AP 8th Class Maths Bits Chapter 11 Algebraic Expressions with Answers

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AP State Syllabus 8th Class Maths Bits 11th Lesson Algebraic Expressions with Answers

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Question 1.
Which of the following is a monomial?
A) 2x + 3
B) \(\frac{-3}{4}\) xy
C) cx² + dx + e
D) \(\frac{5}{7}\)x – \(\frac{2}{3}\)y
Answer:
B) \(\frac{-3}{4}\) xy

Question 2.
The degree of 4xy² z³
A) 4
C) 6
B) 2
D) 3
Answer:
C) 6

Question 3.
The degree of 3x² – 5 + 7x³ – 6x⁵
A) 5
B) 3
C) 2
D) -6
Answer:
A) 5

Question 4.
If A = 5x² + 3xy + 2y², B = – 2y2 – 3xy + 4x² then A + B = ………………..
A) 9x² + 6xy
B) 4y²
C) x² + 4y² + 6xy
D) 9x²
Answer:
D) 9x²

Question 5.
Which of the following is a group of like terms?
A) 2t, \(\frac{5 t}{2}, \frac{-6 s}{7}\)
B) x , 2x², – 7x, 8x³
C) 6p, – 7p, \(\frac{5}{2}\) p
D) 2y, \(\frac{-7}{3}\)x, 5t
Answer:
C) 6p, – 7p, \(\frac{5}{2}\) p

Question 6.
5x × (-3y) =
A) – 15xy
B) – 15x²y
C) 15xy
D) 2xy
Answer:
A) – 15xy

Question 7.
The product of 5x, 6y and 7z
A) 210 (x + y + z)
B) 210 xyz
C) 18 xyz
D) 18 (x + y + z)
Answer:
B) 210 xyz

Question 8.
(a + b)² – (a – b)² =
A) 2(a² + b²)
B) a² + b²
C) 4ab
D) 0
Answer:
C) 4ab

Question 9.
The formula involved in the product of 302 × 298
A) (a + b)²
B) (a – b)²
C) (a + b) (a – b)
D) None
Answer:
C) (a + b) (a – b)

Question 10.
(3m – 2n²) × (- 7 mn) …………………
A) – 21 m² n + 14 mn³
B) 21 m² n – 14 m²
C) – 21 mn² + 14 m³ n
D) 21 m² – 4 mn³
Answer:
A) – 21 m² n + 14 mn³

Question 11.
5x (6y + 3) = …………………..
A) 30x + 15
B) 30x – 15y
C) 3x + 15 y
D) 30xy + 15x
Answer:
D) 30xy + 15x

Question 12.
The product of two monomials is a …………………….
A) Binomial
B) Monomial
C) 0
D) 4
Answer:
B) Monomial

Question 13.
(5x + 6y) (3x – 2y) = ……………………
A) 8x² – 8 xy
B) 15x² + 3xy
C) 15x² – xy
D) 15x² + 8xy – 12y²
Answer:
D) 15x² + 8xy – 12y²

Question 14.
No. of terms in the product of a binomial and a trinomial are …………………
A) 10
B) 9
C) 6
D) 7
Answer:
C) 6

Question 15.
(a + b)² = ………………
A) a² + b²
B) a² – b²
C) 7
D) a² + 2ab + b²
Answer:
D) a² + 2ab + b²

Question 16.
The symbol used for an equation identity is ……………….

C) ≡
D) =
Answer:
C) ≡

Question 17.
(a + b) (a – b) = ………………..
A) a² – b
B) b² – a²
C) a² – b²
D) a – b²
Answer:
C) a² – b²

Question 18.
(a – b)² = ……………..
A) a² – 2ab + b
B) a² – ab + b²
C) a² – 2a + b²
D) a² – 2ab + b²
Answer:
D) a² – 2ab + b²

Question 19.
(x + a) (x + b) = …………………
A) x² + (a + b) x + ab
B) x² – (a-b) x – ab
C) x² – ab
D) x + ab
Answer:
A) x² + (a + b) x + ab

Question 20.
If the equation is true for all values of the variables then it is called an ………………..
A) Equation
B) identity
C) Product
D) None
Answer:
B) identity

Question 21.
The formula used in the product of 96 × 104 is ……………….
A) (a + b) (a – b)
B)(a – b)²
C) (a – b)²
D) a² – b
Answer:
A) (a + b) (a – b)

Question 22.
The formula used in the product of 196² is …………………..
A) (a + b)²
B) (a – b)²
C) a² – b
D) a – b²
Answer:
B) (a – b)²

Question 23.
987² – 13² = ………………….
A) 9,74,000
B) 79,400
C) 14,000
D) 14,009
Answer:
A) 9,74,000

Question 24.
(4x + 5y) (4x – 5y) = ……………………..
A) x² – 16y²
B) 16x² – y²
C) 16x – 25
D) 16x² – 25y²
Answer:
D) 16x² – 25y²

Question 25.
(a – b)² – (a-b)² = ……………….
A) 2ab
B) 0
C) ab
D) \(\frac{\mathrm{ab}}{2}\)
Answer:
B) 0

Question 26.
a² + b² = ……………………
A) (a + b)² – 2ab
B) a² – b²
G) (a – b)² + 4ab
D) None
Answer:
A) (a + b)² – 2ab

Question 27.
(a – b)² + 4ab = ………………
A) (a – b)³
B) (a – b)²
C) (a + b)²
D) a² – b
Answer:
C) (a + b)²

Question 28.
(a – b)² – (a + b)² = ………………
A) 2a² + b²
B) 0
C) 4ab
D) – 4ab
Answer:
D) – 4ab

Question 29.
Degree of 3x² y² z³ is …………………
A) 2
B) 3
C) 7
D) 3
Answer:
C) 7

Question 30.
The value of 2x³ – 2x² + 1 at x = 1 is ………………
A) 4
B) -1
C) 3
D) 1
Answer:
D) 1

Question 31.
a (a² – b²) = ………………
A) a³ – b² a
B) a – b²
C) a³ – b²
D) a – b³
Answer:
A) a³ – b² a

Question 32.
a (a-b) + b (b-c) + c (c – a) = ………………..
A) 0
B) a² – b²
C) a² + b²
D) a² + b² + c² – ab – bc – ca
Answer:
D) a² + b² + c² – ab – bc – ca

Question 33.
83 × 77 = …………………
A) 3691
B) 6391
C) 6091
D) 1391
Answer:
B) 6391

Question 34.
304² = …………………….
A) 82,416
B) 92,416
C) 82,466
D) 93,416
Answer:
B) 92,416

Question 35.
(m + n) (m – n) = ………………….
A) m – n²
B) m² – n
C) m – n
D) None
Answer:
D) None

Question 36.
9k² + 24 kl + 16 l² = ………………
A) (9 k + 3l)²
B) (3k + 4l) (3k + 4l)
C) (3 k – 4l)²
D) None
Answer:
B) (3k + 4l) (3k + 4l)

Question 37.
abc × a²bc = ………………….
A) a²b²c²
B) abc²
C) a³b²c²
D) ab²c
Answer:
C) a³b²c²

Question 38.
(P + q) (P² – pq + q²) = ………………..
A) p³ + q
B) p – q²
C) p² + q²
D) p³ + q³
Answer:
D) p³ + q³

Question 39.
m³ + m² n – n² m – n³ = ………………..
A) (m² – n²) (m + n)
B) (m – n) (m² + n²)
C) (m + n) (m – 1)
D) None
Answer:
A) (m² – n²) (m + n)

Question 40.
– 5 p² × – 2p = ………………
A) 10p³
B) 10p
C) – 10p³
D) – 8p³
Answer:
A) 10p³

Question 41.
92² – 8² = ………………..
A) 1400
B) 1000
C) 8400
D) 8500
Answer:
C) 8400

Question 42.
I = ………………..
A) \(\frac{\text { PTR }}{100}\)
B) \(\frac{P}{100 \mathrm{TR}}\)
C) \(\frac{100 \mathrm{~T}}{\mathrm{PR}}\)
D) \(\frac{100 \mathrm{I}}{\mathrm{PR}}\)
Answer:
A) \(\frac{\text { PTR }}{100}\)

Question 43.
106 × 94 = ……………..
A) 9864
B) 9964
C) 9800
D) 9364
Answer:
B) 9964

Question 44.
– 3x² + 3x² – 5x² – x² = …………….
A) x²
B) – 6x²
C) 3x²
D) 6x²
Answer:
B) – 6x²

Question 45.
Identify like terms.
A) 3x², 2x², – x²
B) xy, xy², – 3y²
C) pq, pq², \(\frac {1}{2}\)pq
D) 8x², 9y², 2pq
Answer:
A) 3x², 2x², – x²

Question 46.
(a + b)² – (a – b)² = ……………….
A) 2ab
B) 2bc
C) 4a²
D) None
Answer:
D) None

Question 47.
The value of 3x + 5 at x = 1 is …………………..
A) 6
B) 8
C) 9
D) 10
Answer:
B) 8

Question 48.
If a = 1, b = 2 then (a – b)² = ………………..
A) – 1
B) 1
C) – 2
D) 3
Answer:
B) 1

Question 49.
At x = \(\frac {1}{2}\) the value of 2x – 1 is ……………….
A) 1
B) 0
C) -1
C) 2
Answer:
B) 0

Question 50.
P = xy, Q = yz, R = zx then PQR = …………………
A) x² y² z²
B) xy² z²
C) xy z
D) \(\frac{x^{2} y^{2}}{z^{2}}\)
Answer:
A) x² y² z²

Question 51.
(5x² – 6x + 9) (2x – 3) = ………………
A) 10x³ – 7x² + 3x
B) 10x³ – 7x² + x + 1
C) 10x³ – 27x² + 7
D) 10x³ – 27x² + 36x – 27
Answer:
D) 10x³ – 27x² + 36x – 27

Question 52.
(3x + 5y) (5x – 7y) = ……………………
A) 15x² – 3y²
B) 15x² + 4xy – 35y²
C) 15x² – 4xy
D) 15x – 13xy²
Answer:
B) 15x² + 4xy – 35y²

Question 53.
Additive Inverse of 6x² – 4x – 1 is ……………….
A) x² – 6x + 1
B) – 6x² + 4x – 3
C) x² – 3x + 7
D) – 6x² + 4x + 1
Answer:
D) – 6x² + 4x + 1

Question 54.
2x² + 5x – 1 + 8x + x² + 7 – 6x + 3 – 3x² = ……………
A) 7x + 9
B) x – 7
C) x – 9
D) x + 3
Answer:
A) 7x + 9

Question 55.
2a + b – (a – b) = ………………..
A) a – b
B) 2a – 2b
C) a + 2b
D) a – 2b
Answer:
C) a + 2b

Question 56.
Degree of zero is ………………..
A) 0
B) -1
C) 3
D) not defined
Answer:
D) not defined

Question 57.
Degree of constant is ………………
A) 0
B) 1
C) 2
D) -1
Answer:
A) 0

Question 58.
(3x² – 7x + 1) (4x – 4x) = ………………
A) 4x³ – x² + 11
B) 0
C) 3x³ – 7x + 1
D) None
Answer:
B) 0

Question 59.
(X – 1) (x + 1) = ………………
A) x² + 1
B) x² – 1
C) x – 1
D) x + 3
Answer:
B) x² – 1

Question 60.
Number of terms in a trinomial is ………………..
A) 0
B) 1
C) 2
D) 3
Answer:
D) 3

Question 61.
(√a + √b)(√a – √b) = ………………….
A) a – b²
B) a – b
C) a² – b
D) a + b
Answer:
B) a – b

Question 62.
\(\left(\frac{\mathbf{a}}{3}+\frac{\mathbf{b}}{5}\right)\left(\frac{\mathbf{a}}{3}-\frac{\mathbf{b}}{5}\right)\) = ……………….
A) \(\frac{a^{2}}{9}+\frac{b}{2}\)
B) \(\frac{\mathrm{a}^{2}}{9}\) – 1
C) \(\frac{a^{2}}{9}-\frac{b^{2}}{25}\)
D) \(\frac{2 a}{3}-\frac{b}{3}\)
Answer:
C) \(\frac{a^{2}}{9}-\frac{b^{2}}{25}\)

Question 63.
Number of terms in ax² + bx + c is ……………….
A) 2
B) 3
C) 4
D) 1
Answer:
B) 3

Question 64.
(a – b) (a² + ab + b²) = ……………
A) a³ – b
B) a – b³
C) a² – b²
D) None
Answer:
D) None

Question 65.
(x + 3) (x + 2) =
A) x² + 5x + 6
B) x² – 5x – 6
C) x² – 3x + 6
D) None
Answer:
A) x² + 5x + 6

Question 66.
9x² – y² = ………………
A) (3x + y) (3x – y)
B) (3x – 1) (3x – y)
C) (3x – y)(3x – 3)
D) None
Answer:
A) (3x + y) (3x – y)

Question 67.
\(\frac{4 a^{2},-1}{2 a+1}\) = ……………..
A) a – 1
B) a +1
C) 2a
D) 2a – 1
Answer:
D) 2a – 1

Question 68.
(3x² – 7x + 9) ÷ 0
A) 0
B) 3x² – 9
C) 9x
D) Not defined
Answer:
D) Not defined

Question 69.
m³ (m – 2) + 2m² (m + 3) – 6m (m – 4) = ………………..
A) m – 24m²
B) m² + 24m
C) m² + 2m
D) m + 4m²
Answer:
B) m² + 24m

Question 70.
Cube of (a + 1) is = …………………
A) a² + 1
B) a + 2a + 1
C) a + 3a + 3
D) 3a – 3
Answer:
C) a + 3a + 3

Question 71.
(99)² = ……………..
A) 1145
B) 8900
C) 9800
D) 9801
Answer:
D) 9801

Question 72.
9.8 × 10.2 = ……………….
A) 39.55
B) 91.99
C) 99.96
D) 96.99
Answer:
C) 99.96

Question 73.
(84)² – (16)² = …………..
A) 3600
B) 6100
C) 6800
D) 6900
Answer:
C) 6800

Question 74.
1010 × 990 = ………………..
A) 999900
B) 99099
C) 99000
D) 98900
Answer:
A) 999900

Question 75.
(705)² – (295)² = ………………
A) 23000
B) 13000
C) 140000
D) 410000
Answer:
D) 410000

Question 76.
(x + 1) (x – 1) (x² + 1) = ……………..
A) x⁴ – 1
B) x² – 1
C) 4x – 1
D) x + 1
Answer:
A) x⁴ – 1

Question 77.
8x = (52)² – (48)² then x = ………………..
A) 12
B) 50
C) 9
D) 26
Answer:
B) 50

Question 78.
13x = (85)² – (84)² then x = ……………….
A) 16
B) 11
C) 13
D) 10
Answer:
C) 13

Question 79.
(11 + x)(11 – x) = ……………….
A) 121 – x²
B) 121 – x
C) 12 – x³
D) 3x – 4
Answer:
A) 121 – x²

Question 80.
11³ = …………………
A) 1221
B) 1331
C) 1441
D) 1113
Answer:
B) 1331

Question 81.
(x + \(\frac{1}{x}\))² = ………………….
A) x + \(\frac{1}{2 x}\)
B) x – \(\frac{1}{\mathrm{x}^{2}}\)
C) 3x – \(\frac{1}{\mathrm{x}^{2}}\)
D) x² + 2 + \(\frac{1}{\mathrm{x}^{2}}\)
Answer:
D) x² + 2 + \(\frac{1}{\mathrm{x}^{2}}\)

Question 82.
(7xy – 1) (7xy + 1) = ………………….
A) 49x² y² – 1
B) 49xy- 1
C) 49xy² – 1
D) 9xy -1
Answer:
A) 49x² y² – 1

Question 83.
The product of two positive numbers is ………………….
A) 0
B) -1
C) Negative
D) Positive
Answer:
D) Positive

Question 84.
3x²y × 4xy² × 7x³y³ = ……………. …………………
A) 84x⁶y⁶
B) 48y⁶
C) 41xy⁶
D) 40x⁶y⁶
Answer:
A) 84x⁶y⁶

Question 85.
The sum of all exponents of variables in a monomial is called ……………… of the
monomial.
A) Expression
B) Degree
C) Like
D) None
Answer:
B) Degree

Question 86.
Degree of the trinomial 3xy + 4y – 8 is ……………..
A) 2
B) 4
C) 3
D) – 8
Answer:
A) 2

Question 87.
5x × 6y × 7z =
A) 2xy
B) 105xy
C) 120x
D) 210xy
Answer:
D) 210xy

Question 88.
In a cuboid l = 2x, b = 3y, h = 4z then volume, v = ………………….
A) 3xyz
B) 2xy
C) 4xyz
D) 24xyz
Answer:
D) 24xyz

Question 89.
The property used in a(b + c) = ab + ac is ………………..
A) Identity
B) Distributive
C) Commutative
D) None
Answer:
B) Distributive

Question 90.
How many terms are there in the product of a binomial and trinomial ?
A) 4
B) 10
C) 9
D) None
Answer:
D) None

Question 91.
a(a + 1) = 6 then a = ………………..
A) 2
B) – 3
C) A&B
D) None
Answer:
C) A&B

Question 92.
a² + b² + c² + 2ab + 2bc + 2ca = ……………….
A) (a + b + c)²
B) (a – b – c)²
C) (2a – b – c)²
D) (a – b)²
Answer:
A) (a + b + c)²

Question 93.
196² – (194 + 2)² = ………………
A) 16
B) 19
C) 10
D) 0
Answer:
D) 0

Question 94.
9672 = …………………
A) 93 × 004
B) 93 × 102
C) 83 × 104
D) 93 × 107
Answer:
A) 93 × 004

Question 95.
The area of adjacent square is …………………

A) 2a⁴
B) 2a²
C) (\(\frac{a}{2}\))²
D) 4a²
Answer:
D) 4a²

Question 96.
a (a – b) + b (a – b) = ………………..
A) a² – b
B) a² – b²
C) a – b²
D) \(\frac{a}{2}\) – b
Answer:
B) a² – b²

Question 97.
a² – b² = (a + b) (a – b) is a ……………….
A) Identity
B) Area
C) Place
D) None
Answer:
A) Identity

Question 98.
(x + a) (x – b) = ………………….=
A) x² + ax – bx – ab
B) x² + (a + b) x – ab
C) x² – ax – ab
D) None
Answer:
A) x² + ax – bx – ab

Question 99.
101² – 101² = ……………..
A) 101
B) 202
C) 0
D) 401
Answer:
C) 0

Question 100.
a = 13, b = 12 then a² – b² = ……………….
A) 16
B) 10
C) 25
D) 12
Answer:
C) 25