Answer:
The figure of speech used in this line is alliteration.

Alliteration is the repetition of a consonant sound in the beginning of consecutive words. In the given line the words ‘ highway, happier’ are alliterative with the repetition in the consonant sound of the phoneme/h/.

AP 7th Class English Important Questions Unit 6 The Why – Why Girl

8. Read the following lines carefully.

We can’t all be captains, we’ve got to be crew,
There’s something for all of us here,
There’s big work to do, and there’s lesser to do,
And the task you must do is the near. (Be The Best of Whatever You Are)
Now, answer the following questions.
1. What should we be if we can’t be a captain?
Answer:
We should be a crew.

2. What is the tone of the poet?
Answer:
Optimism

3. What is the rhyme scheme you find in this stanza?
Answer:
abab

4. What is the message of the poem?
Answer:
One should try to do one’s best with whatever one is.

5. Which word in the poem means the same as ‘piece of work’?
Answer:
Task

9. Read the following lines carefully.

If you can’t be a highway then just be a trail,
If you can’t be the sun be a star;
It isn’t by size that you win or you fail
Be the best of whatever you are! (Be The Best of Whatever You Are)
Now, answer the following questions.
1. What should be our attitude towards our work?
Answer:
Whatever we do, we should do it whole-heartedly.

2. What can one be when one can’t be the sun?
Answer:
One can be a star.

3. What are the two contrasting things mentioned the first two lines?
Answer:
A highway and a trail

4. What decides the winning?
Answer:
The best quality of work

5. What is the tone of the poet?
Answer:
Optimism

Reading Comprehension (Unseen)

1. Read the following passage carefully.

A visit to an exhibition is a novel experience. An exhibition which I visited recently was very interesting. It was one of the largest exhibitions ever held. Being a Sunday there were many visitors that made it difficult to walk.

Men, women, and children in their colourful and best dresses were there. At the booking counter there were long queues. I bought tickets and entered the exhibition grounds. Our parents and I enjoyed the exhibition for a long time. The grounds were tastefully decorated. There were stalls and pavilion of ministries, companies, and states.

There were hundreds of exhibits for the domestic use. By the time we came out of the German pavilion, we were very tired. We went to a coffee shop and had hot coffee. My mother bought a shawl. There was a village complex with many village singers, jugglers, and folk artists. The puppet show was very amusing.
Now answer the following questions
a) What is necessary to visit the exhibition?
Answer:
An entrance ticket

b) Who is a juggler?
Answer:
One who does magic is a juggler.

Choose the correct answer from the choices given.
c) When is it difficult to go around in exhibition?
i) Sunday
ii) Tuesday
iii) Working day
Answer:
i) Sunday

d) What was very entertaining for the author?
i) Stalls
ii) Coffee shop
iii) Puppet show
Answer:
iii) Puppet show

e) What did the writer’s family do when they were tired?
i) They sat down and relaxed.
ii) They went to a coffee shop and had coffee.
iii) They bought toys and shawl
iv) They went home.
Answer:
ii) They went to a coffee shop and had coffee.

2. Read the following passage carefully.

Sally jumped up as soon as she saw the surgeon come out of the operating room. She said : “How is my little boy? Is he going to be alright? When can I see him? The surgeon said, “I’m sorry. We did all we could, but your boy didn’t make it”. Sally said, “Why do little children get cancer? Doesn’t God care anymore? Where were you, God, when my son needed you?”

The surgeon asked, “Would you like some time alone with your son? One of the nurses will be out in a few minutes, before he’s transported to the university”.

Sally asked the nurse to stay with her while she said goodbye to son. She ran her fingers through his curly hair. “Would you like a lock of his hair?” the nurse said. She cut a lock of the boy’s hair and gave it to Sally in a plastic bag. Sally said, “It was Jimmy’s idea to donate his body to the university for study. He said it might help somebody else,” she continued, “My Jimmy had a heart of gold. Always thinking of someone else. Always wanting to help others if he could”.
Now answer the following questions.
a) Who was admitted in the hospital?
Answer:
Sally’s son

b) What was the boy suffering from?
Answer:
Cancer

Choose the correct answer from the choices given.
c) Where will the boy be taken after the surgery?
i) to his home
ii) to hospital
iii) to university
iv) to a clinic
Answer:
iii) to university

d) What did the nurse offer Sally as a token of memory?
i) a gold win
ii) a big chest of clothes
iii) the boy’s clothes
iv) a lock of hair of the boy
Answer:
iv) a lock of hair of the boy

e) Why was the boy taken to the university?
i) to be operated
ii) to get good treatment
iii) to be helpful for the study of others
iv) to help the doctors
Answer:
iii) to be helpful for the study of others

Interpretation of Non-Verbal Information

1. The following table tells us about the population details of five villages.
AP 7th Class English Important Questions Unit 6 The Why – Why Girl 1
Now answer the following questions.
a) What information can we get from the above table?
Answer:
Population details of five villages

b) Which village has the highest number of total population?
Answer:
Suripadu

Choose the correct answer from the choices given below.
c) Which village is in the second place in female population?
i) Veerukonda
ii) Alkapur
iii) Suripadu
Answer:
ii) Alkapur

d) The two villages with the same number of male population are ………
i) Velagalammapudi and Suripadu
ii) Rambedu and Suripadu
iii) Veerukonda and Rambedu
Answer:
iii) Veerukonda and Rambedu

e) Which of the following statements is true with reference to the information given above?
i) The number of males and females in Rambedu is almost equal.
ii) The number of females is higher than the number of males in Velagalammapudi.
iii) Alkapur has the lowest number of families.
Answer:
i) The number of males and females in Rambedu is almost equal.

2. Study the following tree diagram carefully.
AP 7th Class English Important Questions Unit 6 The Why – Why Girl 2
Now answer the following questions.
a) Who is Meena’s mother-in-law?
Answer:
Naveena

b) How many granddaughters does Arjun have?
Answer:
Four

Choose the correct answer from the choices given below.
c) Praveena is the daughter of………….
i) Meena
ii) Ravi
iii) Kavya
Answer:
iii) Kavya

d) Venu and Nikhil are ………
i) brothers
ii) cousins
iii) friends
Answer:
ii) cousins

e) Which of the following statements is true with reference to the information given above?
i) Anil has two daughters.
ii) Anuhya and Rani are sisters.
iii) Kavya is Ravi’s wife.
Answer:
ii) Anuhya and Rani are sisters.

Vocabulary

Synonyms

Choose the words with similar meanings (synonyms) from the list given to the words underlined.
AP 7th Class English Important Questions Unit 6 The Why – Why Girl 3
Answer:
a) a) exhausted, b) strenuously
b) a) stubborn, b) yield
c) a) remained, b)announced
d) a) maketired, h) tend
e) a) Settling, b) chop
f) a) commanding, b) idle

Antonyms

Write the opposites (antonyms) for the underlined words.
a) The question (a) came from a small girl, about ten years old. She was chasing (b) a large snake.
b) “Moyna, don’t forget (a) to thank the Babu for the rice he sent (b) us,” said Khiri.
c) Moyna tended the goats of the village landlords or Babus, but she was neither humble (a) nor grateful (b).
d) When I returned (a) to the village a year later (b), the first thing I heard was Moyna’s voice.
e) If you pass by, you’re sure (a) to hear an impatient (b), demanding voice – “Don’t be lazy. Ask me questions.”.
f) “Don’t be lazy (a). Ask me questions. Ask me why mosquitoes should be destroyed, why the pole star is always (b) in the north sky.”
Answer:
a) a) answer, b) escaping
b) a) remember, b) received
c) a) proud, b) ungrateful
d) a) left, b) earlier
e) a) unsure, b) patient
f) a) industrious, b) never

Right Forms of the Words

Fill in the blanks with the right form of the words given in the brackets.

a) “Aren’t you tired ?” I asked. Moyna shook her head _____ (a) (vigorous / vigorously. “Who will bring the goats home and _____ (b) (collection/collect) firewood, fetch water and lay traps for the birds?” came the questions, one after another.
b) “But she is very, _____ (a) (obstinate / obstinately),” Khiri _____ (b) (retortion/retorted).
c) Moyna tended the goats of the village landlords or Babus, but she was neither _____ (a) (humble / humbly) nor _____ (b) (gratefulness / grateful).
d) “The good snakes I _____ (a) (caught / catch) and give to mother. She makes _____ (b) (love / lovely) snake curry.
e) Moyna was _____ (a) (silence / silent). She tidied the room, watered the flowering tree and fed fish to the mongoose. Then she came up to me and said, “I will _____ (b) (learnt/learn) to read and find the answers to my questions.”
f) If you pass by, you are _____ (a) (sure / surely) to hear her _____ (b) (impatient / impatience), demanding voice, “Don’t be lazy. Ask me questions.”
Answer:
a) p) vigorously, b) collect
b) a) obstinate, b) retorted
c) a) humble, b) grateful
d) a) catch, b) lovely
e) a) silent, b)learn
f) a) sure, b) impatient

Spelling Test

Type — 1 : Vowel Clusters

Complete the following words using “ai, au, ea, ee, ei, eo, la, ie, io, oi, oo, ou, ua, ue or ui”.

a) I ran after her, grabbed her pl _ _ t and held her back, sh _ _ ting. “No, Moyna, don’t!”
b) Moyna sh _ _ k her head vigor _ _ sly.
c) The Shabars were a p _ _ r tribal gr _ _ p.
d) And she came, with one change of clothes and a baby mong _ _ se. “It _ _ ts very little and chases away the bad snakes.” “The good.snakes I catch and give to mother.”
e) The _ _ rth is r _ _ nd, did you know that?
f) If you don’t t _ _ ch me, how will I l _ _ rn?
Answer:
a) plait, shouting
b) shook, vigorously
c) poor, group
d) mongoose, eats
e) earth, round
f) teach, learn

AP 7th Class English Important Questions Unit 6 The Why – Why Girl

Type – 2 : Suffixes

Complete the following words with the suitable suffixes given in the brackets.

a) “Aren’t you tire__ (d / ed)?” I asked. Moyna shook her head vigorous__ (ly /My).
b) Moyna tended the goats of the village land__ (a) (lords / lards) or Babus, but she was neither humble nor grate__ (b) (ful / full).
c) “She makes love__ (lly / ly) snake curry. I’ll bring some for you” said Moyna. Our Samithi teach__ (er / or), Malati, said to me, “She’ll exhaust you with her whys !”
d) Many stars are bigg__ (or / er) than the sun. But they live far away, so they look small. The sun is near__ (er / or).
e) When I return__ (ed / d)“to the village a year later, the first thing I heard was Moyna’s voice. “Why is the school closed?” she challenged Malati as she entered the Samithi’s school, dragg__ (ed / irig) along a bleating goat.
f) If you pass by, you’re sure to hear an impati__ (ent/ant), demanding voice, “Don’t be lazy. Ask me questions. Ask me why mosquitoes should be destroy__ (d / ed), Why the pole star is always in the north sky.”
Answer:
a) tired, vigorously
b) landlords, grateful
c) lovely, teacher
d) bigger, nearer
e) returned, dragging
f) impatient, destroyed

Type – 3 : Wrongly Spelt Words

Identify the wrongly spelt word and write its correct spelling in the space provided.
a) grass, stamped, learn, thousend
Answer:
thousand

b) tribel, chop, river, study
Answer:
tribal

c) office, employer, graze, mosquiteos
Answer:
mosquitoes

d) search, primery, forest, simply
Answer:
primary

e) fetch, mongoose, lovly, hour
Answer:
lovely

Classification of Words

Arrange the following words under the correct headings.
AP 7th Class English Important Questions Unit 6 The Why – Why Girl 4

Choice of the Words

Fill in the blanks choosing the suitable words from those given in the box.
AP 7th Class English Important Questions Unit 6 The Why – Why Girl 5

Answer:
a) 1) dragged, 2) weaving
b) 1) obstinate, 2) retorted
c) 1) delicious, 2) send
d) 1) chases, 2) lovely
e) 1) exhaust, 2) graze
f) 1) stamped, 2) change

Homophones

Fill in the blanks with suitable words using the homophones given in the brackets.

1. Did the ____ win the race? (hair, hare)
2. Farida has gone to visit her ____ . (son, sun)
3. You sound a little ____ . (horse, hoarse)
4. The flu left him ____ . (week, weak)
5. It is rude to ____ at DeoDle.(stare, stair)
6. Can I have a ____ of cake, nlease. (peace, piece)
7. This ____ is interesting. (storey, story)
8. Don’t ____ your valuable time. (waste, waist)
9. I ____ his mobile number. (no, know)
10. Thev like to watch that ____ . (cereal, serial)
Answer:

  1. hare
  2. son
  3. hoarse
  4. weak
  5. stare
  6. piece
  7. story
  8. waste
  9. know
  10. serial

Phrasal Verbs

Fill in the blanks with suitable phrasal verbs given in the box.
AP 7th Class English Important Questions Unit 6 The Why – Why Girl 7

1) Rajkumar ______ his friend admiringly.
2) He ______ his wet boots and sat by the fire.
3) Nandakishore wanted to ______ some business in the city.
4) Kaushik ______ on the sofa and soon fell asleep.
5) She usually ______ at 5 o’clock.
6) Caterpillars ______ butterflies.
Answer:

  1. looked at
  2. took off
  3. set up
  4. lay down
  5. gets up
  6. change into

Grammar

I. Edit the following passage correcting the underlined parts.

1. Abudl Kalam is (a) born on 15th October, 1931 in (b) Rameswaram in Tamil Nadu. She (c) graduated in aeronautical engineering from an (d) Madras Indian Institute of Technology.
Answer:
a) was b) at c) He d) the

2. On one fine sunny day, Akbar and Birbal were taking an (a) leisurely walk in the palace gardens. Immediately (b) Akbar thought of testing Birbal’s wits by asking her (c) a tricky question. The Emperor asked Birbal, “How much (d) crows are there in our kingdom?”
Answer:
a) a b) Suddenly c) him d) How many

3. Born in the sixth century B.C., Susrutha was a descendant of a (a) Vedic sage Viswamitra. He learnt surgery but (b) medicine at the feet of Divodasa Dhanvantari in tier (c) hermitage at Varanasi. Later, he becomes (d) an authority in not only surgery but also in other branches of medicine.
Answer:
a) tHe b) and c) his d) became

4. Snakes are a (a) most specialized group of reptiles. Much (b) species of snakes are find (c) all over the world. Some of they (d) are poisonous and some are not poisonous.
Answer:
a) the b) Many c) f6und d) them

AP 7th Class English Important Questions Unit 6 The Why – Why Girl

II. Complete the passage choosing the right words from those given below. Each blank is numbered and for each blank four choices are given. Choose the correct answer and write (A), (B), (Q or (D) in the. blanks.

1. Pandavas were the five powerful and skilled sons ………. (1) Pandu, the king of Hastinapur and his two wives Kunti and Madri: Hastinapur is ………. (2) with the current modern Indian state of Haryana, South of New Delhi. ………. (3) Pandavas are the central characters in the most applauded epic, the Mahabharata. They were famously involved in the Kurukshetra war with ………. (4) cousins, Kauravas.
1) A) of B) in C) at D) with
2) A) equate B) equates C) will equate D) equated
3) A) The B) A C) An D) This
4) A) our B) their C) my D) his
Answer:
1) A 2) D 3) A 4) B

2. Anacondas are a group ………. (1) large snakes. ………. (2) are found in tropical South America. The green anaconda is ………. (3) largest snake in the world. It can reach a length of 30 feet and ………. (4) up to 550 Pounds.
1) A) on B) with C) of D) to
2) A) We B) They C) She D) It
3) A) the B) an C) this D) a
4) A) weighed B) weight C) will weigh D) weigh
Answer:
1) C 2) B 3) A 4) D

3. Ramzan is one of ………. (1) most important festivals for Muslims. This festival ………. (2) the end of the holy month Ramzan. The month of Ramzan is considered ………. (3) a gift from God and is related ………. (4) mercy and forgiveness.
1) A) a B) the C) an D) this
2) A) marking B) marked C) marks D) mark
3) A) since B) but C) and D) as
4) A) to B) for C) by D) into
Answer:
1) B 2) C 3) D 4) A.

4. A long time ago there ………. (1) a monkey who lived in a rose-apple tree by the side of a river. He lived alone, ………. (2) was very happy. One day, a crocodile came out ………. (3) the river. He swam up to the tree and told ………. (4) monkey that he had travelled a long distance and was in search of food as he was very hungry.
1) A) were B) are C) is D) was
2) A) if B) but G) since D) as soon as
3) A) of B) into C) in D) to
4) A) a B) an C) the D) those
Answer:
1) D 2) B 3) A 4) C

III. Rearrange the words and make meaningful ‘wh’ questions.

a) classes / will / when / begin / our
Answer:
When will our classes begin?

b) going / where / you / are
Answer:
Where are you going?

c) teacher / your / who / favourite / is
Answer:
Who is your favourite teacher?

d) brothers / many / you / how / have?
Answer:
How many brothers have you?

e) come / did / you / why / yesterday / not
Answer:
Why did you not come yesterday?

IV. Read the following statements and frame suitable ‘wh’ questions.

a) This is my father’s car.
Answer:
Whose car is this?

b) Yesterday, I met my friend.
Answer:
Whom did you meet yesterday?

c) This film is very nice.
Answer:
How is this film?

d) She will come tomorrow.
Answer:
When will she come?

e) Viswanathan Anand won the game.
Answer:
Who won the game?

AP 7th Class English Important Questions Unit 6 The Why – Why Girl

V. Complete the following sentences using apprpriate clause.

1) If you work hard, ______. (get success)
2) If you tease the dog, ______. (bite you)
3) If you go to bed early, ______ . (be healthy)
4) ______ you’ll catch the bus. (walk fast)
5) ______ they will also respect you. (give respect to others)
Answer:

  1. you will get success
  2. it will bite you
  3. you will be healthy
  4. If you walk fast
  5. If you give respect to others,….

VI. Interchange the ‘if clause’ and the ‘main clause’ in the above sentences and write them down.
Answer:

  1. You will get success if you work hard.
  2. The dog will bite you if you tease it.
  3. You will be healthy if you go to bed early.
  4. You will catch the bus if you walk fast.
  5. Others will also respect you if you give respect to them.

Creative Writing

1. In the lesson “The Why – Why Girl”, you have learnt that Moyna exhausted others with her ‘whys’. One day she met Malati, their Samithi teacher and asked her why she shouldn’t study too.
Now, write a possible conversation based on the above context.
Answer:
Moyna : Good morning, teacher.
Malati : Good morning, Moyna.
Malati : Why have you come to me?
Moyna : Why is school closed? Why shouldn’t I study too?
Malati : Who’s is stopping you, girl? School is over for the day.
Malati : You know, Moyna, I take the class from 9 to 11 in the morning.
Moyna : Why can’t you change the hours, madam?
Malati : Why should I change the hours, Moyna?
Moyna : I have to graze Babu’s goats in the morning. I can only come after eleven.
Malati : No, I won’t change my time.
Moyna : If you don’t teach, how will I learn?
Moyna : If you don’t change the hours, none of us, goatherds, and cowherds can come.
Malati : O.K., girl. I will change the hours. You can come after eleven.
Moyna : Thank you, madam.
Malati : It’s O.K., girl.

2. In the. lesson “The Why – Why Girl”, you have learnt that Moyna grew up and started teaching at the Samithi school. When she was a girl, she was interested in asking questions others. She almost all exhausted others with her ‘whys’. When she became teacher, she expected a number of questions from the students. She even encouraged them to ask her questions. She asked them not to be lazy.

Imagine that you were Moyna and write a diary entry expressing your feelings at the end of the day on which you have attended the school for the first time as a – teacher.
Answer:

Monday, 10th August, 20xx
8:30 p.m.Dear Diary,
Oh, God ! I am really grateful to you. Finally, my long lasting wish has been fulfilled. It’s all because of your grace. From my childhood onwards, everyone has referred me as ‘why-why’ girl. That ‘why – why’ girl has become a teacher today ! My questioning nature has brought me to today’s position. But, in the morning class, the children did not ask me questions. They were all lazy in that period. Why didn’t they ask me the questions such as, “Why should mosquitoes be destroyed ?”, “Why is the pole star always in the north sky ?” etc. Then only they will shine, they will have a bright future. From tomorrow onwards, I shall make them learn the art of questioning. If one doesn’t question, one doesn’t find anything and one doesn’t achieve anything.Moyna

3. Mother’s Day is celebrated on May 9th. Prepare a script for speech on the role of a mother in a family on the occasion of Mother’s Day.
Answer:
Honorable judges and dear students,

Today, I, Abhilash of Class VII, stand before you to speak on the role of a mother in a family. With Mother’s Day that is celebrated on May 9th, round the corner, I thought of reflecting on the role of a mother and importance in a child’s life.

A mother is like the nucleus around whom everyone else orbits in a family. And the word multitasking was probably coined for a mother, and if not certainly had her in mind 1 After all a mother provides the required structure and balance to the household, lacking which the world would seem chaotic and confusing. She is the one person who. ensures that life functions in an orderly way, right from breakfast, lunch, dinner being served at the table, to clothes being ironed and kept in the cupboard, to the kitchen always being stocked up with food, the beds perfectly made, the bills paid, the list is infinite. However more importantly, a mother brings balance to the family mentally and emotionally.

Needless to say she plays a pivotal role in what a child is tomorrow. A mother is the one person who is responsible for a child’s wholesome development and takes charge of it. Clearly a mother journey is perhaps one of the toughest. There is a saying that the God created mother in his place to look after the family. We should agree to this and be thankful to mother. Showing gratitude is the only tribute that we can give to a mother.

Thank you one and all for giving me this opportunity.

AP 7th Class English Important Questions Unit 6 The Why – Why Girl

4. The locality in which you live is not cleaned properly by the Municipal workers. Heaps of garbage are found everywhere. Foul smell is coming out of it. You sense the danger of spreading diseases.

Write a letter to the Municipal Commissioner about the insanitary conditions.
Answer:

4th February, 20xx.

From
Regd. No. x x x x,
Government College Road,
Bhimavaram.

To
The Municipal Commissioner,
Bhimavaram Municipality.

Sir,
I regret to bring the following to your notice for necessary action.

Our town is suffering a lot due to the negligence of the Municipal helath workers. The sweepers are not regular to their duties. Once in a week they come in a casual way. There are piles of garbage at every corner emitting foul smell.

Some roads have pot-holes and ditches. Water gets stagnated. Recently a girl fell into a ditch. Thank God, a cyclist saw it and saved her. If the same state of affairs continue, I am afraid that diseases may spread. All these things lead to health hazard.
May I request you to take steps in this regard ? You know sir, public health should be the priority of the Municipality.

Thanking you Sir,

Yours faithfully,
xxxxxxxx.

5. Write a story using the hints provided

Hints : Small village – a boy and a mother – poor – collected wood from forest – cut down small trees – one day – a big bird from a tree – don’t cut down this tree – my house – boy agreed – bird pleased – come before sunrise with a bag – next morning – hold on to my tail – flew up – in the sky -to a distant valley – full of gold – filled the bag – flew back – boy and mother rich – happy.
Answer:
The Kindness of a Bird
Once there# lived a boy and his mother in a small village. They were very poor and earned their livelihood by collecting wood from forest. The boy used to cut down small trees.

One day he began to cut a big tree. A bird from the tree pleaded not to cut down the tree because it was her house. The boy agreed.

The bird was pleased and asked the boy to come before sunrise with a bag the next morning. He did as the bird said. The bird asked the boy to hold on to her tail. The boy held her tail tightly and the bird flew up in the sky to a distant valley which was full of gold. The boy filled the bag with gold. Then they flew back. The boy and his mother became rich. They lived happily.

AP 7th Class English Important Questions Unit 6 The Why – Why Girl

6. Write a story using the following hints.

Hints: A crow – thirsty – no Water around – flies around – searches for water – finds water in a pot- water at the bottom – can not reach – thinks of a plan – looks around – found small stones – drops small stones into the pot – water comes up – drinks feels happy – flies away.
Answer:
A Clever Crow

Once upon a time there was a crow. It was clever. It lived on the branch of a tree in. a forest. One day it was very thirsty as it was a hot summer. There was no water around. So it thought to go to the villages around in search of water. It reached a near by village and began to search for water. It searched many places for water. At last it found some water in a pot near a hut. It felt happy on seeing the water in the pot.

But it became very difficult for the crow to reach as the water was at the bottom of the pot. It tried very hard but it could not get the water. So it was disappointed. It looked around and found a heap of small stones. On seeing the heap of stones, there came a thought of bringing the water in the pot from the bottom to the top. It dropped the small stones one by one into the pot. The water came up. The crow drank the water and quenched its thirst. It felt happy and flew away.

Moral: Where there is a will, there is a way.

AP 7th Class English Important Questions Unit 5 The Art of Weaving

These AP 7th Class English Important Questions 5th Lesson The Art of Weaving will help students prepare well for the exams.

AP Board 7th Class English Unit 5 Important Questions and Answers The Art of Weaving

Reading Comprehension (Seen)

1. Read the following passage carefully.

We went to Mangalagiri, one of the famous towns in Guntur District, along with our English teacher on a case study.

First, we consulted a master W&1V€1’, Veertfatf, for the details “where to go?”, “whom to meet?” Mr. Veeraiah cordially welcomed us. He said “Mangalagiri is famous for its sarees and fabrics produced by handicraft weaving. Many families live on the art of weaving here.” (The Art of Weaving)

Now, answer the following questions.
1. What was the case study about?
Answer:
The case study was about the handlooms in Mangalagiri.

2. Who helped the students?
Answer:
Veeraiah

3. What was Veeraiah?
Answer:
A master weaver

4. What is Mangalagiri famous for?
Answer:
Mangalagiri is famous for its sarees and fabrics produced by handicraft weaving.

5. Who took the students to Mangalagiri?
Answer:
Their English teacher

AP 7th Class English Important Questions Unit 5 The Art of Weaving

2. Read the following passage carefully.

We asked him, “Could you please tell us about the fabric of Mangalagiri?” He expressed his gratitude for our concern for them and responded most positively:

“This fabric is the product of weaving with the help of pit looms. It takes much time to weave and requires a lot of patience to prepare everything ready. Mangalagiri sarees are special for their quality and the process we follow. The quality of fabric depends upon the yarn we use. Generally, we purchase cotton yarn from different mills from our state and Jari from Surath, Maharashtra.”

“Sir, can you explain how you begin the process of weaving?” asked one of our classmates.

Veeraiah said, “First, the yarn is boiled in the water, mixed with caustic soda, for a couple of hours and also bleached to make it suitable for dyeing”. (The Art of Weaving)
Now, answer the following questions.
1. Who explained the things to students?
Answer:
Mr. Veeraiah, a master weaver

2. What does the making of this fabric require?
Answer:
It requires a lot of patience.

3. What is the speciality of Mangalagiri sarees?
Answer:
They are special for the quality.

4. What does the quality depend on?
Answer:
It depends on the yarn they use.

5. What is the first step in the process of weaving? .
Answer:
First, the yarn is boiled in the water, mixed with caustic soda, for a couple of hours and also bleached to make it suitable for dyeing.

3. Read the following passage carefully.

While we were going on the streets of Mangalagiri, we met another weaver Sambayya who was selling handloom sarees. We asked him, “Why is the fabric produced in Mangalagiri special from other fabrics?”

His enthusiasm was evidently seen when he said, “The Nizam design is a unique characteristic feature of this fabric. The uniqueness of Mangalgiri cotton is because of its durability. The fabric is woven only on a pit loom, and there are no gaps on the weave towards the edges of the fabric along with the fact that it is created in Mangalgiri alone. The body and the pallu are embellished with zari or golden thread work with a Nizam boarder and geometrical and simple designs. (The Art of Weaving)

Now, answer the following questions.
1. What was Sambayya doing on the street?
Answer:
He was selling handloom sarees.

2. What Was the unique characteristic feature of Managalagiri fabric?
Answer:
The Nizam design

3. How is the fabric woven?
Answer:
It is woven on a pit loom.

4. How is golden thread work used?
Answer:
To embellish the body and the pallu

5. What do you understand about the durability of Mangalagiri fabric?
Answer:
It is of high durability.

AP 7th Class English Important Questions Unit 5 The Art of Weaving

4. Read the following passage carefully.

Around 5000 weavers are working in the Mangalagiri textiles industry in a population of eighty thousand. Mangalagiri has a special place in the world textile map because of the handloom sarees and the dress materials woven here are world famous.

The weavers face many problems in the textile industry. They face tough competition, change in fashion, trends, scarcity of raw material, and the involvement of middle men. However the traditional value of handloom fabric is increasing for their uniqueness. Handloom fabric, thus, has a lot of global demand because of its artistic appeal. (The Art of Weaving)

Now, answer the following questions.
1. What are the main products of Mangalagiri textiles industry?
Answer:
Handloom sarees and dress-materials

2. How many people depend on textiles industry in Mangalagiri?
Answer:
Around 5000 people

3. What problems do the weavers face?
Answer:
They face tough competition, change in fashion, trends, scarcity of raw material, and the involvement of middle men.

4. Why is the traditional value of the fabric increasing?
Answer:
Because of its uniqueness

5. Why does handloom fabric have globcil demand?
Answer:
Because of its artistic appeal

5. Read the following lines carefully.

Weavers, weaving at break of day,
Why do you weave a garment so gay?…
Blue as the wing of the halcyon wild,
We weave the robes of a new-born child. (Indian Weavers)

Now, answer the following questions.
1. What do the weavers weave in the morning (at break of day)?
Answer:
A garment so gay

2. For whom are the special clothes being woven?
Answer:
For a new-born child

3. What are the clothes compared to?
Answer:
The clothes are co.mpared to the wing of a halcyon whose wings are bright colour.

4. Which stage of human life is talked in these lines?
Answer:
Childhood

5. What is the colour of the garment of a new-born child?
Answer:
The colour of the garment of a new-born child is blue.

6. Read the following lines carefully.

Weavers, weaving at fall of night,
Why do you weave a garment so bright?
Like the plumes of a peacock, purple and green,
We weave the marriage-veils of a queen. (Indian Weavers)

Now, answer the following questions.
1. When are the weavers weaving the marriage veil of a queen?
Answer:
The weavers are weaving the marriage veil of a queen at fall of night.

2. What is it compared to?
Answer:
It is compared to the plumes of a peacock.

3. What is the colour of the garment?
Answer:
The colour of the garment is purple and green.

4. Which words rhyme with ‘night’ and ‘green’?
Answer:
‘Night’ rhymes with ‘bright’ and ‘green’ rhymes with ‘queen’.

5. What is the stage of human life discussed here?
Answer:
The stage of youth

AP 7th Class English Important Questions Unit 5 The Art of Weaving

7. Read the following lines carefully.

Weavers, weaving solemn and still,
What do you weave in the moonlight chill?
White as a feather and white as a cloud,
We weave a dead man’s funeral shroud. (Indian Weavers)

Now, answer the following questions.
1. Write name of the poem from which the above stanza has been taken. Who is the poetess of the poem?
Answer:
The name of the poem is ’Indian Weavers’. Its poetess is Sarojini Naidu.

2. What did the weavers weave in the chill moonlight?
Answer:
The weavers are weaving the shroud in the chill moonlight.

3. What is the colour of the shroud?
Answer:
The colour of the shroud is white.

4. Which words rhyme with each other in the above stanza?
Answer:
Still’rhymes with’chill’and’cloud’rhymes with’shroud’.

5. What figure of speech is used in the following lines?
White as a feather and as a cloud,
We weave a dead man’s funeral shroud.
Answer:
Simile

Reading Comprehension (Unseen)

1. Read the following passage carefully.

Mother Teresa is also known as ‘Blessed Teresa of Calcutta”. Her earlier name was “Anjeze Gonxhe Bojaxhiu”. She was born on 26th August, 1910 at the then Yugoslavia. She came to India in 1929. Mother Teresa was Roman Catholic nun moved to Calcutta’s slum “to serve God among the poorest of the poor”.

In 1950, she established the Missionaries of Charity to help the poor, helpless, disabled, diseased refugees and lepers. Today, the missionaries of charity are in more than 100 countries.

She was awarded the title of “Padma Shri” in 1962. She received the Nobel Peace Prize in 1979. Later in 1980, she received the title of ‘Bharat Ratna”, the-highest civil-ian award in India. She was the first citizen of India to win Nobel Peace Prize.

Now, answer the following questions.
a) What is the other name for Mother Teresa?
Answer:
‘Blessed Teresa of Calcutta’

b) What was the birth place of Teresa?
Answer:
Yugoslavia

Choose the correct answer from the choices given.
c) When did Mother Teresa found the Missionaries of Charity?
i) 1980
ii) 1929
iii) 1950
iv) 1919
Answer:
iii) 1950

d) What was the award received by Teresa in 1979?
i) Nobel Prize
ii) Padma Shri
iii) Blessed Teresa
iv) Bharat Ratna
Answer:
i) Nobel Prize

e) Where did Mother Teresa find God?
i) in the city of Calcutta
ii) in the school of charity
iii) in Yugoslavia
iv) in the poorest of the poor
Answer:
iv) in the poorest of the poor

AP 7th Class English Important Questions Unit 5 The Art of Weaving

2. Read the following passage carefully.

There was a Guru who had mastered the scriptures. One day when he was teaching the Vedas to his disciples, a cat started moving around. This did not disturb the Guru, but was a distraction to some of his disciples. So the Guru instructed his disciples to get hold of the cat and tie it to pillar. As the nuisance recurred on the following days, the cat was regularly tethered to the pillar before the Guru began his teaching.

Some years later the Guru died. One of his disciples became the new head. The practice of tethering the cat to the pillar continued. After a few months the cat died. When the Guru began his teaching the next day he noticed that the cat was missing. He said, “Don’t you know that a cat must be tied to the pillar during my teaching? That is our tradition. Go and find a cat”. The disciples immediately obeyed the order. Blindly following traditions, thus, is foolish and serves no purpose.

Now, answer the following questions.
a) Why were the disciples distracted?
Answer:
A cat’s moving around distracted the disciples.

b) What was done to prevent the cat from roaming about?
Answer:
The cat was tied to the pillar.

Choose the correct answer from the choices given.
c) Who became the new head?
i) One of the disciples of the Guru
ii) The cat
iii) All the disciples
Answer:
i) One of the disciples of the Guru

d) What practice continued after the new Guru took charge?
i) Keeping the cat near the Guru
ii) Tethering the cat to the pillar
iii) Making it go round the pillar
Answer:
ii) Tethering the cat to the pillar

e) Choose the correct statement from the following.
i) The new Guru was foolish because he was blindly following a practice.
ii) The new Guru was foolish because he was fond of cats.
iii) The new Guru was foolish because he disliked traditions.
Answer:
i) The new Guru was foolish because he was blindly following a practice.

Interpretation of Non-Verbal Information

1. The bar graph below shows the Sex ratio of females per 1000 males. Study the graph and answer the questions.
AP 7th Class English Important Questions Unit 5 The Art of Weaving 1
Now, answer the following questions.
a) What is the Rural female population during 2001?
Answer:
946 females

b) What is the difference in the population from 2001 to 2011?
Answer:
The population has increased in 10 years of time.

Choose the correct answer from the choices given.
c) How many females are existing in urban areas in 2011?
i) 946
ii) 900
iii) 926
iv) 947
Answer:
iii) 926

d) The ratio of male : female in 2011 in rural area is
i) 1000 : 933
ii) 1000 : 947
iii) 900 : 1000
iv) 946 : 1000
Answer:
ii) 1000 : 947

e) Which of the following statements is true according to the graph representation?
i) In 2011, the urban female population is lesser than the total population.
ii) The female population decreased in 2011 when compared to 2001.
iii) The male and female population is same in 2001 in rural areas.
Answer:
i) In 2011, the urban female population is lesser than the total population.

AP 7th Class English Important Questions Unit 5 The Art of Weaving

2. The pie chart below shows the usage of water for domestic purpose. Study it and answer the questions.
AP 7th Class English Important Questions Unit 5 The Art of Weaving 2
Now, answer the following questions.
a) For which purpose is water mostly used on domestic front?
Answer:
Toilet washing

b) What are the different kinds of washing mentioned in the pie chart?
Answer:
Drinking, washing up, clothes washing, personal washing showers, personal washing baths and taps, etc.

Choose the correct answer from the choices given.
c) Water used for …………. is very less.
i) personal washing showers
ii) toilet flushing
iii) drinking
iv) washing hands
Answer:
iii) drinking

4) What is the percentage of water used for outdoor purpose?
i) 12%
ii) 7%
iii) 21%
iv) 5%
Answer:
ii) 7%

5) Pick out the true statement with reference to the details in the pie chart.
i) Water is best utilized for clothes washing.
ii) Consumption of water for various washing purposes can be minimised/reduced.
iii) Water is the main source for keeping ourselves and surroundings clean.
Answer:
iii) Water is the main source for keeping ourselves and surroundings clean.

Vocabulary

Synonyms

Choose the words with similar meanings (synonyms) from the list given to the words Underlined.
AP 7th Class English Important Questions Unit 5 The Art of Weaving 3
Answer:
a) a) thankfulness, b) replied
b) a) abundant, b) arrange
c) a) Usually, b) buy
d) a) methods, b) long-lasting
e) a) uncomplicated, b) hand-operated
f) a) inexpensive, b) manufactured

Antonyms

Write the opposites (antonyms) for the underlined words.

a) He expressed his gratitude (a) for our concern for them and responded most positively (b).
b) Generally, we purchase (a) cotton yarn from different (b) mills from our state and Jari from Surat, Maharashtra.
c) The fabric which is made on the pit loom with a dobby attachment mechanism is very unique (a) and beautiful (b).
d) “It has a rich appearance (a). The quality of work done by the weavers and the pain (b) the weavers take for weaving a saree keep the love for our Mangalagiri fabric,” he explained.
e) They face tough competition, change in fashion trends, scarcity (a) of raw (b) material, and the involvement of middle men.
f) However the traditional (a) value of handloom fabric is increasing (b) for their uniqueness.
Answer:
a) a) ingratitude, b) negatively
b) a) sell, b) same
c) a) common, b) awful
d) a) disappearance, b) comfort
e) a) abundance, b) processed
f) a) unconventional, b) decreasing

Right Forms of the Words

Fill in the blanks with the right form of the words given in the brackets.

a) We went to Mangalagiri, one of the most _______ (a) (fame / famous) towns in Guntur District, along with our English _______ (b) (teacher / teach) on a case-study.
b) Mangalagiri sarees are _______ (a) (speciality / special) for their quality and the process we follow. The quality of fabric _______ (b) (dependent / depends) upon the yarn we use.
c) No, dyeing is an important and _______ (a) (significance / significant) step in handloom saree _______ (b) (produce / production).
d) Street-sizing is the _______ (a) (extend / extension) of the warp, spraying of starch and brushing followed by drying to get it _______ (b) (ready / readily).
e) One of us _______ (a) (enquiry /enquired) “Sir, what are you doing ?” He _______ (b) (replied / reply), “I am weaving a saree.”
f) The _______ (a) (unique / uniqueness) of Mangalagiri cotton is because of its _______ (b) (durable / durability).
Answer:
a) a) famous, b)teacher
b) a) special, b) depends
c) a) significant, b) production
d) a) extension, b) ready
e) a) enquired, b) replied
f) a) uniqueness b) durability

Spelling Test

Type – 1 : Vowel Clusters

Complete the following words using “ai, au, ea, ee, ei, eo, ia, ie, io, oi, oo, ou, ua, ue or ui”.

a) Many famil _ _ s live on the art of w _ _ ving here.
b) Mangalagiri sarees are spec _ _ l for their q _ _ lity and the process we follow.
c) Our techniq _ _ s give a uniq _ _ and durable colour to the fabric.
d) We n _ _ d an open and a spac _ _ us place for street-sizing.
e) The fabric which is made on the pit l _ _ m with a dobby attachment mechanism is very unique and be _ _ tiful.
f) “Sir, are these fabrics ch _ _ per than fabrics produced in powerloom mills? Could you expl _ _ n?” Our teacher asked.
Answer:
a) families, weaving
b) special, quality
c) techniques, unique
d) need, spacious
e) loom, beautiful
f) cheaper, explain

AP 7th Class English Important Questions Unit 5 The Art of Weaving

Type – 2 : Suffixes

Complete the following words with the suitable suffixes given in the brackets.

a) First, we consulted a master weave___ (r / er), Veeraiah, for the details “where to go?”, “whom to meet?” Mr. Veeraiah cordial___ (ly / by) welcomed us.
b) The fabric is the product of weav___ (eing / ing) with the help of pit looms. It takes much time to weave and requires a lot of pati___ (ence / ance) to prepare everything ready.
c) After dyeing, it is washed, dried at rpom temperat___(ure / are) and brought for the process of spinning, local___(ly / lly) called ‘aasu’.
d) It is a man___ (ual / ial) operating system. The fabric which is made on the pit loom with a dobby attach___ (ment / mant) mechanism is very unique and beautiful.
e) His enthusi___ (asm / astic) was evident___ (ly / lly) seen when he said, “The Nizam design is a unique characteristic feature of this fabric.”
f) The Nizam design is a unique character___ (istic / ism) feature of this fabric. The unique___ (ness /less) of Mangalagiri cotton is because of its durability.
Answer:
a) weaver, cordially
b) weaving, patience
c) temperature, locally
d) manual, attachment
e) enthusiasm, evidently
f) characteristic, uniqueness

Type – 3 : Wronalv Spelt Words

Identify the wrongly spelt word and write its correct spelling in the space provided.

a) special, heartfelt, mekhamism, textile
Answer:
mechanism

b) quality, competetion, process, service
Answer:
competition

c) generally, cotton, involvment, source
Answer:
involvement

d) boil, express, enthusyasm, material
Answer:
enthusiasm

e) woven, evidently, bleach, purchace
Answer:
purchase

f) important, unikness, durability, wash
Answer:
uniqueness

g) technik, feature, problem, raw
Answer:
technique

h) wonderful, durable, spinning, temparature
Answer:
temparature

Classification of Words

Arrange the following words under the correct headings.
AP 7th Class English Important Questions Unit 5 The Art of Weaving 4

Choice of the Words

Fill in the blanks choosing the suitable words from those given in the box.
AP 7th Class English Important Questions Unit 5 The Art of Weaving 5 AP 7th Class English Important Questions Unit 5 The Art of Weaving 6
Answer:
a) 1) cordially, 2) produced
b) 1) fabric, 2) purchase
c) 1) dried, 2) spinning
d) 1) manual, 2) mechanism
e) 1) embellished, 2) geometrical
f) 1) competition, 2) involvement

Formation of Adverbs

a) Make adverbs by adding ‘ly’ to the following adjectives.
AP 7th Class English Important Questions Unit 5 The Art of Weaving 7

b) Complete the following sentences with the correct form of the words in brackets.

1. Sriram speaks _____ English. He Speaks English _____ . (correct)
2. Saleem is a _____ tailor. He makes dresses _____ . (careless)
3. You always speak _____ . Please speak _____ .(loud, quiet)
4. Be _____ and do your homework _____ . (careful, correct)
5. Nandu is a _____ reader.He reads books very (slow)
6. Please be _____ or do your work _____ . I want to sleep. (quiet)
7. My mother shouted _____ when I showed my progress card. (loud)
8. Please listen _____ . (careful)
9. P.T. Usha is a _____ runner. She runs very _____ . (fast)
10. Leelavathi is a _____ teacher. She teaches very _____ . (good, well)
Answer:

  1. correct; correctly
  2. careless ; carelessly
    loudly; quietly
  3. careful; carefully
  4. slow, slowly
  5. quiet; quietly
  6. loudly
  7. carefully
  8. fast; fast
  9. good ; well

Idiomatic Expressions

Use the following idiomatic expressions in your own sentences.

1) walking on floor : ______________
2) over the moon : ______________
3) on top of the world : ______________
4) have stars in your eyes : ______________
5) jump for joy : ______________
6) happy camper : ______________
Answer:
1) After he had won in the elections, he walked on the floor.
2) Akash was over the moon when he got a foreign car.
3) When Dheeraj was selected as a bank officer, he was on the top of the world.
4) The young player has stars in his eyes when he is going to play his first international match.
5) When I heard the good news, I jumped for joy.
6) Nitya was a happy camper when she got a place at IIT, Madras.

Grammar

I. Edit the following passage correcting the underlined parts.

1. Television is the biggest source for (a) entertainment for the world. People gets (b) information about the world through the media. Television has many programmes based in (c) different interests of people. The shows, movies, music, news, cartoon films, business news etc make them (d) very popular.
Answer:
a) of b) get c) on d) it

2. Chandra Sekhar Venkata Raman was a (a) eminent Indian scientist. He was the first Asian but (b) also the first non-white for (c) receive the Nobel Prize in Science. He is (d) born at Tiruchirapalli on November 7, 1888.
Answer:
a) an b) and c) to d) was

3. Once upon a time, there lived a stork at (a) the side of a tank. There were plenty of fish in the tank and a (b) stork always had a full meal. Since (c) the years passed, the stork grew old and found it difficult to caught (d) fish for food.
Answer:
a) by b) the c) As d) catch

4. Thomas Alva Edison a (a) greatest inventor of all times, is the most suitable example of his own saying. This great, outstanding US inventor has (b) the credit of making 1001 inventions. Can you imagine a world without electric light, recorded music, cinema etc. who (c) are the contributions with (d) this great genius?
Answer:
a) the b) had c) which d) of

AP 7th Class English Important Questions Unit 5 The Art of Weaving

II. Complete the passage choosing the right words from those given below. Each blank is numbered and for each blank four choices are given. Choose the correct answer and write (A), (B), (C) or (D) in the blanks.

1. A place …………….. (1) various creatures like animals, birds, reptiles, fishes etc. …………….. (2) kept in the cages or guarded areas for the purpose of display is called a zoo. …………….. (3) maintenance of the zoos requires a large stretch …………….. (4) land.
1) A) when B) which C) where D) how
2) A) is B) are C) was D) were
3) A) These B) A C) An D) The
4) A) of B) with C) at D) by
Answer:
1) C 2) B 3) D 4) A

2. Electricity is …………….. (1) essential resource for a thriving life. It …………….. (2) our daily life. Life without the electricity will be impossible …………….. (3) imagine. Electricity serves mankind greatly. We must stop …………….. (4) wastage of power.
1) A) that B) this C) a D) an
2) A)ran B) running C) runs D) must run
3) A) to B) for C) in D) by
4) A) a B) the C) an D)those
Answer:
1) D 2) C 3) A 4) B

3. Christmas is …………….. (1) most important festival for Christians. It is celebrated to mark the birth of Jesus, …………….. (2) is the supreme lord of the Christians. It marks the …………….. (3) of the days of hope for those oppressed before the birth of Jesus. Christmas is celebrated with the spirit …………….. (4) joy and merry-making.
1) A)the B) a C) an D) these
2) A) which B ) who C) where D) why
3) A) begin B) began C) begun D) beginning
4) A) at B) by C) of D) to
Answer:
1) A 2) B 3) D 4) C

4. A white tiger is a Bengal tiger …………….. (1) very rare, creamy white fur, blue eyes grey or brownish stripes. It …………….. (2) not a special kind of tiger. White tige weigh …………….. (3) 570 pounds and grow up to …………….. (4) than ten feet long.
1) A) at B) by C) with D) to
2) A) were B) are C) was D) is
3) A) as much as B) as C) if D) but
4) A) most B) more C) much D) many
Answer:
1) C 2) D 3) A 4) B

III. Complete the following sentences using “Present Continuous Tense”.

a) She _____ (listen) to music.
b) Listen! He _____ (sing) a Tamil ^ong.
c) Look! The cat _____ (sit) under the table.
d) The two boys _____ (fight) with each other.
Answer:
a) is listening
b) is singing
c) is sitting
d) are fighting
e) is sleeping

AP 7th Class English Important Questions Unit 5 The Art of Weaving

IV. Write meaningful sentences using present continuous tense with the sets of words given below.

a) Sushma – draw – picture of loom
Answer:
Sushma is drawing the picture of a loom.

b) Praveen – fly – kite
Answer:
Praveen is flying a kite.

c) Babu – water – plants
Answer:
Babu is watering plants.

d) They – play – cricket
Answer:
They are playing cricket.

e) I – do – project work
Answer:
I am doing project work.

f) Hemanth – bring – vegetables
Answer:
Hemanth is bringing vegetables.

V. Change the following sentences into Reported Speech.

1. Kavya said, “My new job is very interesting.”
2. Ram said, “I am feeling well now.”
3. He said, “I am sorry.”
4. The teacher said to the boys, “Why are you late ?”
5. Sudha said, “I will go to Delhi tomorrow.”
6. Ravi said to Ashok, “Where are you going ?”
7. He said, “The earth moves round the sun.”
8. Vasanta said to me, “I have passed the exam.”
9. Raju said, “I have met your brother.”
10. Srinivas said, “I am reading a novel.”
11. Karthikeya said to Ajay, “I can do it.”
12. Seshu said, “We are in the playground.”
Answer:

  1. Kavya said that her new job was very interesting.
  2. Ram said that he was feeling well then.
  3. He said that he was sorry.
  4. The teacher asked the boys why they were late.
  5. Sudha said that she would go to Delhi the next day.
  6. Ravi asked Ashok where he was going.
  7. He said that the earth moves round the sun.
  8. Vasanta told me that she had passed the exam.
  9. Raju said that he had met my brother.
  10. Srinivas said that he was reading a novel.
  11. Karthikeya told Ajay that he could do it.
  12. Seshu said that they were in the playground.

VI. Fill in the blanks with a suitable preposition. Use the prepositions given in the box.
AP 7th Class English Important Questions Unit 5 The Art of Weaving 8
a) The girl ____ the picture is my sister.
b) They are living ____ the same roof.
c) There is a temple ____ our school.
d) He is lying ____ the couch.
e) The fishes are moving ____ the aquarium.
f) London lies ____ the Thames.
g) Our house is ____ the railway station.
h) Nitya sat ____ Charitha and Alekhya.
Answer:
a) in
b) under
c) beside
d) on
e) in
f) on
g) beside
h) between

Creative Writing

1. You have learnt in the lesson, “The Art of Weaving” that a group of students visited Mangalagiri. They met Sambayya who was selling handloom sarees.
Now, write a possible conversation based on the above context.
Answer:
Student 1 : Good morning, sir.
Sambayya : Very good morning, students.
Student 2 : What are you doing, sir?
Sambayya : l am selling sarees, boys and girls.
Student 3 : Which type of sarees are they?
Sambayya : They are famous Mangalagiri sarees made on handloom.
Student 4 : What is their speciality, sir?
Sambayya : The Nizam design is a unique characteristic of this fabric.
Student 5 : O.K., Sir How much money do you earn a day by selling these sarees?
Sambayya : Not much, boys and girls. I earn the sufficient money to meet my expenses.
Student 1 : O.K., Sir. Thank you.
Sambayya : It’s O.K, students, bye.

AP 7th Class English Important Questions Unit 5 The Art of Weaving

2. You have known a number of new things about weavers and their art after reading the lesson “The Art of Weaving.”

Imagine that you were one of the students who made a visit to Mangalagiri and attempt a diary entry at the end of the day on which you visited Mangalagiri.
Answer:

Thursday, 15th January, 20xx
7:30 p.m.Dear Diary,

What a lovely sarees ! What a tremendous art! Weaving clothes is really beautiful. It is also very difficult too ! Today, we met four or five weavers and all of them are very skillful. They are all satisfied with their earnings. Tehy are really passionate about . their art. Though it takes much time to weave on a handloom, they don’t mind it. They have a lot of patience. They are not money minded. But Mangalagiri sarees are very

famous. Today, we all came to know many new things about the familiarity of Mangalagiri ; Sarees. Because of this textile industry, Mangalagiri gets a special place. As far as the weavers are concerned, they are facing many problems. They are facing tough competition. They are facing the challenges such as change in fashion, scarcity of raw material and the involvement of middle men. Oh, God ! Please help them with their work. Please make them get rid of their problems.
Kiran

3. Our school is going to celebrate its Annual Day next month. You are going to dance for two songs. The local M.L.A will be the chief guest of the function. Many important people of the village will attend the programme. All the teachers are working very hard to make it a big success. Games are being conducted for the occasion.
Now, write a letter to your friend inviting him to attend the programme.
Answer:

Tenali.
10-3-xx.

Dear Ravi,
It has been a long time since I wrote to you. How are your parents? How are you? How is your little sister? I hope you are studying well. We are all fine here. I am also doing well here. In this letter I would like to describe you about our school Annual Day which we celebrate next month.

On 20th of April our school is going to celebrate the Annual Day. The local M.L.A. will be the Chieft Guest of the function. Our Head Master will preside over the function. Many important people of the village will attend the programme. All the teachers are working hard to make it a big success. Competitions in games and sports are being conducted for the occasion. Many cultural activities are going to be held. I am going to dance for two songs. It is going to be a great fun and enjoyment.

Do you want to grab the fun and entertain yourself by attending our Annual Day? I would like you to be at the function. I am looking forward to seeing you here. Convey my regards to your parents. Hoping you will turn up, I remain.

Yours lovingly,
x x x x x.

Addres on the Envelope :
To
G. Suresh,
S/o G. Satish,
H. No: 8-95/A,
Sai Baba Temple Street,
Brahmin Street,
Nizam Patnam.
Guntur (Dt.)

4. Design an invitation card on the occasion of a dinner.
Answer:

Invitation

Mr and Mrs Prabhakar request the pleasure of Mr. and Mrs. Gautam’s company at dinner on Monday, April 18, 20xx at 8 p.m.
40, Rama Street Hyderabad

AP 7th Class English Important Questions Unit 5 The Art of Weaving

5. Design an invitation card on the occasion of a birthday party.
Answer:

Invitation

Join the fun at Gautam’s 11th Birthday Party!

Time : 3 pm
Venue: 303, Platinum Towers, Eluru

Hi friends! This year I’m having my birthday party at my grandmother’s house! You can bring your grandparents too, if they want to come! It will be fun!
Parents – Please pick up your children at 7 pm.

6. Design an invitation card on the occasion of a wedding.
Answer:

Invitation
Mr. and Mrs. Prabhakar
request the pleasure of all
at the marriage of their son
Rajesh
to
Bindu
At 11, E – Block, Srinagar Colony, Kurnool.
On Monday, 18 April, 20xx at 8 pm.

7. Write a story using the following hints.

Hints : A good boy – disobeys his parents – gets into bad company – father gives him some good apples – tells him to lay them aside for a few days – places a rotten apple among them – the rotten apple spoils the good ones – a lesson on bad company.
Answer:
AVOID BAD COMPANY
Once there lived a good boy. He got into bad company. He disobeyed his parents. His parents were greatly worried. His father thought of a plan of bringing him round. He wished to teach his son a lesson.

One day the father gave his son some good apples. He asked him to lay them aside. After a few days they found the apples still in good condition. Next the father gave him a rotten apple and asked him to place it among the good ones. The boy did so. After a few days they found that all the apples were spoiled. The boy understood that one rotten apple would spoil all the good ones. He learnt a lesson. He avoided bad friends. He kept them at an arm’s length.

Moral: Avoid bad company.

AP 7th Class English Important Questions Unit 5 The Art of Weaving

8. You are Lakshmi, a staff reporter of The Times of India. You have been asked to cover the incident of daylight robbery when the inmates were present in a house in the outskirts of Vizag. Write a report in about 120 words.
Answer:
A Daylight Robbery

Vizag: 20th March, 20xx (Lakshmi) : The Times of India News Service

Vizag is no more a safe city once it used to be. Daylight robberies have become a part of the cultural life of the city. Cases of robbery have become very common. Yesterday, a daring daylight robbery was committed in Telephone Colony, on the outskirts of the city. It was 11.30 am. The robbers broke open a side door and entered the house. They asked for the keys of the cupboards and boxes. They had revolvers and daggers in their hands. Women and children became dumb with fear. The robbers finished their jobs within minutes.

They decamped with all the jewellery and about twenty five thousand rupees in cash. Before running away, they locked the inmates in a room. The neighbours rushed to help only when they heard their cries. The police came an hour late. No one believes if the lost valuables and money would be recovered. The people have doubts about the honest and sincere working of the police.

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4

SCERT AP 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 Textbook Exercise Questions and Answers.

AP State Syllabus 9th Class Maths Solutions 1st Lesson వాస్తవ సంఖ్యలు Exercise 1.4

ప్రశ్న1.
కింది వానిని సూక్ష్మీకరించండి.
i) (5 + \(\sqrt{7}\)) (2 + \(\sqrt{5}\))
సాధన.
(5 + \(\sqrt{7}\)) (2 + \(\sqrt{5}\))
= 10 + 5\(\sqrt{5}\) + 2\(\sqrt{7}\) + \(\sqrt{35}\)

ii) (5+ \(\sqrt{5}\)) (5 – \(\sqrt{5}\))
సాధన.
(5 + \(\sqrt{5}\)) (5 – \(\sqrt{5}\)) = (5)2 – (\(\sqrt{5}\))2
= 25 – 5 = 20

iii) (\(\sqrt{3}\) + \(\sqrt{7}\))2
సాధన.
(\(\sqrt{3}\) + \(\sqrt{7}\))2 = (\(\sqrt{3}\))2 + (\(\sqrt{7}\))2 + 2(\(\sqrt{3}\)) (\(\sqrt{7}\))
= 3 + 7 + 2\(\sqrt{21}\) = 10 + 2\(\sqrt{21}\)

iv) (\(\sqrt{11}\) – \(\sqrt{7}\))(\(\sqrt{11}\) + \(\sqrt{7}\))
సాధన.
(\(\sqrt{11}\) – \(\sqrt{7}\))(\(\sqrt{11}\) + \(\sqrt{7}\))
= (\(\sqrt{11}\))2 – (\(\sqrt{7}\))2
= 11 – 7 = 4

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4

ప్రశ్న2.
కింది వానిలో అకరణీయ సంఖ్యలేవి? కరణీయ సంఖ్య లేవి?
i) 5 – \(\sqrt{3}\)
ii) \(\sqrt{3}\) + \(\sqrt{2}\)
iii) (\(\sqrt{2}\) – 2)2
iv) \(\frac{2 \sqrt{7}}{7 \sqrt{7}}\)
v) 2π
vi) \(\frac{1}{\sqrt{3}}\)
vii) (2 + \(\sqrt{2}\)) (2 – \(\sqrt{2}\))
సాధన.
i) 5 – \(\sqrt{3}\) – కరణీయ సంఖ్య
ii) \(\sqrt{3}\) + \(\sqrt{2}\) – కరణీయ సంఖ్య
iii) (\(\sqrt{2}\) – 2)2 – కరణీయ సంఖ్య
iv) \(\frac{2 \sqrt{7}}{7 \sqrt{7}}\) – అకరణీయ సంఖ్య
v) 2π – కరణీయ సంఖ్య కాదు
vi) \(\frac{1}{\sqrt{3}}\) – కరణీయ సంఖ్య
vii) (2 + \(\sqrt{2}\)) (2 – \(\sqrt{2}\)) – అకరణీయ సంఖ్య

ప్రశ్న3.
కింది సమీకరణాలలో x, y, z మొదలగు చరరాశులు అకరణీయ సంఖ్యలను సూచిస్తాయా ? కరణీయ సంఖ్యలను సూచిస్తాయా ?
i) x2 = 7
ii) y2 = 16
iii) z2 = 0.02
iv) u2 = \(\frac{17}{4}\)
v) w2 = 27
vi) t4 = 256
సాధన.
i) x2 = 7 ⇒ x = \(\sqrt{7}\) ఒక కరణీయ సంఖ్య
ii) y2 = 16 ⇒ y = \(\sqrt{16}\) = 4 ఒక అకరణీయ సంఖ్య
iii) z2 = 0.02 ⇒ z = \(\sqrt{0.02}\) ఒక కరణీయ సంఖ్య
iv) u2 = \(\frac{17}{4}\) ⇒ u = \(\frac{\sqrt{17}}{2}\) ఒక కరణీయ సంఖ్య
v) w2 = 27 ⇒ w = 3\(\sqrt{3}\) ఒక కరణీయ సంఖ్య
vi) t4 = 256 ⇒ t = \(\sqrt[4]{256}=\sqrt[4]{4^{4}}\) = 4 ఒక అకరణీయ సంఖ్య.

ప్రశ్న4.
ఒక వృత్తపరిధికి, దాని వ్యాసానికి గల నిష్పత్తి \(\frac{c}{d}\)ని π సూచిస్తాము. మరి π ను కరణీయసంఖ్య అని ఎందుకు పరిగణిస్తారు ?
సాధన.
వృత్తపరిధి (c) మరియు వ్యాసము (d) లు పోల్చదగిన పొడవులు కావు. అనగా ఆ రెంటిని కచ్చితంగా కొలిచే మాపనము లేదు. కాబట్టి π ను కరణీయ సంఖ్యగా పరిగణిస్తాము.

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4

ప్రశ్న5.
హారాలను అకరణీయం చేయండి.
i) \(\frac{1}{3+\sqrt{2}}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 1

ii) \(\frac{1}{\sqrt{7}-\sqrt{6}}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 2

iii) \(\frac{1}{\sqrt{7}}\)
సాధన.
\(\frac{1}{\sqrt{7}}=\frac{1}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}}=\frac{\sqrt{7}}{7}\)

iv) \(\frac{\sqrt{6}}{\sqrt{3}-\sqrt{2}}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 3

ప్రశ్న6.
హారాలను అకరణీయం చేసి సూక్ష్మీకరించండి.
i) \(\frac{6-4 \sqrt{2}}{6+4 \sqrt{2}}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 4

ii) \(\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 5

iii) \(\frac{3 \sqrt{5}-\sqrt{7}}{3 \sqrt{3}+\sqrt{2}}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 6

iv) \(\frac{3 \sqrt{5}-\sqrt{7}}{3 \sqrt{3}+\sqrt{2}}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 7

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4

ప్రశ్న7.
\(\sqrt{2}\) = 1.414, \(\sqrt{3}\) = 1.732 మరియు \(\sqrt{5}\) = 2.236 అయితే \(\frac{\sqrt{10}-\sqrt{15}}{2 \sqrt{2}}\) విలువను మూడు దశాంశ స్థానాల వరకు కనుగొనండి.
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 8

ప్రశ్న8.
విలువలు కనుగొనండి.
i) 641/6
సాధన.
641/6 = (26)1/6 = 2

ii) 321/5
సాధన.
321/5 = (25)1/5 = 2

iii) 6251/4
సాధన.
6251/4 = (54)1/4 = 5

iv) 163/2
సాధన.
163/2 = (42)3/2 = 43 = 64

v) 2432/5
సాధన.
2432/5 = (35)2/5 = 32 = 9

vi) (46656)-1/6
సాధన.
(46656)-1/6 = (66)-1/6
= 6-1 = \(\frac{1}{6^{1}}\) = \(\frac {1}{6}\)
[∵ 6 × 6 × 6 × 6 × 6 × 6 = 46656]

ప్రశ్న9.
\(\sqrt[4]{81}-8 \sqrt[3]{343}+15 \sqrt[5]{32}+\sqrt{225}\) ను సూక్ష్మీకరించండి.
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 9
= (34)1/4 – 8(73)1/4 + 15(25)1/5 + 15
= 3 – 8 × 7 + 15 × 2 + 15
= 3 – 56 + 30 + 15 = -8

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4

ప్రశ్న10.
‘a’ మరియు ‘b’ లు ఏవైనా అకరణీయసంఖ్యలు అయితే కింది సమీకరణాలలో a, b విలువలు కనుక్కోండి.
i) \(\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}=a+b \sqrt{6}\)
సాధన.
\(\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\)
హారంను అకరణీయం చేయగా,
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 10
5 + 2\(\sqrt{6}\) ను a + b\(\sqrt{6}\) తో పోల్చగా
a = 5 మరియు b = 2

ii) \(\frac{\sqrt{5}+\sqrt{3}}{2 \sqrt{5}-3 \sqrt{3}}=a-b \sqrt{15}\)
సాధన.
\(\frac{\sqrt{5}+\sqrt{3}}{2 \sqrt{5}-3 \sqrt{3}}\)
హారమును అకరణీయం చేయగా,
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.4 11

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

Practice the AP 10th Class Maths Bits with Answers 5th Lesson వర్గ సమీకరణాలు on a regular basis so that you can attempt exams with utmost confidence.

AP Board 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 1.
px + qx2 + r = 0 వర్గ సమీకరణ విచక్షణిని తెల్పండి.
జవాబు.
q2 – 4pr

ప్రశ్న 2.
2x2 – 4x – 3 = 0 యొక్క విచక్షణిని కనుగొనుము.
సాధన.
b2 – 4ac = (- 4)2 – 4(2) (- 3) = 40 .

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 3.
చరరాశి X లో వర్గ సమీకరణం యొక్క సాధారణ రూపంను రాయండి.
జవాబు.
ax2 + bx + c = 0, (a ≠ 0) .

ప్రశ్న 4.
సాధారణంగా వర్గ సమీకరణానికి గల మూలాల సంఖ్య ……………………..
(A) గరిష్టంగా మూడు
(B) గరిష్టంగా రెండు
(C) అనంతం
(D) గరిష్ఠంగా ఐదు
జవాబు.
(B) గరిష్టంగా రెండు

ప్రశ్న 5.
క్రింది ఏ సందర్భంలో px2 + qx + r = 0 వర్గసమీకరణం మూలాలు కల్పితాలు అవుతాయి ?
(A) q2 > 4pr
(B) q2 < 4pr
(C) q2 = 4pr
(D) p = q + r
జవాబు.
(B) q2 < 4pr

ప్రశ్న 6.
2x2 + x – 4 = 0 యొక్క విచక్షణిని లెక్కించండి.
సాధన.
విచక్షణి b2 – 4ac = (1)2 – 4(2) (-4)
= 1 + 32 = 33

ప్రశ్న 7.
ax2 + bx + c = 0 యొక్క మూలాల లబ్ధం …..
(A) \(\frac{c}{a}\)
(B) \(\frac{-b}{a}\)
(C) \(\frac{-c}{a}\)
(D) \(\frac{b}{c}\)
జవాబు.
(A) \(\frac{c}{a}\)

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 8.
‘x’ యొక్క ఏ ధనాత్మక విలువకు 4x2 – 9 = 0 అవుతుంది ?
సాధన.
4x2 – 9 = 0 ⇒ 4x2 = 9
⇒ x2 = \(\frac{9}{4}\)
⇒ x = \(\sqrt{\frac{9}{4}}\) = ± \(\frac{3}{2}\)

ప్రశ్న 9.
క్రిందివానిలో మూలాలు సమానంగా గల వర్గ
సమీకరణం ఏది ?
(A) x2 – 5 = 0
(B) x2 – 10x + 25 = 0
(C) x2 + 5x + 6 =:0
(D) x2 – 1 = 0
జవాబు.
(B) x2 – 10x + 25 = 0

ప్రశ్న 10.
క్రింది వానిలో \(\frac{1}{3}\) మరియు \(\frac{1}{2}\) లను మూలాలుగాకలిగిన వర్గ సమీకరణం ఏది ?
(A) x2 + \(\frac{5 x+1}{6}\) = 0
(B) – 6x2 – 5x + 1 = 0
(C) x2 – \(\frac{5 x-1}{6}\) = 0
(D) 6x2 – 5x -1 = 0
సాధన.
(C) x2 – \(\frac{5 x-1}{6}\) = 0

ప్రశ్న 11.
x2 – px + q = 0 (p, q ∈ R మరియు p ≠ 0, q ≠ 0)కు విభిన్న వాస్తవ మూలాలు ఉంటే క్రింది వానిలో ఏది సత్యం ?
(A) p2 < 4q
(B) p2 > 4q
(C) p2 = 4q
(D ) p2 + 4q = 0
జవాబు.
(B) p2 > 4q

ప్రశ్న 12.
ax2 + bx + c = 0 వర్గ సమీకరణంలో b2 – 4ac> 0 అయిన దాని మూలాల స్వభావాన్ని తెల్పండి.
జవాబు.
అసమాన వాస్తవ సంఖ్యలు.

ప్రశ్న 13.
క్రింది ఏ సందర్భంలో ax2 + bx + c = 0 రేఖాచిత్రము ఇచ్చిన పటాన్ని పోలి ఉంటుంది ?
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 1
(A) b2 – 4ac > 0
(B) b2 – 4ac = 0
(C) b2 – 4ac < 0
(D) ఏదీకాదు
జవాబు.
(A) b2 – 4ac > 0

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 14.
2 + √3, 2 – √3 మూలాలుగా గల వర్గ సమీకరణమును రాయండి.
సాధన.
x2 – (α + β)x + αβ = 0 .
α = 2 + √3, β = 2 – √3
x2 – 4x + 1 = 0

ప్రశ్న 15.
x2 + 6x + 5 = 0 మూలాలు α మరియు β అయిన α + β విలువ ఎంత ?
సాధన.
α + β = \(\frac{-b}{a}\) = \(\frac{-6}{1}\) = – 6

ప్రశ్న 16.
x2 – 10x + 9 = 0కు α, β లు మూలాలైతే |α – β| విలువ ఎంత ?
సాధన.
x2 – 10x + 9 = 0కు α, β లు మూలాలు.
α + β = \(\frac{-b}{a}\) = \(\frac{-(-10)}{1}\) = 10
α, β = \(\frac{\mathrm{c}}{\mathrm{a}}\) = 9
(α – β)2 = (α + β)2 – 4ap .
= (10)2 – 4(9) = 100 – 36 = 64
α – β = √64 = ± 8
∴ |α – β| = 8

ప్రశ్న 17.
ax2 + ax + 2 = 0 మరియు x2 + x + b = 0 అనే వర్గ సమీకరణాలకు ఒకటి ఒక ఉమ్మడి మూలం అయితే a ∙ b = 2 అని చూపుము.
సాధన.
ax2 + ax + 2 = 0 కు 1 ఒక మూలం.
a(1)2 + a(1) + 2 = 0
∴ 2a + 2 = 0 ⇒ a = – 1
అలాగే x2 + x + b = 0 కి కూడా 1 ఒక మూలము.
∴ 1 + 1 + b = 0 ⇒ b = – 2.
∴ a : b = (-1) (-2) = 2.

ప్రశ్న 18.
6x2 – 5x + 1 = 0 యొక్క విచక్షణి విలువను కనుగొనుము.
సాధన.
విచక్షణి b2 – 4ac = (-5)2 – 4(6)(1) = 1

ప్రశ్న 19.
క్రింది వానిలో ఏది x – \(\frac{3}{x}\) = 2 సమీకరణం యొక్క ఒక మూలము ?
(A) 1
(B) 2
(C) 3
(D) 4
జవాబు.
(C) 3

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 20.
x2 + 5x + k = 0 సమీకరణం విభిన్న వాస్తవ మూలాలను కలిగి ఉంటే k విలువను కనుగొనుము.
సాధన.
b2 – 4ac > 0 (మూలాలు విభిన్న వాస్తవ సంఖ్యలు) , .
(5)2 – 4(1) (k) > 0
∴ 25 > 4k ⇒ 4k < 25
⇒ k < \(\frac{25}{4}\)

ప్రశ్న 21.
x2 – 4 = 0 మరియు x2 + px – 4 = 0లు ఒకే
మూలాలను కల్గియున్న p విలువ ఎంత ?
(A) 2
(B) o
(C) 4
(D) 1
జవాబు.
(B) o

ప్రశ్న 22.
క్రింది వానిలో వర్గ సమీకరణము
(A) 5 + \(\frac{3}{x}\) = x
(B) x2 + \(\frac{1}{x^{2}}\) + = \(\frac{17}{4}\)
(C) x (x + 3) = 6x + 3
(D) x(2x + 3) = 2x2 – 7
జవాబు.
(C) x (x + 3) = 6x + 3

ప్రశ్న 23.
క్రింది వానిలో వర్గ సమీకరణము
(A) x2 – 6x – 4
(B) (2x + 1) (3x + 2)=0
(C) 7x = 2x2
(D) పైవన్నీ
జవాబు.
(D) పైవన్నీ

ప్రశ్న 24.
క్రింది వానిలో వర్గ సమీకరణము కానిది
(A) x (x – 3) = x2 + 5
(B) x (x + 5) = 2x2 + 4
(C) x2 – √2x – 1 = 0
(D) పైవన్నీ
జవాబు.
(A) x (x – 3) = x2 + 5

ప్రశ్న 25.
వర్గ సమీకరణం యొక్క సాధారణ రూపాన్ని రాయండి.
జవాబు.
ax2 + bx + c = 0, (a ≠ 0)

ప్రశ్న 26.
a యొక్క ఏ విలువకు ax (x2 – 4) + dx = 2x3 + bx2 + 10, b ≠ 0 ఒక వర్గ సమీకరణాన్ని సూచిస్తుంది ?
సాధన.
ax3 – 4ax + dx = 2x3 + bx2 + 10, (b ≠0) |
(a – 2)x3 = bx2 + (d – 4a)x – 10 = 0
వర్గసమీకరణంలో x3 పదం ఉండదు.
∴ a – 2 = 0 ⇒ a = 2

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 27.
(m + 1)x3 + 6x2 + 5x = 16 ఒక వర్గ సమీకరణాన్ని సూచిస్తే m విలువ ఎంత ?
సాధన.
వర్గ సమీకరణంలో x3 పదం ఉండదు.
∴ m + 1 = 0 ⇒ m = -1

ప్రశ్న 28.
px2 + qx + r = 0 వర్గ సమీకరణ మూలాలను తెల్పండి.
సాధన.
px2 + qx + r = 0 వర్గ సమీకరణ మూలాలు
\(\frac{-\mathrm{q} \pm \sqrt{\mathrm{q}^{2}-4 \mathrm{pr}}}{2 \mathrm{p}}\)

ప్రశ్న 29.
‘రెండు వరుస ధన సంఖ్యల లబ్ధం 132” అయిన ఆ సంఖ్యలను కనుగొనుటకు అవసరమయ్యే వర్గ సమీకరణంను రాయండి.
సాధన.
రెండు వరుస ధన సంఖ్యలు x, x + 1 అనుకొనుము.
∴ x(x + 1) = 132 (లెక్క ప్రకారం లబ్ధం 132)
x2 + x – 132 = 0

ప్రశ్న 30.
“రెండు వరుస బేసి సంఖ్యల లబ్దము 399” అయిన ఆ రెండు సంఖ్యలను కనుగొనుటకు ఉపయోగపడే వర్గ సమీకరణము (x చిన్న బేసి సంఖ్య అయిన)ను కనుగొనుము.
సాధన.
రెండు వరుస బేసి సంఖ్యలలో చిన్న బేసి సంఖ్య x.
∴ రెండవ బేసి సంఖ్య = x + 2 .
వీని లబ్ధం x(x + 2) = 399
కావలసిన వర్గసమీకరణం = x2 + 2x – 399 = 0

ప్రశ్న 31.
“రెండు వరుస సరి సంఖ్యల లబ్దము 120” అయిన ఆ సంఖ్యలను కనుగొనుటకు అవసరమగు వర్గ సమీకరణంను రాబట్టుము.
సాధన.
రెండు, వరుస సరి సంఖ్యలలో చిన్న సరి సంఖ్య x అనుకొనుము.
∴ రెండవ సరి సంఖ్య = x + 2
వీని లబ్ధం x(x + 2) = 120
కావలసిన వర్గసమీకరణం = x2 + 21 – 120 = 0

ప్రశ్న 32.
“ఒక సంఖ్య మరియు ఆ సంఖ్య యొక్క వ్యుత్రమంల మొత్తం \(\frac{5}{2}\)” ను సూచించు వర్గ సమీకరణమును కనుగొనుము.
సాధన.
x + \(\frac{1}{x}\) = \(\frac{5}{2}\) (ఒక సంఖ్య x అనుకొనుము. దాని వృత్రమం \(\frac{1}{x}\))
⇒ \(\frac{x^{2}+1}{x}\) = \(\frac{5}{2}\)
⇒ 2x2 + 2 = 5x
⇒ 2x2 – 5x + 2 = 0

ప్రశ్న 33.
“ఒక సంఖ్య మరియు ఆ సంఖ్య యొక్క వ్యుత్తమంల మొత్తం 2” ను సూచించు వర్గ సమీకరణము
(A) x2 – 2x + 1= 0
(B) x2 + 2x + 1 = 0
(C) x2 + 25 – 1= 0
(D) x2 + 2x + 2 = 0
సాధన.
(A) x2 – 2x + 1= 0

x + \(\frac{1}{x}\) = 2
⇒ \(\frac{x^{2}+1}{x}\) = 2
⇒ x2 + 1
⇒ 2x = x2 – 2x + 1 = 0

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 34.
A = {x/x అనేది (x – 4) (x + 2) = 0 యొక్క మూలము}, B అనే సమితి 2x – 8 యొక్క శూన్య విలువల సమితి అయిన A ∩ Bను కనుగొనుము.
సాధన.
A = {4, – 2}
2x – 8 = 0 ⇒ 2x = 8
⇒ x = 4 శూన్యవిలువ = 4
∴ B = {4}
∴ A ∩ B = {4}

ప్రశ్న 35.
A = {x/x అనేది (x – 4) (x + 2) = 0 యొక్క మూలము}, B అనే సమితి 2x – 8 యొక్క శూన్య విలువల సమితి అయిన A – Bను కనుగొనుము.
సాధన.
A = {4, – 2}
2x – 8 = 0 ⇒ 2x = 8 ⇒ x = 4
శూన్యవిలువ = 4
∴ B = {4}
A – B = {4, – 2} – {4} = {- 2}

ప్రశ్న 36.
క్రింది వానిలో ఏది “రెండు వరుస ధన బేసి సంఖ్యల వర్గాల మొత్తం 290”ను సూచించు వర్గ సమీకరణం ?
(A) x2 + (x + 2)2 = 290
(B) x2 + (x + 2)2 = 2902
(C) x2 – (x + 2)2 = 290
(D) x2 – (x – 2)22 = 2902
జవాబు.
(A) x2 + (x + 2)2 = 290

ప్రశ్న 37.
ఒక సంఖ్య మరియు దాని యొక్క వర్గాల మొత్తం
56నకు సరియగు వర్గ సమీకరణమును రాబట్టుము.
(A) x + 2x2 = 56
(B) 2x + x2 = 56
(C) x + x2 = 56
(D) x – x – 56 = 0
జవాబు.
(C) x + x2 = 56

సాధన.
x + x2 = 56
= x2 + x – 56 = 0.

ప్రశ్న 38.
2x2 – 5x + 3 = 0 యొక్క ఒక మూలము
(A) – 1
(B) 1
(C) 0
(D) 2
జవాబు.
(B) 1 (యత్న-దోష పద్దతి)

సాధన.
2x2 – 5x + 3 = 0
x = – 1 ⇒ 2(- 1)2 – 5 (- 1) + 3
⇒ 2 + 5 + 3 = 10 ≠ 0
x = 1 ⇒ 2(1)2 – 5 (1) + 3
⇒ 2 – 5 + 3 = 0
∴ 1 ఒక మూలము.

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 39.
(x – 4) (x + 2) = 0 యొక్క మూలాలు ఏవి ?
సాధన.
(x – 4) (x + 2) = 0
∴ x – 4 = 0 (లేదా) x + 2 = 0
x = 4 (లేదా) x = – 2
∴ మూలాలు’ = – 2, 4.

ప్రశ్న 40.
(2x + 3) (3x – 7) = 0 వర్గ సమీకరణ మూలాలు కనుగొనుము.
సాధన.
(2x + 3) (3x – 7) = 0
= 2x + 3 = 0 (లేదా) 3x-7 = 0
∴ x = \(\frac{-3}{2}\) (లేదా) x = \(\frac{7}{3}\)
∴ మూలాలు = \(\frac{-3}{2}, \frac{7}{3}\)

ప్రశ్న 41.
2x2 – 6x = 0 వర్గ సమీకరణ మూలాలు కనుగొనుము.
సాధన.
2x2 – 6x = 0 ⇒ 2x(x – 3) = 0
∴ 2x = 0 ⇒ x = 0 లేదా x – 3 = 0 ⇒ x = 3
∴ మూలాలు = 0, 3.

ప్రశ్న 42.
x2 – 5x + 6 = 0 యొక్క ఒక మూలం 3 అయిన రెండవ మూలాన్ని కనుగొనుము.
సాధన.
x2 – 5x + 6 = 0
ఒక మూలం α = 3, రెండవ మూలం β అనుకొనుము.
∴ α + β = \(\frac{-b}{a}\) ⇒ 3 + β = \(\frac{-(-5)}{1}\) = 5
∴ β = 5 – 3 = 2
(లేదా)
మూలాల లబ్ధం αβ = \(\frac{c}{a}\)
⇒ 3β = \(\frac{6}{1}\) ⇒ β = 2
(లేదా)
x2 – 3x – 2x + 6 = 0
⇒ x(x – 3) – 2 (x – 3) = 0
⇒ (x – 3) (x – 2) = 0
∴ మూలాలు α = 3, β = 2.

ప్రశ్న 43.
x2 + 6x + 5 = 0 యొక్క మూలాలు α మరియు β అయిన α + β విలువ ఎంత ?
సాధన.
α + β = \(\frac{-b}{a}\) = \(\frac{-6}{1}\) = – 6

ప్రశ్న 44.
x2 – 5x + 6 = 0 యొక్క మూలాలు α మరియు β, α > β అయిన α – β విలువను కనుగొనుము.
సాధన.
x2 – 5x + 6 = 0 ,
x2 – 3x – 2x + 6 = 0
⇒ x(x – 3) – 2 (x – 3) = 0
⇒ (x – 3) (x – 2) = 0
∴ మూలాలు α = 3, β = 2.
∴ α – β = 3 – 2 = 1.
(లేదా) .
α + β = 5, αβ = 6
∴ (α – β)2 = (α + β)2 – 4αβ
= 52 – 4(6) = 25 – 24 = 1
∴ (α – β)2 = 1 ⇒ α – β = √1 = 1

ప్రశ్న 45.
x2 – 3x- 10 = 0 యొక్క మూలాలు α, β అయిన – α2 + β2 విలువను గణించండి.
(A) 21
(B) 25
(C) 29
(D) 10
సాధన.
(C) 29

x2 – 3x – 10 = 0 యొక్క మూలాలు α, β. ,
∴ α + β = \(\frac{-b}{a}\) = 3, αβ = \(\frac{c}{a}\) = – 10
∴ (α + β)2 = α2 + β2 + 2αβ
⇒ (3)2 = α2 + β2 + 2(-10)
⇒ 9 + 20 = α2 + β2
∴ α2 + β2 = 29
(లేదా)
x2 – 3x – 10 = 0
x2 – 5x + 2x – 10 = 0
⇒ x(x – 5) + 2(x – 5) = 0
⇒ (x – 5) (x + 2) = 0
α = 5, β = -2.
∴ α2 + β2 = (5)2 + (-2)2
= 25 + 4 = 29

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 46.
x2 – 3x – 4 = 0 యొక్క మూలాలు α, β అయిన α3 + β3 విలువను కనుగొనుము.
(A) 64
(B) 63
(C) – 1
(D) 17
జవాబు.
(B) 63

సాధన.
x2 – 3x – 4 = 0 యొక్క మూలాలు α, β.
∴ α + β = 3, αβ = – 4
∴ α3 + β3 = (α + β)3 – 3αβ(α + β)
⇒ (3)3 – 3(-4) (3) = 27 + 36 = 63

ప్రశ్న 47.
x2 + 4x + 4 = 0వర్గ సమీకరణ మూలాలు p, q అయిన క్రింది వానిలో ఏది సత్యం ?
(A) pq = 4
(B) p = – 2, q = -2
(c) p + q = – 4
(D) పైవన్నీ
జవాబు.
(D) పైవన్నీ

ప్రశ్న 48.
x2 – 6x + 8 = 0 వర్గ సమీకరణ మూలాలు p, q అయిన p ∙ q విలువ ఎంత ?
సాధన.
మూలాల లబ్ధం pq = \(\frac{c}{a}\) = \(\frac{8}{1}\) = 8

ప్రశ్న 49.
x2 + 2kx + 16 = 0 కు 4 ఒక మూలము అయితే k విలువను కనుగొనుము.
సాదన.
x2 + 2kx + 16 = 0కు 4 ఒక మూలము.
(4)2 + 8k + 16 = 0
⇒ 8k + 32 = 0 ⇒ k = \(\frac{- 32}{8}\) = – 4

ప్రశ్న 50.
x2 + 2√2x – k = 0 కు /Z ఒక మూలము అయితే k విలువను కనుగొనుము.
సాధన.
(√2)2 + 2√2(√2) – k = 0
⇒ 2 + 4 – k = 0 ⇒ k = 6

ప్రశ్న 51.
ax2 + ax + 8 = 0 మరియు x2 + x + c = 0 వర్గ సమీకరణాలకు x = 1 ఒక ఉమ్మడి మూలం అయిన ac = 8 అని చూపుము.
సాధన.
ax2 + ax + 8 = 0 మరియు x2 + x + c = 0కు
1 ఒక ఉమ్మడి మూలము.
∴ a(1)2 + a(1) + 8 = 0 మరియు
(1)2 + 1 + c ⇒ 0 = c = -2
2a = – 8 ⇒ a = -4
∴ ac = (- 4) (- 2) = 8

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 52.
a యొక్క ఏ విలువకైనా (a + 2)x2 – ax – 2 = 0 కు క్రింది వానిలో ఏది ఒక మూలం ?
(A) 1
(B) – 1
(C) 0
(D) 2
జవాబు.
(A) 1

సాధన.
గుణకాల మొత్తం (a + 2) + (- a) + (- 2) = 0
కావున 1 ఒక శూన్యం అవుతుంది.
(లేదా )
యత్న-దోష పద్దతిలో సాధించాలి.
1 ఒక శూన్యం అనుకొనుము.
(a + 2)(1)2 – a(1) – 2
= a + 2 – a – 2 ≠ 0
కావున 1 ఒక మూలము.
– 1 ఒక శూన్యం అనుకొనుము.
(a + 2) (- 1)2 – a (- 1) – 2
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 2
∴ – 1 మూలము కాదు.
ఇదే విధంగా 0, 2 కు కూడా సరిచూడగలరు.

ప్రశ్న 53.
ax2 + bx + c = 0 వర్గ సమీకరణ మూలాలు సమానం అయిన c = \(\frac{b^{2}}{4 a}\) అని చూపుము. .
సాధన.
b2 – 4ac = 0 ⇒ 4ac = b2 ⇒ c = \(\frac{b^{2}}{4 a}\)

ప్రశ్న 54.
ax2 + bx + c = 0 వర్గ సమీకరణ మూలాలు సమానం అయిన
(A) b2 – 4ac > 0
(B) b2 – 4ac < 0
(C) b2 – 4ac = 0
(D) పైవి ఏవీకాదు
జవాబు..
(C) b2 – 4ac = 0

ప్రశ్న 55.
ax2 + bx + c = 0 వర్గ సమీకరణ విచక్షణిని రాయండి.
జవాబు.
b2 – 4ac

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 56.
ax2 + bx + c = 0 వర్గ సమీకరణ మూలాలు సమానమైనచో సమాన మూలంను తెల్పండి.
జవాబు.
\(\frac{-b}{2 a}\)

ప్రశ్న 57.
x2 + px – q = 0 వర్గసమీకరణ విచక్షణిని రాయండి.
సాధన.
p2 – 4(1) (-q) = p2 + 4q

ప్రశ్న 58.
ఒక లంబకోణ త్రిభుజం యొక్క ఒక భుజం మరొక భుజం కన్నా 3 సెం.మీ. ఎక్కువ మరియు కర్ణము 15 సెం.మీ., చిన్న భుజం x సెం.మీ. అయిన క్రింది ఏ వర్గ సమీకరణాన్ని తృప్తి పరుస్తుంది ?
(A) 3x2 + 6x – 108 = 0
(B) x2 + 6x – 108 = 0
(C) x2 + 3x – 108 = 0
(D) 2x2 + 3x + 108 = 0
జ.
(C) x2 + 3x – 108 = 0

సాధన.
చిన్న భుజం X అనుకొనుము.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 3
AB2 + BC2 = AC2
x2 + (x + 3)2 = 152
x2 + x2 + 6x + 9 = 225
2x2 + 6x + 9 – 225 = 0
2x2 + 6x – 216 = 0
2(x2 + 3x – 108) = 0
∴ x2 + 3x – 108 = 0

ప్రశ్న 59.
మొత్తము 27, లబ్దము 180 అయ్యే విధంగా రెండు సంఖ్యలను కనుగొనుటకు ఉపయోగపడే వర్గ సమీకరణంను కనుగొనుము.
సాధన.
రెండు సంఖ్యలు x, 27 – x అనుకొనుము.
x(27 – x) = 180 ⇒ 27x – x2 = 180
∴ x2 – 27x + 180 = 0
(లేదా)
ఆ రెండు సంఖ్యలు α, β అనుకొనుము.
– α + β = 27, αβ = 180
∴ వర్గ సమీకరణం = x2 – (α + β)x + αβ = 0
x2 – 27x + 180 = 0

ప్రశ్న 60.
ఒక త్రిభుజం యొక్క భూమి, దాని ఎత్తు కంటే 4 సెం.మీ. ఎక్కువ. ఈ త్రిభుజ వైశాల్యము 48 చ.సెం.మీ. త్రిభుజ ఎత్తును లెక్కించుటకు సరియగు వర్గ సమీకరణమును ఎత్తు X సెం.మీ. అయిన సందర్భంలో రాయండి.
సాధన.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 4
త్రిభుజ వైశాల్యం = \(\frac{1}{2}\) bh = 48
⇒ \(\frac{1}{2}\)(x + 4)x = 48
∴ x2 + 4x = 96 ⇒ x2 + 4x – 96 = 0

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 61.
2x2 – 8x + p = 0 వర్గ సమీకరణం వాస్తవ మూలాలను కలిగి ఉండటానికి అవసరమయ్యే p యొక్క గరిష్ఠ విలువ ఎంత ?
సాధన.
2x2 – 8x + p = 0 యొక్క మూలాలు వాస్తవ మూలాలను కలిగి ఉంటే b2 – 4ac ≥ 0.
∴ (-8)2 – 4(2)p ≥ 20
⇒ 64 ≥ 8p ≥ 0
⇒ 64 ≥ 8p ⇒ 8 ≥ p ⇒ p ≤ 8
∴ p గరిష్ట విలువ = 8.

ప్రశ్న 62.
3x2 + 6x + k = 0కు వాస్తవ విభిన్న మూలాలుంటే k < 3 అని చూపుము.
సాధన.
3x2 + 6x + k = 0కు వాస్తవ విభిన్న మూలాలుంటే
b2 – 4ac > 0 ⇒ (6)2 – 4(3)k > 0
∴ 36 – 12k > 0 ⇒ 12k < 36
⇒ k < \(\frac{36}{12}\) = 3
∴ k < 3.

ప్రశ్న 63.
x2 + kx + 25 = 0 వర్గ సమీకరణ మూలాలు వాస్తవాలైతే k2 ≥ 100 అని చూపుము.
సాధన.
x2 + kx + 25 = 0 మూలాలు వాస్తవ మూలాలైతే
k2 – 4(1)(25) ≥ 0
⇒ k2 – 100 ≥ 0 ⇒ k2 ≥ 100

ప్రశ్న 64.
kx2 – 6x + 9 = 0 యొక్క మూలాలు వాస్తవాలు కాకపోతే k విలువను కనుగొనుము.
సాధన.
kx2 – 6x + 9 = 0 యొక్క మూలాలు వాస్తవాలు కాకపోతే
(- 6)2 – 4(k)(9) < 0 (∵ b2 – 4ac < 0)
36 – 36k < 0 36k > 36 ⇒ k > \(\frac{36}{36}\) = 1
∴ k > 1

ప్రశ్న 65.
3x2 + 6x + k = 0 యొక్క మూలాలు సంకీర్ణ సంఖ్యలు అయితే k > 3 అని చూపుము.
సాధన.
3x2 + 6x + k = 0 యొక్క మూలాలు సంకీర్ణ
సంఖ్యలు అనగా వాస్తవ సంఖ్యలు కావు.
∴ (6)2 – 4(3)k < 0 (∵ b2 – 4ac < 0)
36 – 12k < 0 ⇒ 12k > 36 ⇒ k > 3 .

ప్రశ్న 66.
2x2 + kx + 3 = 0 వర్గ సమీకరణానికి రెండు సమాన వాస్తవ మూలాలుంటే k విలువ ఎంత ?
సాధన.
2x2 + kx + 3 = 0 మూలాలు సమానాలు .
∴ k2 – 4(2) (3) = 0 (∵ b2 – 4ac = 0)
k2 = 24 = k ⇒ √24

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 67.
k యొక్క ఏ విలువకు kx (x – 2) + 6 = 0 వర్గ సమీకరణ మూలాలు సమాన వాస్తవ సంఖ్యలు అవుతాయి ?
సాధన.
kx2 – 2kx + 6 = 0 యొక్క మూలాలు సమానాలు.
∴ (- 2k)2 – 4(k) (6) = 0
⇒ 4k2 – 24k = 0 ⇒ 4k (k – 6) = 0
k ≠ 0, ∴ k – 6 = 0 ⇒ k = 6 .

ప్రశ్న 68.
x22 – k2 = 0 యొక్క ఒక మూలం – 3 అయిన మరొక మూలంను కనుగొనుము.
సాధన.
x2 – k2 = 0 యొక్క ఒక మూలము α = – 3, β = ?
α + β = \(\frac{-b}{a}\) = 0 ⇒ – 3 + β = 0, β = 3
(లేదా)
– 3 ఒక మూలము.
∴ (-3)2 – k2 = 0 ⇒ k2 = 9
⇒ k = √9 = ± 3,
రెండవ మూలము 3.

ప్రశ్న 69.
క్రింది వానిలో మూలాలు సమానంగా గల వర్గ సమీకరణము ఏది ?
(A) x2 + 4x + 4 = 0
(B) x2 – 4x + 4 = 0
(C) A మరియు B
(D) ఏదీకాదు
జవాబు.
(C) A మరియు B

ప్రశ్న 70.
విభిన్న వాస్తవ మూలాలు కలిగిన వర్గ సమీకరణం ఒకదానిని రాయండి.
సాధన.
(ఏవైనా రెండు వాస్తవ సంఖ్యలు మూలాలుగా గల వర్గ సమీకరణం కనుగొనాలి)
2, 3 మూలాలుగా గల వర్గసమీకరణం కనుగొందాం.
(x – 2) (x – 3) = 0
x2 – 5x + 6 = 0

ప్రశ్న 71.
2x2 – 3x + 5 = 0 వర్గ సమీకరణ మూలాల స్వభావాన్ని రాయండి.
సాధన.
విచక్షణి b2 – 4ac = (- 3)2 – 4(2)(5)
= 9 – 40 = – 31 < 0
కావున, మూలాలు వాస్తవ సంఖ్యలు కావు.

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 72.
3x2 – 4√3x + 4 = 0 వర్గ సమీకరణ మూలాలు సమాన వాస్తవ సంఖ్యలని చూపండి.
సాధన.
b2 – 4ac = (- 4√3)2 – 4(3)4
= 48 – 48 = 0
కావున, మూలాలు సమాన వాస్తవ సంఖ్యలు.

ప్రశ్న 73.
2x2 + 6x + 3 = 0 వర్గ సమీకరణ మూలాల స్వభావాన్ని రాయండి.
సాధన.
b2 – 4ac = (6)2 – 4(2)(3)
= 36 – 24 = 12 > 0 0
∴ మూలాలు అసమాన వాస్తవ సంఖ్యలు.

ప్రశ్న 74.
x2_5x + 4 = 0 యొక్క మూలాలు α, β మరియు α, k, P లు గుణశ్రేణిలో ఉంటే k విలువ ఎంత ?
సాధన.
x2 – 5x + 4 = 0 యొక్క మూలాలు α, β.
∴ α + β = 5, αβ = 4
α, k, β లు గుణశ్రేణిలో కలవు.
∴ \(\frac{\mathrm{k}}{\alpha}\) = \(\frac{\beta}{\mathrm{k}}\) ⇒ k2 = αβ = 4
∴ k = √4 = ± 2.

ప్రశ్న 75.
ax2 + bx + c = 0 వర్గ సమీకరణ మూలాలు : సమాన వాస్తవ సంఖ్యలు కావడానికి గల నియమాన్ని రాయండి.
జవాబు.
b2 – 4ac = 0

ప్రశ్న 76.
ax2 + bx + c = 0 వర్గసమీకరణ విచక్షణి b2 – 4ac > 0 అయితే మూలాలు గూర్చి నీవు ఏమి చెప్పగలవు ?
జవాబు.
మూలాలు విభిన్న వాస్తవ సంఖ్యలు.

ప్రశ్న 77.
వర్గ సమీకరణ విచక్షణి b2 – 4ac < 0 అయిన మూలాల స్వభావమును తెల్పండి.
(A) వాస్తవ సమాన సంఖ్యలు
(B) వాస్తవ విభిన్నాలు
(C) వాస్తవ సంఖ్యలు కావు
(D) మూలాలు శూన్యాలు
జవాబు.
(C) వాస్తవ సంఖ్యలు కావు (మూలాలు వాస్తవ సంఖ్యలు కావు).

ప్రశ్న 78.
ax2 + bx + c = 0 వర్గ సమీకరణ గ్రాను b2 – 4ac < 0 అయినప్పుడు చిత్తు పటంలో చూపండి.
జవాబు.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 5

ప్రశ్న 79.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 6
(A) b2 – 4ac = 0
(B) b2 – 4ac < 0
(C) b2 – 4ac0
(D) b2 – 4ac > 0
జవాబు.
(D) b2 – 4ac > 0

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 80.
ax2 + bx + c = 0 యొక్క మూలాలు సంకీర్ణ సంఖ్యలు (వాస్తవ సంఖ్యలు కాకపోతే) అయితే ఆ వర్గ సమీకరణ గ్రాను చిత్తుపటంలో చూపండి.
జవాబు.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 7

ప్రశ్న 81.
b24ac > 0 అయిన ax2 + bx + c = 0వర్గ సమీకరణ గ్రాఫ్ క్రింది వానిలో ఏది కాదు ?
(A)
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 8
(B)
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 9
(c)
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 10
(D) పైవన్నీ
జవాబు.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 10

ప్రశ్న 82.
b2 – 4ac = 0 అయినప్పుడు 2 + bx + c = 0 వర్గ సమీకరణ (ను చిత్తు పటంగా గీయండి.
జవాబు.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 11

ప్రశ్న 83.
x2 + bx + c = 0 వర్గ సమీకరణ గ్రాఫ్ కు చెందిన క్రింది వాటిలో ఏది అసత్యము ?
(A) b2 – 4ac > 0 అయిన గ్రాఫ్ X – అక్షాన్ని రెండు బిందువుల వద్ద ఖండిస్తుంది.
(B) B2 – 4ac < 0 అయిన గ్రాఫ్ X – అక్షాన్ని ఖండించదు.
(C) b2 – 4ac = 0.అయిన గ్రాఫ్ X – అక్షాన్ని రెండు బిందువుల వద్ద ఖండిస్తుంది.
(D) పైవన్నీ
జవాబు.
(C) b2 – 4ac = 0.అయిన గ్రాఫ్ X – అక్షాన్ని రెండు బిందువుల వద్ద ఖండిస్తుంది.

ప్రశ్న 84.
విభాగం-I లోని విచక్షణి విలువకు, విభాగం-IIలోని మూలాల స్వభావానికి జత చేయండి.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 12
(A) i-b, ii-a, iii-c
(B) i-c, ii-a, iii-b
(C) i-c, ii-b, iii-a
(D) i-b, ii-c, iii-a
జవాబు.
(B) i-c, ii-a, iii-b

ప్రశ్న 85.
√3x2 – 6x + 12√3 = 0 వర్గ సమీకరణ విచక్షణిని కనుగొనుము.
సాధన.
విచక్షణి b2 – 4ac
= (- 6)2 – 4(√3)12√3
= 36 – 144
= – 108

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 86.
x2 – 3x – k = 0 వర్గ సమీకరణ విచక్షణి 25 అయిన ఓ విలువ ఎంత ?
సాధన.
b2 – 4ac = 25
⇒ (-3)2 – 4(1) (- k) = 25
⇒ 9 + 4k = 25
⇒ 4k = 25 – 9
∴ 4k = 16 ⇒ k = 4

ప్రశ్న 87.
3x2 – 5x + 2 = 0 యొక్క ఒక మూలము 1 అయిన రెండవ మూలం ఎంత ?
సాధన.
మూలాల మొత్తం α + β = \(\frac{-b}{a}\) = \(\frac{-(-5)}{3}\)
∴ 1 + β = \(\frac{5}{3}\) (∵ ఒక మూలం 1)
రెండవ మూలం β = \(\frac{5}{3}\) – 1 = \(\frac{2}{3}\)
(లేదా) ..
మూలాల లబ్ధం αβ = \(\frac{c}{a}\) = \(\frac{2}{3}\)
(1) β = \(\frac{2}{3}\)
∴ β = \(\frac{2}{3}\)

ప్రశ్న 88.
విభాగం-Iలోని విచక్షణి విలువకు, విభాగం-II లోని గ్రాఫ్ రూపానికి జత చేయండి.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 13
(A) i-a, ii-c, iii-b
(B) i-a, ii-b, iii-c
(C) i-b, ii-a, iii-c
(D) i-b, ii-c, iii-a
జవాబు.
(A) i-a, ii-c, iii-b

ప్రశ్న 89.
వాదన I : x2 – 6x + 9 = 0 వర్గసమీకరణ మూలాలు సమాన వాస్తవ సంఖ్యలు.
వివరణ II : ax2 + bx + c = 0 యొక్క విచక్షణి b2 – 4ac = 0 అయిన మూలాలు. సమాన వాస్తవ సంఖ్యలు. (A) I అసత్యం , II సత్యం , I & II సరైన వివరణ
(B) I సత్యం, II సత్యం, I & II సరైన వివరణ కాదు
(C) I సత్యం, II సత్యం , I & II సరైన వివరణ
(D) I అసత్యం, II అసత్యం
జవాబు.
(D) I అసత్యం, II అసత్యం

ప్రశ్న 90.
x2 – x – 20 = 0 సమీకరణానికి చెందిన క్రింది ఏది అసత్యం ?
(A) వేర్వేరు వాస్తవ మూలాలను కలిగి ఉంటుంది
(B) – 4 మరియు 5 లు మూలాలు
(C) వాస్తవ సమాన మూలాలను కలిగి ఉంటుంది
(D) A మరియు B
జవాబు.
D

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 91.
a = 1 అయిన ax2 + 2x + a = 0 కు గల : మూలాలు సమానం అని చూపుము.
సాధన.
b2 – 4ac = (2)2 – 4(a)(a) = 4 – 4a2,
a = 1 అయితే 4 – 4a2 = 4 – 4(1)2 = 0
a = 1 అయినప్పుడు b2 – 4ac = 0 కావున మూలాలు సమానము.
(లేదా)
a = 1 అయిన ఇచ్చిన వర్గసమీకరణం
= x2 + 2x + 1 = 0
∴ b2 – 4ac = (2)2 – 4(1) (1) = 0. కావున మూలాలు సమానం.

ప్రశ్న 92.
b2 – 4ac > 0 అయిన సందర్భంలో వర్గ సమీకరణం యొక్క రేఖాచిత్రం చిత్తుపటం గీయండి.
సాధన.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 14

ప్రశ్న 93.
x2 + 6x + λ = 0 ఖచ్చిత వర్గం అయిన 7 విలువ ఎంత ?
సాధన.
x2 + 6x + λ = 0 ఖచ్చిత వర్గం అయితే
(a + b)2 = a2 + 2ab + b2 రూపంలో ఉంటుంది.
∴ x2 + 2 ∙ 3 ∙ x + λ = 0
ఇక్కడ, a = x, b = 3, λ = b2
λ = (3)2 = 9
(లేదా)
x2 + 6x + λ = 0 ఖచ్చిత వర్గం అయితే మూలాలు ‘సమానాలు.
∴ b2 – 4ac = 0
⇒ (6)2 – 4(1)λ = 0
⇒ 36 – 4λ = 0 ⇒ 36 = 4λ.
∴ λ = 9

ప్రశ్న 94.
3, 3 మూలాలుగా గల వర్గ సమీకరణం యొక్క రేఖాచిత్రం చిత్తుపటం గీయండి.
జవాబు.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 15

ప్రశ్న 95.
x2 + 2x + (λ2 + 1) = 0 వర్గ సమీకరణ మూలాలు సమానం అయితే λ విలువను కనుగొనుము.
సాధన.
b2 – 4ac = 0
⇒ (2)2 – 4(1)(λ2 + 1) = 0
⇒ 4 – 4λ2 – 4 = 0
⇒ 4λ2 = 0
∴ λ2 = 0 ⇒ λ = 0

ప్రశ్న 96.
b2 – 4ac< 0 అయినపుడు ax2 + bx + c = 0 మరియు a < 0 అయిన సందర్భంలో వర్గ సమీకరణం యొక్క గ్రాఫ్ (రేఖాచిత్రం)ను గీయండి..
జవాబు.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 16

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 97.
(2x + 3)2 = 0 వర్గ సమీకరణం యొక్క విచక్షణిని కనుగొనుము.
సాధన.
0 (∵ ఇచ్చిన వర్గసమీకరణం (a + b)2 = 0 రూపంలో కలదు. కావున మూలాలు సమానం. కావున విచక్షణి ‘0’).
(లేదా )
(2x + 3)2 = 4x2 + 12x + 9
b2 – 4ac = (12)2 – 4(4)(9)
= 144 – 144 = 0

ప్రశ్న 98.
3x2 + 2√5x – 5 = 0 వర్గ సమీకరణం యొక్క విచక్షణిని కనుగొనుము.
సాధన.
3x2 + 2√5x – 5 = 0
విచక్షణి b2 – 4ac = (2√5)2 – 4(3)(- 5)
= 20 + 60 = 80

ప్రశ్న 99.
(3x – 2)2 = – 2 (3x – 2)2 యొక్క మూలాలు
(A) \(\frac{-2}{3}, \frac{-2}{3}\)
(B) \(\frac{2}{3}, \frac{2}{3}\)
(C) \(\frac{3}{2}, \frac{3}{2}\)
(D) \(\frac{-2}{3}, \frac{2}{3}\)
జవాబు.
(B) \(\frac{2}{3}, \frac{2}{3}\)

సాధన.
(3x – 2)2 = -2 (3x – 2)2
⇒ (3x – 2)2 + 2(3x – 2)2 = 0
⇒ 3(3x – 2)2 = 0
∴ (3x – 2)2 = 0 ⇒ (3x – 2) (3x – 2) = 0 2
∴ మూలాలు \(\frac{2}{3}, \frac{2}{3}\)

ప్రశ్న 100.
3(x – 4)2 = (x – 4)2 + 8 యొక్క ఒక మూలం ‘6’ అవుతుందని చూపండి.
సాధన.
3(x – 4)2 = (x – 4)2 + 8
x = 6 అయిన 3(6 – 4 )2 = (6 – 4)2 + 8
12 = 4 + 8 ⇒ 12 = 12
కావున, 6 ఒక శూన్యం అవుతుంది.

ప్రశ్న 101.
వర్గ బహుపది ax2 + bx + c యొక్క శూన్య విలువలు 2, -3 అయిన ax2 + bx + c = 0 – యొక్క మూలాలను రాయండి.
సాధన.
(2, – 3) (∵ ax2 + bx + c యొక్క శూన్యాలు
ax2 + by + c = 0 క్క మూలాలు అవుతాయి.)

ప్రశ్న 102.
(x + 2)2 – 9 = 0 వర్గ సమీకరణ మూలాలను కనుగొనుము.
సాధన.
(x + 2)2 – 9 = 0 ⇒ (x + 2)2 = 9
x + 2 = √9 = ± 3.
∴ x + 2 = 3 ⇒ x = 1
x + 2 = – 3 ⇒ x = – 5
∴ మూలాలు = 1, – 5.

ప్రశ్న 103.
x2 – 4x + 2 = 0 వర్గ సమీకరణ మూలాలను కనుగొనుము.
సాధన.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 17

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 104.
“రెండు సంఖ్యల మొత్తం 15, వాని వర్గాల మొత్తం 117” అయిన ఆ సంఖ్యలను కనుగొనుటకు అవసరమగు వర్గసమీకరణాన్ని రాబట్టుము.
సాధన.
ఆ సంఖ్యలు α, β అనుకొంటే,
α + β = 15, αβ = 117.
వర్గ సమీకరణం = x2 – (α + β)x + αβ = 0
∴ కావలసిన వర్గసమీకరణం x2 – 15x + 117 = 0.

ప్రశ్న 105.
ax2 + bx + c = 0 యొక్క సాధనకు ఉపయోగించే వర్గసూత్రాన్ని రాయండి.
(లేదా)
ax2 + bx + c = 0 వర్గ సమీకరణ సాధన (మూలాలను) రాయండి.
సాధన.
\(\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\)

ప్రశ్న 106.
“3x2 – 4√5x + 4 = 0 వర్గ సమీకరణ మూలాలు సమాన వాస్తవ సంఖ్యలు”. ఇచ్చిన వర్గ సమీకరణ – మూలాలను తెల్పండి.
సాధన.
సమాన వాస్తవ మూలాలు = \(\frac{-b}{2 a}, \frac{-b}{2 a}\)
= \(\frac{-(-4 \sqrt{3})}{6}\) = \(\frac{2}{\sqrt{3}}, \frac{2}{\sqrt{3}}\)

ప్రశ్న 107.
ప్రవచనం-I: ax2 + bx + c = 0 యొక్క విచక్షణి b2 – 4ac > 0 అయిన మూలాలు సమాన వాస్తవ సంఖ్యలు.
ప్రవచనం-II: ax2 + bx + c = 0 యొక్క విచక్షణి b2 – 4ac < 0 అయిన మూలాలు అసమాన ‘వాస్తవ సంఖ్యలు.
(A) I, II లు రెండూ సత్యము
(B) I సత్యం, II అసత్యం
(C) I సత్యం, II అసత్యం
(D) I మరియు II లు రెండూ అసత్యం
జవాబు.
(D) I మరియు II లు రెండూ అసత్యం

ప్రశ్న 108.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 18
పై పటంలోని గ్రాను సూచించే వర్గ సమీకరణ మూలాలు రాయండి.
సాధన. మూలాలు – 1 మరియు 2.

ప్రశ్న 109.
2x2 – 2√2x + k= 0 వర్గ సమీకరణ మూలాలు సమానాలు అయినపుడు k విలువను కనుగొనుము.
సాధన.
b2 – 4ac = 0 (∵ మూలాలు సమానం)
(- 2√2)2 – 4(2)k = 0
⇒ 8 – 8k = 0 ⇒ 8 = 8k
∴ k = 1.

ప్రశ్న 110.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 19
పై లంబకోణ త్రిభుజం ABC యొక్క మిగిలిన రెండు భుజాలను కనుగొనుటకు అవసరమైన వర్గ సమీకరణమును రాబట్టుము.
సాధన.
(x + 5)2 + x2 = 252 (∵ ∠B = 90°
= AC2 = AB + BC2)
x2 + 10x + 25 + x2 = 625
2x2 + 10x – 600 = 0.

ప్రశ్న 111.
2x2 – 2√2x + 1 = 0 వర్గ సమీకరణ మూలాలు సమానం అయితే ఆ మూలాలను కనుగొనుము.
సాధన.
సమాన మూలాలు \(\frac{-b}{2 a}, \frac{-b}{2 a}\) = \(\frac{2 \sqrt{2}}{4}\)
= \(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\) = \(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\)
(లేదా)
మూలాలు సమానం కావున b2 – 4ac = 0
∴ మూలాలు = \(\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\)
= \(\frac{-(-2 \sqrt{2}) \pm 0}{2(2)}\)
= \(\frac{2 \sqrt{2}}{4}\)
= \(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\)

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 112.
(2x + 1)3 = px3 + 5 ఒక వర్గ సమీకరణం అయితే p = ……………
(A) 8
(B) 4
(C) 2
(D) 0
జ.
(A) 8

సాధన.
p = 8 (L.H.S. మరియు R.H.S. లలో 3 గుణకం సమానం కావాలి)
⇒(2x + 1)3 = px3 + 5
⇒ (2x)3 + 13+ 3(2x)(1)(2x + 1) = px3 + 5
⇒ 8x3 + 13 + 12x2 + 6x = px3 + 5
∴ p = 8
[∵ (a + b)3 = a3 + B3 + 3ab (a + b)]

ప్రశ్న 113.
ఒక వర్గ సమీకరణానికి గల గరిష్ఠ మూలాల సంఖ్య ఎంత ?
జవాబు.
2

ప్రశ్న 114.
స్థిరపదం లోపించిన వర్గ సమీకరణమునకు ఎల్లప్పుడు ‘0’ ఒక మూలం అని చూపుము.
సాధన.
ax2 + bx + c = 0 లో స్థిరపదం లోపిస్తే అది
ax2 + bx = 0 ⇒ x(ax + b) = 0
x = 0 (లేదా) ax + b = 0
∴ ‘0’ ఒక మూలము.
(లేదా)
మూలాల లబ్ధం αβ = \(\frac{c}{\mathrm{a}}\) = \(\frac{0}{\mathrm{a}}\) = 0 (∵ c = 0)
∴ α = 0 (లేదా) β = 0
కావున ‘0’ ఒక మూలము.

ప్రశ్న 115.
x (x + 4) = 12 కు వర్గ సమీకరణ ప్రామాణిక రూపం తెల్పండి.
జవాబు.
x2 + 4x – 12 = 0

ప్రశ్న 116.
(2x – 1) (2x + 1) = 0 వర్గ సమీకరణ మూలాలు రాయండి.
జవాబు.
మూలాలు \(\frac{1}{2}\), –\(\frac{1}{2}\).

ప్రశ్న 117.
క్రింది ఏ సందర్భంలో వర్గ సమీకరణం యొక్క మూలాలు వాస్తవ సంఖ్యలు అవుతాయి ?
(A) b2 – 4ac > 0 ‘
(B) B2 – 4ac = 0 i
(C) b2 – 4ac < 0
(D) A మరియు B
జవాబు.
(D) A మరియు B

ప్రశ్న 118.
ఈ క్రింది గ్రాఫ్ సూచించే వర్గ సమీకరణము యొక్క మూలాలు
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 20
(A),సమాన వాస్తవసంఖ్యలు
(B) విభిన్న వాస్తవసంఖ్యలు
(C) వాస్తవసంఖ్యలు కాదు
(D) ఏమీ చెప్పలేము
జవాబు.
(C) వాస్తవసంఖ్యలు కాదు

ఈ క్రింది పటాన్ని పరిశీలించి, 119, 120 ప్రశ్నలకు సమాధానాలు రాయండి.

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 21

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 119.
గ్రాఫ్ సూచించే వర్గ సమీకరణమును రాయండి.
సాధన.
(x + 2)2 = 0 = x2 + 2x + 4 = 0

ప్రశ్న 120.
గ్రాఫ్ సూచించే వర్గ సమీకరణ మూలములను తెల్పండి.
జవాబు.
-2, -2 (లేదా) – 2

ప్రశ్న 121.
ఒక వర్గ సమీకరణ గ్రాఫ్ X – అక్షాన్ని (2, 0) బిందువు వద్ద స్పర్శిస్తుంటే ఆ వర్గసమీకరణ ఒక మూలంను ” తెల్పండి.
జవాబు.
2.

ప్రశ్న 122.
ఓ యొక్క ఏ విలువకు 3x2 – 2x + k= 0 యొక్క విచక్షణి శూన్యం అవుతుంది ?
సాధన.
b2 – 4ac = 0 = (- 2)2 – 4(3)(k) = 0
⇒ 4 – 12k = 0
⇒ 12k = 4
⇒ k = \(\frac{1}{3}\)

ప్రశ్న 123.
నిత్య జీవితంలో వర్గ సమీకరణాలను ఉపయోగించే ఒక సందర్భాన్ని తెల్పండి.
జవాబు.
రాకెట్ ను ప్రయోగించే సందర్భంలో, రాకెట్ గమన మార్గాన్ని నిర్వచించడంలో వర్గ సమీకరణాన్ని ఉపయోగిస్తారు.
(లేదా)
డిష్ యాంటెనాల తయారీలో / కంటి అద్దాల తయారీలో వర్గసమీకరణంను ఉపయోగిస్తారు.

ప్రశ్న 124.
x2 – 3x + 2 = 0 వర్గ సమీకరణ మూలాల మొత్తం ఎంత ?
సాధన.
మూలాల మొత్తం = \(\frac{-b}{a}\) = \(\frac{-(-3)}{1}\) = 3

ప్రశ్న 125.
x2 + kx + 50 = 0 యొక్క ఒక మూలము 5 అయిన k విలువ ఎంత ?
సాధన.
x2 + kx + 50 = 0 యొక్క ఒక మూలము 5.
∴ (5)2 + k(5) + 50 = 0
= 5k = – 75
⇒ k = \(\frac{-75}{5}\) = – 15

ప్రశ్న 126.
ప్రవచనం-I: ax2 + bx + c = 0 యొక్క మూలాల మొత్తం \(\frac{-b}{a}\) కు సమానము.
‘ప్రవచనం-II : ax2 + bx + c = 0 వర్గ సమీకరణం ఎల్లప్పుడు రెండు వాస్తవ మూలాలను కలిగి ఉంటుంది.
(A) I సత్యం , II అసత్యం .
(B) I సత్యం, II సత్యం
(C) I అసత్యం, II సత్యం
(D) I అసత్యం, II అసత్యం
జవాబు.
(A) I సత్యం , II అసత్యం .

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 127.
మూలాలు సమానంగా గల వర్గసమీకరణానికి ఒక ఉదాహరణనివ్వండి.
సాధన.
మూలాలు సమానంగా గల వర్గసమీకరణానికి ఉదాహరణ
(x – 2) (x – 2) = 0 = x2 – 4x + 4 = 0

ప్రశ్న 128.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 22
పై లంబకోణ త్రిభుజం ABCలో AB భుజం పొడవును సాధనగా గల వర్గ సమీకరణ ప్రామాణిక రూపంను రాయండి.
సాధన.
AC2 = AB + BC2
= (x + 2)2 = x2 + (x + 1)2
= x2 + 4x + 4 = x2 + x2 + 2x + 1 [∵ (a + b)2 = a2 + 2ab + b2]
∴ x2 – 2x – 3 = 0

ప్రశ్న 129.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 23
పై పటంలో ‘0’ వృత్త కేంద్రము మరియు AC = (x + 3) సెం.మీ. AB = x సెం.మీ. BC = √3 x సెం.మీ అయిన x విలువ కలిగిన వర్గ సమీకరణంను కనుగొనుము.
సాధన.
∠B = 90° (∵ B అర్ధవృత్తంలోని కోణము) 3
∴ AB2 + BC2 = AC2
⇒ x2 + (√3 x)2 = (x + 3)2
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 24
∴ 3x2 – 6x – 9 = 0

ప్రశ్న 130.
kx (x – 2) + 6 = 0 యొక్క ఒక సాధన 3 అయిన k = ……………
(A) 2
(B) – 2
(C) 1
(D) – 1
జవాబు.
(B) – 2

సాధన.
kx (x – 2) + 6 = 0 యొక్క సాధన 3.
∴ k(3) (3 – 2) + 6 = 0
3k + 6 = 0 = 3k =-6 -6
∴ k = \(\frac{-6}{3}\) = – 2

ప్రశ్న 131.
α, β లు శూన్యాలుగా గల వర్గబహుపది k(x2 – (α + β)x + αβ) అయిన α, β లు మూలాలుగా గల వర్గ బహుపదిని తెల్పండి.
జవాబు.
x2 – (α + β)x + αβ = 0

ప్రశ్న 132.
క్రింది పటంలో గ్రాఫ్ సూచించే వర్గ సమీకరణం యొక్క మూలాలు ఏవి ?
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 25
జవాబు.
మూలాలు 1, 4.

ప్రశ్న 133.
మొత్తము 27, లబ్ధము 182 అయ్యే విధంగా గల రెండు సంఖ్యలను కనుగొనుటకు అవసరమైన వర్గ సమీకరణం x2 – kx + 182 = 0 అయిన kను కనుగొనుము.
జవాబు.
k = 27 (∵ k విలువ మూలాల మొత్తానికి సమానము)

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 134.
“ఒక సంఖ్య మరియు సంఖ్య యొక్క వ్యుత్రమాల మొత్తం \(\frac{10}{3}\)” అయిన ఇచ్చిన నియమాలను తృప్తిపరిచే వర్గ సమీకరణం
(i) x + \(\frac{1}{x}\) = \(\frac{10}{3}\)
(ii) 3x2 = 10x + 3 = 0
(A) i మాత్రమే సత్యం
(B) ii మాత్రమే సత్యం
(C) i మరియు ii లు రెండూ సత్యం
(D) i మరియు ii’లు రెండూ అసత్యం
జవాబు.
(C) i మరియు ii లు రెండూ సత్యం

ప్రశ్న 135.
x2 – 5x + 6 = 0 మూలాలు α, β అయిన \(\frac{1}{\alpha}+\frac{1}{\beta}\) విలువను కనుగొనుము.
సాధన.
x2 – 5x + 6 = 0 యొక్క మూలాలు α, β
∴ α + β = 5, αβ = 6
\(\frac{1}{\alpha}+\frac{1}{\beta}\) = \(\frac{\beta+\alpha}{\alpha \beta}\) = \(\frac{5}{6}\)
(లేదా)
x2 – 5x + 6 = 0 యొక్క మూలాలను α, β
విలువలు కనుగొని \(\frac{1}{\alpha}+\frac{1}{\beta}\) విలువ కనుగొనవచ్చును.

ప్రశ్న 136.
x – \(\frac{1}{3}\) = 3 వర్గ సమీకరణంను ప్రామాణిక రూపులోకి మార్చండి.
సాధన.
x – \(\frac{1}{x}\) = 3 ⇒ \(\frac{x^{2}-1}{x}\) = 3 ⇒ x2 – 1 = 3x
⇒ x2 – 3x – 1 = 0

ప్రశ్న 137.
x – \(\frac{1}{x}\) = 0 మరియు x ≠ 0 అయిన X ధన విలువ ఎంత ?
సాధన.
x = \(\frac{1}{x}\) ⇒ x2 = 1 ⇒ x = √1 = ± 1
∴ x యొక్క ధన విలువ = 1

ప్రశ్న 138.
6x2 – x – 2 = 0 వర్గ సమీకరణ మూలాలు \(\frac{2}{3}\) మరియు –\(\frac{1}{2}\) అయిన p(x) = 6x2 – x – 2 వర్గబహుపది యొక్క శూన్యాలు ఏవి ?
సాధన.
p(x) = 6x2 – x – 2 యొక్క శూన్యాలు \(\frac{2}{3}, \frac{-1}{2}\)

ప్రశ్న 139.
1, 2 శూన్యాలుగాగల వర్గబహుపది p(x) = x2 – 3x + 2 అయిన log1010, log10100 విలువలు మూలాలుగా గల -వర్గ సమీకరణాన్ని తెల్పండి.
సాధన.
log1010 = 1,
log10100 = log10102 = 2log1010 = 2
∴ 1, 2 శూన్యాలుగా గల వర్తబహుపది
= x2 – 3x + 2 = 0 (ఇవ్వబడినది).

ప్రశ్న 140.
x – \(\frac{3}{x}\) = 2 వర్గ సమీకరణ మూలాలలో ఒకటి – 1 అయిన రెండవ మూలము ఏది ?
సాధన.
x – \(\frac{3}{x}\) = 2 = x2 – 2x – 3 = 0 యొక్క ఒక
మూలం α = – 1.
α + β = 2 ⇒ – 1 + β = 2 ⇒ β = 3,
రెండవ మూలం = 3

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 141.
క్రింది వానిలో ax2 + bx + c = 0కు సంబంధించి నది ఏది సత్యం ?
(A) b2 – 4ac > 0 అయిన మూలాలు విభిన్న వాస్తవ సంఖ్యలు.
(B) b2 – 4ac = 0 అయిన మూలాలు సమాన వాస్తవ సంఖ్యలు.
(C) b2 – 4ac < 0 అయిన వాస్తవ సంఖ్యలు కావు.
(D) పైవి అన్నీ
జవాబు.
(D) పైవి అన్నీ

ప్రశ్న 142.
x2 – 7x + 12 = 0 నకు మూలాల స్వభావం తెల్పండి.
సాధన.
x2 – 7x + 12 = 0 యొక్క విచక్షణి
b2 – 4ac = (- 7)2 – 4(1)(12)
= 49 – 48 = 1 > 0
∴ మూలాలు విభిన్న వాస్తవ సంఖ్యలు.

ప్రశ్న 143.
x2 – kx + 16 = 0 నందు మూలాలు అసమానాలు, వాస్తవాలు అయిన క్రింది వానిలో ఏది సత్యం ?
(A) k = 8.
(B) k > 8
(C) k < 8
(D) ఏదీకాదు
జవాబు.
(D) ఏదీకాదు

సాధన.
x2 – kx + 16 = 0 యొక్క మూలాలు అసమాన వాస్తవ సంఖ్యలు.
∴ b2 – 4ac > 0 ⇒ (- k)2 – 4(1)16 > 0
k2 – 64 > 0 ⇒ k2 > 64 ⇒ k > √64
∴ k > 8 (లేదా) k < – 8.

ప్రశ్న 144.
క్రింది పటంలోని వర్గ సమీకరణం యొక్క మూలాల గూర్చి నీవు ఏమి చెప్పగలవు ?
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 26
జవాబు.
మూలాలు వాస్తవ సంఖ్యలు కావు.

ప్రశ్న 145.
x2 – 36 = 0 యొక్క గ్రాఫ్ 20 అయిన a + b విలువ ఎంత ?
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 27
సాధన.
a, b లు ఇచ్చిన వర్గసమీకరణం మూలాలు.
∴ a + b = \(\frac{-b}{a}\) = \(\frac{0}{1}\) = 0
(లేదా)
x2 – 36 = 0 ⇒ x2 = 36 ⇒ x = √36 = ±6
గ్రాఫ్ ప్రకారం మూలాలు a, b
∴ a = – 6, b = 6
∴ a + b = (- 6) + 6 = 0

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 146.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 28
పై పటం సూచించే వర్గ సమీకరణం నందు మూలాల మొత్తంను తెల్పండి.
(A) 2
(B) 4
(C)8
(D)
సాధన.
(B) 4
మూలాలు సమానాలు మరియు 2, 2.
∴ మూలాల మొత్తం = 2 + 2 = 4

ప్రశ్న 147.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 29
(A) 1
(B) 2
(C) 3
(D) 6
జవాబు.
C

సాధన.
మూలాలు 1,3
p మూలాల మొత్తం అవుతుంది.
∴ p = 1 + 3 = 4
q మూలాల లబ్ధం అవుతుంది.
∴ q = (1) (3) = 3

ప్రశ్న 148.
x2 – 4x + 3 = 0 యొక్క మూలాలు 1, 3 అయిన x2 – 4x + 3 = 0 యొక్క రేఖాచిత్రం (గ్రాఫ్) X- అక్షాన్ని ఖండించే బిందువులను తెల్పండి.
సాధన.
X – అక్షాన్ని ఖండించే బిందువులు (1, 0) మరియు (3, 0).

ప్రశ్న 149.
sin 90°, sec 60° విలువలు శూన్యాలుగా గల వర్గ సమీకరణాన్ని రాయండి.
సాధన.
sin 90° = 1, sec 60° = 2.
∴ 1, 2 శూన్యాలుగా గల వర్గ సమీకరణం
x2 – (1 + 2)x + (1) (2) = 0 .
x2 – 3x + 2 = 0

ప్రశ్న 150.
ax2 + bx + c = 0 యొక్క మూలాల మొత్తంను రాయండి.
సాధన.
\(\frac{-b}{a}\)

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 151.
ax2 + bx – c = 0 యొక్క మూలాల లబ్దంను – తెల్పండి.
జ.
\(\frac{c}{a}\)

ప్రశ్న 152.
(x + 5) (x – 6) = 0 తో సూచింపబడే వర్గ సమీకరణం యొక్క మూలాల మొత్తం ఎంత ?
సాధన.
మూలాలు – 5, 6 .
∴ మూలాల మొత్తం = (- 5) + 6 = 1

ప్రశ్న 153.
2x2 – 1 = 0 వర్గ సమీకరణమునకు sin θ ఒక మూలము (0 ≤ 90°) అయిన ‘θ’ విలువను కనుగొనుము.
సాధన.
2x2 – 1 = 0కు sin θ ఒక మూలము.
∴ 2 sin2θ – 1 = 0
⇒ 2 sin2θ = 1 ⇒ sin2θ = \(\frac{1}{2}\)
∴ sin θ = \(\sqrt{\frac{1}{2}}\) = \(\frac{1}{\sqrt{2}}\)
∴ θ = 45°

ప్రశ్న 154.
ఒక వర్గ సమీకరణం మూలాలు వాస్తవ సంఖ్యలు అయిన ఆ మూలాల సంఖ్య.
(A) 0
(B) కనీసం
(C) గరిష్ఠంగా 2
(D) B మరియు C
జవాబు.
(D) B మరియు C

ప్రశ్న 155.
x2 – 7x + 12 = 0 వర్గ సమీకరణం యొక్క మూలాల లబ్ధంను కనుగొనుము.
సాధన:
మూలాల లబ్ధం = \(\frac{c}{a}\) = \(\frac{12}{1}\) =12

ప్రశ్న 156.
AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు Bits 30
వర్గ సమీకరణ గ్రాఫ్ పటంలో చూపిన విధంగా X- అక్షాన్ని ఒకే బిందువు వద్ద తాకిన పై సందర్భంలో విచక్షణి గూర్చి నీవు ఏమి చెప్పగలవు?
జవాబు.
విచక్షణి = 0

ప్రశ్న 157.

ను సూచించు వర్గ బహుపది మూలాల స్వభావాన్ని రాయండి.
జవాబు.
మూలాలు సమాన వాస్తవ సంఖ్యలు.

గమనిక: ఇచ్చిన సమాచారం ఆధారంగా 158 – 160 వరకు గల ప్రశ్నలకు సమాధానాలు రాయండి. వర్గసమీకరణము x2 – 7x + 12 = 0.

ప్రశ్న 158.
ఇచ్చిన వర్గసమీకరణ విచక్షణిని కనుగొనుము.
సాధన.
విచక్షణి. b2 – 4ac = (-7)2 – 4(1) (12)
= 49 – 48 = 1

ప్రశ్న 159.
ఇచ్చిన వర్గసమీకరణ మూలాలను పొడవు, వెడల్పులుగా గల దీర్ఘచతురస్ర చుట్టుకొలత ఎంత ?
సాధన.
మూలాలు α, β అనుకొనుము.
l = α, b = β అనుకొనుము.
దీర్ఘచతురస్ర చుట్టుకొలత = 2(1 + b)
= 2(α + β)
= 2\(\left(\frac{-b}{a}\right)\)
= 2\(\left(\frac{-(-7)}{1}\right)\)
= 14 యూనిట్లు

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 160.
ఇచ్చిన వర్గసమీకరణ మూలాలను పొడవు, వెడల్పులుగా గల దీర్ఘచతురస్ర వైశాల్యమును లెక్కించండి.
సాధన.
దీర్ఘచతురస్ర వైశాల్యం = lb = αβ
= \(\frac{c}{a}\) = \(\frac{12}{1}\) = 12 చ.యూ.

ప్రశ్న 161.
వెడల్పు కంటె పొడవు 5 ఎక్కువగా గల దీర్ఘచతురస్ర వైశాల్యం a2 చ.యూ. పై సమాచారాన్ని సూచించు వర్గ సమీకరణం ఏది ?
(A) x2 + 5x – 25 = 0
(B) x(x + 5) = a
(C) x2 + 6x – a = 0
(D) పైవేవీకావు
సాధన.

దీర్ఘచతురస్ర వైశాల్యం = lb = a2
∴ (x + 5)x = a2
∴ కావలసిన వర్గసమీకరణం x2 + 5x – a2 = 0.

ప్రశ్న 162.
2 sin2 θ – 3 sin e + 10 = 0 సమీకరణంలో sin θ = x అయిన ఏర్పడే x లో వర్గసమీకరణాన్ని రాయండి.
జవాబు.
2x2 – 3x + 10 = 0.

ప్రశ్న 163.
ax2 + bx + c = 0 వర్గసమీకరణం యొక్క మూలాలు సమానమయ్యే సందర్భంలో వర్గసమీకరణ గ్రాఫ్ X – అక్షాన్ని స్పర్శించే బిందువును తెల్పండి.
జవాబు.
\(\left(\frac{-b}{2 a}, 0\right)\)

ప్రశ్న 164.
x2 – 3x + p= 0 యొక్క ఒక మూలం ‘0’ అయిన ‘p’ విలువ ఎంత ?
సాధన.
x2 – 3x + p = 0 యొక్క ఒక మూలం
(0)2 – 3(0) + p = 0 ⇒ p = 0

ప్రశ్న 165.
రెండు వరుస ధనపూర్ణ సంఖ్యల లబ్దం 306. ఈ ధన పూర్ణసంఖ్యలను కనుగొనుటకు అవసరమైన వర్గ సమీకరణాన్ని రాబట్టుము.
సాధన.
చిన్న ధన సంఖ్య = x అనుకొనుము.
పెద్ద ధన సంఖ్య = x + 1
x(x + 1) = 306 ⇒ x2 + x – 306 = 0
(లేదా)
పెద్ద ధన సంఖ్య = x అనుకొనుము
చిన్న ధన సంఖ్య = x – 1
x(x – 1) = 306 ⇒ x2 – x – 306 = 0

ప్రశ్న 166.
x + \(\frac{1}{x}\) = వర్గ సమీకరణమున 1 ఒక మూలం అని చూపుము.
సాధన.
x + \(\frac{1}{x}\) లో x = 1 ని ప్రతిక్షేపించగా
(1) + \(\frac{1}{(1)}\) = 2
1 + 1 = 2
2 = 2
∴ L.H.S. = R.H.S.
∴ 1 ఒక మూలము.

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 167.
క్రింది వానిలో సమాన మూలాలు – 1 గా గల వర్గ సమీకరణం ఏది ?
(A) x2 + 2x = – 1
(B) (x + 1)2 = 0
(C) x2 = – (2x + 1)
(D) పైవన్నీ
జవాబు.
(D) పైవన్నీ

ప్రశ్న 168.
ఈ క్రింది వానిలో వర్గ సమీకరణం కానిది ఏది ?
(A) x2 = 5
(B) (x + 1)2 = (2x – 3)2
(C) (2x + 5)2 = (2x – 1)2
(D) x3 + 3×22 + 1 = (x – 4)3
జవాబు.
(C) (2x + 5)2 = (2x – 1)2

ప్రశ్న 169.
జతపరుచుము. వర్గ సమీకరణం x2 – 10x + 9 = 0

(A) i-a, ii-c, iii-b, iv-d
(B) i-d, ii-b, iii-c, iv-a
(C) i-b, ii-a, iii-d, iv-c
(D) i-c, ii-b, iii-d, iv-a
జవాబు.
(B) i-d, ii-b, iii-c, iv-a

ప్రశ్న 170.
30 మీ. ఎత్తుగల కొబ్బరి చెట్టు నుండి ఒక కొబ్బరికాయ h = 30 + 7t – t2ను తృప్తిపరిచేటట్లు పడుతుంది. అయితే అది భూమిని చేరుటకు పట్టు కాలమును లెక్కించుటకు ఈ క్రింది వానిలో ఏది సరైన వర్గ సమీకరణము?
(A) 30 = 30 + 7t – t2
(B) – 30 = 30 + 7t + t2
(C) 0 = 30 + 7t – t2
(D) 0 = 7t – t2
జవాబు.
(C) 0 = 30 + 7t – t2

ప్రశ్న 171.
నిలకడ నీటిలో బోటు వేగం 18 mps, ప్రవాహ వేగం x mps అయిన ప్రవాహానికి ఎదురు దిశలో బోటు , వేగము ……….. mps.
జవాబు.
18 – x

ప్రశ్న 172.
క్రింది ఏ సందర్భంలో వర్గసమీకరణ భావనను ఉపయోగించుకొంటాము ?
(A) ప్రయోగించిన రాకెట్ యొక్క గమన మార్గాన్ని నిర్ణయించడంలో .
(B) పైకి విసిరిన వస్తువు యొక్క పదాన్ని నిర్ణయించడంలో
(C) వాహనం యొక్క బ్రేకును వేసినప్పుడు అది ప్రయాణించే మార్గాన్ని లెక్కించడం
(D) పై అన్ని సందర్భాలలో
జవాబు.
(D) పై అన్ని సందర్భాలలో

ప్రశ్న 173.
x2 – 8x + 16 = 0 యొక్క మూలాలను భుజాలుగా గల చతురస్రం యొక్క వైశాల్యము ఎంత ?
సాధన.
మూలాలు చతురస్ర భుజాలు α, β అనుకొనుము. (α = β).
చతురస్ర వైశాల్యం = మూలాల లబ్ధం .
= \(\frac{c}{a}\) = 16

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 174.
క్రింది వర్గసమీకరణాలను వాని మూలాలకు జత చేయడంలో సరైన సమాధానాన్ని ఎన్నుకొనుము.

(A) i-b, ii-a, iii-c, iv-d
(B) i-c, ii-b, iii-a, iv-d
(C) i-b, ii-c, iii-d, iv-a
(D) i-b, ii-d, iii-a, iv-c
జవాబు.
(C) i-b, ii-c, iii-d, iv-a

ప్రశ్న 175.
x2 – 6x + 8 = 0 యొక్క మూలాల సగటు ఎంత ?
సాధన.
మూలాలు α, β అనుకొనుము.
α + β = \(\frac{-b}{a}\) = \(\frac{-(-6)}{1}\) = 6
α, β ల సగటు = \(\frac{\alpha+\beta}{2}=\frac{6}{2}\) = 3

ప్రశ్న 176.
x2 – 2x – 8 = 0 యొక్క మూలాలు α, β మరియు α, k, β లు అంకశ్రేణిలో ఉంటే k విలువ ఎంత ?
సాధన.
x2 – 2x – 8 = 0 యొక్క మూలాలు α, β.
∴ α + β = \(\frac{-b}{a}\) = \(\frac{-(-2)}{1}\) = 2
α, k, β లు A.P లో ఉంటే k = \(\frac{\alpha+\beta}{2}=\frac{2}{2}\) = 1

ప్రశ్న 177.
3 మరియు 4 మూలాలుగా కల్గిన వర్గసమీకరణాన్ని రాయండి.
జవాబు.
x2 – 7x + 12 = 0

AP 10th Class Maths Bits 5th Lesson వర్గ సమీకరణాలు

ప్రశ్న 178.
వర్గసమీకరణం ax2 + bx + c = 0 యొక్క విచక్షణి b2 – 4ac< 0 అయ్యే సందర్భానికి చిత్తు రేఖాచిత్రం (గ్రాఫ్) గీయండి.
జవాబు.

AP 7th Class English Important Questions Unit 4 The Brave Little Bowman

These AP 7th Class English Important Questions 4th Lesson The Brave Little Bowman will help students prepare well for the exams.

AP Board 7th Class English Unit 4 Important Questions and Answers The Brave Little Bowman

Reading Comprehension (Seen)

1. Read the following passage carefully.

Once there lived a little wise man with a crooked back. He was a skilled archer. His only wish was to join the army. He thought that the king might not give him the job because of his crooked back. The little wise man wanted to find a strong man and ask him to take him as his assistant. Then the king would take both of them. He went in search of a big man.

One day he saw a big man digging a ditch.

The Little Man : You are a big and strong man. Why are you digging ditches? Can’t you find some other work?
The Big Man : I don’t know any other work, and I have to earn my living.
The Little Man : Don’t do this work anymore. Come with me. We will go to the king and ask for a job in the army for you.
The Big Man : I can’t do that. I am not a skilled warrior and can’t fight.
The Little Man : Don’t worry about that. Just go to the King, ask for a job in the army, and introduce me as your assistant.
The Big Man : But, how cap, a little man like you assist me?
(The Brave Little Bowman)

Now, answer the following questions. ,
1. What was the disadvantage that the little man had?
Answer:
He was short and had a crooked back.

2. What was the little man good at?
Answer:
He was good at archery.

3. What was the little man in search of?
Answer:
A big man

4. What was the big man doing when the little man approached him?
Answer:
The big man was digging ditches.

5. How would the little man be introduced?
Answer:
As an assistant of the big man

AP 7th Class English Important Questions Unit 4 The Brave Little Bowman

2. Read the following passage carefully.

They went to the palace gates. The big man sent a word to the king that there was a skilled bowman at the gate. The king sent for the big man.

The King : What do you want? Why did you come here?
The Big Man : My greetings to you, your Majesty. I want to join your army.
The King : Who is this little man?
The Big Man : He is my assistant, your Majesty. I want you to take him too along with me.
The King : I will take the both of you and give a thousand silver coins a month.
The Big Man : Thank you very much, your Highness! We will serve you to the best of our abilities.
(The Brave Little Bowman)

Now, answer the following questions.
1. What was the word sent by the big man to the king?
Answer:
That there was a skilled bowman at the gate

2. What were the phrases used by the big man to address the king?
Answer:
Your Majesty! and Your Highness!

3. Who was introduced as the assistant?
Answer:
The little man

4. How much did the king offer them a month?
Answer:
A thousand silver coins

5. Who joined the big man and the little man in the army?
Answer:
The king

3. Read the following passage carefully.

One day, the King was informed that a wild elephant was creating panic among the people: running up and down the road, tossing people in the air, causing injuries and in some cases death to the people. Immediately the king ordered the big man fo meet him. The big man reported to the king.
The King : Have you heard about the wild elephant?
The Big Man : Yes, your Majesty!
The King : Go and kill the wild elephant and put the people’s fears to rest.
The Big Man : Certainly, your Highness!
The big man and the little man went to look out for the wild elephant. The little man shot the elephant and killed it and they reported it to the king.
The Big Man : I have killed the wild elephant, your Majesty.
The King : Bravo! You have once again proved that you are a very brave man. I am happy to have you in my army. Take your reward. (The Brave Little Bowman)

Now, answer the following questions.
1. What was informed to the king?
Answer:
That a wild elephant was creating panic among the people

2. Who ordered to kill the elephant?
Answer:
The king

3. What was the king’s order to the big man?
Answer:
To kill the wild elephant and put the people’s fears to rest

4. Who killed the elephant?
Answer:
The little man

5. Whom did the king praise?
Answer:
The big man

AP 7th Class English Important Questions Unit 4 The Brave Little Bowman

4. Read the following passage carefully.

The war elephant went out of the city and entered the battlefield. Then at the sound of the first drum beat, the big man shook with fear.
The Little Man : Hang in there. You need not be afraid. If you fall off now, you will be killed.
The Big Man slipped off the elephant’s back, and ran back to the city.
The Big Man : I don’t want this job. I don’t want your money either. I can do any job as long as I live.
The Little man : Oh! what a coward he is! though big and strong! However, this is a blessing in disguise. I will fight for the king and prove that I am , better than the big man, though I don’t have a big and strong body.

The little bowman drove the war elephant into the fight. The army broke into the enemy king’s camp. The little man’s army drove the enemy out of their kingdom and won the battle. The king heard about the little bowman. The people called him ‘The Brave Little Bowman.’ The king made him the chief of the army and gave him rich gifts. The big man was ashamed of himself and went back to his work of digging ditches. As per the saying, ‘better late than never’, the little man received the much-deserved honour at last. (The Brave Little Bowman)

Now, answer the following questions.
1. Where did the war elephant enter?
Answer:
The battlefield

2. What did the big man do in the battlefield?
Answer:
He slipped off the elephant’s back and ran back to the city.

3. How is it a blessing in disguise?
Answer:
Though he had to fight the battle, it was a great opportunity for him to prove his skill.

4. Who won the battle?
Answer:
The little man’s army

5. What did the people call the little man?
Answer:
The Brave Little Bowman

5. Read the following lines carefully.

Over hill, over dale,
Thorough bush, thorough brier,
Over park, over pale,
Thorough flood, thorough fire!
I do wander everywhere,
Swifter than the moon’s sphere;
And I serve the Fairy Queen,
To dew her orbs upon the green; (A Fairy Song)

Now, answer the following questions.
1. Who is the speaker of these lines?
Answer:
A fairy

2. What is the poetic device used in the fourth and the sixth line?
Answer:
Hyperbole

3. Who moves faster, the moon or the speaker?
Answer:
The speaker

4. Who does the speaker serve?
Answer:
The Fairy Queen

5. How is the speaker serving her / him?
Answer:
By dropping dewdrops upon the green.

AP 7th Class English Important Questions Unit 4 The Brave Little Bowman

6. Read the following lines carefully.

The cowslips tall her pensioners be;
In their gold coats spots you see;
Those be rubies, fairy favours;
In those freckles live their savours;
1 must go seek some dewdrops here,
And hang a pearl in every cowslip’s ear. (A Fairy Song)

Now, answer the following questions.
1. What are the cowslips?
Answer:
Yellow flowers

2. What are the spots on the cowslips compared with?
Answer:
The spots on the cowslips are compared with rubies.

3. What is figure of speech used in the line ‘And hang a pearl in every cowslip’s ear.’?
Answer:
Personification

4. How do the spots look like?
Answer:
Like rubies

5. What are the ‘gold coats’ referred to?
Answer:
The yellow petals of the flowers

Reading Comprehension (Unseen)

1. Read the following passage.
After the war, our church was in a very bad condition. So we decided to build a new one on the top of a hill just outside the town. We used many different kinds of materials. We built the walls of stone and glass, the heavy doors of wood and metal. From the top of the church there was a wonderful view. You can see the entire town and countryside for miles around. People from all parts of the country visit the church every day. It is such an interesting building. ‘

Now, answer the following questions.
a) What was the condition of the church after the war?
Answer:
The church was in a very bad condition after the war.

b) Where did the people want to build the church?
Answer:
on the top of the hill

Choose the correct answer from the choices given.
c) The walls of the new church were made of?
i) wood and glass
ii) wood and metal
iii) stone and glass
Answer:
iii) stone and glass

d) The doors were made of…….
i) metal and wood
ii) cement and bricks
iii) glass and marble
Answer:
i) metal and wood

e) Choose the correct statement from the following.
i) The new church was built in a town.
ii) The new church was an interesting building.
iii) The new church had no walls and doors.
Answer:
ii) The new church was an interesting building.

AP 7th Class English Important Questions Unit 4 The Brave Little Bowman

2. Read the following passage.

Penny-wise Monkey
Once upon a time, there lived the king of a big and affluent country. The king was quite fond of travelling. Usually, he didn’t like to visit his own country; instead he went to other countries. One day, he assembled his army to move out for a holiday to some distant country. The king and his soldiers walked for the whole morning in the forest. After this, they went into the camp to take some rest.

The horses were also tired, so they were fed with peas. One of the monkeys, who lived in the forest, was keeping a track of the things done by the king’s men from a distance. When he saw peas offered to the horses, he jumped down from the tree at once to get some of them. He quickly gobbled some peas, also filled his mouth and hands with them. Then, he went up the tree and sat down to eat the peas.

As and when, he sat there to eat peas; one pea fell from his hand to the ground. The greedy monkey dropped all the peas he had in his hands and ran down to look for the lost pea at once. Unluckily, he could not find that one pea. He climbed up the ‘tree again and sat at rest. He was looking very sad. He said to himself, “To get one pea, 1 threw away what I had”.

The king was watching the monkey from the camp and said to himself, “I would not be like this stupid monkey, who lost much to gain a little. I will go back to my own country and enjoy what I have”. Thus, the king and his army marched back to their own country.
Now, answer the following questions.
a) Why did the king want to visit other countries?
Answer:
because he was quite fond of travelling.

b) What did the monkey see?
Answer:
The monkey saw peas being offered to the horses.

Choose the correct answer from the choices given.
c) The monkey gobbled the peas in a particular way.
From this, we know that ………..
i) the monkey was kind
ii) the monkey was greedy
iii) the monkey wanted just enough to eat
Answer:
ii) the monkey was greedy

d) Another possible title to the story is ………..
i) The Horses and the Monkey
ii) The Wise Monkey
iii) Penny-wise and Pound-foolish
Answer:
iii) Penny-wise and Pound-foolish

e) Choose the correct statement from the following.
i) The king learnt that it is foolish to lose more to gain little.
ii) The king learnt that it is good to take risk in life.
iii) The king learnt that without pain there cannot be any gain.
Answer:
i) The king learnt that it is foolish to lose more to gain little

Interpretation Of Non-Verbal Information

1. Read the following table showing Endocrine glands, hormones they release and their functions.

Endocrine gland Hormone Functions of Hormone
Pituitary growth hormone Stimulates growth and DNA synthesis
Pancreas insulin glucagon Stimulates glucose uptake in all cells; breaks down glycogen into glucose.
Thyroid thryoxin Stimulates metabolism and heart rate.
Adrenal adrenalin Stimulates heart rate and blood pressure.
Parathyroid parathyroid harmone Stimulates calcium ion release in bones

Now, answer the following questions.
a) What does the table show?
Answer:
The table shows endocrine glands, hormones they secrete and their functions.

b) Which gland stimulates glucose uptake in all cells?
Answer:
Pancreas stimulates glucose uptake in all cells.

Choose the correct answer:
c) Which of the following glands stimulates heart rate and blood pressure?
i) pituitary
ii) parathyroid
iii) adrenal
Answer:
iii) adrenal

d) Which of the following glands releases growth hormone?
i) pancreas
ii) parathyroid
iii) pituitary
Answer:
iii) pituitary

e) Which of the following glands stimulates metabolism and heart rate?
i) pituitary
ii) thyroid
iii) adrenal
Answer:
ii) thyroid

2. Study the following table :

Openers with more than 8000 runs in One Day Internationals (ODIs)
AP 7th Class English Important Questions Unit 4 The Brave Little Bowman 1

Now, answer the following questions.
a) What does the table show?
Answer:
The table shows the openers with more than 8000 runs in One Day Internationals.

b) Who was the highest scorer as an opener in ODIs?
Answer:
Sachin Tendulkar was the highest scorer in ODIs as an opener.

Choose the correct answer:
c) How many centuries were scored by Sachin as an opener?
i) 75
ii) 28
iii) 45
Answer:
iii) 45

d) Who was the second highest scorer as an opener?
i) Adam Gilchrist
ii) Sanath Jayasurya
iii) Sourav Ganguly
Answer:
ii) Sanath Jayasurya

e) The average of which two openers is almost equal?
i) Desmond Haynes and Chris Gayle
ii) Sourav Ganguly and Desmond Haynes
iii) Chris Gayle and Saeed Anwar
Answer:
ii) Sourav Ganguly and Desmond Haynes

Vocabulary

Synonyms

Choose the words with similar meanings (synonyms) from the list given to the words underlined.
AP 7th Class English Important Questions Unit 4 The Brave Little Bowman 2
Answer:
a) a) talented, b) hope
b) a) heavy, b) supporter
c) a) divided, b) equitably
d) a) At once, b) commanded
e) a) applauded, b) courage
f) a) give in, b) war

Antonyms

Write the opposites (antonyms) for the underlined words.
a) He was a skilled (a) archer. His only wish was to join (b) the army.
b) The Big Man : Thank you very much, your Highness ! We will serve (a) you to the best of our abilities (b).
c) Immediately (a) the king ordered (b) the big man to meet him.
d) A few days later (a), as a bolt from the blue for the big man, the kingdom was attacked (b) by an enemy.
e) The Big Man : Today is my last (a) day in this world. I am definitely (b) going to die.
f) I will fight (a) for the king and prove that I am better (b) than the big man, though I don’t have a big and strong body.
Answer:
a) a) unskilled, b) leave
b) a) neglect, b) inabilities
c) a) Eventually, b) obeyed
d) a) earlier, b) defended
e) a) first, b) doubtfully
f) a) yield, b) worse

Right Forms of the Words

Fill in the blanks with the right form of the words given in the brackets.

a) Once there lived a little _____ (a).(wisely / wise) man with a crooked back. He was a skilled _____ (b) (archery / archer).
b) I will do the work _____ (a) (assigned / assignment) to you and we will divide the pay _____ (b) (equally / equal).
c) They joined the army and were _____ (a) (happy / happily). One day the king sent for the big man and told him that there was a tiger in the forest who was _____ (b) (kill/ killing) people.
d) All the people in the _____ (a) (king / kingdom) praised the big man for his _____ (b) (brave / bravery).
e) The king _____ (a) (received / reception) a message either to surrender his kingdom to him or to get _____ (b) (ready / readily) for the battle.
f) As per the saying, ‘better late than never’, the little man _____ (a) (receive / received) the much deserved _____ (b) (honour / honourable).
Answer:
a) a) wise, b) archer
b) a) assigned, b) equally
c) a) happy, b) killing
d) a) kingdom, b) bravery
e) a) received, b)ready
f) a) received, b) honour

Spelling Test

Type – 1 : Vowel Clusters

Complete the following words using “ai, au, ea, ee, ei, eo, eu, ia, ie, io, oi, oo, ou, ua, ue or ui”.
a) He th _ _ ght that the king might not give him the job bec _ _ se of his crooked back.
b) Then the king w _ _ Id take both of them. He went in s _ _ rch of a big man.
c) The Big Man : My gr _ _ tings to you, your Majesty. I want to join y _ _ r army.
d) Immed _ _ tely the king ordered the big man to m _ _ t him.
e) The king rec _ _ ved a message either to surrender his kingdom to him or to get r _ _ dy for the battle.
f) The p _ _ ple called him ‘The Brave Little Bowman’. The king made him the ch _ _ f of the army and gave him rich gifts.
Answer:
a) thought, because
b) would, search
c) greetings, your
d) Immediately, meet
e) received, ready
f) people, chief

AP 7th Class English Important Questions Unit 4 The Brave Little Bowman

Type – 2 : Suffixes

Complete the following words with the suitable suffixes given in the brackets.

a) He was a skilled arch __(er /ery). His only wish was to join the army. He thought that the king might not give him the job because of his crook __(d /ed) back.
b) The little wise man want __(d / ed) to find a strong man and ask him to take him as his assist __(ant / ent).
c) The Big Man : Thank you very much, your High __(nes / ness)! We will serve you to the best of our abilit __(yes / ies).
d) All the people in the king __(dom / dome) praised the big man for his brav __(ary /ery).
Answer:
a) archer, crooked
b) wanted, assistant
c) Highness, abilities
d) kingdom, bravery

Type – 3 : Wronalv Spelt Words

Identify the wrongly spelt word and write its correct spelling in the space provided.

a) messege, report, country, archer
Answer:
message

b) palace, asistant, equally, shoot
Answer:
assistant

c) earn, thousand, battle, apreciate
Answer:
appreciate

d) worry, happy, imediatly, blessing
Answer:
immediately

e) praise, cheif, ashamed, shoulder
Answer:
chief

Classification of Words

Arrange the following words under the correct headings.
AP 7th Class English Important Questions Unit 4 The Brave Little Bowman 3

Choice of the Words

Fill in the blanks choosing the suitable words from those given in the box.
AP 7th Class English Important Questions Unit 4 The Brave Little Bowman 4
Answer:
a) 1) strong, 2) assistant
b) 1) happy, 2) killing
c) 1) informed, 2) creating
d) 1) praised, 2) bravery
e) 1) surrender, 2) ready
f) 1) ashamed, 2) digging

Verb Forms

Read the table given below and fill in the blank with the correct forms of the verbs. Write ‘Regular’ or ‘Irregular’ in the third column.

Present Tense Past Tense Regular or Irregular
1. buy bought Irregular
2. clean cleaned Regular
3. close closed Regular
4. dance danced Regular
5. take took Irregular
6. eat ate Irregular
7. think thought Irregular
8. fly flew Irregular
9. write wrote Irregular
10. do did Irregular

Grammar

I. Edit the following passage correcting the underlined parts.

1. Speech is a great blessing, and (a) it can also be an (b) great – curse, for it helped (c) us to make our intentions and desires knowing (d) to our friends.
Answer:
a) but b) a c) helps d) known

2. Once upon a time there lived a king in central India. He is (a) handsome and (b) very vain. He looked after (c) himself constantly in mirrors, in pools of water even in other people’s eyes when they spoke to him.
“I am the handsomest (d) king on earth,” he said to his courtiers.
Answer:
a) was b) but c) at d) most handsome

3. The green cells of leaves are wonderful little laboratories, there (a) all the starch in the world is produced. Since starch forms a (b) important part of the food of men and animals, their life depend (c) on the work done by the green cells of plants. Thus trees are such great friends to (d) man.
Answer:
a) where b) an c) depends d) of

4. Deforestation in a (a) Himalayas have become (b) major ecological problem. Its results are felt not only in the hill regions and (c) hundreds of miles downstream in the Ganges plain, who (d) feeds and waters about one-third of India’s 840 million people.
Answer:
a) the b) has become c) but d) which

AP 7th Class English Important Questions Unit 4 The Brave Little Bowman

II. Complete the passage choosing the right words from those given below. Each blank is numbered and for each blank four choices are given. Choose the correct answer and write (A), (B), (Q or (D) in the blanks.

1. A.P.J. Abdul Kalam ………….. (1) born in ………….. (2) middle-class Tamil family in the island town ………….. (3) Rameswaram. He was a short boy with rather ordinary looks ………….. (4) his parents were tall and handsome. His father was neither highly educated nor very rich.
1) A) is B) was C) being D) were
2) A) one B) the C) a D) an
3) A) of B) near C) by D) off
4) A) and B) if C) though D) but
Answer:
1) B 2) C 3) A 4) D

2. Ramesh ………….. (1) Mohan went ………….. (2) the cinema on Saturday ………….. (3) was a long queue. It was a cold evening and they ………….. (4) to stand in the queue for nearly an hour.
1) A) or B) and C) but D) so
2) A) to B) for C) by D) into
3) A) Their B) There C) They D) The
4) A) have B) had C) has D) will have
Answer:
1) B 2) A 3) B 4) B

3. Lai Bahadur Shastri ………….. (1) born on 2nd October, 1904 ………….. (2) Mogul Sarai ………….. (3) Varanasi. His father was below two years of age ………….. (4) ordinary teacher and died when he was below two years of age.
1) A) is B) was C) are D) were
2) A) at B) in C) from D) on
3) A) of B) from C) in D) at
4) A) the B) an C) a D) one
Answer:
1) B 2) A 3) C 4) B

4. One day a Brahmin was walking ………….. (1) a forest ………….. (2) suddenly he ………….. (3) someone crying out for help. He ………….. (4) in the direction of the sound and came upon a well that was dried up.
1) A) by B)through C) in D) from
2) A) or B)through C) when D) but
3) A) heard B) hear C) hears D) hearing
4) A) go B) went C) goes D) going
Answer:
1) B 2) C 3) A 4) B

III. Fill in the blanks with the verb in Simple Future Tense.

1) Our exams ______ (postpone) because of the second wave Corona.
2) I ______ (meet) you this evening.
3) I don’t think she ______ (accept) your proposal.
4) I ______ (tell) you about it later.
5) I ______ (write) to you as early as possible.
6) Next week, we ______ (buy) a new car.
7) This shop ______ (close) by 8 p.m. today.
8) She ______ (come) to the party.
9) I think, they ______ (lose) their match against Australia.
10) Tomorrow, my father ______ (take) us to circus.
Answer:

  1. will be posponed
  2. will meet
  3. will accept
  4. will tell
  5. shall write
  6. shall buy
  7. will be closed
  8. will come
  9. will lose
  10. will take

IV. Fill in the blanks with the verb in Simple Future Tense.

1) My father _____ (be) in Guntur tomorrow.
2) I _____ (see) you on Sunday.
3) They _____ (sell) their house.
4) I _____ (do) it for you.
5) I _____ (go) to school tomorrow.
6) _____ you _____ (ring) the bell?
7) I am angry, I _____ (beat) you if you continue to argue with me.
8) They _____ (play) a match in the next month.
9) I _____ (have) my lunch at 2 p.m. this afternoon.
10) I am thirsty, I _____ (drink) a bottle of lemonade.
Answer:

  1. will be
  2. will see
  3. will sell
  4. shall do
  5. will go
  6. will, ring
  7. shall beat
  8. will play
  9. shall have
  10. will drink

V. Write negative sentences for the given positive sentences.

1) I will see you tomorrow.
2) Tonight, we will go to the cinema.
3) I shall display my product at the exhibition which is going to be held in Vijayawada.
4) I shall attend the programme.
5) He will join us in the webex meeting.
6) They will play a match tomorrow.
7) They will get married in August.
8) It will rain soon.
9) Sushma will be in 8th class by this time, next year.
10) She will dance with me.
Answer:

  1. I won’t see you tomorrow.
  2. Tonight, we won’t go to the cinema.
  3. I shan’t display my product at the exhibition which is going to be held in Vijayawada.
  4. I shan’t attend the programme.
  5. He won’t join us in the webex meeting.
  6. They won’t play a match tomorrow.
  7. They won’t get married in August.
  8. It won’t rain soon.
  9. Sushma won’t be in 8th class by this time, next year.
  10. She won’t dance with me.

Creative Writing

1. You have read the lesson “The Brave Little Bowman”. You have come to know about the little man’s crooked back though he was a skilled archer. His wish was to join the army. But, he couldn’t get a job in the army because of his crooked back.
Now, describe the feelings of the little bowman about his crooked back and how he could get a job in the army.
Answer:
The little man was very wise. He was a skilled archer too. But he was unhappy with his crooked back. His strong desire was to join the army. But he knew that he would be refused to join the army because of his crooked back. He thought, “How unlucky fellow I am! Though I am a skilled archer 1 could not fulfil my wish. Oh, God! Why did you give me this crooked back? What can I do now? Shall I go to the king and request him to take me into his army? No, it is not good. He should not give me the job because of my crooked back.

Oh, God! Please show me a way to join the army. If I don’t get a job in the army, my life is futile. What will happen if I assist a strong man? Why can’t I use a strong man to join the army? Yes, it is a good idea! I must find out a strong man and ask him to take me as his assistant. Then we will go to the king and he will give jobs to both of us in the army. Thank God! You have given me a right idea. Now, I am hopeful of fulfilling my wish.”

AP 7th Class English Important Questions Unit 4 The Brave Little Bowman

2. You have learnt that the little bowman was made the chief of the army by the king. The king and all the people came to know about his abilities. The little man’s joy knew no bounds when he was made the chief of the army.
Imagine that you are the little bowman and make a diary entry describing the feelings of the little bowman after he was made the chief of the army.
Answer:

15th November, 20xx
Friday
7:30 p.m.
Dear Diary,Today is a very good day. It is really an unforgettable day in my life. Finally, I have fulfilled my long-lasting wish. Thank God! You only have given me this chance. It’s all because of that big man. What a coward he is! Though big and strong, he is timid. However, his leaving the battlefield is a blessing in disguise for me. Though I don’t have a big body, I have fought for the kingdom and proved that I am better than the big man. The king has made me the chief of the army and given me a number of rich gifts. It is a great honour for me. I am very happy. Oh, God! I am grateful to you. I shall do my level best as the chief of the army. I shall discharge all my duties upto the king’s entire satisfaction I can’t believe my eyes. Today is a memorable day for me.

The Little Bowman

3. Write about an act of bravery that you or your family member or any one of your friends may have shown at some stage in your life.
Answer:
An act of my bravery

My father runs a jewellery shop. The shop is open on all days. But it is closed on Sundays.

One Sunday evening. 1 was returning home after playing cricket with my friends. I was coming on my bicycle. On my way home, when 1 came to my father s shop, I found #my father’s shop was kept open. I was surprised to see it open as it was a Sunday. I got down my bicycle and put it behind a tree and stood there silently to see what was going to happen. A few minutes later, I saw two thieves coming from the shop with a bag of jewellery and keeping it in their car, kept outside the shop. They later, went again into the shop to bring some more.

At once, without any hesitation, I ran towards the car and took out the air from all the tyres. Then I rode on my bicycle to the nearby police station and informed the police about the theft.

The police took me in their jeep and came to the spot. Seeing the police, the thieves began to run. But the police chased them and caught hold of them. All our jewellery was kept back in the shop and then it was locked.

The police congratulated me on my act of bravery. All my friends and neighbours praised me for my bravery. I felt happy as 1 had saved our property.

4. You know that Dr. B.R. Ambedkar was a social reformer and a politician. He was the chairman of the drafting committee of the Indian Constitution. Now write a brief biographical sketch using the facts given below.
Birth : 14 April, 1891
Place of Birth : Mhow in Central Provinces (currently Madhya Pradesh)
Parents : Ramji Maloji Sakpal (father) and Bhimabai Murbadkar Sakpal (mother)
Wife : Ramabai Ambedkar
Education : Elphinstone High School, University of Bombay, Columbia University, London School of Economics
Associations : Samata Sainik Dal, Independent Labour Party. Scheduled Castes Federation
Political Ideology : Right winged; Equalism
Religious Beliefs : A Hindu by birth; a Buddhist 1956 onwards
Books written : Essays on Untouchables and Untouchability, The Annihilation of Caste, Waiting for a Visa
Death : 6, December, 1956
Answer:
Dr. B.R. Ambedkar was a social reformer and a politician. He was the chairman of the drafting committee of the Indian Constitution. He was born on 14 April, 1891 in Mhow in Central Provinces (currently Madhya Pradesh). His parents were Ramji Maloji Sakpal (father) and Bhimabai Murbadkar Sakpal (mother). Ramabai Ambedkar was his wife. He had his schooling from Elphinstone High School. He took his university education from University of Bombay, Columbia University and London School of Economics.

He worked for the organizations of Samaita Sainik Dal, Independent Labour Party and Scheduled Castes Federation. He was right winged. He fought for equal rights for all people. He was a Hindu by birth and turned a Buddhistl956 onwards. He wrote ‘Es¬says on Untouchables’, ‘Untouchability’, ‘The Annihilation of Caste’ and ‘Waiting for a Visa’ describing the problems of the untouchables in society. He passed away on 6th December 1956.

5. Write a story using the following hints.

Hints : Woodcutter – cutting tree – on river bank – axe slips – falls into water – woodcutter sad – river god appears from water – offers golden axe – woodcutter refuses – god offers silver axe – woodcutter refuses- god offers iron-own axe – woodcutter happy – accepts axe – god very pleased- honest woodcutter – gives all three axes.
Answer:
Title : AN HONEST WOODCUTTER
Once upon a time there was a woodcutter. The woodcutter lived in a village with his family. Though he was poor, he was honest. He had to earn money by selling firewood. He used to cut trees on the nearby river bank.

One day he went to the nearby river bank and started cutting a tree. Unfortunately while he was cutting the tree, his iron axe slipped and fell into water. The woodcutter felt sad as he lost his iron axe. Moreover it would be difficult for him to buy a new axe. He prayed to god for help. Immediately the river god came out of the water and appeared before him. The river god asked the woodcutter what his problem was. The woodcutter told the god that his axe slipped and fell into the river water. He requested the god to bring his axe back. The god took pity on him and disappeared. He brought a golden axe instead of the iron axe and offered it to the woodcutter. But the woodcutter refused to take the golden axe offered by the river god as it was not his own axe. Then the river god disappeared again and came out of water with a silver axe. The god offered him to take the silver axe. But the woodcutter refused the silver axe also, as it was not his own axe.

The river god disappeared once again and came out of water with the woodcutter’s own iron axe. He offered it to the woodcutter. The woodcutter was happy on seeing his own iron axe and accepted to take the iron axe. The river god was pleased with the . honesty of the woodcutter. He gave all the three axes to him and disappeared. The woodcutter went home happily.

Moral: Honesty will be rewarded.

AP 7th Class English Important Questions Unit 4 The Brave Little Bowman

6. Write a story using the hints provided :

Hints : Small village – a boy and a mother – poor – collected wood from forest – cut down small trees – one day – a big bird from a tree – don’t cut down this tree – my house – boy agreed – bird pleased – come before sunrise with a bag – next morning – hold on to my tail – flew up – in the sky – to a distant valley – full of gold – filled the bag – flew back – boy and mother rich – happy.
Answer:
The Kindness of a Bird
Once there lived a boy and his mother in a small village. They were very poor and earned their livelihood by collecting wood from forest. The boy used to cut down small trees.

One day he began to cut a big tree. A bird from the tree pleaded not to cut down the tree because it was her house. The boy agreed.

The bird was pleased and asked the boy to come before sunrise with a bag the next morning. He did as the bird said. The.bird asked the boy to hold on to her tail. The boy held her tail tightly and the bird flew up in the sky to a distant valley which was full of gold. The boy filled the bag with gold. Then they flew back. The boy and his mother became rich. They lived happily.

AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys

These AP 7th Class English Important Questions 3rd Lesson A Journey through the Hills and Valleys will help students prepare well for the exams.

AP Board 7th Class English Unit 3 Important Questions and Answers A Journey through the Hills and Valleys

Reading Comprehension (Seen)

1. Read the following passage carefully.

It has been my longing since childhood to visit the Eastern Ghats. I’ve heard about the stunning beauty of the valleys, caves, tunnels, and the journey through ghat roads. The geographical magic of the Eastern Ghats and frequent appearance of Lambasingi in both the print and electronic media has always tempted me.

During the period from November to January, the hills with lushing greenery and blossoms welcome the visitors. The beauty of the valleys attracts even the movie makers.

I set off from Visakhapatnam along with my friends at 6 a.m. to catch the Kirandul Passenger, the only train from Visakhapatnam.to Berra Caves. Had 1 missed this mode of travel, I would have missed the most exciting moments of the train journey. And of course, there is a lot of scope to plan our journey on road hut it’s different. The first task that we had finished was taking breakfast after boarding the train. (A Journey through the Hills and Valleys)

Now, answer the following questions.
1. What was the longing wish of the speaker?
Answer:
To visit the Eastern Ghats

2. What were the things that tempted the author?
Answer:
The geographical magic of the Eastern Ghats and frequent appearance of lambasingi in both the print and electronic media

3. What was the attraction for the movie makers?
Answer:
The beauty of the valleys

4. What was the name of the train they caught?
Answer:
The Kirandul Passenger

5. What did they do after boarding the train?
Answer:
They took their breakfast.

AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys

2. Read the following passage carefully.

When the train was crossing the tunnels, we felt as if it were night because of the darkness for a few minutes even after the dawn. I could still remember the astounding experience in the longest tunnel among the 58 tunnels. Particularly the special coach called Vista dome coach, the air-conditioned tourist compartment with wide windows and LCD TV, .is a special attraction to this train journey After Chimidipalli station, just after a tunnel, a grand waterfall made us spellbound. I could not account all the water falls like this during the journey. The train reached Borra Caves by 9.40 a.m. We got down with our baggage. The train journey from Visakhapatnam to Borra Caves gave us an unforgettable experience which made us speechless. (A Journey through the Hills and Valleys)

Now, answer the following questions.
1. When did they feel as if it were night?
Answer:
When the train was crossing the tunnels

2. How many tunnels were there in their journey?
Answer:
58 tunnels

3. What is a Vista dome coach?
Answer:
It was the air-conditioned tourist compartment with wide windows and LCD TV.

4. Where did they see a grand waterfall?
Answer:
After Chimidipalli station, just after a tunnel

5. How was their journey to Borra Caves?
Answer:
It was an unforgettable experience.

3. Read the following passage carefully.

It was no exaggeration what t came to know about this God’s Architecture. At a height of 705 metres above the. sea level, made of Karstic limestone, manifested with magnificence, the Borra Caves are the largest caves in the country. While entering the caves everyone in our group enjoyed the echo of shouts of visitors. Unknowingly, we also shouted in excitement. You can understand the feelings of the boulders there. The chilled weather in the caves gave us a different experience. These caves are a good source of enjoyment and also experiential learning. Out of the caves, on either side of the road, the tribes sell their handicrafts made with bamboos, spices collected from forests and products of their farming, etc. to make their living. •

We had lunch at Borra Caves at 1 p.m. We had a very sumptuous lunch. Very special dishes of this agency area, which were differently cooked with local spices. (A Journey through the Hills and Valleys)

Now, answer the following questions.
1. What are the caves made of?
Answer:
They are made of Karstic limestone.

2. At what height were the caves located?
Answer:
At a height of 705 metres above the sea level

3. What did they enjoy while entering the caves?
Answer:
The echo of shouts of visitors

4. How was the weather in the caves?
Answer:
Chilly

5. What were the things sold by the tribes?
Answer:
Handicrafts made with bamboos, spices collected from forests and products of their farming, etc.

AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys

4. Read the following passage carefully.

We reached Araku Valley, the Andhra Ooty, and a monumental vacation spot in Andhra Pradesh. Wow! The aroma of coffee all over the surroundings certainly gets the exhausted minds energized. It was the Coffee Museum where one may be tempted to relish the taste of the coffee made with different aromas. Really, it’s the best beverage that I have ever had.

Here, we visited the Tribal Museum, the exhibition of many interesting things like the traditional art, handicrafts, ornaments and dresses used by the tribes, etc. It is an apt place for those who are enthusiastic to learn more about the culture and tradition of the local tribes. I was surprised to know the life style of tribal people. Kodus, a Primitive Tribal Group (PTG) use a different language which is a non-scripted dialect of Oriya. (A Journey through the Hills and Valleys)

Now, answer the following questions.
1. What is called the Andhra Ooty?
Answer:
Araku Valley

2. What is the beverage mentioned in the first paragraph?
Answer:
Coffee

3. What were the museums visited by the author?
Answer:
The Coffee Museum and the Tribal Museum

4. What was the apt place to learn more about the culture and tradition of the local tribes?
Answer:
The Tribal Museum

5. What was the thing that surprised the author?
Answer:
The lifestyle of the tribal people

5. Read the following passage carefully.

Lambasingi, the Kashmir of Andhra Pradesh, a small hamlet in Visakhapatnam district, is known for the snowfall with a record fall of 0°C and sometimes – 3°C temperatures particularly between November and January. It is also called ‘Korra Bayalu’ in their local language. Fenced by towering hills, tall green trees and surrounded by the mist, the area provides a perfect magical setting to enjoy winters. If anyone stays out in the open, one will be frozen.

Feeling the warmth of the sunrise at Lambasingi made an auspicious start of the day that lasts forever. After having breakfast, we visited Kondakarla Bird Sanctuary, one of the best places of visit. I was glad to see the strange visitors, the birds. I wonder how they survive in the intense cold weather. But their joy knew no bounds as they live in their natural habitat. (A Journey through the Hills and Valleys)

Now, answer the following questions.
1. What is Lambasingi called?
Answer:
The Kashmir of Andhra Pradesh or Korra Bayalu

2. What is Lambasingi known for?
Answer:
It is known for the.snowfall with a record fall of 0°C and sometimes – 3°C temperatures particularly between November and January.

3. What is the best seasbn to enjoy the weather of Lambasingi?
Answer:
Winter

4. What happens if anyone stays out in the open at Lambasingi?
Answer:
One will be frozen.

5. What was the nearby attraction to Lambasigi?
Answer:
Kondakarla Bird Sanctuary

AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys

6. Read the following passage carefully.

Gandikota, the magnificient piece of nature’s architecture, has come to be known as the Hidden Grand Canyon of India. The travelers who visit will be stunned by its beauty. It is located in Kadapa District of Andhra Pradesh. It resembles the Grand Canyon, Arizona, US. There are many astounding areas that are alluring to the visitors in and around Gandikota. ‘Gandi’ means ‘Canyon’ and ‘Kota’ means ‘Fort’. The village nearby this area is known to be Gandikota. ‘ ‘

The spectacular gorge formed by the Penna River that cuts through Erramala hills offers a beautiful view. A gorge is a narrow valley between hills or mountains, with steep rocky walls and a stream running through it. In fact, gorges are formed because of erosion of rock over a long period of time. (Gandikota – The Grand Canyon of India)

Now, answer the following questions.
1. What is Gandikota to be known as?
Answer:
The Hidden Grand Canyon of India

2. What makes the travelers stunned?
Answer:
The beauty of Gandikota

3. Where is Gandikota located?
Answer:
In Kadapa District

4. What is a gorge?
Answer:
A gorge is a narrow valley between hills or mountains, with steep rocky walls and a stream running through it.

5. How are gorges formed?
Answer:
Because of erosion of rock over a long period of time

7. Read the following passage carefully.

The Fort made of red stone has excellent palaces adorned with fine carvings. It is very exciting to walk along the fort’s wall and .spend a few moments by the serene river. A trip to this place is worth it, considering the fact that you can peep into history through the walls of Gandikota Fort, which narrates the tale of various civilizations that existed thousands of years ago.

The best time to visit this place is between September and February, as the weather ‘ during this time is comparatively pleasant. Summers are too hot and there will be significantly low water levels, the canyon seems less appealing. (Gandikota – The Grand Canyon of India)

Now, answer the following questions.
1. How is the fort made?
Answer:
It is made of excellent palaces adorned with fine carvings.

2. What is an exciting thing to do at the fort?
Answer:
Walking along the fort’s wall.

3. Which narrates the tale of various civilizations?
Answer:
The walls of Gandikota Fort

4. What is the best time to visit the fort?
Answer:
Between September and February

5. When does the fort Seem less appealing?
Answer:
In summer

Reading Comprehension (Unseen)

1. Read the following passage carefully.

Have you ever seen a UFO? A UFO is an Unidentified Flying Object, a strange object or light that people see in the sky. Many people believe that these strange lights are really spaceships from another planet.

For years people have seen and heard many odd things in the sky, blinking and glowing lights, flying objects shaped like saucers, and moving objects making strange noises. Some people have even taken pictures of these unusual sights.

Some of these UFOs are really aeroplanes, weather balloons or meteors. But many UFO reports are still a mystery.

Now, answer the following questions.
a) What do people believe about these strange lights?
Answer:
People believe that these strange lights are really spaceships from other planets.

b) What are these UFOs really?
Answer:
These UFOs are really aeroplanes, weather balloons or meteors.

Choose the correct answer from the choices given.
c) U.F.O stands for:
i) Unknown Flying Object
ii) Unidentified Flying Object
iii) Unseen Flying Object
Answer:
ii) Unidentified Flying Object

d) U.F.Os are believed to be spaceships from other
i) countries
ii) continents
iii) planets
Answer:
iii) planets

e) Which of the following statements is true?
i) UFOs are make-believe.
ii) Moving objects with blinking lights have to be UFOs
iii) People have seen moving objects making strange noises.
Answer:
i) UFOs are make-believe.

AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys

2. Read the following passage carefully.

Do you know about one of the most famous monsters in the world? The Loch Ness Monster is a large animal that some people believe lives in Loch Ness, a deep dark lake in Scotland. For many years, hundreds of people have reported seeing something strange in the lake. They have even given it the nick name “Nessie’.

Nessie is said to be about 30 feet long, with a long slender neck, one or two humps and flippers.

There are even pictures that have been taken of a large animal-like shape in the water. Scientists are still trying to solve the mystery of Nessie.

Now, answer the following questions.
a) Where do the Loch Ness Monsters live?
Answer:
Loch Ness Monsters are said to be lived in the Loch Ness lake in Scotland.

b) How is Nessie?
Answer:
Nessie is said to be about 30 feet long with a long slender neck, one or two humps and flippers.

Choose the correct answer from the choices given,
c) Actually the Loch Ness is the name of a
i) country.
i) city.
iii) lake.
Answer:
iii) lake.

d) Which of the following is a fact about Nessie?
i) Nessie has a long slender neck.
ii) Nessie has flippers.
iii) Nessie is a mystery.
Answer:
iii) Nessie is a mystery.

e) What was the Nickname given to Loch Ness Monster?
i) Nest
ii) Nestle
iii) Nessie
Answer:
iii) Nessie

Interpretation Of Non-Verbal Information

1. Read the following tree diagram carefully.
AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 1

Now answer the following questions.
a) What does the above diagram show?
Answer:
The above diagram shows a tree diagram of musical instruments.

b) What are the three main categories of musical instruments?
Answer:
Three catagories : (1) Wind instruments, (2) Percussion instruments, (3) Stringed instruments.

Choose the correct answer from the choices given below.
c) Which of the following is a stringed instrument?
i) Harp
ii) Horn
iii) Tabla
Answer:
i) Harp

d) What type of musical instrument is Xylophone?
i) Percussion instrument
ii) Wind instrument
iii) Stringed instrument
Answer:
i) Percussion instrument

e) Which of the following statements is TRUE based on the information given?
i) All string instruments are a type of percussion instruments.
ii) Wood block is a wind instrument.
iii) Guitar and Violin are stringed instruments.
Answer:
iii) Guitar and Violin are stringed instruments.

AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys

2. Study the family tree of Bala Krishna.
AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 2

Now answer the following questions.
a) Who are the grandparents of Praveen?
Answer:
Balakrishna and Ragini

b) How many granddaughters does Bala Krishna have?
Answer:
Five granddaughters

Choose the correct answer from the choices given below.
c) Medha is the daughter of ……………..
i) Rohit
ii) Veena
iii) Bhavya
Answer:
ii) Veena

d) Praveen and Raasi are ……………
i) brothers
ii) cousins
iii) friends
Answer:
ii) cousins

e) Which of the following statements is TRUE based on the information given?
i) Rohit has two daughters.
ii) Ananya and Raasi are cousins.
iii)Rohit’s wife is Bhavya.
Answer:
i) Rohit has two daughters.

Vocabulary

Synonyms

Choose the words with similar meanings (synonyms) from the list given to the words underlined.
AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 3
AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 4
Answer:
a) a) fascination, b) induced
b) a) thrilling, b) abundant
c) a) surprising, b) broad
d) a) alighted, b) memorable
e) a) surroundings, b) peaceful
e) a) advantage, b) panoramic

Antonyms

Write the opposites (antonyms) for the underlined words.
a) I could still remember (a) the astounding (b) experience in the longest tunnel among the 58 tunnels.
b) We got down (a) with our baggage. The train journey from Visakhapatnam to Borra Caves gave us an unforgettable (b) experience which made us speechless.
c) Log huts, tents set in tribal environment for the tourists’ night stay are more enjoyable (a) as they offer pleasant (b) and serene atmosphere that is not found in concrete jungles.
d) Here, we visited the Tribal Museum, the exhibition of many interesting (a) things like the traditional (b) art, handicrafts, ornaments and dresses used by the tribes, etc.
e) I feel proud (a) to visit this garden for its great history. This popular (b) botanical garden, built in 1942 in 26 acres, was the source of cultivating vegetables for the soldiers who fought in the World War II.
f) Lambasingi, the Kashmir of Andhra Pradesh, a small (a) hamlet in Visakhapatnam district, is known (b) for the snowfall with a record fall of 0°C and sometimes -3°C temperatures particularly between November and January.
Answer:
a) a) forget, b) unimpressive
b) a) board / got in, b) forgettable
c) a) unenjoyable, b) nasty
d) a) uninteresting, b) unconventional
e) a) sorry, b) unpopular
f) a) big, b) unfamiliar

Right Forms of the Words

Fill in the blanks with the right form of the words given in the brackets.

a) The _____ (a) (beauty / beautiful) of the valleys _____ (b) (attacts / attraction) even the movie makers.
b) It was no _____ (a) (exaggerate / exaggeration) what I came to know about this God’s _____ (b) (Architecture / Architect).
c) These caves are a good source of _____ (a) (enjoyment / enjoyed) and also _____ (b) (experientially / experiential) learning.
d) Here, we visited the Tribal Museum, the _____ (a) (exhibited / exhibition) of many interesting things like the _____ (b) (tradition / traditional) art, handicrafts, ornaments and dresses used by the tribes, etc.
e) This _____ (a) (popular1 / popularity) botanical garden, built in 1942 in 26 acres, was the source of _____ (b) (cultivate / cultivating) vegetables for the soldiers who fought in the the World War II.
f) Feeling the _____ (a) (warmly / warmth) of the sunrise of Lambasingi made an _____ (b) (auspicious / auspiciously) start of the day that lasts forever.
Answer:
a) a) beauty, b) attracts
b) a) exaggeration, b) Architecture
c) a) enjoyment, b) experiential
d) a) exhibition, b) traditional
e) a) popular, b) cultivating
f) a) warmth, b) auspicious

Spelling Test

Type – 1 : Vowel Clusters

Complete the following words using “ai, au, ea, ee, ei, eo, ia, ie, io, oa, oi, oo, ou, ua, ui or uo”.

a) aftern _ _ n b) sh _ _ ting c) pi _ _ sant
d) f _ _ nd e) of c _ _ rse f) coff _ _
g) plantat _ _ ns h) betw _ _ n i) vacat _ _ n
j) surr _ _ ndings k) cert _ _ nly l) exh _ _ sted
m) mus _ _ m n) r _ _ lly o) exhibit _ _ n
p) tradit _ _ nal q) enthus _ _ tic r) p _ _ pie
s) lang _ _ ge t) d _ _ lect u) b _ _ n
v) s _ _ m w) picturesq _ _ x) h _ _ rt
y) self _ _ s z) ind _ _ d

Answer:

a) afternoon b) shouting c) pleasant
d) found e) of course f) coffee
g) plantations h) between i) vacation
j) surroundings k) certainly 1) exhausted
m) museum n) really o) exhibition
p) traditional q) enthusiastic r) people
s) language t) dialect u) boon
v) seem w) picturesque x) heart
y) selfies z) indeed

Exercise – 2

a) f _ _ St b) mov _ _ s c) f _ _ l
d) pr _ _ d e) gr _ _ t f) b _ _ lt
g) s _ _ rce h) sold _ _ r i) f _ _ ght
j) tr _ _ ning k) tr _ _ l) h _ _ se
m) f _ _ t n) ceremon _ _ l o) b _ _ t
p) gr _ _ n q) auspici _ _ s r) sanct _ _ ry
s) b _ _ nd t) p _ _ ce u) pi _ _ sure
v) adventur _ _ s w) destinat _ _ n x) b _ _ r
y) rem _ _ ning z) l _ _ k

Answer:

a) feast b) movies c) feel
d) proud e) great f) built
g) source h) soldier i) fought
j) training k) tree 1) house
m) feet n) ceremonial o) beat
p) green q) auspicious r) sanctuary
s) bound t) peace u) pleasure
v) adventurous w) destination x) bear
y) remaining z) look

Type – 2 : Suffixes

Complete the following words with the suitable suffixes given in the brackets.

a) During the period from November to January, the hills with lushing green ___ (ery / ary) and blossoms welcome the visit ___ (ers / ors).
b) The train journey from Visakhapatnam to Borra Caves gave us an unforgett ___ (eble/ able) experience which made us speech ___ (loss / less).
c) These caves are a good source of enjoy ___ (ment / mant) and also experien ___ (tial / cial) learning.
d) Log huts, tents set in tribal environ ___ (ment / mant) for the tourists’ night stay are more enjoy ___ (eble /able) as they offer pleasant and serene atmosphere that is not found in concrete jungles.
e) It is indeed, a wonder ___ (ful / full) feast for the eyes. Here, the rail ___ (way / weigh) track and the roadway seem to go parallel.
f) At night, there was an unforget ___ (teble / table) camp fire in which we all enjoyed Dhimsa, the local ceremon ___ (yal / ial) dance of the agency, performed by 12 to 16 women while men beating the drums.
Answer:
a) greenery, visitors
b) unforgettable, speechless
d) environment, enjoyable
f) unforgettable, ceremonial
c) enjoyment, experiential
e) wonderful, railway

Type – 3 : Wronalv Spelt Words

Identify the wrongly spelt word and write its correct spelling in the space provided.

a) exageration, valley, popular, entire
Answer:
exaggeration

b) pleasure, cultivating, magnifisense, frequent
Answer:
magnificence

c) aspicious, aspect, enjoyable, stunning
Answer:
auspicious

d) experience, parallel, sumptus, intense
Answer:
sumptuous

e) atraction, concrete, glance, amazing
Answer:
attraction

f) convert, unforgetable, trekking, compensating
Answer:
unforgettable

Classification of Words

Arrange the following words under the correct headings.
AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 5

Choice of the Words

Fill in the blanks choosing the suitable words from those given in the box.
AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 6 AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 7
Answer:
a) 1) sumptuous, 2) cooked
b) 1) environment, 2) atmosphere
c) 1) monumental, 2) exhausted
d) 1) apt, 2) enthusiastic
e) 1) tribal, 2) dialect
f) 1) boon, 2) scenic
g) 1) parallel, 2) phenomenon
h) 1) aspect, 2) contrasting
i) 1) Compensating, 2) ceremonial
j) 1) surrounded, 2) frozen

Prefixes / Suffixes

Add appropriate prefixes / suffixes to the following roots to make new words.
AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 8

Grammar

I. Edit the following passage correcting the underlined parts.

1. Dolphins are very interesting animals. They, looks (a) like fish but they are not fish. Fish has (b) cold blood but dolphins have warm blood. Fish can live under water and (c) dolphins cannot. They can stay in (d) water for a long time.
Answer:
a) look b) have c) but d) under

2. An (a) Olympic Games are the great (b) celebrations of sport in the world. They are held once in four years. The Olympic Games began at (c) Olympia in 776 B.C. They took place from time to time till (d) 393 A.D.
Answer:
a) The b) greatest c) in d) until

3. Dhyanchand is (a) a very well-known hockey player. He was born at (b) 29 August 1905 in Allahabad. He studied in the (c) local secondary high school. In 1922, he joined a (d) British army as a sepoy.
Answer:
a) was b) on c) a d) the

4. Vikram Sarabhai was responsible to (a) the setting up of the Rocket Launching station or (b) Space Science and Technology Centre in (c) Thumba in Kerala. A (d) Rocket and Launching Ranger at Srihaj-i Kota in Andhra Pradesh was set up by Dr. Sarabhai only.
Answer:
a) for b) and c) at d) The

AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys

II. Complete the passage choosing the right words from those given below. Each blank is numbered and for each blank four choices are given. Choose the correct answer and write (A), (B), (Q or (D) in the blanks.

1. Have you ever ____ (1) people putting ____ (2) thumb impression on important documents? This is done mainly ____ (3) illiterate people ____ (4) they cannot put their signatures.
1) A) see B) sees C) seen D) seeing
2) A) its B) his C) their D) her
3) A) with . B) from C) by D) of
4) A) so B) because C) as D) since
Answer:
1) C 2) C 3) C 4) B

2. The finger prints ____ (1) the police to ____ (2) the thieves and criminals. ____ (3) ____ keep a record of the finger prints of thieves and criminals ____ (4)
to them.
1) A) helps B) help C) helped D) helping
2) A) identify B) identifying C) identified D) identifies
3) A) He B) She C) They D) It
4) A) knows B) know C) known D) knowing
Answer:
1) B 2) A 3) C 4)C

3. A cell phone is ____ (1) extremely sophisticated radio. ____ (2) cell phones ____ (3) can talk to anyone ____ (4) the planet from just about anywhere.
1)A) a B) an C) the D) any
2) A) By B) With C) From D) On
3) A) she B) he C)they D) you
4) A) on B) in C) over D) above
Answer:
1)B 2) B 3) D 4) A

4. Abdul is ____ (1) friend. One evening he ____ (2) home from school. He‘saw a boy ____ (3) in a tank. Suddenly he jumped ____ (4) the tank and saved the boy.
1) A) I B) my G) me D) mine
2) A) is returning B) returns C) was returning D) returned
3) A) drowns B) drowning C) drowned D) drown
4) A) in B) on C)into . D) over
Answer:
1) B 2) C 3) B D) C

III. Fill in the blanks with suitable prepositions given in the box.
AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 9
1) There is a box ______ the table.
2) I will meet you ______ the evening.
3) He reached the place ______ 8.30 a.m.
4) Rahul went ______ a movie his friends.
5) The cat jumped ______ the well.
6) She hurried ______ the entrance to receive the guest.
7) His house is ______ the sea.
8) A number of colourful butterflies are flying ______ us.
9) We are living ______ the same roof.
10) They are going to travel the ______ world.
Answer:

  1. on
  2. in
  3. at
  4. to with
  5. into
  6. towards
  7. by
  8. above
  9. under
  10. around

IV. Fill in the blanks with suitable prepositions given in the box.
AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys 10
1) She is walking ______ the road slowly.
2) The Palk strait is located ______ India and Sri Lanka..
3) The Thames river flows ______ London.
4) She will conje to India ______ November.
5) Mr. Alexander has taught in this school ______ one year.
6) He put a paper weight ______ the papers.
7) She always holds an umbrella ______ her head.
8) There is a temple ______ our school.
9) It is easier to walk ______ the hill than go up.
10) I saw your friend ______ the park.
Answer:

  1. along
  2. between
  3. through
  4. in
  5. for
  6. on
  7. over
  8. beside
  9. down
  10. at

V. Write the other degrees of the following adjectives.

Positive Degree Comparative Degree Superlative Degree
small smaller smallest
safe safer safest
clever cleverer cleverest
bright brighter brightest
hot hotter hottest
beautiful more beautiful most beautiful
precious more precious most precious
hard-working more hard-working most hard-morking
much more most
good better best
bad worse worst
far farther / further farthest / furthest

VI. Read the following sentences. Label them with ‘P’ for Positive, ‘C’ for Comparative and ‘S’ for ‘Superlative’.

1. Rahul Dravid is one of the greatest batsmen in the world.
2. Alexander was the greatest soldier in the world.
3. India is one of the fastest developing countries in the world.
4. No other river in the world is as long as the Nile.
5. Hindi is one of the most popular languages in India.
6. Lara is not as great as Tendulkar.
7. Rekha is one of the most beautiful girls in the class.
8. Very few metals are as expensive as platinum.
9. Shimla is colder than all hill stations in the Himachal Pradesh.
10. Delhi is one of the most crowded cities of India. ‘
Answer:

  1. Superlative Degree
  2. Superlative Degree
  3. Superlative Degree
  4. Positive Degree
  5. Superlative Degree
  6. Positive Degree
  7. Superlative Degree
  8. Positive Degree
  9. Comparative Degree
  10. Superlative Degree

Creative Writing

1. Describe a journey with your family.
Answer:
Recently we planned a tour to Araku Valley. Dad said it’s a very pleasant and cool hill station that can be visited in summer. Charan and I were so excited and told our friends about our trip to Araku. Mom also said its a worthy sight seeing place.

We started early in the morning of Monday by a train to Vishakhapatnam. I enjoyed the climate and scenic beauty sitting by the window. Mom made some snacks and lunch for us to enjoy during the journey. We reached Vishakhapatnam in the after¬noon. We took rest in a hotel and went to see R.K. Beach in the evening. First time, to go near the heavy waters scared me a lot. But my father held our hands and gave the courage to go near the waters. We enjoyed a lot with the on and off movements of tides.

We took rest for the night and started for Araku early in the morning by train. The journey was pleasant and exciting as we passed through forests and tunnels. Children in the train shouted with joy. We reached Araku, hired a room and got fresh. We hired a taxi to see some old temples. Borra caves, tea and coffee plantations and beautiful gardens. We enjoyed the trip. The garden was beautiful with flower beds, bushes and decorated trees.

The trip was a memorable experience in my life.

2. One of your Mends wishes to visit the place you have visited recently. Write a letter to your Mend giving suggestions to help him make his/her Mp successful.
Answer:

5 – 23 – 13/B,
6/18 Brodipet,
GUNTUR.
6th June, 20xx.

My dear Sriram,

I am fine and pink in health. I hope the same with you there.

I would like to describe the place, Hyderabad which I have visited recently. Hyderabad is thexapital of Telangana. It is a big cosmopolitan city. People of different languages, cultures and traditions live harmoniously together. There are many places worth-seeing in Hyderabad. Some of them are -1) the Charminar 2) the Salarjung Museum 3) the Legislative Assembly 4) the Birla Mandir 5) Nehru Zoological Park 6) Planetarium 7) The Tank Bund 8) Rajiv International Airport 9) Ramoji Film City 10) Hussain Sagar and the Buddha Statue.

It is a lovely city. The clim’ate is fine. The Hussain Sagar joins the twin cities namely Hyderabad and Secunderabad. You should visit it soon.

Please convey my regards to your parents.

Yours lovingly,
Hanuman

Address on the envelope :
M. Sriram,
S/o Mr. M. Suryaprakash,
1-2-34 A,
Temple Street,
Kandukur.
Prakasam. (dt)

AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys

3. You have read that the author and his friends planned a tour to Araku Valley in the lesson, “A Journey through the Hills and Valleys”. He travelled by the Kirandul Passenger up to Borra Caves. The author and his friends enjoyed themselves the train journey. Their travel in Vista dome coach of Kirandul Passenger gave them memorable experience.

Now, describe the feelings of the author while he was travelling by the Kirandul Passenger along with his Mends.
Answer:
The author felt very happy when they planned to visit Araku Valley. He started from Visakhapatnam along with his friends and travelled by the Kirandul Passenger, the only train from Visakhapatnam to Borra Caves. As soon as he boarded the train, he started thinking. He thought, “What a wonderful occasion it is ! The travel in Vista dome coach with wide windows and LCD TV is really a special attraction to this train journey. The scenery of the hills with lushing greenery and blossoms is magnificent to watch. Oh, now, I think we are crossing the longest tunnel on our way. It gives me an astounding experience. Oh, here comes a grand waterfall which makes all the travellers spellbound. I can’t account all the waterfalls like this during the journey. The sheer beauty of the lushing greenery, various coloured blossoms, tunnels, waterfalls, valleys, ghat roads, etc. has taken my breath away. This train journey from Visakhapatnam to Borra Caves has given us an unforgettable experience and has made us speechless !”

4. Do you have any memorable day in your life ? Narrate about it in a paragraph.
Answer:
A DAY THAT I CAN’T FORGET
There are many unforgettable days in my life. Of these is the day when the result of my class VI examination was declared. I had done all my papers well. I expected a good result. But I had stood first in the entire district. I felt very very happy. My parents and other family members were very happy. All my friends and teachers came to congratualte me on this great success. Sweets were distributed in the colony. My father decided to send me to a very good school for further education. I can’t forget that day.

5. Recently you have spent a week in hills at your grandparents’ house.’You enjoyed your stay. Write a paragraph about 100 words describing the joy of living in the lap of nature.
Answer:
How I spent a week in hills
Last month I spent a week in hills in my grandparents’ house. My grandparents live in Rishikesh at the foothills of the great Himalayas. This year it was very hot in the plains. So I went to them. First, the weather was pleasant though days were hot. Sitting on the banks of holy Ganges in the background of lush green forest and hills gave us peace. We went to Chamoli for two days. There we enjoyed our stay. The nature looked fresh and pure. The distant hills and snow-covered tops added glory to natural beauty. We ate seasonal fruits and tasted local food to our fill. There was no tension or pressure of any kind. It was a blessing to be in the lap of nature.

6. Write a Biographical sketch of Mr. Ramnath Kovind, the President of India, using the information given below :
Birth : 1st October, 1945
Paraunk near Kanpur, Uttar Pradesh.
Parents : Sri Maiku Lal
Smt. Kalavathi
Education : School education in Kanpur – B. Com, LL.B, Kanpur University.
Spouse : Smt. Savitha
Positions held : * Advocate for Government of India at the Delhi High Court from 1977 to 1981.
* Junior Council for Government of India in Supreme Court from 1982 to 1984.
* Governor of Bihar from 2015 to 2017.
Parliamentary life : Member of Rajya Sabha from Uttar Pradesh from 1994 to 2000.
Assumed the office as President : 25th July, 2017
Answer:
Ramnath Kovind was born on 1st October, 1945 in Paraunk, near Kanpur, Uttar Pradesh. His parents were Sri Maikulal and Smt. Kalavathi. He completed his school education in Kanpur and obtained the degrees of B.Com and L.L.B from Kanpur University. He married Savitha. He was an advocate of Indian Government in the Delhi High Court from 1977 to 1981 and Indian Government Junior Council in the Supreme Court from 1982 to 1984. Before assuming charge of the office of the 14th President of India on July 25,2017, Kovind served as the 36th Governor of the state of Bihar from 2015 to 2017. He was elected as a member of Rajya Sabha from Uttar Pradesh from 1994 to 2000.

7. Write a story using the following hints.

Hints: Four bulls in a field – very good friends – lion feared to near them – thought of a plan – said bad words against friends – then bulls grazed separately – lion killed one after the other – united – strength.
Answer:
FOUR FOOLISH BULLS
Once there lived four bulls by the side of a forest. They were strong and sturdy. They were united. They grazed together. A lion, which lived in the forest, very much wished to make a feast of the bulls. The lion, did not dare to go near the bulls. He thought of a plan. He met each bull in turn and said bad words against the other bulls. The foolish bulls believed his words. They started grazing separately. The lion took advantage of the disunity of the bulls. He killed one after the other and ate all the four bulls.

Moral: Unity is strength, (or) United we stand, divided we fall.

AP 7th Class English Important Questions Unit 3 A Journey through the Hills and Valleys

8. Write a story using the following hints:
Hints : A king very fond of stories – man who tells a story that never ends to marry his daughter – a handsome young man begins his story – a little ant – nothing to eat – sees a big building – decides to take some rice from it – crawls inside – carries a grain of rice on back – crawls home – the young man goes on about little ant – king understands – marries off his daughter to him.
Answer:
THE CLEVER MAN’S ENDLESS STORY
Once there lived a king. He was very much fond of stories. He declared that he would give his daughter in marriage to the man who would tell him an endless story.

One day a clever and handsome young man came to the king.. He started telling an endless story. The story ran like this. “Once there was a little ant. It was hungry. It had nothing to eat. It saw a big building. It crawled inside it. There was a heap of rice. It carried a grain of rice on its back to its hole. It came back. Again it carried another grain of rice”.

The young man repeated the same story of the ant several times. The story seemed endless. The king got vexed. He understood the cleverness of the young man. He mar-ried off his daughter to him.

Moral: Your wisdom comes to your help, (or) Knowledge is power.

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3

SCERT AP 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3 Textbook Exercise Questions and Answers.

AP State Syllabus 9th Class Maths Solutions 1st Lesson వాస్తవ సంఖ్యలు Exercise 1.3

ప్రశ్న1.
2.874 ను సంఖ్యారేఖపై క్రమానుగత వర్ధన పద్ధతిలో చూపించండి.
సాధన.
సోపానం – 1:
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3 1

సోపానం – 2:
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3 2

సోపానం – 3:
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3 3

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3

ప్రశ్న2.
\(5 . \overline{28}\) ను సంఖ్యారేఖపై క్రమానుగత వర్ధన పద్ధతిలో 2 స్థానాల వరకు చూపించండి.
సాధన.
సోపానం – 1:
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3 4

సోపానం – 2:
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3 5

సోపానం – 3:
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3 6

సోపానం – 4:
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.3 7

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.2

SCERT AP 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.2 Textbook Exercise Questions and Answers.

AP State Syllabus 9th Class Maths Solutions 1st Lesson వాస్తవ సంఖ్యలు Exercise 1.2

ప్రశ్న1.
కింది సంఖ్యలను కరణీయ మరియు అకరణీయ సంఖ్యలుగా వర్గీకరించండి.
i) \(\sqrt{27}\)
ii) \(\sqrt{441}\)
iii) 30.232342345…
iv) 7.484848…
v) 11.2132435465…
vi) 0.3030030003…
సాధన.
i) కరణీయ సంఖ్య
ii) అకరణీయ సంఖ్య
iii) కరణీయ సంఖ్య
iv) అకరణీయ సంఖ్య
v) కరణీయ సంఖ్య
vi) కరణీయ సంఖ్య

ప్రశ్న2.
అకరణీయ సంఖ్యలకు, కరణీయ సంఖ్యలకు మధ్యగల నాలుగు భేదాలను ఉదాహరణలతో తెలుపండి.
సాధన.
i) కరణీయ సంఖ్యను \(\frac{\mathrm{p}}{\mathrm{q}}\) రూపంలో వ్యక్తపరచలేము.
ఇక్కడ p మరియు q లు పూర్ణసంఖ్యలు మరియు q ≠ 0.
ఉదా : \(\sqrt{2}, \sqrt{3}, \sqrt{5}, \sqrt{7}\) మొ॥నవి.

ii) అకరణీయ సంఖ్యను \(\frac{\mathrm{p}}{\mathrm{q}}\) రూపంలో వ్యక్తపరచవచ్చును.
ఉదా : – 3 = \(\frac {-3}{1}\) మరియు \(\frac {5}{4}\) మొ॥నవి.

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.2

ప్రశ్న3.
\(\frac {5}{7}\) మరియు \(\frac {7}{9}\) ల మధ్యగల ఒక కరణీయ సంఖ్య కనుగొనండి.
సాధన.
\(\frac {5}{7}\) మరియు \(\frac {7}{9}\) ల యొక్క దశాంశ రూపములు
\(\frac {5}{7}\) = \(0 . \overline{714285}\) …., \(\frac {7}{9}\) = 0.7777 ….. = \(0 . \overline{7}\)
∴ \(\frac {5}{7}\) మరియు \(\frac {7}{9}\) ల మధ్యన గల కరణీయ సంఖ్య 0.727543 ……

ప్రశ్న4.
0.7 మరియు 0.77 ల మధ్య గల రెండు కరణీయ సంఖ్యలు కనుగొనండి.
సాధన.
0.7 మరియు 0.77 ల మధ్యగల రెండు కరణీయ సంఖ్యల రూపము
0.70101100111000111……. మరియు 0.70200200022…

ప్రశ్న5.
\(\sqrt{5}\) విలువను 3 దశాంశ స్థానాల వరకు కనుగొనండి.
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.2 1
∴ \(\sqrt{5}\) = 2.236
[\(\sqrt{5}\) విలువ కచ్చితముగా 2.23606 కు సమానం కాదు]

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.2

ప్రశ్న6.
భాగహార పద్ధతిలో \(\sqrt{7}\) విలువను ఆరు దశాంశ స్థానాల వరకు కనుగొనండి.
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.2 2

ప్రశ్న7.
\(\sqrt{10}\) ను సంఖ్యారేఖపై సూచించండి.
సాధన.
సోపానం-1 : సంఖ్యారేఖను గీయుము.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.2 3
సోపానం-2 : OABC దీర్ఘచతురస్రమును పొడవు 3 యూనిట్లు మరియు వెడల్పు 1 యూనిట్ ఉండేలా గీయుము.
సోపానం-3 : OB కర్ణమును గీయుము.
సోపానం-4 : ‘O’ కేంద్రంగా OB వ్యాసార్ధముతో ఒక చాపమును గీయగా అది సంఖ్యారేఖను D వద్ద ఖండించును.
సోపానం-5 : సంఖ్యారేఖ పై గల ‘D’ విలువ \(\sqrt{10}\) ను సూచిస్తుంది.

ప్రశ్న8.
2, 3 ల మధ్య గల రెండు కరణీయ సంఖ్యలు కనుగొనండి.
సాధన.
ab ఒక సంపూర్ణవర్గం కాకుండునట్లు a, b లు ఏవైనా రెండు ధన అకరణీయ సంఖ్యలయితే \(\sqrt{a b}\) అనునది
a, b ల మధ్య ఉండే కరణీయ సంఖ్య అవుతుంది.
∴ 2 మరియు 3ల మధ్యన గల కరణీయ సంఖ్య \(\sqrt{6}\)
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.2 4

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.2

ప్రశ్న9.
కింది వాక్యాలు సత్యమా ? అసత్యమా ? ఒక ఉదాహరణతో సమర్థించండి.
i) ప్రతి కరణీయ సంఖ్య ఒక వాస్తవ సంఖ్య అవుతుంది.
సాధన.
సత్యము (∵ వాస్తవ సంఖ్యల సమితి కరణీయ మరియు అకరణీయ సంఖ్యలు రెండింటినీ కలిగి ఉంటుంది.)

ii) ప్రతి అకరణీయ సంఖ్య ఒక వాస్తవ సంఖ్య అగును.
సాధన.
సత్యము (∵ వాస్తవ సంఖ్యల సమితి కరణీయ మరియు అకరణీయ సంఖ్యలు రెండింటినీ కలిగి ఉంటుంది.)

iii) ప్రతి వాస్తవ సంఖ్య అకరణీయ సంఖ్య కొనవసరం లేదు.
సాధన.
అసత్యము
(∵ అకరణీయ సంఖ్యలన్నియూ వాస్తవ సంఖ్యలే.)

iv) n ఒక సంపూర్ణవర్గం అయితే \(\sqrt{n}\) ఒక కరణీయ సంఖ్య కాదు.
సాధన.
సత్యము (∵ కరణీయ సంఖ్య నిర్వచనం ప్రకారం)

v) n ఒక సంపూర్ణవర్గం అయితే \(\sqrt{n}\) ఒక కరణీయ సంఖ్య.
సాధన.
అసత్యము (∵ అకరణీయ సంఖ్య నిర్వచనం ప్రకారం)

vi) ప్రతి వాస్తవ సంఖ్య ఒక కరణీయ సంఖ్యయే.
సాధన.
అసత్యము (∵ వాస్తవ సంఖ్యలు కరణీయ సంఖ్యలతో పాటు అకరణీయ సంఖ్యలను కూడా కలిగి ఉంటాయి.)

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1

SCERT AP 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 Textbook Exercise Questions and Answers.

AP State Syllabus 9th Class Maths Solutions 1st Lesson వాస్తవ సంఖ్యలు Exercise 1.1

ప్రశ్న1.
a) ఏవైనా మూడు అకరణీయ సంఖ్యలు రాయండి.
సాధన.
\(\frac{3}{4}, \frac{5}{9}, \frac{2}{7}\)

b) అకరణీయ సంఖ్యను మీ సొంత మాటలలో వివరించండి.
సాధన.
\(\frac{\mathrm{p}}{\mathrm{q}}\) రూపంలో వ్యక్తపరచగలిగిన ఏ సంఖ్యనైనా అకరణీయ సంఖ్య అంటారు.
ఉదా: \(\frac{3}{5}, \frac{-4}{9}, \frac{5}{6}, \ldots \ldots \ldots\)

ప్రశ్న2.
కింది వాక్యాలకు ఒక్కొక్క ఉదాహరణను ఇవ్వండి.
i) అకరణీయ సంఖ్య అయి పూర్ణ సంఖ్య కాని సంఖ్య.
సాధన.
\(\frac {7}{11}\)

ii) పూర్ణాంకమయి సహజ సంఖ్య కాని సంఖ్య.
సాధన.
‘0’ (సున్న)

iii) పూర్ణ సంఖ్యయై పూర్ణాంకం కాని సంఖ్య.
సాధన.
-8

iv) సహజ సంఖ్య, పూర్ణాంకము, పూర్ణ సంఖ్య మరియు అకరణీయ సంఖ్య అన్నీ అయ్యే సంఖ్య.
సాధన.
5

v) పూర్ణ సంఖ్యయై సహజ సంఖ్య కాని సంఖ్య.
సాధన.
– 4

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1

ప్రశ్న3.
1 మరియు 2ల మధ్యగల ఐదు అకరణీయ సంఖ్యలు కనుగొనండి.
సాధన.
1 మరియు 2ల మధ్య 5 అకరణీయ సంఖ్యలుండాలి.
కావున 1 మరియు 2 ల హారాలను 1 + 5 = 6 గా వ్రాస్తాము.
∴ 1 = 1 × \(\frac {6}{6}\) మరియు 2 = \(\frac{2 \times 6}{6}=\frac{12}{6}\)
ఇప్పుడు
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 1

ప్రశ్న4.
\(\frac {2}{3}\) మరియు \(\frac {3}{5}\) ల మధ్య మూడు అకరణీయ సంఖ్యలుంచుము.
సాధన.
a, b ల మధ్యగల అకరణీయ సంఖ్య \(\frac{a+b}{2}\) కావున
అదే విధముగా a = \(\frac {2}{3}\), b = \(\frac {3}{5}\) అనుకొనుము.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 2

ప్రశ్న5.
\(\frac {8}{5}\) మరియు \(\frac {-8}{5}\) లను సంఖ్యారేఖపై సూచించండి.
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 3
సోపానం-1 : – 3, – 2, – 1, 0, 1, 2, 3 లను సూచిస్తూ ఒక సంఖ్యారేఖను గీయండి.
సోపానం-2 : ఆ సంఖ్యారేఖ పై సున్నాకు కుడి మరియు ఎడమవైపు ప్రతి యూనిట్ ను ఐదు సమాన భాగాలుగా చేయండి.
సోపానం-3 : సున్నా నుండి కుడివైపు గల ఎనిమిదవ బిందువు \(\frac {8}{5}\)ను మరియు ఎడమవైపు గల ఎనిమిదవ బిందువు \(\frac {-8}{5}\)ను సూచిస్తుంది.

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1

ప్రశ్న6.
కింది అకరణీయ సంఖ్యలను దశాంశ రూపంలో రాయండి.
I. i) \(\frac {242}{1000}\)
సాధన.
\(\frac {242}{1000}\) = 0.242

ii) \(\frac {354}{500}\)
సాధన.
\(\frac {354}{500}\)
= \(\frac{354 \times 2}{500 \times 2}\)
= \(\frac {708}{1000}\)
= 0.708

iii) \(\frac {2}{5}\)
సాధన.
\(\frac {2}{5}\)
= \(\frac{2 \times 2}{5 \times 2}\)
= \(\frac {4}{10}\)
= 0.4

iv) \(\frac {115}{4}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 4
∴ \(\frac {115}{4}\) = 28.75

II. i) \(\frac {2}{3}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 5
∴ \(\frac {2}{3}\) = 0.6666 ……. = \(0 . \overline{6}\)

ii) \(\frac {-25}{36}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 6
∴ \(\frac {-25}{36}\) = -0.6944 ….. = \(-0.69 \overline{4}\)

iii) \(\frac {22}{7}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 7
∴ \(\frac {22}{7}\) = 3.14285 ……

iv) \(\frac {11}{9}\)
సాధన.
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 8
∴ \(\frac {11}{9}\) = 1.222 …… = \(1 . \overline{2}\)

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1

ప్రశ్న7.
కింది వాటిని \(\frac{\mathrm{p}}{\mathrm{q}}\) (p, q లు పూర్ణసంఖ్యలు మరియు – q ≠ 0) రూపంలో రాయండి.
i) 0.36
సాధన.
0.36 = \(\frac{36}{100}=\frac{9}{25}\)

ii) 15.4
సాధన.
15.4 = \(\frac{154}{10}=\frac{77}{5}\)

iii) 10.25
సాధన.
10.25 = \(\frac{1025}{100}=\frac{41}{4}\)

iv) 3.25
సాధన:
3.25 = \(\frac{325}{100}=\frac{13}{4}\)

ప్రశ్న8.
కింది వాటిని \(\frac{\mathrm{p}}{\mathrm{q}}\) (p, q లు పూర్ణసంఖ్యలు మరియు q ≠ 0) రూపంలో రాయండి.
i) \(0 . \overline{5}\)
సాధన.
x = \(0 . \overline{5}\) = 0.5555……… అనుకొనుము.
అవధి ‘1’ కావున ఇరువైపులా 10 చే గుణించగా
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 9
∴ \(0 . \overline{5}\) యొక్క \(\frac{\mathrm{p}}{\mathrm{q}}\) రూపము \(\frac {5}{9}\) అగును.

ii) \(3 . \overline{8}\)
సాధన.
x = \(3 . \overline{8}\) అనుకొనుము.
x = 3.888 ………
అవధి ‘1’ కావున ఇరువైపులా 10 చే గుణించగా
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 10
∴ \(3 . \overline{8}\) యొక్క \(\frac{\mathrm{p}}{\mathrm{q}}\) రూపము \(\frac {35}{9}\) అగును.

iii) \(0 . \overline{36}\)
సాధన.
x = \(0 . \overline{36}\) అనుకొనుము.
x = 0.363636 …………
అవధి ‘2’ కావున ఇరువైపులా 100 చే గుణించగా
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 11
∴ \(0 . \overline{36}\) యొక్క \(\frac{\mathrm{p}}{\mathrm{q}}\) రూపము \(\frac {4}{11}\) అగును.

iv) \(0 . \overline{36}\)
సాధన.
x = \(3.12 \overline{7}\) అనుకొనుము.
x = 3.12777 ……….
అవధి ‘1’ కావున ఇరువైపులా 10 చే గుణించగా
AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1 12
∴ \(3.12 \overline{7}\) యొక్క \(\frac{\mathrm{p}}{\mathrm{q}}\) రూపము \(\frac {563}{180}\) అగును.

AP Board 9th Class Maths Solutions Chapter 1 వాస్తవ సంఖ్యలు Ex 1.1

ప్రశ్న9.
కింద ఇచ్చిన ఏ సంఖ్యలు అంతమయ్యే దశాంశాలో భాగహారం చేయకుండానే గుర్తించండి.
i) \(\frac{3}{25}\)
సాధన.
ఇచ్చిన సంఖ్య యొక్క హారంను గమనించుము.
హారంలో ‘2’ లేక ‘5’ లేక “2 మరియు 5”ల లబ్దముగాని వుంటే ఆ అకరణీయ సంఖ్య అంతమయ్యే దశాంశమగును.
∴ ఇచ్చిన సంఖ్య యొక్క హారము 25 = 5 × 5
కావున \(\frac{3}{25}\) అంతమగు దశాంశము.

ii) \(\frac{11}{18}\)
సాధన.
ఇచ్చిన సంఖ్య హారము 18 = 2 × 3 × 3
∴ \(\frac{11}{18}\) అంతము కాని దశాంశము.

iii) \(\frac{13}{20}\)
సాధన.
ఇచ్చిన సంఖ్య యొక్క హారము 20 = 2 × 2 × 5
∴ \(\frac{13}{20}\) అంతమగు దశాంశము.

iv) \(\frac{41}{42}\)
సాధన.
ఇచ్చిన సంఖ్య యొక్క హారము 42 = 2 × 3 × 7
∴ \(\frac{41}{42}\) అంతము కాని దశాంశము.

AP 7th Class English Important Questions Unit 2 The Turning Point

These AP 7th Class English Important Questions 2nd Lesson The Turning Point will help students prepare well for the exams.

AP Board 7th Class English Unit 2 Important Questions and Answers The Turning Point

Reading Comprehension (Seen)

1. Read the following passage carefully.

I was in class V when the Second World War, the largest conflict in human history, was at its peak- Because of the war all the resources were scarce and the prices were not affordable. So, 1 had to take up my first job as a newspaper boy My task was to pick up a bundle of Tamil Newspapers and to deliver them to some local offices, some tea stalls and occasionally a few homes. Before I set out to distribute, I used to sit on the bench there at the station, open the bundle and carefully pluck out a copy of the daily newspaper Dinamani. The first page always caught my attention as it was usually filled with the photos of fighter aircrafts and stories of the Second World War. The German air force called Luftwaffe was sending hundreds of planes and bombers to attack the city and the British Royal Air Force had to deploy their full air force to defend their motherland. The stories would be about brave pilots from both the sides, and how they manoeuvred their aircraft and bombers. As a young boy I used to love the stories of the pilots and their planes. I was curious about planes. I wanted to be a pilot myself. (The Turning Point)

Now, answer the following questions.
1. What was the class that Kalam was in at the time of the Second World’ War?
Answers:
In class V

2. What made the resources scarce?
Answers:
The Second World War

3. What was his first job?
Answers:
He worked as a newspaper boy.

4. What was the news that was published on the first page of the newspaper?
Answers:
The photos of fighter aircrafts and stories of the Second World War

5. What made the speaker want to become a pilot?
Answer:
The stories of the pilots and their planes in the Second World War

AP 7th Class English Important Questions Unit 2 The Turning Point

2. Read the following passage carefully.

My curiosity grew in science because of a very special teacher when I was a ten-year-old boy in Class V. This was indeed a life-changing event. My science teacher’s name was Shri Siva Subramania Iyer. One day the topic of discussion in our class of sixty-five was ‘how birds fly? He drew a sketch of a bird with a tail, wings, feathers, and head on the board and explained how a bird flew. He explained how a bird could lift elf, fly and change direction by using its wings and the tail. He asked us whether we understood.

We gave a gloomy reply – no. Mr. Iyer did not get upset. That evening he took all of us to the seashore. The sunset, waves, cool breeze, and the chirping of birds all together made it a very pleasant atmosphere. He asked all of us to notice how the birds make a formation in a group and fly. He also told us to notice the shape of the formation made by the birds while flew. He drew our attention towards how they flap their wings to fly higher and how they use the tail to propel directions. Mr. Iyer also made us notice how the bird is powered to fly by itself. In 15 minutes, all the students cheerfully shouted “yes sir, we now understand how birds fly on their own.” (The Turning Point)

Now, answer the following questions.
1. What was the speaker curious for?
Answer:
Science

2. What was the topic of discussion in the class?
Answer:
How birds fly

3. What did the teacher explain?
Answer:
The flight or flying of the bird

4. What did the teacher do to make his students understand the topic well?
Answer:
He took his students to the seashore and showed them how the birds really fly.

5. How was the atmosphere at the seashore?
Answer:
It was very pleasant.

3. Read the following passage carefully.

The flight principle got imprinted in my mind and I decided that in the future I will study subjects related to flight. However, as a little boy I needed guidance to pursue this field. I asked my teacher Mr. Iyer to guide and tell me how to pursue my interest. He told me to study and explore the field of aviation science and aeroplanes.

Whatever I had learnt that day changed my life. 1 was inspired to have an aim. Later I realized how important it was to study Physics. I chose Physics. I opted for Aeronautical Engineering at the Indian Institute of Technology, Madras. Then, I became an Aeronautical Engineer and a space technologist. Mr. Iyer’s class had transformed my life which led me to make a profession out of my passion. Aeronautics, or the science of flight, was special to me. My career began in this field. (The Turning Point)

Now, answer the following questions.
1. What was imprinted in the speaker’s mind?
Answer:
The flight principle

2. What decision did the speaker take to do in future?
Answer:
He wanted to study subjects related to flight.

3. Who guided the speaker to pursue his interest?
Answer:
Mr. Siva Subramania Iyer, his science teacher

4. What did the speaker study at IIT, Madras?
Answer:
Aeronautical Engineering

5. How did the speaker start his career?
Answer:
He started his career as an aeronautical scientist.

AP 7th Class English Important Questions Unit 2 The Turning Point

4. Read the following lines carefully.

This is my prayer to thee, My Lord – strike, strike at the root of penury in my heart.
Give me the strength lightly to bear my joys and sorrows.
Give me the strength to make my love fruitful in service.
Give me the strength never to disown the poor or bend my knees before insolent might.
Give me the strength to raise my mind high above daily trifles.
And give me the strength to surrender my strength to thy will with love. (Give Me Strength)
Now, answer the following questions.

1. Who is praying to whom?
Answer:
The post is playing to God

2. What does the poet pray for?
Answer:
For strength to bear his joys end sorrows

3. What does the poet want the Lord to strike?
Answer:
The root of penury in his hear

4. Who are not to be disowned?
Answer:
The poor

5. What is ‘thy will’ according to the poet?
Answer:
To serve human beings

Reading Comprehension (Unseen)

1. Read the following passage carefully.

Up the river Hudson in North America are the Catskill mountains. They are not so high as the Himalayas in India. In a certain village at the foot of these mountains there lived long ago a man called Rip Van Winkle. He was simple and good natured. A very kind neighbour and a great favourite of all the good wives in the neighbourhood. The women took his side and put the blame on Dam Van Winkle. .

The children of the village too would shout with joy whenever they saw him. He made play things for them. He told them fairy tales. So they liked him.

Now, answer the following questions.
a) Why did children like Rip Van Winkle?
Answer:
Rip Van Winkle used to make play things for children. He told them fairy tales. So children liked Rip Van Winkle very much.

b) What kind of man was Rip Van Winkle?
Answer:
Rip Van Winkle was simple and good natured. He was a very kind neighbour and a great favourite of all the women and children in the village.

Choose the correct answer from the choices given.
c) Where are the Catskill mountains?
i) In South America
ii) In Africa
iii) In North America
Answer:
iii) In North America

d) Where did Rip Van Winkle live?
i) On the top of Catskill mountains
ii) In a village at the foot of the Catskill mountains
iii) In a city in North America
Answer:
ii) In a village at the foot of the Catskill mountains

e) Who liked Rip Van Winkle very much?
i) All the wives in the neighbourhood
ii) All the husbands in the neighbourhood
iii)All the friends in the village
Answer:
i) All the wives in the neighbourhood

AP 7th Class English Important Questions Unit 2 The Turning Point

2. Read the following passage carefully.

In the American War of Independence, a Corporal and a party of soldiers were ordered to raise a heavy beam for a battery that was being repaired. There were too few men for the work, but the Corporal, full of his dignity did nothing but stand by and shout orders, presently an officer, not in uniform rode up. “Hallo,” he said to Corporal, ‘why don’t you lend your men a hand to get that beam up?” “Don’t you know that I am a Corporal ?” was the reply, “Are you ?” said the officer, who then got down from his horse and joined the men. He worked till the sweat streamed down his face. When the beam had been raised and put to its place, he turned to the Corporal and bade him a low bow, “Good day Mr. Corporal. Next time when you have too few men for this kind of work, send for the Commander in Chief and I shall be happy to help you again.”

It was George Washington himself.

Now, answer the following questions.
a) Why did the officer get down from the horse?
Answer:
The officer got down from his horse to help the men in their work.

b) Who was the person that helped the men and the Corporal?
Answer:
The person that helped the man and the Corporal was none other than the President of America, George Washington.

Choose the correct answer from the choices given.
c) What was to be raised?
i) A battery
ii) A cannon
iii) A beam
Answer:
iii) A beam

d) Who was the person that was having dignity?
i) The Corporal
ii) The Soldier
iii) The President
Answer:
i) The Corporal

e) What did the Corporal have?
i) Very few men
ii) Many ment
iii) A lot of soldiers
Answer:
i) Very few men

Interpretation Of Non-Verbal Information

1. In the table given below the data is given about different age groups in different employment sectors.

Read the table and answer the following questions :
AP 7th Class English Important Questions Unit 2 The Turning Point 1
Now answer the following questions.
a) What does the above table show?
b) In which sector are very small member of people working?
c) In which sector are maximum number of people working?
d) In which sector are maximum number of young people working?
e) In which sector are maximum number of old people working?
Answer:
a) The above table shows people of different age groups working under different employment sectors.
b) In accountancy very small number of people are working.
c) In manufacturing sector maximum number of people are working.
d) In retail sector maximum number of young people are working.
e) In manufacturing sector maximum number of old people are working.

2. Study the table given below and observe the changing patterns of unemployment in some advanced countries.
AP 7th Class English Important Questions Unit 2 The Turning Point 2
Now answer the following questions.
a) How many countries are compared in the given table?
b) What period does the table represent?
c) Which country has the least unemployment rate in 2005?
d) Which country has a decrease of nearly 6% in unemployment rate between 2000 and 2006?
e) In the case of every country we can notice that (Choose the correct answer.)
i) The unemployment rate is steadily increasing.
ii) The unemployment rate is steadily decreasing.
iii) The unemployment rate is fluctuating, i.e. sometimes it rises and sometimes it falls.
f) Which year recorded the highest unemployment rate for many countries?
g) Which country recorded the least fluctuations in the unemployment rate?
Answer:
a) Eight countries are compared in the given table.
b) The table represents the period 2000 – 2006.
c) Japan has the least unemployment rate in 2005.
d) Spain has a decrease of nearly 6% in unemployment rate between 2000 and 2006.
e) iii
f) 2003
g) Germany

Vocabulary

Synonyms
Choose the words with similar meanings (synonyms) from the list given to the words underlined.

AP 7th Class English Important Questions Unit 2 The Turning Point 3
AP 7th Class English Important Questions Unit 2 The Turning Point 4
Answer:
a) a) hand over, b) sometimes
b) a) strike, b) place
c) a) benefit, b) presence
d) a) refreshing, b) observe
e) a) driven, b) joyfully
f) a) direct, b) curiosity

Antonyms

Write the opposites (antonyms) for the underlined words.

a) Because of the war all the resources were scarce (a) and the prices were not affordable (b).
b) Before I set out to distribute (a), I used to sit on the bench there at the station, open (b) the bundle and carefully pluck out a copy of the daily newspaper Dinamani.
c) The stories would be about brave (a) pilots from both the sides, and how they maneuvered their aircraft and bombers. As a young (b) boy, I used to love the stories of the pilots and their planes.
d) My curiosity (a) grew in science because of a very special (b) teacher when I was a ten-year-old boy in class V.
e) The sunset (a), waves, cool breeze, and the chirping of birds all together made it a very pleasant (b) atmosphere.
f) Mr. Iyer also made us notice how the bird is powered (a) to fly by itself. In 15 minutes, all the students cheerfully (b) shouted, “Yes sir, we now understand how birds fly on their own.”
Answer:
a) a) abundant / plentiful, b) unaffordable
b) a) collect, b) close
c) a) timid, b) old
d) a) disinterest, b) ordinary
e) a) sunrise, b) unpleasant
0 a) exhausted, b) sorrowfully

Right Forms of the Words

Fill in the blanks with the right form of the words given in the brackets.

a) I was in class V when the Second World War, the ____ (a) (larger / largest) conflict in human history, was at its peak. Because of the war all the resources were ____ (b) (scarce / scarcity) and the prices were not affordable.
b) The German air force called Luftwaffe was ____ (a) (sending / send) hundreds of planes and bombers to attack the city and the British Royal Air Force had to ____ (b) (deploy / deployment) their full air force to defend their motherland.
c) As a young boy, I used to ____ (a) (love / lover) the stories of the pilots and their planes. I was ____ (b) (curiosity / curious) about planes.
d) My ____ (a) (curious / curiosity) grew in science because of a very ____ (b) (special / speciality) teacher when I was a ten-year-old boy in class V.
e) The sunset, waves, cool breeze and the chirping of birds all together made it a very ____ (a) (pleasant / pleasantly) atmosphere. He asked all of us to notice how the birds make a ____ (b) (formed / formation) in a group and fly.
f) Mr. Iyer’s class had ____ (a) (transformation / transformed) my life which ____ (b) (led / leader) me to make a profession out of my passion.
Answer:
a) a) largest, b) scarce
b) a) sending, b) deploy
c) a) love, b) curious
d) a) curiosity, b) special
e) a) pleasant, b) formation
f) a) transformed, b) led

AP 7th Class English Important Questions Unit 2 The Turning Point

Spelling Test

Type – 1 : Vowel Clusters

Complete the following words using “ae, ai, au, ea, ee, ei, eo, eu, ia, ie, io, oa, oo, ou, ua, ue or ui”.

a) The first page always c _ _ ght my attent _ _ n as it was usually filled with the photos of fighter aircrafts and stories of the Second World War.
b) As a y _ _ ng boy, I used to love the stories of the piiots and their planes. I was cur _ _ us about planes.
c) My curiosity grew in science bee _ _ se of a very special t _ _ cher when 1 was a ten-year-old boy in class V.
d) He asked us whether we underst _ _ d. We gave a gl _ _ my reply – no.
e) The sunset, waves, c _ _ i breeze and the chirping of birds all together made it a very pi _ _ sant atmosphere.
f) Whatever I had l _ _ rnt that day changed my life. I was Inspired to have an _ _ m.
Answer:
a) caught, attention
b) young, curious
c) because, teacher
d) understood, gloomy
e) cool, pleasant
f) learnt, aim

Type – 2 : Suffixes

Complete the following words with the suitable suffixes given in the brackets.

a) The first page always caught my attent ___ (ion / ian) as it was usual ___ (liy / ly) filled with the photos of figher aircrafts and stories of the Second World War.
b) My curio ___ (city / sity) grew in science because of a very special teach ___ (er / or) when 1 was a ten-year-old boy in class V.
c) He explained how a bird could lift itself, fly and change direct ___ (ion/ian) by using its wings and the tail. He asked us whether we understood. We gave a gloom ___ (y / ey) reply – no.
d) He drew our attention towards how they flap their wings to fly high ___ (est /er) and how they use the tail to propel direct ___ (ions / ians).
e) I opted for aero ___ (nautic / nautical) engineering at the Indian Institute of Technology, Madras. Then, I became a space techolog ___ (yist / ist).
Answer:
a) attention, usually
b) curiosity, teacher
c) direction, gloomy
d) higher, directions
e) aeronautical, technologist

Type – 3 . Wronalv Spelt Words

Identify the wrongly spelt word and write its correct spelling in the space provided.
a) canflict, seashore, direction, realize
Answer:
conflict

b) resorce, discussion, chirp, career
Answer:
resource

c) important, field, plesant, deliver
Answer:
pleasant

d) technology, interest, ocassionally explain
Answer:
occasionally

e) caught, discuss, skech, flight
Answer:
sketch

Classification of Words

Arrange the following words under the correct headings.
AP 7th Class English Important Questions Unit 2 The Turning Point 5

Choice of the Words

Fill in the blanks choosing the suitable words from those given in the box.
AP 7th Class English Important Questions Unit 2 The Turning Point 6
Answer:
a) 1) set out, 2) carefully
b) 1) explained, 2) direction
c) 1) attention, 2) propel
d) 1) pursue, 2) explore

Compound Adjectives

1. Fill in the blanks to complete the given paragraph using the compound adjectives given in the box.
long-sleeved high-heeled open-mouthed sweet-looking well-dressed odd-looking part-time

Mrs. Das has a __(1)__ job in a clothes shop. Yesterday, an __(2)__ woman walked into the shop. She was wearing __(3)__ shoes. A __(4)__ dog was with her. “I want a __(5)__ shirt for my dog, please,” she said. “For your dog?” asked Mrs.Das, __(6)__ in surprise. “Yes,” replied the woman. “I want him to be __(7)__ for my next party.”
Answer:
1) part-time,
2) odd-looking,
3) high-heeled,
4) sweet-looking,
5) long-sleeved,
6) open-mouthed,
7) well-dressed.

2. Match the following words in Set – A with Set – B to make compound adjectives and write them in the space given.

Set – A Set – B Compound Adjective
1. cold A) lasting cold-blooded
2. four B) blooded four-day
3. well C) day well-read
4. five D) read five-star
5. long E) star long-lasting

Grammar

I. Edit the following passage correcting the underlined parts.

1. Tigers lives (a) in different parts of Asia and Siberia. The tiger or (b) the lion are the biggest animals in the cat family. An (c) male tiger is about 10 feet long. Their (d) coat is yellow and black.
Answer:
a) live, b) and, c) A, d) Its

2. Around the earth there was (a) atmosphere who (b) is like a rind round the (c) fruit. It is made up of oxygen, nitrogen, water vapour or (d) a number of other gases.
Answer:
a) is, b) which, c) a, d) and

3. In a village there lived a boy and his mother. There (a) are (b) very poor. The boy collected wood in (c) the forest and sold it. He cuts (d) down small trees also.
Answer:
a) They, b) were, c) from, d) cut

4. The Banyan tree is possibly a (a) biggest and friendliest of all our trees. We did (b) not see many banyan trees in our cities nowadays. This (c) trees require plenty of space for (d) spread themselves.
Answer:
a) the, d) do, c) These, d) to

AP 7th Class English Important Questions Unit 2 The Turning Point

II. Complete the passage choosing the right words from those given below. Each blank is numbered and for each blank four choices are given. Choose the correct answer and write (A), (B), (Q) or (P) in the blanks.

1. Every Sunday Daniel and his family ____(1) to the beach. They live far ____(2) the beach. ____(3) once a week the family gets into the car and Daniel’s father for hours ____(4) they reach the beach.
1) A) goes B) went C) go D) going
2) A) away B) from C) to D) of
3) A) And B) But C) Or D) Yet
4) A) till B) to C) until D) up to
Answer:
1) C 2) B 3) B 4) C

2. Mahatma Gandhi freed India from ____(1) British Empire. He did not ____(2) the British ____(3) guns ____(4) he loved all people.
1) A) a B) an C) the D) some
2) A) fight B)fought C) fighted D) fighting
3) A) from B) by C) with D) ou
4) A) so B) because C) why D) for
A. 1) C 2) A 3) C 4) B

3. Of all ____(1) creatures, butterflies are perhaps ____(2) most beautiful. Thev have such briehtlv ____(3) wings. If vou look at the wings ____(4) a magnifying glass, you will see that they are covered by tiny scales.
1) A) fly B) flying C) flew D) flown
2) A) a B) an C) the D) some
3) A) colour B) colours C) coloured D) colouring
4) A) from B) in C) into D)through
Answer:
1) B 2) C 3) C 4) D

4. Atmosphere makes ____(1) earth a planet of life. It ____(2) us with the air to breathe, protects ____(3) from dangerous solar ravs ____(4) saves us from the extremes of heat and cold.
1) A) a B) an C) the D) that
2) A) supply B) supplies C) supplied D) supplying
3) A) we B) us C) our D) ours
4) A) but B) and C) or D) yet
Answer:
1) C 2) B 3) B 4) B

III. Write the past forms of the words given below.
AP 7th Class English Important Questions Unit 2 The Turning Point 7
Answer:
1) belonged
2) grew
3) explained
4) directed
5) understood
6) made
7) shouted
8) decided
9) told
10) opted

IV. Fill in the blanks with past form of the verb given in brackets.

1) He _____ (go) home very late last night.
2) I _____ (meet) her two years ago.
3) They _____ (buy) a new flat last month.
4) Columbus _____ (discover) America.
5) The teacher _____ (appreciate) the students.
Answer:

  1. went
  2. met
  3. bought
  4. discovered
  5. appreciated

AP 7th Class English Important Questions Unit 2 The Turning Point

V. Fill in the blanks with suitable adverbs of time given iii the box.

1) She has _____ finished training.
2) Have you _____ been to Agra?
3) I have lived in Guntur _____ 2015.
4) He has loved in Chennai _____ a long time.
5) Subhash hasn’t arrived _____ .
6) What time does the film start? It has _____ started.
Answer:

  1. just
  2. ever
  3. since
  4. for
  5. yet
  6. already

Creative Writing

1. In Kalam’s autobiography “The Turning Point”, you have learnt that Kalam worked as a newspaper boy while he was studying in class V. You know that those were the days of the Second World War. Kalam used to sit on the bench there at the station and read the stories of war. Kalam was very enthusiastic about those stories. One day he read the war story of the previous day. Then, he distributed the daily newspaper and went to school. That evening, he started to write a diary.
Imagine that you were Kalam and attempt a diary entry.
Answer:
Friday, 10th September 2021
7:30 p.m.

Dear Diary,
In the morning, the photos I saw are really magnificent. They are the photos of war between Britain and Germany. How attractive they are ! The first page of the daily newspaper Dinamani is totally filled with the photos of fighter aircrafts and stories of the Second World War. The German Air Force is sending hundreds of planes and bombers to attack the city and the British Royal Air Force is deploying their full force to defend their motherland. 1 like those stories of brave pilots from both the sides, and how they manoeuvre their aircrafts and bombers. I love the stories of the pilots and their planes. I am really curious about planes. I love the profession of a pilot. I too shall become a pilot myself. I shall operate the planes. But my family is a poor one where nobody is a literate. What can I do ? Yes, I shall take the guidance from our teachers. That’s all for now! I’m really tired and I am going to sleep.
Kalam

2. In the lesson The Turning Point’ you have learnt that the science teacher Mr. Siva Subramania Iyer took the students of class V to the seashore and taught them how birds fly on their own. The flight priniciple got imprinted in Kalam’s mind and he decided that in the future he would study subjects related to flight. He met Mr. Iyer to seek his guidance.

Now, write a possible conversation between Mr. Iyer and Kalam on the above context.
Answer:
Kalam : Good morning, Sir!
Mr. Iyer : Good morning. What brings you here, Kalam?
Kalam : Sir, yesterday you taught us how birds fly. I now understand how they fly on their own.
Mr. Iyer : Very good.
Kalam : Sir, the flight principle got imprinted in my mind and so I decided
Mr. Iyer : Why do you hesitate, boy? You can express your feelings with me freely.
Kalam : I decided that in the future I will study subjects related to flight.
Mr. Iyer : Oh, very nice to hear.
Kalam : Sir, I need your guidance to pursue my interest.
Mr. Iyer : Certainly, I’ll guide you. If you work hard, you’ll achieve your aim.
Kalam : Thank you very much, sir.

3. Use the following information and write a bio-sketch of Dr. Kalam.
Dr. Avul Pakir Jainulabdeen Abdul Kalam
Birth : 15th October 1931 at Rameswaram in Tamil Nadu
Died on : 27th July 2015
Parents : Ashiamma (mother), Jainulabdeen (father)
Education : Schooling at Rameswaram
Childhood friends : Ramanadha Sastry, Aravindan and Sivaprakasan
Alma Matter : St. Joseph’s College, Tiruchirapalli
Madras Institute of Technology
Profession : Professor, author, aerospace scientist
Presidency : 11th President of India on 25th July 2002
Achievements : Evolution of ISRO’s launch vehicle programme, operationalisation of AGNI, PRITHVI missiles
Literary pursuits : Four of his books
– Wings of Fire
– India 2020 – A Vision for the New Millennium
– My Journey
– Ignited Minds
Honours : Honorary doctorate from 30 universities
Awards : Padma Bhushan (1981)
Padma Vibhushan (1990)
Bharat Ratna (1997)
Answer:
Dr. Avul Pakir Jainulabdeen Abdul Kalarn

Abdul Kalam was the 11th President of India. He was born on 15th October 1931 at Rameswaram in Tamil Nadu. His mother was Ashiamma and father Jainulabdeen. He did his schooling at Rameswaram. His childhood friends are Ramanadha Sastry, Aravindan and Sivaprakasan.

He studied at St. Joseph’s College in Tiruchirapalli and completed his professional course at Madras Institute of Technology. He stepped into the shoes of many professions such as a professor, author, and an aerospace scientist.

He was elected as 11th President of India on 25th July 2002. He played a key role in the evolution of ISRO’s launch vehicle programme and in the operationalisation of AGNI, PRITHVI missiles.

The four important literary pursuits of Kalam are Wings of Fire, India 2020 – A Vision for the New Millennium, My Journey and Ignited Minds. He was honoured with a honorary doctorate from 30 universities. He got awards like Padma Bhushan in 1981 and Padma Vibhushan in 1990. He also got the most prestigious award Bharat Ratna in 1997. He passed away on 27th July 2015.

AP 7th Class English Important Questions Unit 2 The Turning Point

4. Write a letter to your father requesting him to allow you to go on an educational tour with your Mends.
Answer:

12-25, Ashok Nagar
Mangalagiri.

15 June, 20xx

My dear father
I am safe here and I hope that you are also safe there. I am studying well and I got 90% of marks in the last monthly tests and I hope that I can get more than 90% in the coming exams.

I am very happy to inform you that our school is arranging an educational tour to visit Mysore and surrounding places. We will visit Brundavan gardens, some industries and educational institutes there. It is a two day programme. Our school teachers will also accompany us. All our friends are going on the trip. I am also interested to go on the tour for which 1 require Rs. 3,000/- for expenses.

Hence, I request you to kindly allow me to go on the tour along with my friends and teachers and send the amount as early as possible. 1 am waiting for your reply. Convey my profound regards to Mummy and best wishes to my brother and sister.

With love
Yours lovingly
Aditya

Address on the Envelope :
To
P. Krishnamurthy
17-761/A
Nehru Nagar
Madanapalli
Chittoor dist.

5. Write a story using the following hints :

Hints : A crow – find a peice of meat – take the piece of meat fly – about to eat – a cunning fox – sees piece of meat – wants to take it – fox says – crow has a sweet voice – to sing a song – vexed with his repeated requests – put the piece of meat – under his leg says – that he has already read the story – get away from there.
Answer:
One day a crow found a piece of meat somewhere. The crow took the piece of the meat in its beak and flew off to a tree nearby. As it was about to eat the meat, a cunning fox came there. The fox saw the piece of the meat. Somehow he wanted to take it away from the crow. Then the fox said that the crow had a sweet voice. He asked the crow to sing a song for him. He repeatedly requested the crow for a song. Having been vexed with his repeated requests, the crow put the piece of the meat under his claw and asked the fox to get away from there. He told the fox that he had already read the story of stupid crow and cunning fox.

AP 7th Class English Important Questions Unit 2 The Turning Point

6. Write a story using the following hints.

Hints : An old farmer – five sons – lazy and selfish – quarrelled one another – old man worried about – his good words – sons did not care – asked servants – bring a bundle of sticks – sons asked to break – but none – bundle loosened – single stick – broken easily – sons understood – unity is strength.
Answer:
The Farmer and His Five Sons
Once there was an old farmer. He had five sons. The sons were lazy and selfish. They always quarrelled with one another. The old man was worried about his sons’ future. He tried to mend their behaviour by saying a few good words. But the sons did not care arid they did not change their ways. So, the old man wanted to teach his sons a lesson and he asked his servants to bring a bundle of sticks. He called his sons and asked them to break the bundle one after another. But they could not break the bundle as it was not an easy task. Then the old man loosened the bundle and gave them a stick each. They could break the sticks easily. Thus the old man tried to make them understand the value of unity like a bundle of sticks. The sons understood the value of unity and they started to believe that unity is strength.
Moral: Unity is strength.