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Practice the AP 10th Class Maths Bits with Answers Chapter 10 Mensuration on a regular basis so that you can attempt exams with utmost confidence.

AP State Syllabus 10th Class Maths Bits 10th Lesson Mensuration with Answers

Question 1.
The volume of right circular cylinder with radius 6 cm and height 7 cm is ……………. cm³
A) 642
B) 927
C) 264
D) 792
Answer:
D) 792

Question 2.
A sphere of radius ‘r’ is inscribed in a cylinder. The surface area of the sphere is ……………. of the cylinder.
A) total surface area
B) curved surface area
C) volume
D) none of these
Answer:
B) curved surface area

Question 3.
The maximum length of the stick that can be placed in a cuboid, whose measurements are 8 × 4 × 1, is ……………………
A) 8
B) 9
C) 12
D) 13
Answer:
B) 9

Question 4.
The volume of a cube will be ………………… (in cm³), whose total surface area is 216 cm².
A) 216
B) 196
C) 212
D) 144
Answer:
A) 216

Question 5.
Which of the following vessel can be filled with more water (A, B are in cylindrical shape) ?

A) A
B) B
C) Both are equal
D) Cannot be determined
Answer:
B) B

Question 6.
The curved surface area of a sphere will be ………………………… , whose radius is 10 cm.
A) 239π
B) 400π
C) 221π
D) 129π
Answer:
B) 400π

Question 7.
Base area of the prism is 30 cm² and its height is 10 cm. Then the volume of the prism is …………………
A) 300 cm³
B) 300 cm²
C) 150 cm²
D) 150 cm³
Answer:
A) 300 cm³

Question 8.
If the total surface area of cube is 96 cm³, then side of cube is ……………..
A) 3 cm
B) 5 cm
C) 6 cm
D) 4 cm
Answer:
D) 4 cm

Question 9.
Ratio of volumes of cylinder and cone whose radii are equal and having same height is
A) 1 : 3
B) 1 : 2
C) 3 : 1
D) 2 : 1
Answer:
C) 3 : 1

Question 10.
To find out the slant height of a cone, we use ………….. theorem.
A) Thales
B) S.A.S
C) Pythagoras
D) S.S.S
Answer:
C) Pythagoras

Question 11.
A.solid iron cuboid of dimensions 49 cm × 33 cm × 24 cm is melted to form a solid sphere, then its radius is
A) 21 cm
B) 13 cm
C) 24 cm
D) 18 cm
Answer:
A) 21 cm

Question 12.
In a right circular cone, \(\sqrt{(l+\mathbf{r})(l-\mathbf{r})}\) =
A) slant height
B) vertical height
C) radius of the base
D) diameter of the base
Answer:
B) vertical height

Question 13.
Volume of a cube is 512 cm³, then its edge is
A) 8 cm
B) 6 cm
C) 14 cm
D) 18 cm
Answer:
A) 8 cm

Question 14.
T.S.A of a solid hemisphere whose radius is x cm is 147 π cm². Then ‘x’ is
A) 21
B) 15
C) 8
D) 7
Answer:
D) 7

Question 15.
The number of cubes of edge 2 cm which can be cut out from a cube of edge 6 cm is
A) 9
B) 18
C) 27
D) 3
Answer:
C) 27

Question 16.
A cylinder and cone have bases of equal radii and arc of equal heights then the volumes are in the ratio is ……………….
A) 1 : 2
B) 2 : 1
C) 3 : 1
D) 1 : 3
Answer:
C) 3 : 1

Question 17.
A heap of the rice is in the form of cone. Its diameter is 12 m, height is 8 m, then the volume is ……………………
A) 200.5 Cu.cm
B) 300.14 Cu.cm
C) 301.44 Cu.m
D) 200.15 Cu.m
Answer:
C) 301.44 Cu.m

Question 18.
Combination shape of tanker is
A) Cylinder + 2 hemispheres
B) Cylinder + Circle
C) Cylinder + hemisphere
D) Cone + Circle
Answer:
A) Cylinder + 2 hemispheres

Question 19.
A hemisphere is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the length of the cube, then the surface area of the remaining solid is …………………… sq. units.
A) a²(5 + \(\frac{\pi}{2}\))
B) a²(6 + \(\frac{\pi}{2}\))
C) a²(6 + \(\frac{\pi}{4}\))
D) a²(4 + \(\frac{\pi}{4}\))
Answer:
B) a²(6 + \(\frac{\pi}{2}\))

Question 20.
The height of a cone and its base radius are 4 cm and 3 cm respectively. Then its slant height is ……………… cm.
A) 4
B) 3
C) 5
D) 6
Answer:
C) 5

Question 21.
A vessel is in the form of a hollow hemisphere mounted by hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm, then the inner surface area of the vessel is ………………..
A) 308 cm²
B) 572 cm²
C) 672 cm²
D) 472 cm²
Answer:
B) 572 cm²

Question 22.
The radii of the base of cylinder and a cone are in the ratio of 3 : 4 and their heights are in the ratio of 2 : 3, then the ratio of the volumes is …………………….
A) 9 : 8
B) 9 : 4
C) 3 : 1
D) 27 : 64
Answer:
A) 9 : 8

Question 23.
A circus tent is cylindrical up to a height of 4 m and cone above it. If the diameter is 105 m and its slant height of cone is 40 m., then the total area of canvas required to built the tent is ……………..
A) 7920 m²
B) 7820 m²
C) 9720 m²
D) 2645 m²
Answer:
A) 7920 m²

Question 24.
An iron spherical ball of volume 232848 cm³ has been melted and converted into a cone with vertical angle of 120°. Then the height of the cone is
A) 42√3 cm
B) 42 cm
C) 21 cm
D) None
Answer:
A) 42√3 cm

Question 25.
If a cylinder and cone have bases of equal radii and are equal heights, then the ratio of their volumes is
A) 1 : 3
B) 2 : 3
C) 3 : 1
D) 3 : 2
Answer:
C) 3 : 1

Question 26.
If the curved surface area of a cone is 4070 cm² and its diameter is 70 cm, then its slant height is
A) 27 cm
B) 37 cm
C) 47 cm
D) 57 cm
Answer:
B) 37 cm

Question 27.
Under the usual notations, the total surface area of a cuboid is
A) lb + bh + hl
B) \(\frac{l \mathrm{~b}+\mathrm{bh}+\mathrm{h} l}{2}\)
C) 2(lb + bh + hl)
D) None
Answer:
C) 2(lb + bh + hl)

Question 28.
A joker’s cap is in the form of a right- circular cone whose base radius is 7 cm and height is 24 cm. The area of the sheet required to make 10 such caps is
A) 550 cm²
B) 5500 cm²
C) 55000 cm²
D) None
Answer:
B) 5500 cm²

Question 29.
A right-circular cylinder has base radius 14 cm and height 21 cm. The curved surface area is
A) 1848 cm²
B) 616 cm²
C) 3080 cm²
D) 12936 cm²
Answer:
A) 1848 cm²

Question 30.
The volume of the sphere of radius 21 cm is
A) 5544 cm³
B) 38808 cm³
C) 1155 cm³
D) 8983 cm³
Answer:
B) 38808 cm³

Question 31.
A sphere, a cylinder and a cone have the same radius and same height, then the ratio of their curved surface areas is
A) 2 : √3 : 4
B) 4 : 4 : √5
C) 3 : √5 : 4
D) None
Answer:
B) 4 : 4 : √5

Question 32.
The volume of the cone =
A) \(\frac {4}{3}\)πr²
B) \(\frac {1}{3}\)πr²h
C) πr²h
D) \(\frac {1}{2}\)πr²h
Answer:
B) \(\frac {1}{3}\)πr²h

Question 33.
If the diagonal of a cube ia 4√3, then the side of the cube is
A) 1
B) 2
C) 3
D) 4
Answer:
D) 4

Question 34.
If the volume of a hemisphere is 19404 cm3 then its radius is
A) 7
B) 14
C) 21
D) 28
Answer:
C) 21

Question 35.
A metallic sphere of radius 2 cm is melted to recast into the shape of a cylinder of radius 4 cm. Then the height of the cylinder is
A) \(\frac {1}{3}\) cm
B) \(\frac {4}{3}\) cm
C) \(\frac {2}{3}\) cm
D) 1 cm
Answer:
C) \(\frac {2}{3}\) cm

Question 36.
Three spheres of radii 6 cm, 1 cm and 8 cm are melted so as to form a single sphere. Then the radius of the new sphere is
A) 11 cm
B) 9 cm
C) 8 cm
D) 10 cm
Answer:
B) 9 cm

Question 37.
The radius and height of a right circular cone are 6 cm and 7 cm respectively. Then the volume of the cone is
A) 264 cu.cm
B) 300 cu.cm
C) 246 cu.cm
D) 256 cu.cm
Answer:
D) 256 cu.cm

Question 38.
Volume of a regular circular cylinder is ………….. cu. units.
A) πr²h
B) πrl
C) 2πrh
D) 2h(l + b)
Answer:
A) πr²h

Question 39.
Total surface area of cube is 54 cm² . Then its side is ………………… cm.
A) 6
B) 9
C) 12
D) 3
Answer:
D) 3

Question 40.
For a right circular cone with radius = r, height = h and slant height = l, which of the following is not true ?
A) Always l > h
B) Always l > r
C) Always r > π
D) l² = r² + h²
Answer:
C) Always r > π

Question 41.
Lateral surface area of a right circular cone = πrl, where ‘l’ is ……………….
A) height of the cone
B) diameter of the cone
C) slant height of the cone
D) none of these
Answer:
C) slant height of the cone

Question 42.
The length, breadth and height of a room are 8 m, 6.5 m and 3.5 m respectively. Then the volume of air contained in the room is
A) 162 m³
B) 172 m³
C) 182 m³
D) 192 m³
Answer:
C) 182 m³

Question 43.
The diagonal of the cuboid with dimensions 9cm × 12cm × 20cm is ……………….
A) 41 cm
B) 32 cm
C) 25 cm
D) 21 cm
Answer:
C) 25 cm

Question 44.
Total Surface Area of the cuboid with dimensions 8 cm × 4 m × 2 cm is
A) 158 cm²
B) 112 cm²
C) 320 cm²
D) 191 cm²
Answer:
B) 112 cm²

Question 45.
The volume of a cuboid is 440 cm³ and the area of its base is 88 cm², then its height is ………………. m.
A) 4
B) 5
C) 6
D) 7
Answer:
B) 5

Question 46.
Volume of the cube is 125 m³, then its side is ………………… cm.
A) 12
B) 6
C) 5
D) 10
Answer:
C) 5

Question 47.
Total Surface Area (TSA) of cube is 2400 cm2, then its side is ……………. cm.
A) 80
B) 60
C) 40
D) 20
Answer:
D) 20

Question 48.
Edge of a cube is 2 cm then Lateral Surface Area (LSA) is ……………….. cm².
A) 13
B) 31
C) 61
D) 16
Answer:
D) 16

Question 49.
Total Surface Area of a cube whose side is 0.5 cm is ………………..
A) \(\frac {1}{4}\) cm²
B) \(\frac {1}{8}\) cm²
C) \(\frac {3}{4}\) cm²
D) \(\frac {3}{2}\)cm²
Answer:
D) \(\frac {3}{2}\)cm²

Question 50.
The volume of a cube is 27 cm³, then its surface area is
A) 36cm²
C) 64 cm²
B) 54 cm²
D) 82 cm²
Answer:
B) 54 cm²

Question 51.
The radius of a conical tent is 7 m and its height is 10 m. Then the slant height of the cone is ………………..
A) 11.2 m
B) 10.2 m
C) 12.2 m
D) 14.2 m
Answer:
C) 12.2 m

Question 52.
The volume of a cone is 462 cm³. Its base radius is 7 cm then its height is ……………… cm.
A) 10.3
B) 7
C) 8
D) 9
Answer:
D) 9

Question 53.
Height of the cone is 15 cm, slant height is 17 cm, then radius of the cone is ………………… cm.
A) 8
B) 10
C) 16
D) 14
Answer:
A) 8

Question 54.
In a cone, Lateral Surface Area (LSA) is …………….. if slant height and radius of the base are 25 cm and 7 cm respectively.
A) 450 cm²
B) 550 cm²
C) 650 cm²
D) 150 \(\frac {1}{7}\) cm²
Answer:
B) 550 cm²

Question 55.
The slant height of a cone is 10 cm and radius of the base is 7 cm, then Total Surface Area (TSA) = …………….. cm².
A) 374
B) 478
C) 474
D) 378
Answer:
A) 374

Question 56.
The area of the base of a right circular cone is 78.5 cm². If its height is 12 cms, then its volume is ………………. cm³.
A) 31.4
B) 314
C) 304
D) 404
Answer:
B) 314

Question 57.
The diameter of the base of a right circular cylinder is 14 cm and its height is 20 cm. Then its curved surface area is
A) 594 cm²
B) 1188 cm²
C) 440 cm²
D) 1540 cm²
Answer:
B) 1188 cm²

Question 58.
A solid iron rod has a cylindrical shape. Its height is 10 cm and base radius is 7 cm. Then volume of the.rod is
A) 1640 cm³
B) 1740 cm³
C) 1440 cm³
D) 1540 cm³
Answer:
D) 1540 cm³

Question 59.
The volume of a cylinder is 49,896 cm³ and its curved surface area is 4752 sq.cm. Then its radius is ……………… cm.
A) 12.3
B) 10
C) 21
D) 13.7
Answer:
C) 21

Question 60.
The ratio of the radius and height of a cylinder is 3 : 2. The radius is 21 cm, then Lateral Surface Area (LSA) = ………………… cm³
A) 2043
B) 1949
C) 1848
D) 1948
Answer:
C) 1848

Question 61.
In a cylinder d = 40 cm, h = 56 cm, then Curved Surface Area (CSA) = ……………. cm³.
A) 7040
B) 6040
C) 4040
D) 3040
Answer:
A) 7040

Question 62.
Volume of cylindrical bottle is 88 cm³, radius is 2 cm, then h = ……………… cm
A) 12
B) 10
C) 9
D) 7
Answer:
D) 7

Question 63.
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio of 5 : 3. Then the ratio of their volumes is ………………
A) 4 : 9
B) 9 : 4
C) 20 : 27
D) 27 : 20
Answer:
C) 20 : 27

Question 64.
The ratio of volumes of a cone and a cylinder whose diameters And heights are equal is
A) 3 : 1
B) 1 : 2
C) 2 : 1
D) 1 : 3
Answer:
D) 1 : 3

Question 65.
The length of equator on the globe is 88 cm, then r is ……………………..
A) 12 cm
B) 10 cm
C) 16 cm
D) 14 cm
Answer:
D) 14 cm

Question 66.
Two spheres are of radii in the ratio 3 : 5, then ratio of their surface areas is
A) 16 : 1
B) 25 : 9
C) 9 : 16
D) 9 : 25
Answer:
D) 9 : 25

Question 67.
If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, then the diameter of the sphere is ………………….
A) 12 cm
B) 16 cm
C) 20 cm
D) 24 cm
Answer:
D) 24 cm

Question 68.
The surface areas of two spheres are in the ratio 1:4, then the ratio of their volumes is …………………
A) 1 : 8
B) 1 : 64
C) 1 : 12
D) 1 : 16
Answer:
B) 1 : 64

Question 69.
Surface area of a sphere is 576π cm², then volume is ……………….
A) 2304 π cm³
B) 1403 π cm³
C) 3404 π cm³
D) 4010 π cm³
Answer:
A) 2304 π cm³

Question 70.
The outer and inner radii of a hemisphere are 3 cm and 2 cm, then Total Surface Area (TSA) is ……………….. cm²
A) 9.7
B) 97 \(\frac {3}{7}\)
C) 96 \(\frac {1}{2}\)
D) 16 \(\frac {1}{4}\)
Answer:
B) 97 \(\frac {3}{7}\)

Question 71.
The surface area of sphere is 550 cm². Its radius is ………………
A) 6.6 cm
B) 5.6 cm
C) 5.5 cm
D) 7.6 cm
Answer:
A) 6.6 cm

Question 72.
Volume of the possible biggest cylinder that can be made of a cube of side 14 cm is …………………… (in cm³)
A) 2156
B) 1078
C) 539
D) 428
Answer:
A) 2156

Question 73.
Height of a cylindrical iron rod is four times to its radius of the base. If it is melted and recast into spherical balls, number of balls thus formed
A) 4
B) 3
C) 2
D) 1
Answer:
B) 3

Question 74.
If a cuboid of dimensions 49 cm × 33 cm × 24 cm is melted and recast into a sphere, then radius of the sphere is
A) 24 cm
B) 21 cm
C) 18 cm
D) 13 cm
Answer:
B) 21 cm

Question 75.
Volume of the possible biggest cone that can be made out of a cube of side 4.2 cm is …………………. (in cm³)
A) 19.4
B) 14.6
C) 9.7
D) 8.4
Answer:
A) 19.4

Question 76.
The diameter of a metallic sphere is 6 cm. It is melted and drawn into a wire having diameter as 2 cm. Then the length of the wire (in cm) ………………….
A) 48
B) 12
C) 36
D) 24
Answer:
C) 36

Question 77.
In a cuboid if l = b = h, then it is a
A) cone
B) cube
C) cylinder
D) sphere
Answer:
B) cube

Question 78.
The base of a cone is ……………….
A) hemisphere
B) sphere
C) circle
D) square
Answer:
C) circle

Question 79.
The volume of cone of diameter’d’ and height ‘h’ is ………………. units³.
A) \(\frac{\pi \mathrm{d}^{2}}{2}\)
B) \(\frac{\pi d^{2} h}{12}\)
C) \(\frac{\pi \mathrm{dh}^{2}}{12}\)
D) \(\frac{\pi d^{2}}{12}\)
Answer:
B) \(\frac{\pi d^{2} h}{12}\)

Question 80.
Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. Then the ratio of their volumes is …………………
A) 3 : 1
B) 1 : 4
C) 1 : 3
D) 1 : 9
Answer:
A) 3 : 1

Question 81.
The vertical cross section of a cone is …………………
A) right triangle
B) scalene triangle
C) isosceles triangle
D) circle
Answer:
C) isosceles triangle

Question 82.
The horizontal cross section of a cylinder is
A) rectangle
B) square
C) circle
D) triangle
Answer:
C) circle

Question 83.
The vertical cross section of a cylinder is
A) rectangle
B) square
C) circle
D) right triangle
Answer:
A) rectangle

Question 84.
If ‘d’ is the diameter of a sphere, then its volume is …………………
A) \(\frac {2}{3}\)πd³
B) \(\frac {1}{6}\)πd³
C) \(\frac {4}{3}\)πd³
D) \(\frac {1}{24}\)πd³
Answer:
B) \(\frac {1}{6}\)πd³

Question 85.
In what ratio are the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height
A) 1 : 3 : 2
B) 2 : 3 : 1
C) 3 : 1 : 2
D) 3 : 2 : 1
Answer:
C) 3 : 1 : 2

Question 86.
The surface area of a sphere 4 cm its diameter is ……………………
A) 16 πcm²
B) 23 π cm²
C) 64 π cm²
D) 12 π cm²
Answer:
A) 16 πcm²

Question 87.
The radius of a hemisphere is 7 cm, then its surface area is ………………….. cm²
A) 10
B) 150
C) 300
D) 462
Answer:
D) 462

Question 88.
The internal and external radii of a hemispherical bowl are r₁ and r₂ respectively. Then the surface area of the bowl is …………………..
A) 2π(r₁² + r₂²)
B) π(r₁² + r₂²)
C) π(r₁² – r₂²)
D) 2π(r₁² – r₂²)
Answer:
A) 2π(r₁² + r₂²)

Question 89.
If the radius of a cylinder is doubled and its height remains unchanged, then its curved surface area is increased by times.
A) 2
B) 3
C) half
D) unchange
Answer:
B) 3

Question 90.
If a cone and a hemisphere have bases of equal radii, then its ratio of volumes is …………………
A) 2 : 1
B) 3 : 1
C) 4 : 1
D) 1 : 1
Answer:
A) 2 : 1

Question 91.
From a wooden cube of side Y cm, a right circular cylinder of maximum volume is cut. Then the volume of this cylinder is ………………. cm³.
A) \(\frac {1}{3}\)πX³
B) πX³
C) \(\frac{\pi}{4}\)X³
D) \(\frac {4}{3}\) πX³
Answer:
C) \(\frac{\pi}{4}\)X³

Question 92.
Three shots are made by melting a solid metallic sphere of radius 6 cm. If the radii of the two spheres are 3 cm and 4 cm respectively, then the radius of the third shot is ………………… cm.
A) 5
B) 2
C) 4
D) 3
Answer:
A) 5

Question 93.
The volume and the surface area of a sphere are numerically the same. Then the volume of the smallest cylinder in which the sphere is exactly kept is
A) 18π
B) 54π
C) 27π
D) 36π
Answer:
B) 54π

Question 94.
Lateral Surface Area of four walls of a room is ……………….. sq.units
A) 2h(l + b)
B) 2(l + b)
C) h(l + b)
D) 2 lbh
Answer:
A) 2h(l + b)

Question 95.
The radius of the base and height of a right circular cone are 9 cm and 15 cm respectively. Then volume of the cone is …………………. cm³.
A) 405 π
B) 1215 π
C) 81 π
D) 225 π
Answer:
A) 405 π

Question 96.
The heights of two cylinders are equal. The radii are R and r. Then the ratio of their volumes is
A) R² : r²
B) R : r³
C) R : r²
D) R² : r
Answer:
A) R² : r²

Question 97.
The volume of a sphere of radius ‘r’ is obtained by multiplying its surface area by
A) \(\frac{4}{3}\)
B) \(\frac{\mathrm{r}}{3}\)
C) \(\frac{4 r}{3}\)
D) 3r
Answer:
B) \(\frac{\mathrm{r}}{3}\)

Question 98.
The ratio between the volumes of a sphere and a cylinder, if in cylinder, height is equal to the radius of base is ………………….
A) 3 : 1
B) 1 : 3
C) 3 : 4
D) 4 : 3
Answer:
D) 4 : 3

Question 99.
A solid sphere of radius ‘r’ is melted and cast into the shape of a solid cone of height ‘r’. The radius of the base of the cone is
A) 2r
B) 3r
C) 4r
D) 6r
Answer:
A) 2r

Question 100.
If a metallic sphere of radius ‘r’ is melted and recast into a metallic cone of height V units, then radius of the cone is …………………..
A) 2r
B) r
C) 3r
D) 4r
Answer:
A) 2r

Question 101.
To find out quantity of water inside a bottle, we measure
A) surface area
B) total surface area
C) volume
D) base area
Answer:
C) volume

Question 102.
To find out canvas needed for making a tent, we measure
A) area
B) volume
C) base area
D) radius of the base
Answer:
A) area

Question 103.
Geometry box is an example of
A) sphere
B) cone
C) cube
D) cuboid
Answer:
D) cuboid

Question 104.
Chalk-box is an example of
A) sphere
B) cone
C) cube
D) cuboid
Answer:
C) cube

Question 105.
If the radius of the base of a right circular cylinder is halved, keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of the original cylinder is
A) 2 : 1
B) 1 : 2
C) 4 : 1
D) 1 : 4
Answer:
C) 4 : 1

Question 106.
The ratio of volumes of a cone and a cylinder whose radii and height are equal is
A) 3 : 1
B) 1 : 3
C) 1 : 2
D) 1 : 1
Answer:
B) 1 : 3

Question 107.
The radii of two spheres are in the ratio 2 : 3, then the ratio of their surface areas is ……………..
A) 3 : 2
B) 27 : 8
C) 8 : 27
D) 4 : 9
Answer:
D) 4 : 9

Question 108.
A cylinder, a cone and a hemisphere have bases of equal radii and are of equal heights. Then the ratio of their volumes is ………………
A) 3 : 1 : 2
B) 3 : 2 :1
C) 1 : 2 : 3
D) 1 : 3 : 2
Answer:
A) 3 : 1 : 2

Question 109.
Ratio between the volume of a cone and a cylinder is ……………………
A) 3 : 1
B) 1 : 3
C) 1 : 1
D) 4 : 1
Answer:
B) 1 : 3

Question 110.
The ratio between the surface area of sphere and hemisphere is ………………
A) 3 : 1
B) 1 : 3
C) 4 : 3
D) 3 : 4
Answer:
C) 4 : 3

Question 111.
In the adjacent figure, l is called

A) length
B) height
C) slant height
D) volume
Answer:
C) slant height

Question 112.
Identify cuboid from the following

Answer:

Question 113.
Identify the shapes in the funnel
A) Cone, Circle
B) Cylinder, Rectangle
C) Cone, Cylinder
D) Sphere, Cylinder
Answer:
C) Cone, Cylinder

Question 114.
Which of the following item is in spherical shape ?
A) Laddu
B) Cricket Ball
C) Foot Ball
D) All the above
Answer:
D) All the above

Practice the AP 10th Class Maths Bits with Answers Chapter 9 Tangents and Secants to a Circle on a regular basis so that you can attempt exams with utmost confidence.

AP State Syllabus 10th Class Maths Bits 9th Lesson Tangents and Secants to a Circle with Answers

Question 1.
The number of parallel tangents of a circle with a given tangent is
A) 1
B) 2
C) 0
D) infinite
Answer:
A) 1

Question 2.
PA and PB are two tangents drawn to a circle with centre O from an external point P. If ∠APB = 30°, then ∠AOB =
A) 60°
B) 90°
C) 70°
D) 150°
Answer:
D) 150°

Question 3.
Radius of a circle with centre ‘O’ is 5 cm. P is a point at a distance of 3 cm from ‘O’. Then the number of tangents that can be drawn to the circle is ………………
A) 1
B) 2
C) 0
D) 3
Answer:
C) 0

Question 4.
Angle made by the minutes – hand in a clock during a period of 20 minutes is ……………….
A) 120°
B) 20°
C) 360°
D) 90°
Answer:
A) 120°

Question 5.
From the adjacent figure, ∠APB = 40°, then ∠AOB = ……………….

A) 110°
B) 140°
C) 80°
D) 160°
Answer:
B) 140°

Question 6.
The length of a tangent to a circle from a point P is 12 cm and the radius of the circle is 5 cm, then the distance from point P to the centre of the circle is ……………..
A) 11 cm
B) 10 cm
C) 13 cm
D) 14 cm
Answer:
C) 13 cm

Question 7.
Perimeter of a sector is ………………….. units.
A) \(\frac{l \mathrm{r}}{2}\)
B) \(\frac{\mathbf{x}^{0}}{360^{0}}\) × πr²
C) 2 (l + r)
D) l + 2r
Answer:
D) l + 2r

Question 8.
Angle of a sector is 60° and radius is 14 cm, then its area is ……………….. cm².
A) 100.6
B) 102.67
C) 111.6
D) 98.66
Answer:
B) 102.67

Question 9.
The longest chord in a circle is …………………
A) diameter
B) radius
C) arc
D) perimeter
Answer:
A) diameter

Question 10.
A circle can have …………….. parallel tangents.
A) 1
B) 3
C) 2
D) 4
Answer:
C) 2

Question 11.
How many tangent lines can be drawn to a circle from a point outside the circle?
A) 1
B) 2
C) 3
D) 4
Answer:
B) 2

Question 12.
Two circles with centres A and B touches each other at the point C. If AC = 8 cm and AB = 3 cm, then area of shaded region is…………………..

A) 13π
B) 5π
C) 39π
D) 8π
Answer:
C) 39π

Question 13.
The C.S.A. and T.S.A. of a cylinder are in the ratio 2 : 3. Its T.S.A. is 924 cm² then
its volume is ……………….. cm³.
A) 2156
B) 1256
C) 1265
D) 2516
Answer:
A) 2156

Question 14.
The minutes hand of a clock length is 10.5 cm. Then area swept by it in 10 minutes is ……………….. cm².
A) 115.5
B) 57.75
C) 11.55
D) 575.5
Answer:
B) 57.75

Question 15.
Two circles of radius 15 cm and 13 cm intersect at A and B, such that \(\overline{\mathbf{A B}}\) = 24 cm. The distance between their centres is …………… cm
A) 28
B) 14
C) 18
D) 16
Answer:
B) 14

Question 16.
The distance between the two parallel tangents of a circle whose radius is 12 cm is ………………. cm.
A) 14
B) 24
C) 28
D) 36
Answer:
B) 24

Question 17.
The end points of diameter of a circle are (2, 4) and (-3, -1). The radius of the circle is ……………..
A) \(\frac{5 \sqrt{2}}{2}\)
B) 5√2
C) 3√2
D) \(\frac{5 \sqrt{2}}{\pm 2}\)
Answer:
A) \(\frac{5 \sqrt{2}}{2}\)

Question 18.
The area of a circle is 220 cm². Then the area of square inscribed in it is……………..
A) 49 cm²
B) 70 cm²
C) 140 cm²
D) 150 cm²
Answer:
C) 140 cm²

Question 19.
Area of segment of a circle …………………….
A) area of sector
B) area of corresponding sector / area of corresponding triangle
C) 2(l + r)
D) area of segment sector + πr²
Answer:
B) area of corresponding sector / area of corresponding triangle

Question 20.
If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to
A) 60°
B) 70°
C) 80°
D) 90°
Answer:
B) 70°

Question 21.
What is the area of the shaded region in the figure ? In which two circles with centres A and B touch each other at the point C, if AC = 8 cm and AB = 3 cm, is

A) 24π cm²
B) 39π cm²
C) 11π cm²
D) 57π cm²
Answer:
A) 24π cm²

Question 22.
If all the sides of a parallelogram touch a circle, then the parallelogram is
A) a square
B) a rhombus
C) a rectangle
D) None
Answer:
C) a rectangle

Question 23.
PQ is chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Then the length of TP is
A) \(\frac{10}{3}\)cm
B) \(\frac{25}{3}\)cm
C) \(\frac{20}{3}\)cm
D) \(\frac{16}{3}\)cm
Answer:
D) \(\frac{16}{3}\)cm

Question 24.
The number of circles passing through three collinear points in a plane is
A) 1
B) 0
C) 9
D) 12
Answer:
B) 0

Question 25.
The number of pairs of parallel tangents to a circle is
A) 2
B) 4
C) 1
D) infinitely many
Answer:
D) infinitely many

Question 26.
The length of the tangent to a circle with centre O and radius = 6 cm from a point P outside tlie circle such that OP = 10 cm is
A) 6 cm
B) 8 cm
G) 4 cm
D) 5 cm
Answer:
B) 8 cm

Question 27.
If PA and PB are the lengths of tangents drawn from an external point P to a circle, then
A) PA ≠ PB
B) PA > PB
C) PA < PB
D) PA = PB
Answer:
D) PA = PB

Question 28.
The area of the sector, whose radius is 7 cm with angle 60°, is
A) 52.66 cm²
B) 25.66 cm²
C) 62.56 cm²
D) 65.62 cm²
Answer:
B) 25.66 cm²

Question 29.
In the adjacent figure, x =

A) 5.8 cm
B) 6.8 cm
C) 4.8 cm
D) 3.8 cm
Answer:
C) 4.8 cm

Question 30.
In the figure, x =

A) 100°
B) 90°
C) 110°
D) 80°
Answer:
A) 100°

Question 31.
How many tangents can be drawn to a circle from a point outside the circle ?
A) 1
B) 2
C) 3
D) None
Answer:
B) 2

Question 32.
A secant intersects the circle at ……………… point (s).
A) single
B) two
C) three
D) none
Answer:
B) two

Question 33.
The tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Then the length of the tangent is

A) 13 cm
B) \(\sqrt{119}\) cm
C) 14 cm
D) 11 cm
Answer:
B) \(\sqrt{119}\) cm

Question 34.
A parallelogram circumscribing a circle is a
A) trapezium
B) rhombus
C) square
D) rectangle
Answer:
B) rhombus

Question 35.
If the radius of a circle is 4 cm and the sector angle is 30°, then the area of the sector is
A) \(\frac{3 \pi}{4}\)sq.cm
B) 3π\(\)
C) 4π sq.cm
D) \(\frac{4 \pi}{3}\)sq.cm
Answer:
D) \(\frac{4 \pi}{3}\)sq.cm

Question 36.
In the figure below, which of the following are tangents to the circle?

A) A, B, C
B) A, D
C) A, C
D) A, B, D
Answer:
C) A, C

Question 37.
In the figure below, OP = 3 cm and OB = 5 cm. Then AB =

A) 8 cm
B) 9 cm
C) 4 cm
D) 10 cm
Answer:
A) 8 cm

Question 38.
In the figure if ∠APB = 60° and OP = 10 cm, then PA = …………….. cm

A) 5
B) 5√2
C) 5√3
D) 20
Answer:
C) 5√3

Question 39.
The angle between a tangent to a circle and the radius drawn at the point of contact is ………………
A) 60°
B) 30°
C) 45°
D) 90°
Answer:
D) 90°

Question 40.
A line which intersects the given circle at two distinct points is called a
A) tangent
B) transversal
C) direct line
D) secant
Answer:
D) secant

Question 41.
The number of pair of tangents can be drawn to a circle, which are parallel to each other, are ……………….
A) 0
B) 2
C) 4
D) infinite
Answer:
B) 2

Question 42.
The number of tangents that can be drawn to a circle from an external point is ……………….
A) 0
B) 3
C) 2
D) 1
Answer:
C) 2

Question 43.
If PA and PB are tangents to a circle of radius 5 cm, then their lengths are ……………. cm.
A) 5, 13
B) 13, 13
C) 12, 12
D) 13, 12
Answer:
C) 12, 12

Question 44.
The angle between a tangent and the radius drawn at the point of contact is
A) 60°
B) 30°
C) 90°
D) 45°
Answer:
C) 90°

Question 45.
From a point Q, the length of the tangent to a circle is 24 cm, and the distance of Q from the centre is 25 cm, then the radius of the circle is
A) 7 cm
B) 12 cm
C) 15 cm
D) 24 .5 cm
Answer:
A) 7 cm

Question 46.
The length of the tangent drawn from a point 17 cm away from the centre of a circle of radius 8 cm is
A) 25 cm
B) 9 cm
C) 15 cm
D) 8.5 cm
Answer:
C) 15 cm

Question 47.
If the length of a tangent to a circle of radius 6 cm is 8 cm, then the distance from which the tangent is drawn to the centre of the circle is
A) 7 cm
B) 8 cm
C) 9 cm
D) 10 cm
Answer:
D) 10 cm

Question 48.
Two concentric circles are of radii 5 cm and 3 cm. Length of the chord of the larger circle which touches the smaller circle is
A) 8 cm
B) 5 cm
C) 7. 5 cm
D) 9 cm
Answer:
A) 8 cm

Question 49.
If tangents PA and PB from a point P to a circle with centre ‘O’ are inclined to each other at angle of 80°, then ∠POA =
A) 50°
B) 60°
C) 70°
D) 80°
Answer:
A) 50°

Question 50.
AP and AQ are two tangents of a circle with centre ‘O’ and ∠POQ = 60°, then ∠OPQ =
A) 30°
B) 45°
C) 60°
D) 90°
Answer:
C) 60°

Question 51.
If two tangents to a circle of radius 3 cm are inclined to each other at angle of 60°, then length of each tangent =
A) 6 cm
B) 3√3 cm
C) 3 cm
D) \(\frac{3 \sqrt{3}}{4}\)cm
Answer:
B) 3√3 cm

Question 52.
The area of a sector of a circle of radius 7 cm and central angle 60° is …………………….
A) \(\frac{77}{3}\)
B) \(\frac{77}{6}\)
C) \(\frac{77}{9}\)
D) \(\frac{154}{5}\)
Answer:
A) \(\frac{77}{3}\)

Question 53.
In the figure if BP = 5cm,QC = 7cm and AR = 6 cm, then AB + BC + CA =

A) 18 cm
B) 36 cm
C) 25 cm
D) 30 cm
Answer:
B) 36 cm

Question 54.
The parallelogram circumscribing a circle is a ……………………
A) Trapezium
B) Triangle
C) Rectangle
D) Square
Answer:
C) Rectangle

Question 55.
Cyclic rhombus is a …………………
A) Parallelogram
B) Square
C) Trapezium
D) Rectangle
Answer:
B) Square

Question 56.
In the adjacent figure if quadrilateral PQRS circumscribes a circle, then PB + SD =

A) SR
B) PR
C) QS
D) PS
Answer:
D) PS

Question 57.
In the figure ∠AOB =

A) 80°
B) 90°
C) 100°
D) 20°
Answer:
B) 90°

Question 58.
In the figure ∠ACB =
A) 60°
B) 80°
C) 90°
D) 45°
Answer:
C) 90°

Question 59.
The set of all points which are equidistant from a fixed point is called a
A) line
B) ray
C) circle
D) triangle
Answer:
C) circle

Question 60.
The line segment joining any two points oq a circle is called
A) radius
B) diameter
C) chord
D) tangent
Answer:
C) chord

Question 61.
The set of all points which are equidistant from a fixed point is a circle, then the fixed distance is called
A) diameter
B) radius
Cj centre
D) chord
Answer:
B) radius

Question 62.
A line meeting a circle only in one point is called a
A) secant
B) tangent
C) chord
D) arc
Answer:
B) tangent

Question 63.
A line, which intersects a circle in two distinct points, is called
A) secant
B) tangent
C) chord
D) arc
Answer:
A) secant

Question 64.
The point at which the tangent touches the circle is called
A) point of intersection
B) centre of the circle
C) point of contact
D) external point of the circle
Answer:
C) point of contact

Question 65.
Number of tangents that can be drawn at point on a circle is
A) 1
B) 2
C) 3
D) infinite
Answer:
A) 1

Question 66.
Number of tangents that can be drawn through a point inside a circle is
A) 0
B) 1
C) 2
D) infinite
Answer:
A) 0

Question 67.
How many tangents a circle can have?
A) 1
B) 2
C) 0
D) infinite
Answer:
D) infinite

Question 68.
Number of parallel tangents that a circle can have at the most is
A) 1
B) 2
C) 3
D) infinite
Answer:
B) 2

Question 69.
A line drawn through the end of a radius and perpendicular to it, is a …………….. to the circle.
A) secant
B) tangent
C) chord
D) arc
Answer:
D) arc

Question 70.
The tangent at any point of a circle is to the …………………. radius through the point of contact.
A) equal
B) similar
C) parallel
D) perpendicular
Answer:
D) perpendicular

Question 71.
The length of a tangent from a point d cm away from the centre of a circle of radius ‘r’ is
A) \(\sqrt{d^{2}-r^{2}}\)
B) \(\sqrt{\mathrm{d}^{2}+\mathrm{r}^{2}}\)
C) \(\sqrt{\mathrm{dr}}\)
D) \(\sqrt{\mathrm{d}+\mathrm{r}}\)
Answer:
A) \(\sqrt{d^{2}-r^{2}}\)

Question 72.
Two concentric circles are of radii a and b (a>b). Length of the chord of the larger circle which touches the small circle is
A) 2\(\sqrt{a^{2}-b^{2}}\)
B) \(\sqrt{a^{2}-b^{2}}\)
C) 2\(\sqrt{a^{2}+b^{2}}\)
D) \(\sqrt{a^{2}+b^{2}}\)
Answer:
A) 2\(\sqrt{a^{2}-b^{2}}\)

Question 73.
If AP and AQ are two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PAQ = ………………..
A) 60°
B) 70°
C) 80°
D) 90°
Answer:
B) 70°

Question 74.
The shaded portion represents

A) Minor segment
B) Major segment
C) Centre
D) Sector
Answer:
A) Minor segment

Question 75.
Number of chords of a circle is
A) 1
B) 2
C) 3
D) infinite
Answer:
D) infinite

Question 76.
Number of tangents that can be drawn from outside the circle is
A) 0
B) 1
C) 2
D) infinite
Answer:
C) 2

Question 77.
The distance between two parallel tangents to a circle of diameter 8 cm is
A) 8
B) 6
C) 4
D) 2
Answer:
A) 8

Question 78.
The limit of a secant line of a circle is
A) chord
B) diameter
C) tangent
D) secant
Answer:
A) chord

Question 79.
A tangent PA touches a circle with centre ‘O’ at A, then
A) ∠OPA = 90°
B) ∠POA = 90°
C) ∠OAP = 45°
D) ∠OAP = 90°
Answer:
D) ∠OAP = 90°

Question 80.

In the figure XY and XY are two parallel tangents to a circle with centre ‘O’ and other tangent AB with point of contact ‘C’ intersecting XY at A and X’Y’ at B, then ∠AOB =
A) 80°
B) 100°
C) 90°
D) 60°
Answer:
C) 90°

Question 81.
Two tangents TP and TQ are drawn to a circle with centre ‘O’ from an external point T. The ∠PTQ =
A) ∠OPQ
B) 2∠OPQ
C) ∠POQ
D) 2∠POQ
Answer:
B) 2∠OPQ

Question 82.
In the adjacent figure PA and PB are tangents to a circle with centre ‘O’ then ∠OPA =

A) 45°
B) 50°
C) 70°
D) 35°
Answer:
A) 45°

Question 83.
In the adjacent figure if PA = 4 cm, BP = 3 cm and AC = 11 cm then BC =

A) 15 cm
B) 14 cm
C) 7 cm
D) 10 cm
Answer:
D) 10 cm

Question 84.
In the figure AB = 4cm, then BC = ……………….. cm
A) 6
B) 4
C) 2
D) 8
Answer:
C) 2

Question 85.
In the figure diametre of smaller circle is (in cms)

A) 4
B) 2
C) 1
D) 5
Answer:
C) 1

Practice the AP 10th Class Maths Bits with Answers Chapter 8 Similar Triangles on a regular basis so that you can attempt exams with utmost confidence.

AP State Syllabus 10th Class Maths Bits 8th Lesson Similar Triangles with Answers

Question 1.
In ΔABC, E and F are the points on the sides AB and AC respectively.
If AE = 2 cm, EB = 2.5 cm, AF = 4 cm and FC = 5 cm, then
A) EF ⊥ BC
B) EF ⊥ AB
C) EF || BC
D) EF || AB
Answer:
C) EF || BC

Question 2.
From the given figure, the value represented by ‘x’ is …………………

A) 12 cm
B) 11 cm
C) 13 cm
D) 16 cm
Answer:
C) 13 cm

Question 3.
From the given figure, ar (ΔADE): ar (ΔABC) =

A) 25 : 9
B) 9 : 64
C) 25 : 64
D) 9 : 25
Answer:
B) 9 : 64

Question 4.
The altitude of an equilateral triangle of side ‘x’ cm is
A) \(\frac{\sqrt{3}}{2}\) x
B) \(\frac{2}{\sqrt{3}}\) x
C) \(\frac{\sqrt{3}}{4}\) x²
D) \(\frac{\sqrt{3}}{2}\) x²
Answer:
A) \(\frac{\sqrt{3}}{2}\) x

Question 5.
Areas of two similar triangles are 100 cm² and 64 cm². If the median of bigger triangle is 10 cm, then the median of the smaller triangle is …………………..
A) 10 cm
B) 6 cm
C) 4 cm
D) 8 cm
Answer:
D) 8 cm

Question 6.
If ΔPQR ~ ΔXYZ and ∠X= 30°, ∠Q=50°, then ∠Z = ………………….
A) 100°
B) ∠R
C) both A and B
D) not known
Answer:
C) both A and B

Question 7.
From the given figure, x = ……………….

A) 3
B) 2
C) 5
D) 1
Answer:
A) 3

Question 8.
In Heron’s formula, area of triangle = \(\sqrt{\mathbf{S ( S – a ) ( S – b ) ( S – c )}}\), S is ……………… of the triangle.
A) Perimeter
B) Height
C) Half of perimeter
D) None
Answer:
C) Half of perimeter

Question 9.
In Δ ABC with ∠A = 90°; from A, perpendicular AD is drawn on BC. Which one of the following is not correct?
A) ∠A = ∠B
B) Δ DAC ~ Δ DBA
C) Δ ABC ~ Δ DBA
D) Δ ABC ~ Δ DBA ~ Δ DAC .
Answer:
A) ∠A = ∠B

Question 10.
If Δ PQR – ΔXYZ, QR = 3 cm, YZ = 4 cm, ar ΔPQR= 54 cm², then ar ΔXYZ = ………………
A) 13.5 cm²
B) 46 cm²
C) 96 cm²
D) 12 cm²
Answer:
C) 96 cm²

Question 11.
In the adjacent figure, AB = 3 cm, AC = 8 cm, BE = 4.5 cm, then CD = ………………..

A) 10.5 cm
B) 9.5 cm
C) 16 cm
D) 12 cm
Answer:
D) 12 cm

Question 12.
If ΔABC ~ ΔDEF and area (ΔABC) : area (ΔDEF) = 49 : 100. Then DE : AB = ………………….
A) 9 : 10
B) 10 : 7
C) 10 : 9
D) 7 : 10
Answer:
B) 10 : 7

Question 13.
In ΔABC, \(\overline{\mathrm{DE}} \| \overline{\mathrm{BC}}\) and \(\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{3}{5}\) ,AC = 5.6, then AE =
A) 1.8 cm
B) 3.5 cm
C) 1.2 cm
D) 2.1 cm
Answer:
D) 2.1 cm

Question 14.
ΔABC ~ ΔPQR, ∠A = 50°, then ∠Q + ∠R =
A) 120°
B) 110°
C) 130°
D) 80°
Answer:
C) 130°

Question 15.
Area of regular hexagon of side ‘a’ units is …………….. sq. units
A) \(\frac{6 \sqrt{3}}{4}\) a
B) \(\frac{6 \sqrt{3}}{7}\) a²
C) \(\frac{6 \sqrt{3}}{2}\) a²
D) \(\frac{6 \sqrt{3}}{4}\) a²
Answer:
D) \(\frac{6 \sqrt{3}}{4}\) a²

Question 16.
If ΔABC ~ ΔDEF, BC = 4 cm, EF = 5 cm area of ΔABC = 80 cm², then area of
ΔDFF = ……………. cm².
A) 64
B) 125
C) 144
D) 169
Answer:
B) 125

Question 17.
In a square, the diagonal is ……………… times of its side.
A) √7
B) √3
C) √2
D) 2
Answer:
C) √2

Question 18.
In a quadrilateral ABCD, if AB = CD, BC = AD and AC ≠ BD, then ABCD is ………………
A) parallelogram
B) trapezium
C) rhombus
D) square
Answer:
A) parallelogram

Question 19.
In ΔPQR, ∠R = 90° then hypotenuse is …………………..
A) PQ
B) PR
C) RP
D) PP
Answer:
A) PQ

Question 20.
ΔABC ~ ΔDEF if ∠E + ∠F = 130° then ∠A = …………………..
A) 60°
B) 70°
C) 80°
D) 50°
Answer:
D) 50°

Question 21.
The length of the diagonal of a square is 7√2 cm, then the area of the square is …………….cm².
A) 28
B) 14√2
C) 21
D) 49
Answer:
D) 49

Question 22.
In the given figure DE || BC and AE : EC = 4 : 7, then BC: DE = ………………

A) 11 : 4
B) 4 : 11
C) 11 : 3
D) 3 : 11
Answer:
A) 11 : 4

Question 23.
In a equilateral triangle ABC, D is a point on side BC, such that BD = \(\frac {1}{3}\) BC.
Then 9 AD² = ………………
A) 3AB²
B) 5AB²
C) 7AB²
D) 4AB²
Answer:
C) 7AB²

Question 24.
The angles of a triangle are 30°, 60° and 90°. The ratio of its sides is ……………
A) 1 : 2 : √3
B) 1 : √3 : 2
C) √3 : 1 : 2
D) 1 : 2 : 3
Answer:
B) 1 : √3 : 2

Question 25.
In a equilateral triangle ABC, if AD ⊥ BC, then …………………..
A) 5AB² = 4AD²
B) 3AB² = 4AD²
C) 4AB² = 3AD²
D) 2AB² = 3AD²
Answer:
B) 3AB² = 4AD²

Question 26.
Two isosceles triangles have equal angles and their areas are in the ratio of 16 : 25, then the ratio of their corresponding heights is …………………
A) 4 : 5
B) 5 : 4
C) 3 : 2
D) 1 : 4
Answer:
A) 4 : 5

Question 27.
In ΔABC, AD is bisector of ∠A if BD = 5 cm, BC = 7.5 cm, then AB: AC = …………..
A) 2 : 1
B) 1 : 2
C) 4 : 5
D) 3 : 5
Answer:
A) 2 : 1

Question 28.
In the quadrilateral DEFG a circle is inscribed touching quadrilateral at R, S, P, Q. If ES = 5 cm, PF = 7 cm, QG = 5 cm, DR = 4 cm; then perimeter of the quadrilateral is …………………..

A) 40 cm
B) 21 cm
C) 42 cm
D) 20 cm
Answer:
C) 42 cm

Question 29.
If ΔABC ~ ΔEFD and ∠A = 40°, ∠F = 80° then ∠C = ………………….
A) 40°
B) 80°
C) 50°
D) 60°
Answer:
D) 60°

Question 30.
ΔABC ~ ΔPQR, AB = 3.6 cm, PQ = 24 cm and AC = 8.1 cm, PR = ……………. cm.
A) 3.6
B) 5.4
C) 7.8
D) 7.3
Answer:
B) 5.4

Question 31.
In ΔABC, D and E are midpoints of AB and AC then DE : BC
A) 4 : 1
B) 1 : 1
C) 1 : 2
D) 2 : 1
Answer:
C) 1 : 2

Question 32.
ΔABC ~ ΔDEF and perimeters of ΔABC and ΔDEF are 30 cm and 18 cm respectively. If BC = 9 cm, then EF =………………..
A) 6.3 cm
B) 5.4 cm
C) 7.2 cm
D) 4.5 cm
Answer:
B) 5.4 cm

Question 33.
According Baudhayan theorem AC² = ………………
A) AB/BC
B) AB² + BC²
C) AB + BC + AD
D) None of these
Answer:
B) AB² + BC²

Question 34.
ABC is a right triangle and right angled at C. If p is the length of perpendicular from C to AB with AB = c, BC = a, AC = b, then ………………..
A) \(\frac{1}{\mathrm{a}^{2}}=\frac{1}{\mathrm{~b}^{2}}-\frac{1}{\mathrm{p}^{2}}\)
B) \(\frac{1}{p^{2}}=\frac{1}{a^{2}}-\frac{1}{b^{2}}\)
C) \(\frac{1}{b^{2}}=\frac{1}{p^{2}}-\frac{1}{a^{2}}\)
D) \(\frac{1}{p^{2}}=\frac{1}{a^{2}}+\frac{1}{b^{2}}\)
Answer:
D) \(\frac{1}{p^{2}}=\frac{1}{a^{2}}+\frac{1}{b^{2}}\)

Question 35.
The diagonals of a trapezium ABCD with AB || DC, intersect each other at the point O. If AB = 2 CD, then the ratio of areas of triangles AOB and COD is

A) 4 : 1
B) 1 : 4
C) 3 : 4
D) 4 : 3
Answer:
A) 4 : 1

Question 36.
AB, CD, PQ are perpendicular to BD. If AB = x, CD = y and PQ = z, then \(\frac{1}{z}\) =

A) \(\frac{1}{x}+\frac{1}{y}\)
B) xy
C) \(\frac{1}{x}-\frac{1}{y}\)
D) 1
Answer:
A) \(\frac{1}{x}+\frac{1}{y}\)

Question 37.
In the given fighre if LM || AB, AL = x – 3, AC = 2x,BM = x – 2 and BC = 2x + 3. Then the value of x is ……………..

A) 7
B) 8
C) 9
D) Cannot be determined
Answer:
C) 9

Question 38.
The diagonals of a quadrilateral ABCD intersect each other at a point O such that \(\frac{\mathrm{AO}}{\mathrm{BO}}=\frac{\mathrm{CO}}{\mathrm{DO}}\) = . Then the quadrilateral ABCD is …………………….
A) trapezium
B) square
C) rectangle
D) parallelogram
Answer:
B) square

Question 39.
In the given figure, if AB || CD || EF given that AB = 7.5 cm, DC = y cm, EF = 4.5 cm, CF = 3 cm BC = x cm, then the value of x is ………………..

A) 4 cm
B) 5 cm
C) 6 cm
D) None
Answer:
C) 6 cm

Question 40.
If BL and CM are the medians of a triangle ABC right angled at A, then the value of 4(BL² + CM²) =
A) 3BC²
B) 5BC²
C) 7BC²
D) BC²
Answer:
B) 5BC²

Question 41.
If ABD is a triangle right angled at A and AC ⊥ BD, then AC² =
A) BC . BD
B) BD . CD
C) BC. DC
D) AD . AB
Answer:
C) BC. DC

Question 42.
In ΔABC, DE || BC and \(\frac{A D}{D B}=\frac{3}{5} .\). If AC = 5.6 cm, then AE =

A) 2 cm
B) 2.1 cm
C) 2.2 cm
D) 2.5 cm
Answer:
B) 2.1 cm

Question 43.
In a trapezium ABCD, AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF || AB. Then \(\frac{\mathrm{AE}}{\mathrm{ED}}\) =

A) \(\frac{\mathrm{FC}}{\mathrm{BF}}\)
B) \(\frac{\mathrm{ED}}{\mathrm{AE}}\)
C) \(\frac{\mathrm{BF}}{\mathrm{FC}}\)
D) None
Answer:
C) \(\frac{\mathrm{BF}}{\mathrm{FC}}\)

Question 44.
Given that ΔABC ~ ΔDEF and their areas are 64 cm² and. 121 cm² respectively. If EF = 15.4 cm, then BC=
A) 2.11 cm
B) 21.1 cm
C) 1.21 cm
D) 11.2 cm
Answer:
D) 11.2 cm

Question 45.
If two triangles have the same base and area then they lies between …………….
A) parallel lines
B) two straight lines
C) perpendicular lines
D) intersecting lines
Answer:
A) parallel lines

Question 46.
A flagpole 4 m tall casts a 6m shadow. At the same time, a nearby building casts a shadow of 24 m. Then the height of the building is
A) 16 m
B) 20 m
C) 24 m
D) 18 m
Answer:
A) 16 m

Question 47.
In the figure below, PQ || BC. If AP = 3, PB = 4 and AQ = 4, then QC =

A) \(\frac{7}{3}\)
B) \(\frac{4}{3}\)
C) \(\frac{16}{3}\)
D) \(\frac{3}{4}\)
Answer:
C) \(\frac{16}{3}\)

Question 48.
ΔABC ~ ΔDEF and their areas are 16 cm² and 81 cm² respectively.
If BC = 4 cm, then EF =
A) 5 cm
B) 4 cm
C) 11 cm
D) 9 cm
Answer:
A) 5 cm

Question 49.
In the figure below, DE || BC. If AD = x, AE = x + 2, DB = x – 2 and CE = x – 1, then x =

A) 4
B) 5
C) 6
D) 7
Answer:
A) 4

Question 50.
In the figure, x = ………………

A) 45°
B) 135°
C) 90°
D) 15°
Answer:
B) 135°

Question 51.
In the figure if MN || BC, AN = 3, NC = 18, MB = 24, then AM =

A) 2
B) 4
C) 6
D) 8
Answer:
B) 4

Question 52.
An observer of height 1.8 m is 13.2 m away from a palm tree. The angle of elevation of the top of the tree from his eyes is 45°. Then the height of the palm tree is
A) 13.2 m
B) 15 m
C) 14 m
D) 11.4 m
Answer:
C) 14 m

Question 53.
A boy goes 5m due west and then 5m due north. How far is he from the starting point?
A) 10 m
B) 10 √2 m
C) 5 m
D) 5 √2 m
Answer:
C) 5 m

Question 54.
In the figure CD = DA, and EF || BD, CF then \(\frac{\mathrm{CF}}{\mathbf{F B}}\) = ………………

A) \(\frac{\mathrm{CD}}{\mathrm{DA}}\)
B) \(\frac{C E}{D A}\)
C) \(\frac{\mathrm{CE}}{\mathrm{ED}}\)
D) \(\frac{\mathrm{CD}}{\mathrm{CA}}\)
Answer:
C) \(\frac{\mathrm{CE}}{\mathrm{ED}}\)

Question 55.
From the diagram, LM||CB and LN || CD. Which of the following is true?

A) \(\frac{\mathrm{AM}}{\mathrm{AB}}=\frac{\mathrm{AN}}{\mathrm{AD}}\)
B) \(\frac{\mathrm{AM}}{\mathrm{MB}}=\frac{\mathrm{AN}}{\mathrm{ND}}\)
C) \(\frac{\mathrm{AL}}{\mathrm{LC}}=\frac{\mathrm{AM}}{\mathrm{AN}}\)
D) \(\frac{\mathrm{AD}}{\mathrm{BC}}=\frac{\mathrm{AD}}{\mathrm{DC}}\)
Answer:
A) \(\frac{\mathrm{AM}}{\mathrm{AB}}=\frac{\mathrm{AN}}{\mathrm{AD}}\)
or
B) \(\frac{\mathrm{AM}}{\mathrm{MB}}=\frac{\mathrm{AN}}{\mathrm{ND}}\)

Question 56.
When we construct a triangle similar to a given triangle as per given scale f actor, we construct on the basis of ……………….
A) SSS similarity
B) AAA similarity
C) Basic proportionality theorem
D) A and C are correct
Answer:
C) Basic proportionality theorem

Question 57.
In ΔABC, DE || BC, If \(\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{2}{3}\) and AC = 18, then AE =
A) 36
B) 3.6
C) 72
D) 7.2
Answer:
D) 7.2

Question 58.
In the figure, DE || BC. AD = x, DB = x – 2, AE = x + 2 and CE = x – 1, then x =

A) 1
B) 2
C) 3
D) 4
Answer:
D) 4

Question 59.
If ΔABC ~ ΔXYZ, ∠C = 60° and ∠B = 75°, then ∠Z = ……………….
A) 45°
B) 60°
C) 75°
D) 90°
Answer:
A) 45°

Question 60.
If ΔABC ~ ΔDEF, ∠A = 50°, then ∠E + ∠F = ………………
A) 100°
B) 125°
C) 130°
D) 140°
Answer:
C) 130°

Question 61.
If ΔABC ~ ΔDEF, ∠A + ∠B = 130°, then ∠F = ……………..
A) 130°
B) 140°
C) 50°
D) 40°
Answer:
C) 50°

Question 62.
ΔABC ~ ΔPQR, If AB = 3.6, PQ = 2.4, PR = 5.4, then AC =
A) 3.6
B) 8.1
C) 5.4
D) 7.8
Answer:
B) 8.1

Question 63.
In ΔABC, \(\overline{\mathbf{P Q}} \| \overline{\mathbf{A B}}\) , P, Q are on BC and AC. If CQ : QA = 1 : 3 and CP = 4, then BC =
A) 8
B) 12
C) 16
D) 4
Answer:
C) 16

Question 64.
If ΔABC ~ ΔDEF, such that 2AB = DE and BC = 8 cm, then EF = ……………. cm
A) 16
B) 12
C) 9
D) 4
Answer:
A) 16

Question 65.
ΔABC ~ ΔPQR, if AB = 6, BC = 4, AC = 8 and PR = 6, then PQ + QR = …………..
A) 8
B) 10
C) 7.5
D) 9
Answer:
C) 7.5

Question 66.
The ratio of perimeters of two similar triangles is 4 : 9, then the ratio of their areas is …………….
A) 16 : 9
B) 2 : 3
C) 16 : 81
D) 61 : 81
Answer:
C) 16 : 81

Question 67.
The perimeters of two similar triangles are 20 cm and 30 cm then the ratio of the areas of the triangles is ………………
A) 2 : 3
B) 3 : 2
C) 4 : 9
D) 9 : 4
Answer:
C) 4 : 9

Question 68.
The areas of two similar triangles are 16 cm² and 25 cm² respectively, then the ratio of their corresponding sides is ………………..
A) 5 : 4
B) 4 : 5
C) 16 : 25
D) 25 : 16
Answer:
B) 4 : 5

Question 69.
ΔABC ~ ΔDEF. If BC = 3 cm, EF = 4 cm and ar (ΔABC) = 54 cm² then ar (ΔDEF)=
A) 66 cm²
B) 79 cm²
C) 100 cm²
D) 96 cm²
Answer:
D) 96 cm²

Question 70.
The ratio of altitudes of two similar triangles is 4 : 9, then ratio of their areas is
A) 2 : 3
B) 4 : 9
C) 81 : 16
B) 4 : 9
D) 16 : 81
Answer:
D) 16 : 81

Question 71.
The areas of two similar triangles are 25 m² and 36 m². Median of smaller triangle is 10m, then median of the bigger triangle is
A) 15 m
B) 18 m
C) 16 m
D) 12 m
Answer:
D) 12 m

Question 72.
The ratio of areas of two similar triangles is 1: 2, then the ratio of their altitudes is
A) 1 : √2
B) 1 : 2
C) 2 : 1
D) √2 : 1
Answer:
A) 1 : √2

Question 73.
D, E are the mid-points of the sides AB and AC of ΔABC., then DE : BC = …………………
A) 3 : 1
B) 1 : 1
C) 2 : 1
D) 1 : 2
Answer:
D) 1 : 2

Question 74.
D, E are the mid-points of the sides AB and AC of ΔABC. Then DE : BC =
A) 8 cm
B) 6 cm
C) 4 cm
D) 12 cm
Answer:
A) 8 cm

Question 75.
In ΔABC, DE intersects AB and AC in the ratio 1 : 3, if DE = 2.4 cm, then BC = ……………..
A) 4.8 cm
B) 7.2 cm
C) 9.6 cm
D) 12.0 cm
Answer:
B) 7.2 cm

Question 76.
The ratios of corresponding medians of two similar triangles is 2 : 3, then the ratio of their perimeters is
A) 2 : 3
B) 3 : 2
C) 1 : 2
D) 2 : 1
Answer:
A) 2 : 3

Question 77.
The ratio of perimeters of two similar triangles is 9 : 16, then ratio of their altitudes is
A) 9 : 16
B) 3 : 4
C) 16 : 9
D) 4 : 3
Answer:
A) 9 : 16

Question 78.
In a ΔABC, if ∠A = 90°, and AD ⊥ BC, then AD² =
A) BD . DC
B) BC . BD
C) BD . BA
D) BA . BC
Answer:
A) BD . DC

Question 79.
Praveen goes 3 m due East and then 4 m due North. Then, his distance from the starting point is
A) 3 m
B) 4 m
C) 5 m
D) 7 m
Answer:
C) 5 m

Question 80.
In an equilateral triangle ABC, AD ⊥ BC, then 4 AD² =
A) 3 AC²
B) 3 AB²
C) 3 BC²
D) 2 BC²
Answer:
B) 3 AB²

Question 81.
In the rhombus ABCD, AB = 6 cm, then AC² + BD² =
A) 36
B) 144
C) 72
D) 90
Answer:
B) 144

Question 82.
ΔABC ~ ΔPQR, AB = 6, BC = 4, AC = 8, PR = 6, then PQ + QR =
A) 8
B) 10
C) 7.5
D) 9
Answer:
C) 7.5

Question 83.
Two figures are said to be similar if they have same
A) shape
B) size
C) size or shape
D) both size and shape
Answer:
A) shape

Question 84.
Two polygons with the same number of sides are similar if
A) corresponding angles are equal
B) corresponding sides are in proportion
C) corresponding angles are not equal
D) corresponding angles are equal and sides are in proportion
Answer:
D) corresponding angles are equal and sides are in proportion

Question 85.
Which of the following are not similar?
A) Allcircies
B) All squares
C) All quadrilaterals
D) All equilateral triangles
Answer:
C) All quadrilaterals

Question 86.
In ΔABC, DE || BC, then
A) \(\frac{\mathrm{AB}}{\mathrm{AC}}=\frac{\mathrm{AD}}{\mathrm{AE}}\)
B) \(\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{EC}}{\mathrm{AE}}\)
C) \(\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}\)
D) \(\frac{\mathrm{AD}}{\mathrm{DE}}=\frac{\mathrm{AE}}{\mathrm{EC}}\)
Answer:
C) \(\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{EC}}\)

Question 87.
In ΔABC, l intersects AB and AC in D and E such that \(\) , then
A) DE ⊥ BC
B) DE || BC
C) DE ~ BC
D) DE ≅ BC
Answer:
B) DE || BC

Question 88.
ΔPQR is formed by joining the midpoints of the sides of ΔABC, then the ratio of the areas of ΔPQR and ΔABC is
A) 4 : 1
B) 1 : 2
C) 2 : 1
D) 1 : 4
Answer:
D) 1 : 4

Question 89.
Which of the following is not the sides of a right triangle ?
A) 3, 4, 5
B) 5, 12, 13
C) 7, 24, 25
D) 4, 5, 6
Answer:
D) 4, 5, 6

Question 90.
In ΔABC, BC² + AB² = AC², then is a right angle.
A) ∠A
B) ∠B
C) ∠C
D) ∠A and ∠B
Answer:
B) ∠B

Question 91.
The adjacent figures state ……………… criterion of similarity.

A) AA
B) AAA
C) SAS
D) SSS
Answer:
A) AA

Question 92.
Which of the following figures are similar?

Answer:

Question 93.
In a ΔXYZ, if the internal bisector of ∠X meets YZ in P. Then
A) \(\frac{X Y}{X Z}=\frac{Y P}{P Z}\)
B) \(\frac{\mathrm{XY}}{\mathrm{PZ}}=\frac{\mathrm{XZ}}{\mathrm{YP}}\)
C) \(\frac{\mathrm{XY}}{\mathrm{XZ}}=\frac{\mathrm{PZ}}{\mathrm{XP}}\)
D) \(\frac{X Z}{X Y}=\frac{Y Z}{Y P}\)
Answer:
A) \(\frac{X Y}{X Z}=\frac{Y P}{P Z}\)

Question 94.
In ΔABC and ΔA’B’C’, A’ corresponds to vertex A. We denote it symbolically as
A) A’ = A
B) A’ ~ A
C) A’ || A
D) A’ ↔ A
Answer:
D) A’ ↔ A

Question 95.
Two figures are said to be congruent if they have same
A) shape
B) size
C) size or shape
D) both size and shape
Answer:
B) size

Question 96.
Two triangles are similar if their corresponding
A) angles are equal
B) sides are in proportion
C) angles are equal (or) sides are in proportion
D) sides are not in proportion
Answer:
C) angles are equal (or) sides are in proportion

Question 97.
Symbol for “is similar to” is
A) =
B) ~
C) ≅
D) ⇒
Answer:
B) ~

Question 98.
Symbol for “is congruent to” is
A) =
B) ~
C) ≅
D) ⇒
Answer:
C) ≅

Question 99.
Basic proportionality theorem is also known as ……………… theorem.
A) Pythagoras
B) Thales
C) Similar
D) Perpendicular
Answer:
B) Thales

Question 100.
In a rhombus ABCD, AC² + BD² =
A) 4 AB²
B) 4 BC²
C) 4 CA²
D) All of these
Answer:
D) All of these

Question 101.
In a trapezium ABCD, AB || DC, and also EF || AB, then \(\frac{\mathrm{AE}}{\mathrm{ED}}\) =
A) \(\frac{\mathrm{AB}}{\mathrm{DC}}\)
B) \(\frac{\mathrm{AB}}{\mathrm{EF}}\)
C) \(\frac{\mathrm{BF}}{\mathrm{AE}}\)
D) \(\frac{\mathrm{BF}}{\mathrm{FC}}\)
Answer:
D) \(\frac{\mathrm{BF}}{\mathrm{FC}}\)

Question 102.
In ΔABC, D is the mid point of BC. Then AB² + AC² =
A) AD² + BD²
B) 2AD² + 2BD²
C) BD² + DC²
D) 2AC² + 2CD²
Answer:
B) 2AD² + 2BD²

Question 103.
In ΔABC, if ∠B = 90°, BD ⊥ AC, then
A) ΔADB ~ ΔBDC
B) ΔADB ~ ΔABC
C) ΔBDC ~ ΔABC
D) All of these
Answer:
D) All of these

Question 104.
Two ……………. are always similar
A) Triangles
B) Rectangles
C) Squares
D) Trapeziums
Answer:
C) Squares

Question 105.
Two ……………. are always similar
A) Triangles
B) Circles
C) Trapeziums
D) Rectangles
Answer:
B) Circles

Question 106.
The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 12 cm, then the corresponding side of the second triangle is …………….. cm
A) 8
B) 10
C) 12
D) 20
Answer:
A) 8

Question 107.
In a ΔABC, the bisector of ∠A intersects BC at D. If BD: DC = 4 : 7 and AC = 3.5 then AB =
A) 2
B) 3
C) 4
D)5
Answer:
A) 2

Question 108.
AD is the angular bisector of ‘A’. If AB = 6 cm, BD = 8 cm and DC = 6 cm, then AC = …………………. cm.
A) 4.5
B) 4
C) 4.8
D) 5.6
Answer:
A) 4.5

Question 109.
ΔABC is similar to ΔDEF is denoted as
A) ΔABC = ΔDEF
B) ΔABC ~ ΔDEF
C) ΔABC ≅ ΔDEF
D) ΔABC || ΔDEF
Answer:
B) ΔABC ~ ΔDEF

Question 110.
ΔABC is congruent to ΔDEF is denoted as
A) ΔABC = ΔDEF
B) ΔABC ~ ΔDEF
C) ΔABC ≅ ΔDEF
D) ΔABC || ΔDEF
Answer:
C) ΔABC ≅ ΔDEF

Question 111.
In the given figure , we observe the following relationship

A) \(\frac{\mathrm{PE}}{\mathrm{EQ}}=\frac{\mathrm{PE}}{\mathrm{FR}}\)
B) EF ⊥ QR
C) EF || QR
D) EF = QR
Answer:
C) EF || QR

Question 112.
In the given figure, DE || BC, If \(\frac{\mathbf{A D}}{\mathbf{D B}}=\frac{1}{2}\) and AE = 1.2 cm then EC = …………….. cm

A) 7.2
B) 4.7
C) 3.6
D) 2.4
Answer:
D) 2.4

Question 113.
In the adjacent figure, x = …………….., if AB || QR.

A) 4
B) 8
C) 12
D) 16
Answer:
A) 4

Question 114.
In the figure DE || BC, then x = …………………..

A) 2
B) 3
C) 4
D) 1.5
Answer:
A) 2

Question 115.
Observe the given figures and name the criterion of similarity.

A) AAA
B) ASA
C) SAS
D) No similarity
Answer:
D) No similarity

Question 116.
The adjacent figures state ………………… criterion of similarity.

A) AAA
B) SSS A
C) SAS
D) ASA
Answer:
C) SAS

Question 117.
Write the similarity relation in symbolic form.

A) Δ FGH ~ Δ HIK
B) Δ FGH ~ Δ KIH
C) Δ GFH ~ Δ HKI
D) Δ FHG ~ Δ IKH
Answer:
B) Δ FGH ~ Δ KIH

Question 118.
Write the similarity relation of triangles in symbolic form.

A) Δ AXY ~ Δ ABC
B) Δ XYA ~ Δ BAC
C) Δ YXA ~ Δ BCA
D) Δ XAY ~ Δ CAB
Answer:
A) Δ AXY ~ Δ ABC

Question 119.
In the given similar triangles, the value of x =

A) 4.5
B) 6.5
C) 7.5
D) 8.5
Answer:
C) 7.5

Question 120.
Find the value of y if the given triangles are similar.

A) 1.5
B) 2.5
C) 3.5
D) 4.5
Answer:
B) 2.5

Question 121.
In the given figure, DE || BC and AD : DB = 5 : 4, then =

A) \(\frac{81}{25}\)
B) \(\frac{5}{9}\)
C) \(\frac{5}{4}\)
D) \(\frac{25}{81}\)
Answer:
D) \(\frac{25}{81}\)

Question 122.
In ΔABC, D, E are the mid-points of the sides AB and AC, then ar (ΔADE ) : ar ( BCED) =
A) 1 : 4
B) 1 : 3
C) 2 : 1
D) 3 : 2
Answer:
B) 1 : 3

Question 123.
In figure, QA ⊥ AB, PB ⊥ AB. If AO = 10 cm, BO = 6 cm and PB = 9 cm, then AQ = …………………. cm

A) 15
B) 30
C) 45
D) 70
Answer:
A) 15

Question 124.
In the given figure, if ar (ΔPOB) =32 cm², then ar(ΔQOA) is

A) 40 cm²
B) 50 cm²
C) 75 cm²
D) 150 cm²
Answer:
B) 50 cm²

Question 125.
In figure, ΔABC ~ ΔDEF. AB = 5 cm, area (ΔABC) = 20 cm², area (ΔDEF) = 45 cm² then DE =

A) 2.0 cm
B) 4.5 cm
C) 7.5 cm
D) 9.5 cm
Answer:
C) 7.5 cm

Question 126.
In the given figure, CD is

A) 16 cm
B) 64 cm
C) 4 cm
D) 36 cm
Answer:
A) 16 cm

Question 127.
Diagonal of right angled triangle ABC is 8 cm, then its median BM =

A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm
Answer:
C) 4 cm

Question 128.
In the fig. ΔABC ~ ΔDEF. Name the criterion of similarity.

A) SSS
B) SAS
C) AAA
D) RHS B
Answer:
B) SAS

Question 129.
The adjacent figures state …………….. criterion of similarity.

A) SSS
B) SAS
C) AAA
D) AA
Answer:
C) AAA

Question 130.
In the given fig. LM || CB and LN || CD, then

A) \(\frac{A N}{N D}=\frac{A M}{A B}\)
B) \(\frac{\mathrm{AN}}{\mathrm{AL}}=\frac{\mathrm{AM}}{\mathrm{ML}}\)
C) \(\frac{\mathrm{AM}}{\mathrm{MB}}=\frac{\mathrm{AN}}{\mathrm{ND}}\)
D) \(\frac{A M}{M B}=\frac{A N}{A D}\)
Answer:
C) \(\frac{\mathrm{AM}}{\mathrm{MB}}=\frac{\mathrm{AN}}{\mathrm{ND}}\)

Practice the AP 10th Class Maths Bits with Answers Chapter 7 Coordinate Geometry on a regular basis so that you can attempt exams with utmost confidence.

AP State Syllabus 10th Class Maths Bits 7th Lesson Coordinate Geometry with Answers

Question 1.
If a line is passing through (2, 3) and (2, -3), then
1) the line is parallel to X – axis.
2) the line is parallel to Y – axis.
3) the slope of the line is not defined.
4) the slope of the line is zero.
A) 2 and 3 are correct.
B) 1 and 3 are correct.
C) 1 and 2 are correct.
D) 2 and 4 are correct.
Answer:
A) 2 and 3 are correct.

Question 2.
If A(log₂8, log₅25) and B(log₁₀10, log₁₀100), then the mid-point of AB is
A) (2, 2)
B) (3, 2)
C) (1, 2)
D) (4, 4)
Answer:
D) (4, 4)

Question 3.
The nearest point to origin is
A) (2, -3)
B) (5, 0)
C) (0,-5)
D) (1, 3)
Answer:
A) (2, -3)

Question 4.
The point (0, 5) lies on ……………….
A) Both X and Y – axes
B) Origin
C) Y-axis
D) X – axis
Answer:
C) Y-axis

Question 5.
If origin is the centroid of a triangle, whose vertices are (3, 2), (-6, y) and (3,-2), then y = ………………….
A) 0
B) 3
C) 2
D) 6
Answer:
A) 0

Question 6.
Which of the following cannot be a point on X-axis ?
A) (-2, 0)
B) (0, 2)
C) (2, 0)
D) (4, 0)
Answer:
B) (0, 2)

Question 7.
Which of the following is the point of intersection of X – axis and the line y = x + 5?
A) (0, 5)
B) (5, 0)
C) (0, -5)
D) (-5, 0)
Answer:
D) (-5, 0)

Question 8.
The area of the triangle BOA is ……………… sq units.

A) 1
B) 2
C) 3
D) 4
Answer:
C) 3

Question 9.
The distance between two points A(a cosθ, 0), B(0, asinθ) is ……………….
A) a
B) a²
C) √a
D) 0
Answer:
A) a

Question 10.
(x, y), (2, 0), (3, 2) and (1, 2) are vertices of a parallelogram then (x, y)
A) (0, 0)
B) (4, 8)
C) (1, 0)
D) (5, 0)
Answer:
A) (0, 0)

Question 11.
Total distance from X-axis to A(3, 4) and Y-axis to B(5, 7) is ……………………..
A) 8
B) 10
C) 11
D) 9
Answer:
D) 9

Question 12.
Distance between the points A(log₁₀100, tan 45°),
B(cosec 30°.log₇343) is
A) \(\sqrt{13}\)T units
B) \(\sqrt{10}\) units
C) \(\sqrt{34}\) units
D) √5 units
Answer:
D) √5 units

Question 13.
The point (-5, -8) lies in ………. quadrant.
A) I
B) II
C) III
D) IV
Answer:
C) III

Question 14.
The line x = -3 is
A) parallel to X – axis
B) parallel to Y – axis
C) passes through origin
D) passes through (0, -3)
Answer:
B) parallel to Y – axis

Question 15.
The area of a triangle is zero means …………………
A) points are parallel
B) points are collinear
C) points are equal
D) points are negative
Answer:
B) points are collinear

Question 16.
The formula of the area of a triangle is ………………….

Answer:

Question 17.
Slope of the line 3x – αy +1 = 0 is 4 then α = …………………..
A) \(\frac {3}{4}\)
B) \(\frac{-3}{4}\)
C) \(\frac {1}{3}\)
D) \(\frac{-1}{3}\)
Answer:
D) \(\frac{-1}{3}\)

Question 18.
Sides of two similar triangles are in the ratio of 4:9. Area of these triangles are in the ratio of ………………
A) 2 : 3
B) 4 : 9
C) 81 : 16
D) 16 : 81
Answer:
D) 16 : 81

Question 19.
The point at which the line 2x + y = 8 intersects the X-axis is ………………….
A) (8, 0)
B) (0, 8)
C) (0, 4)
D) (4, 0)
Answer:
D) (4, 0)

Question 20.
Three consecutive vertices of a parallelogram are (-2, 1), (1, 0) and (4, 3). Then 4^th vertex is ………………
A) (1, 4)
B) (1, -2)
C) (-1, 2)
D) (-1, -2)
Answer:
A) (1, 4)

Question 21.
The ratio in which the line segment joining the points (4, 6) and (-7, -1) divided by X- axis is ………………….
A) 6 : 1
B) 1 : 6
C) 4 : 7
D) 7 : 4
Answer:
A) 6 : 1

Question 22.
Slope of the line joining (-α, α) and (α, α + α√3) is …………………
A) \(\frac{2}{\sqrt{3}}\)
B) \(\frac{1}{\sqrt{3}}\)
C) √3
D) \(\frac{\sqrt{3}}{2}\)
Answer:
D) \(\frac{\sqrt{3}}{2}\)

Question 23.
If the centroid of the triangle formed with (a, b), (b, c) and (c, a) is O(0,0), then
a³ + b³ + c³ =
A) a + b + c
B) \(\frac{a+b+c}{3}\)
C) \(\frac{a b c}{3}\)
D) 3abc
Answer:
D) 3abc

Question 24.
If A(p, q), B(m, n) and C(p-m, q-n) are collinear, then……………….
A) \(\frac{\mathrm{p}}{\mathrm{n}}=\frac{\mathrm{q}}{\mathrm{m}}\)
B) \(\frac{\mathrm{p}}{\mathrm{m}}=\frac{\mathrm{q}}{\mathrm{n}}\)
C) p + q = m + n
D) p + q + m + n = 0
Answer:
B) \(\frac{\mathrm{p}}{\mathrm{m}}=\frac{\mathrm{q}}{\mathrm{n}}\)

Question 25.
If P = {3x/x ∈N,x ≤ 50},
Q = {5x/x ∈N, x ≤ 30}, then n(P ∩ Q) =……………..
A) 5
B) 8
C) 10
D) 15
Answer:
C) 10

Question 26.
(3, -1), (2, 6) and (-5, 7) are the midpoints of the sides of the triangle ABC. The area of triangle ABC is ………………. sq. units
A) 96
B) 69
C) 86
D) 110
Answer:
A) 96

Question 27.
The ratio in which X-axis divides the line segment joining the points (5, 4) and (5, -3) is ……………..
A) 5 : 2
B) 3 : 4
C) 2 : 5
D) 4 : 3
Answer:
D) 4 : 3

Question 28.
AOBC is a rectangle with A = (0, 3), O (0, 0) and B (5, 0), then the length of
its diagonals is ………………
A) 5
B) 3
C) \(\sqrt{34}\)
D) 4
Answer:
C) \(\sqrt{34}\)

Question 29.
The points (-4, 0), (4, 0), (0, 3) are vertices of ……………….
A) right angled triangle
B) isosceles triangle
C) equilateral triangle
D) scalene triangle
Answer:
B) isosceles triangle

Question 30.
In the given figure AC pass through center of the circle, then the area of the shaded region
region in the given figure is ………………

A) \(\frac{x^{2}}{2}\) (3 – π)
B) x²(\(\frac{\pi}{2}\) – 1)
C) 2x²(π – 1 )
D) \(\frac{x^{2}}{2}\left(\frac{\pi}{2}-1\right)\)
Answer:
D) \(\frac{x^{2}}{2}\left(\frac{\pi}{2}-1\right)\)

Question 31.
The points of trisection of the line segment joining (2, -2), (-7, 4) are
A) (1, 0), (-4, 2)
B) (-1, 0), (-4, 2)
C) (-1, 0), (-4, -2)
D) (1, 0), (4, 2)
Answer:
B) (-1, 0), (-4, 2)

Question 32.
The points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts are)

Answer:

Question 33.
The end points of a line are (2, 3), (4, 5). Then its slope is
A) 4
B) 3
C) 2
D) 1
Answer:
D) 1

Question 34.
The value of k for which the points (7, -2), (5, 1), (3, k) are collinear is
A) 4
B) 3
C) 2
D) 1
Answer:
A) 4

Question 35.
The points A(7, 3), B(6, 1), C(8, 2) and D(9, 4) taken in that order are the vertices of
A) square
B) rhombus
C) parallelogram
D) trapezium
Answer:
B) rhombus

Question 36.
If (a, 2) lies in II quadrant, then (-a, -2) lies in which quadrant ?
A) I
B) II
C) III
D) IV
Answer:
D) IV

Question 37.
The quadrilateral formed by the points A(0, -1), B(2, 1), C(0, 3) and D(-2, 1) taken in the same order is
A) rectangle
B) parallelogram
C) square
D) rhombus
Answer:
C) square

Question 38.
If P(3, 4) and Q(7, 7) are two points and PR = 10, where P, Q and R are collinear, then R =
A) (10,10)
B) (11, 11)
C) (11, 10)
D) (11, -10)
Answer:
C) (11, 10)

Question 39.
If (-2, 1), (1, 0) and (4, 3) are three consecutive vertices of a parallelogram, then the fourth vertex is
A) (2, 1)
B) (1, 4)
C) (0, 0)
D) (2, 2)
Answer:
A) (2, 1)

Question 40.
(0, 0), (1, 0), (0, -4) are the vertices of a …………….. triangle.
A) equilateral
B) isosceles
C) right-angled isosceles
D) right-angled
Answer:
D) right-angled

Question 41.
If (8,1), (k, -4), (2, -5) are collinear, then k =
A) 1
B) 2
C) 3
D) 4
Answer:
C) 3

Question 42.
If the slope of the line through (2, -7) and (x, 5) is 3 then x =
A) 4
B) 5
C) 6
D) 7
Answer:
C) 6

Question 43.
The distance between the points (cosθ, sinθ) and (-sinθ, cosθ) is
A) 1
B) √2
C) 2
D) √3
Answer:
B) √2

Question 44.
The number of elements in a triangle is
A) 3
B) 4
C) 6
D) 5
Answer:
C) 6

Question 45.
The graph of y + x² = 0 lies in the quadrants
A) Q₁, Q₂
B) Q₂, Q₃
C) Q₃, Q₄
D) Q₄, Q₁
Answer:
C) Q₃, Q₄

Question 46.
The line x = 2017 is
A) Slope not defined
B) Parallel to Y – axis
C) 1 and 2
D) None
Answer:
C) 1 and 2

Question 47.
If (k, 2) lies in II quadrant then (-k, -2) lies in the quadrant
A) I
B) II
C) III
D) IV
Answer:
D) IV

Question 48.
The points A(1, 7), B(4, 2), C(-1, -1) and D(-4, 4) are
A) collinear
B) vertices of a square
C) vertices of a rectangle
D) None of these
Answer:
B) vertices of a square

Question 49.
If P divides the line joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁ : m₂, then P is

Answer:

Question 50.
The distance between the points A(4, 3) and B(8, 6) is …………… units.
A) 5
B) 6
C) 4
D) 7
Answer:
C) 4

Question 51.
The points A(1, 5), B(2, 3) and C(-2, -1) are
A) vertices of a right-angled triangle
B) vertices of an isosceles triangle
C) collinear
D) non-collinear
Answer:
D) non-collinear

Question 52.
The midpoint of A(1, 5) and B (-2, -1) is
A) (\(\frac {1}{2}\), 2)
B) (2, \(\frac {1}{2}\))
C) (-\(\frac {1}{2}\), 2)
D) (-\(\frac {1}{2}\), -2
Answer:
C) (-\(\frac {1}{2}\), 2)

Question 53.
If a line makes an angle 45° with positive X-axis, then its slope is
A) \(\frac{1}{\sqrt{2}}\)
B) \(\frac {1}{2}\)
C) \(\frac{\sqrt{3}}{2}\)
D) 1
Answer:
A) \(\frac{1}{\sqrt{2}}\)

Question 54.
The area of the triangle formed by three vertices O(0, 0), A(1, 0), B(0, 1) is ………………. sq. units.
A) o
B) 1/2
C) 1
D) 2
Answer:
B) 1/2

Question 55.
At which point does the straight line y = x + 7 intersect X – axis ?
A) (7, 0)
B) (0, 7)
C) (0, -7)
D) (-7, 0)
Answer:
D) (-7, 0)

Question 56.
Where do the following points (-4, 0), (2, 0), (6, 0), (-8, 0) lie in the coordinate axes ?
A) First Quadrant
B) Y-axis
C) X-axis
D) Fourth Quadrant
Answer:
C) X-axis

Question 57.
The distance between the points (0, 0), (X₁,Y₁) is ………………units.
A) \(\sqrt{x_{1}^{2}+y_{1}^{2}}\)
B) \(\sqrt{x_{1}+y_{1}}\)
C) \(\sqrt{x^{2}+y^{2}}\)
D) \(\sqrt{x+y}\)
Answer:
A) \(\sqrt{x_{1}^{2}+y_{1}^{2}}\)

Question 58.
The slope of a ladder making an angle 60° with the floor is ……………………..

A) 1
B) \(\frac {1}{2}\)
C) \(\frac{1}{\sqrt{3}}\)
D) √3
Answer:
D) √3

Question 59.
The mid point of the line joining the points (4, 5), (- 6, 3) is ………………
A) (1, 4)
B) (-1, 4)
C) (1, -4)
D) (-1, – 4)
Answer:
B) (-1, 4)

Question 60.
The distance of the point (3, – 4) from X- axis is ………………..
A) 3
B) 4
C) 5
D) 1
Answer:
C) 5

Question 61.
The slope of the line joining (2, 1) (3, 6) is …………………..
A) 5
B) 4
C) 3
D) 2
Answer:
A) 5

Question 62.
The line passing through the point (0,0) is
A) y = 2
B) x = 5
C) y = x
D) y = 2x + 3
Answer:
C) y = x

Question 63.
Slope of the line 5x – 6y + 10 = 0 is
A) \(\frac{5}{6}\)
B) \(\frac{-5}{6}\)
C) \(\frac{6}{5}\)
D) \(\frac{-6}{5}\)
Answer:
A) \(\frac{5}{6}\)

Question 64.
The distance between the points (3, 2) and (2, 4) is …………………. units.
A) √5
B) √6
C) √3
D) √2
Answer:
A) √5

Question 65.
The centroid of the triangle with vertices (2, 1), (3, 2), (1, 3) is
A) (3, 5)
B) (2, 2)
C) (3, 3)
D) (3, 6)
Answer:
B) (2, 2)

Question 66.
If the line 4x + 5y = k passing through the origin, then k is
A) -1
B) 2
C) 0
D) 3
Answer:
C) 0

Question 67.
The area of the triangle whose vertices are (0, 0), (x, 0) and (0, y) is
A) xy
B) \(\frac {1}{2}\) xy
C) \(\frac {1}{2}\) x + y
D) x + y
Answer:
B) \(\frac {1}{2}\) xy

Question 68.
The slope of the line perpendicular to the line 2x + y + 4 = 0 is
A) -2
B) 2
C) \(\frac {1}{2}\)
D) –\(\frac {1}{2}\)
Answer:
D) –\(\frac {1}{2}\)

Question 69.
The slope of the line parallel to the line 2x + y + 4 = 0 is
A) 2
B) -2
C) \(\frac {1}{2}\)
D) –\(\frac {1}{2}\)
Answer:
A) 2

Question 70.
The equation of the line having slope 1 and passing through (3, 2) is
A) x + y = 1
B) x – y = 1
C) 2x – y + 1 = 0
D) x – 2y + 1 = 0
Answer:
B) x – y = 1

Question 71.
Slope of the line joining the points (a, 0) and (0, 5) is
A) -b
B) \(\frac{a}{b}\)
C) – \(-\frac{b}{a}\)
D) \(\frac{1}{a}\)
Answer:
C) – \(-\frac{b}{a}\)

Question 72.
The distance of the point (3, p) from origin is 5 units then p is
A) 7
B) 6
C) 5
D) 4
Answer:
D) 4

Question 73.
A = (8, 3), B= (x, 3) and \(\overline{\mathbf{A B}}\) = 12 units then x is
A) -4
B) 14
C) 8
D) 20
Answer:
D) 20

Question 74.
Distance of the point (tanθ, 1) from origin is
A) cotθ
B) sinθ
C) tanθ
D) secθ
Answer:
D) secθ

Question 75.
The perimeter of a triangle formed by the points (0,0), (1,0)and (0, 1) is ………………….units.
A) √2
B) 2 + √2
C) 2 – √2
D) 2 √2
Answer:
B) 2 + √2

Question 76.
Find the value of k for which of (7, -2), (5, 1), (3, k) are collinear
A) \(\frac {4}{5}\)
B) \(\frac {11}{5}\)
C) \(\frac {5}{5}\)
D) \(\frac {7}{5}\)
Answer:
B) \(\frac {11}{5}\)

Question 77.
Find the centroid of (-1, 3), (6, -3), (-3, 6)
A) (\(\frac {2}{3}\), 2)
B) (1, \(\frac {2}{3}\))
C) (-1, \(\frac {2}{3}\))
D) (-\(\frac {2}{3}\), 1)
Answer:
A) (\(\frac {2}{3}\), 2)

Question 78.
A = (4, 2); B = (1, y) and AB = 5 then y = ………………..
A) 6
B) 3
C) 9
D) 2
Answer:
A) 6

Question 79.
A straight line which is parallel to x – y + 1 = 0 is ………………..
A) x – y + k = 0
B) x + y + k = 0
C) ax + by + c = 0
D) 2x + 3y + k = 0
Answer:
A) x – y + k = 0

Question 80.
If the distance of a point from X – axis is 8 units and its distance from Y – axis is 3 units then the point is denoted by
A) (8, 3)
B) (-8, 3)
C) (-3, 8)
D) (3, 8)
Answer:
D) (3, 8)

Question 81.
The slope of the line parallel to 3x – by + 7 = 0 is 3 then b = ………………..
A) 3
B) 4
C) 1
D) 5
Answer:
C) 1

Question 82.
The slope of the line perpendicular to 13x – 7y + 1 = 0 is ……………….
A) \(\frac{-7}{13}\)
B) \(\frac{7}{3}\)
C) –\(\frac{7}{3}\)
D) \(\frac{13}{7}\)
Answer:
A) \(\frac{-7}{13}\)

Question 83.
The coordinates of the centre of the circle having the points (9, 3) and (1, -1) as the end points of the diameter is ………………..
A) (6, 9)
B) (5, 1)
C) (1, 3)
D) (- 1, – 3)
Answer:
B) (5, 1)

Question 84.
One end of the diameter of a circle is (3, 2) and the centre is (0, 0) then the other end point is
A) (8, 4)
B) (3, 2)
C) (- 3, – 2)
D) (5, 1)
Answer:
C) (- 3, – 2)

Question 85.
The mid point of the line segment (3, x) and (1, – 4) is (2, 1) then x =
A) 2
B) – 1
C) 6
D) 0
Answer:
C) 6

Question 86.
The point that lies in IV quadrant
A) (2, 3)
B) (-3, -2)
C) (4, -3)
D) (-2, 3)
Answer:
C) (4, -3)

Question 87.
The point that lies in III quadrant
A) (5, 4)
B) (-5, -4)
C) (-5, 4)
D) (5, -4)
Answer:
B) (-5, -4)

Question 88.
The point that lies in II quadrant is ………………
A) (-2, 3)
B) (2, -3)
C) (2, 3)
D) (0, 0)
Answer:
A) (-2, 3)

Question 89.
x > 0, y > 0, then (x, y) ∈ ………………..
A) Q₁
B) Q₂
C) Q₃
D) Q₄
Answer:
A) Q₁

Question 90.
x < 0, y > 0 then (x, y) ∈ ……………..
A) Q₁
B) Q₂
C) Q₃
D) Q₄
Answer:
B) Q₂

Question 91.
x < 0, y < 0 then (x, y) ∈ ………………
A) Q₁
B) Q₂
C) Q₃
D) Q₄
Answer:
C) Q₃

Question 92.
x > 0, y < 0 then (x, y) ∈ ……………..
A) Q₁
B) Q₂
C) Q₃
D) Q₄
Answer:
D) Q₄

Question 93.
Slope of the line \(\frac{x}{a}+\frac{y}{b}\) = 1 is
A) \(\frac{1}{b}\)
B) \(\frac{1}{a}\)
C) \(\frac{a}{b}\)
D) –\(\frac{\mathrm{b}}{\mathrm{a}}\)
Answer:
D) –\(\frac{\mathrm{b}}{\mathrm{a}}\)

Question 94.
Slope of the line x = 9 is
A) 9
B) – 9
C) 0
D) 5
Answer:
A) 9

Question 95.
The distance between the pointsP(x, y) from origin O (0, 0) is
A) \(\sqrt{x+y}\)
B) \(\sqrt{x^{2}+y^{2}}\)
C) x² + y²
D) x + y
Answer:
B) \(\sqrt{x^{2}+y^{2}}\)

Question 96.
A point on the X – axis
A) (3, 3)
B) (4, 5)
C) (2, 0)
D) (0, 2)
Answer:
C) (2, 0)

Question 97.
A point on the Y – axis
A) (4, 5)
B) (0, 3)
C) (3, 0)
D) (4, 3)
Answer:
B) (0, 3)

Question 98.
The ratio in which the centroid divides the median of a triangle is
A) 1 : 2
B) 2 :1
C) 1 : 3
D) 3 : 1
Answer:
C) 1 : 3

Question 99.
Intercept form of a line is …………….
A) \(\frac{x}{a}+\frac{y}{b}\) = 1
B) x – y = 7
C) \(\frac{x}{a}+\frac{y}{b}\) = 1
D) y = mx + c
Answer:
A) \(\frac{x}{a}+\frac{y}{b}\) = 1

Question 100.
X – intercept of the line ax + by + c = 0 is
A) \(\frac{-\mathrm{c}}{\mathrm{a}}\)
B) \(\frac{c}{a}\)
C) \(\frac{a}{c}\)
D) \(\frac{1}{c}\)
Answer:
C) \(\frac{a}{c}\)

Question 101.
The line y = mx + c meets Y – axis at the point ……………..
A) (0, 0)
B) (c, 0)
C) (0, c)
D) (0, m)
Answer:
C) (0, c)

Question 102.
The line y = mx + c meets X – axis at the point ………………..
A) (0, 0)
B) (c, 0)
C) (0, c)
D) (0, m)
Answer:
B) (c, 0)

Question 103.
Slope of a line can be taken as ………………
A) cosθ
B) tanθ
C) cosecθ
D) sinθ
Answer:
B) tanθ

Question 104.
The mid point of a line segment divides in the ratio
A) 2 : 1
B) 1 : 2
C) 1 : 1
D) 8 : 7
Answer:
C) 1 : 1

Question 105.
x = 0 represents …………………
A) X – axis
B) Y – axis
C) (0, 0)
D) y = mx + C
Answer:
B) Y – axis

Question 106.
y = 0 represents ………………….
A) X – axis
B) Y – axis
C) (0, 0)
D) y = mx + C
Answer:
A) X – axis

Question 107.
x = k represents ……………….
A) parallel to X – axis
B) parallel to Y – axis
C) parallel to X, Y axes
D) (0, 0)
Answer:
B) parallel to Y – axis

Question 108.
y = k represents ………………
A) parallel to X – axis
B) parallel to Y – axis
C) parallel to X, Y axes
D) (0, 0)
Answer:
A) parallel to X – axis

Question 109.
In the coordinate plane the axes are ……………. to each other.
A) parallel
B) perpendicular
C) either perpendicular or parallel
D) neither parallel nor perpendicular
Answer:
B) perpendicular

Question 110.
The distance of a point from Y – axis is called …………………..
A) y – coordinate
B) x – coordinate
C) origin
D) (0, 0)
Answer:
B) x – coordinate

Question 111.
The distance of a point from X – axis is called ………………..
A) x – coordinate
B) y – coordinate
C) origin
D) coordinate
Answer:
B) y – coordinate

Question 112.
The coordinates of origin are
A) (0, 0)
B) (1, 1)
C) (1, 0)
D) (0, 1)
Answer:
A) (0, 0)

Question 113.
The point which is not on the X – axis
A) (-1, 0)
B) (8, 0)
C) (0, 8)
D)(-2, 0)
Answer:
C) (0, 8)

Question 114.
The point which is not on the Y – axis is
A) (-2, 0)
B) (0, 2)
C) (0, -3)
D) (0, 4)
Answer:
A) (-2, 0)

Question 115.
Area of a triangle enclosed by the axis and the line \(\frac{x}{a}+\frac{y}{b}\) = 1 is a b
A) \(\frac{\mathrm{ab}}{3}\)
B) \(\frac{a^{2} b^{2}}{2}\)
C) \(\frac{\mathrm{ab}}{2}\)
D) \(\frac{a+b}{2}\)
Answer:
C) \(\frac{\mathrm{ab}}{2}\)

Question 116.
If G is the centroid of ΔABC, then ΔGAB = ……………….
A) \(\frac {1}{13}\)ABC
B) \(\frac {1}{4}\)ABC
C) \(\frac {1}{2}\)ABC
D) \(\frac {1}{3}\)ABC
Answer:
D) \(\frac {1}{3}\)ABC

Question 117.
The two lines x = 2 and y = -3 will meet at ………………….
A) (1, 8)
B) (2, 4)
C) (-2, 1)
D) (2, -3)
Answer:
D) (2, -3)

Question 118.
Angle made by the line y = x with the positive direction of X – axis is
A) 80°
B) 45°
C) 90°
D) 100°
Answer:
B) 45°

Question 119.
To locate the exact position of a point the number of references we need is ……………….
A) 0
B) 1
C) 2
D) 3
Answer:
C) 2

Question 120.
In a coordinate system the horizontal line is called ………………………
A) Y – axis
B) X – axis
C) origin
D) reference
Answer:
B) X – axis

Question 121.
In a coordinate system the vertical line is called …………………..
A) Y – axis
B) X – axis
C) origin
D) reference
Answer:
A) Y – axis

Question 122.
The meeting point of the two axis in the coordinate plane is called
A) origin
B) X – axis
C) Y – axis
D) (2, 3)
Answer:
A) origin

Question 123.
The point which lies on both the axis is
A) (1, 1)
B) (2, 2)
q (-1, -1)
D) (0, 0)
Answer:
D) (0, 0)

Question 124.
The x – coordinate of a point is also called
A) ordinate
B) 2^nd coordinate
C) abscissa
D) origin
Answer:
C) abscissa

Question 125.
The y – coordinate of a point is also called
A) ordinate
B) abscissa
C) 1^st coordinate
D) origin
Answer:
A) ordinate

Question 126.
The coordinates of a point are (0,0) then the point is
A) origin
B) X – axis
C) ordinate
D) abscissa
Answer:
A) origin

Question 127.
Indentify the point in Q₁

Answer:

Question 128.
A line parallel to x = 3 is ………………….

Answer:

Question 129.
Which of the following line passing through (0,0) ?

Answer:

Question 130.
The location of points (1, 1)(2, 2)(3, 3)in a graph sheet may represents as ………………..

Answer:

Question 131.
Q₁ ∩ Q₂
A) {1,2}
B) Φ
C) {0,1}
D) {1,2,3}
Answer:
B) Φ

Practice the AP 10th Class Maths Bits with Answers Chapter 6 Progressions on a regular basis so that you can attempt exams with utmost confidence.

AP State Syllabus 10th Class Maths Bits 6th Lesson Progressions with Answers

Question 1.
Which term of the G.P. \(\frac{1}{3}, \frac{1}{9}, \frac{1}{27},\) …………………… is \(\frac{1}{2187}\)
A) 5^th
B) 6^th
C) 7^th
D) 8^th
Answer:
C) 7^th

Question 2.
The 21^st term of an A.P., whose first two terms are -3 and 4 is …………………
A) 143
B) -143
C) 137
D) 17
Answer:
C) 137

Question 3.
The common difference of an A.P. for which a₁₈ – a₁₄ = 32 is ……………..
A) 8
B) -8
C) -4
D) 4
Answer:
A) 8

Question 4.
In an A.P., if a = 1, a_n = 20 and S_n = 399, then n = ………………
A) 19
B) 42
C) 28
D) 38
Answer:
D) 38

Question 5.
Which term of G.P. 3, 3√3,9, …………….. equals to 243?
A) 6
B) 7
C) 8
D) 9
Answer:
B) 7

Question 6.
If x, x + 2, x + 6 are three consecutive terms in G.P, find the value of ‘x’.
A) 3
C) 2
B) 4
D) 1
Answer:
D) 1

Question 7.
If a_n = \(\frac{n(n+3)}{n+2}\) , then find a₁₇ = ………………….
A) \(\frac{340}{20}\)
B) \(\frac{341}{19}\)
C) \(\frac{340}{19}\)
D) \(\frac{341}{20}\)
Answer:
C) \(\frac{340}{19}\)

Question 8.
A famous book written by ancient mathematician Aryabhatta is …………………
A) Arya Tharkam
B) Aryabhatteeyam
C) Siddhantha Siromani
D) Karana Kuthuhalam
Answer:
B) Aryabhatteeyam

Question 9.
The sum of first 100 natural numbers is ………………….
A) 4050
B) 4500
C) 5500
D) 5050
Answer:
D) 5050

Question 10.
If a, b, c are in G.P., then b = ……………….
A) ac
B) \(\sqrt{\mathrm{ac}}\)
C) \(\frac{a+c}{2}\)
D) a²c²
Answer:
B) \(\sqrt{\mathrm{ac}}\)

Question 11.
Which term of the A.P -18, -16, -14, …………………. is first positive term ?
A) t₉
B) t₁₀
C) t₁₁
D) t₁₂
Answer:
C) t₁₁

Question 12.
If 16, x, 36 are in G.P. then x =
A) 24
B) 26
C) 28
D) 30
Answer:
A) 24

Question 13.
The next term of the A.P(a + 3d),(a + d). (a – d), ………………….. is
A) a + 2d
B) a – 2d
C) a – 4d
D) a – 3d
Answer:
D) a – 3d

Question 14.
In an A.P the n^th term a_n is ………………….
A) a_n = a + (n – 1)d
B) d + (n – 1)a
C) a + d
D) \(\frac{(n-1)}{d}\) + a
Answer:
A) a_n = a + (n – 1)d

Question 15.
In a G.P. the 3^rd term is 24 and 6^th term is 192 then 10^th term is …………………….
A) 2062
B) 3072
C) 4072
D) 1072
Answer:
B) 3072

Question 16.
In a G.P. a_{P + Q} = m,a _{P – Q} = n then
a_P= …………………..
A) mn
B) \(\sqrt{m n}\)
C) \(\frac{\mathrm{mn}}{2}\)
D) \(\frac{\mathrm{m}}{2}\)
Answer:
B) \(\sqrt{m n}\)

Question 17.
If a_n = \(\frac{n(n+1)(2 n+1)}{6}\) then a₆ = ……………….
A) ±1
B) n(n + 1)
C) 55
D) 91
Answer:
D) 91

Question 18.
If the sum of first ‘n’ terms of an A.P. 2, 5, 8, ………………… is equal to the sum of first n
terms of the A.P. 57, 59, 61, …………………… then ‘n’ is equal to …………………..
A) 110
C) 112
B) 111
D) 113
Answer:
B) 111

Question 19.
If p, q, r are in A.P. and x, y, z in G.P., then X^{q – r} × Y^{r – p} × Z^{p – q} is equal to …………………..
A) p + q + r
B) x × y × z
C) 1
D) px + qy + rz
Answer:
C) 1

Question 20.
In an A.P., p^th term is q and q^th term is p, then its common difference is ………………….
A) 1
B) -1
C) 2
D) -2
Answer:
B) -1

Question 21.
The next term of √2, √8, √18, √32, …………………. is …………………..
A) \(\sqrt{34}\)
B) \(\sqrt{38}\)
C) \(\sqrt{42}\)
D) \(\sqrt{50}\)
Answer:
D) \(\sqrt{50}\)

Question 22.
The common difference of an AP in which a₂₅ – a₁₂ = -52 is ………………….
A) 4
B) -4
C) -3
D) 3
Answer:
B) -4

Question 23.
What will be the value of x if 8x + 4 , 6x – 2 and 2x + 7 are in arithmetic progression?
A) \(\frac{-15}{2}\)
B) \(\frac{15}{2}\)
C) 15
D) -15
Answer:
B) \(\frac{15}{2}\)

Question 24.
The n^th term of an arithmetic progression is -11 while sum of the first n terms is 66, when its first term is 22 then the value of n is
A) 12
B) 13
C) 14
D) 15
Answer:
A) 12

Question 25.
If the first and fifth term’s sum is 10, then the third term of an arithmetic progression is………………
A) 3
B) 1
C) 5
D) 2
Answer:
C) 5

Question 26.
If the 10^th term of the sequence \(\sqrt{3}, \sqrt{12}, \sqrt{27}\) ……………..is \(\sqrt{3 n^{2}}\) then the value of \(\frac{\mathbf{n}}{2}\) is ………………..
A) 3
B) √3
C) 5
D) √5
Answer:
C) 5

Question 27.
If the product of five numbers in GP is 1024, then the middle number is
A) 8
B) 4
C) 2
D) None
Answer:
B) 4

Question 28.
If the second term of a GP is 2 and the sum of infinite terms is 8, then the first term is
A) 8
B) 6
C) 4
D) 3
Answer:
B) 6

Question 29.
If a, b and c are in AP and also in GP, then
A) a = b ≠ c
B) a ≠ b = c
C) a ≠ b ≠ c
D) a = b = c
Answer:
A) a = b ≠ c

Question 30.
The least value of n for which 1 + 2 + 2² + ……………….. (n terms) is greater than 1000 is
A) 7
B) 8
C) 9
D) 10
Answer:
D) 10

Question 31.
The number of numbers between 100 and 1000 which are divisible by 7 is
A) 7
B) 128
C) 132
D) None
Answer:
B) 128

Question 32.
Which is the three digit number divisible by 7 ?
A) 100
B) 133
C) 137
D) 143
Answer:
B) 133

Question 33.
The 6th term in the GP 2, 8, 32, ……………….. is
A) 512
B) 128
C) 2048
D) 256
Answer:
C) 2048

Question 34.
1 + 1 + 1 + ………….. n terms =
A) \(\frac{\mathrm{n}}{2}\)
B) \(\frac{\mathrm{n}-1}{2}\)
C) n
D) \(\frac{n+1}{2}\)
Answer:
C) n

Question 35.
1 + 3 + 6 + 10 + …………………. n terms =
A) \(\frac{n(n+1)(n+2)}{4}\)
B) \(\frac{n(n+1)(n+2)}{8}\)
C) \(\frac{n(n+1)(n+2)}{6}\)
D) None
Answer:
C) \(\frac{n(n+1)(n+2)}{6}\)

Question 36.
How many two-digit numbers are divisible by 6 ?
A) 12
B) 15
C) 10
D) 17
Answer:
B) 15

Question 37.
If the 2nd term of an AP is 4 and the 6th term is 16, then its 11th term is
A) 29
B) 33
C) 34
D) 31
Answer:
A) 29

Question 38.
Which term of the AP 24, 21, 18,……………. is the first negative ?
A) 10th
B) 8th
C) 7th
D) 6th
Answer:
C) 7th

Question 39.
If a = 2 and d = 2, then S₁₅ =
A) 220
B) 230
C) 240
D) 245
Answer:
C) 240

Question 40.
The n^th term of a Geometric Progression is a_n = ar^{n – 1}, where ‘ r ‘ represents
A) Common difference
B) Common ratio
C) First term
D) Radius
Answer:
B) Common ratio

Question 41.
If the n^th term of an A.P. is a_n = 3 + 2n, then the common difference d is ……………………
A) 2
B) 3
C) 4
D) 5
Answer:
A) 2

Question 42.
The common difference of the AP, x – y, x, x + y,………… is ……………….
A) x
B) y
C) – x
D) -y
Answer:
B) y

Question 43.
Common difference of an Arithmetic Progression, whose 3rd term is 5 and 7th term is 9, is
A) 1
B) 2
C) 3
D) 4
Answer:
A) 1

Question 44.
If (i) -1.0, -1.5, -2.0, -2.5, …………………. and (ii) -1,-3, -9, -27,…………….. are two progressions, then which of them is a Geometric Progression ?
A) (i) only
B) (ii) only
C) (i) and (ii) both
D) None of them
Answer:
B) (ii) only

Question 45.
If n^th term of a series is \(\frac{3 n-4}{7}\), then 6^th term =
A) \(\frac{15}{7}\)
B) 1
C) 2
D) \(\frac{18}{7}\)
Answer:
C) 2

Question 46.
If n^th term of a series is \(\) then 7^th term =
A) \(\frac{73}{90}\)
B) \(\frac{5}{9}\)
C) \(\frac{49}{9}\)
D) \(\frac{7}{9}\)
Answer:
B) \(\frac{5}{9}\)

Question 47.
Which of the following is an A.P ?
A) 1 + 8 +27 + ……………….
B) 1 + 4 + 9 + ……………….
C) 1 – 2 + 3 – 4 + …………….
D) 1 + 2 + 3 + ……………
Answer:
D) 1 + 2 + 3 + ……………

Question 48.
10^th term of 4 + 6 + 8 + ………….. is
A) 26
B) 18
C) 22
D) 20
Answer:
C) 22

Question 49.
27^th term of 5, 14, 23, ……………… is
A) 900
B) 101
C) 100
D) 239
Answer:
D) 239

Question 50.
12^th term of the series 5, 14, 23, ……………. is
A) 900
B) 104
C) 239
D) 100
Answer:
B) 104

Question 51.
18^th term of 13, 8, 3, -2, ……………….. is
A) -32
B) -72
C) 32
D) -57
Answer:
B) -72

Question 52.
Common difference of x + \(\frac{4 x}{3}+\frac{5 x}{3}\) + 2x + ……………… is
A) \(\frac{x}{3}\)
B) \(\frac{1}{3}\)
C) x
D) \(\frac{2 x}{3}\)
Answer:
A) \(\frac{x}{3}\)

Question 53.
The common difference of the A.P 13, 8, 3, -2, …………… is
A) 10
B) 4
C) 5
D) -5
Answer:
D) -5

Question 54.
If a = -1, d = -3 in an A.P, then 12^th term is
A) 17
B) -23
C) -34
D) -17
Answer:
C) -34

Question 55.
If the first term of an A.P is -2 and common difference is -5, then 12^th term is
A) -32
B) 32
C) -57
D) 34
Answer:
C) -57

Question 56.
If n^th term of an A.P is \(\frac{5 n-4}{7}\) then common difference is
A) \(\frac{-4}{7}\)
B) \(\frac{5}{7}\)
C) \(\frac{1}{7}\)
D) \(\frac{3}{7}\)
Answer:
B) \(\frac{5}{7}\)

Question 57.
In an A.P if 8^th term is 23 and 102^nd term is 305, then common difference is
A) 5
B) 2
C) 1
D) 3
Answer:
D) 3

Question 58.
In an A.P. if first term is 4,9^th term is 20, then 15^th term is
A) 32
B) 36
C) 16
D) 18
Answer:
A) 32

Question 59.
In an A.P if third term is 7 and seventh term is 15, then first term is
A) 2
B) 0
C) 5
D) 3
Answer:
D) 3

Question 60.
In an A.P, if 16^th term is 47 and 31^st term is 92, then 27^th term is
A) 86
B) 120
C) 80
D) 116
Answer:
C) 80

Question 61.
In an A.P, if 7 times of 7th term is equal to 11 times of 11th term, then 18th term is
A) 7
B) 0
C) 11
D) 18
Answer:
B) 0

Question 62.
If 3rd term of an A.P is 11 and 15th term is 59, then 24th term is
A) 89
B) 95
C) 109
D) 79
Answer:
B) 95

Question 63.
If 10th term of an A.P is 0 and 42nd term is -32, then nth term is ………………
A) 10 – n
B) 8 – n
C) 11 – n
D) 9 – n
Answer:
A) 10 – n

Question 64.
Sum of 20 terms of 3 + 5 + 7 + 9 + ………………. is
A) 440
B) 220
C) 410
D) 460
Answer:
A) 440

Question 65.
How many terms are to be added to make the sum 52 in the series (-8) + (-6) + (-4) + ……………… ?
A) 31
B) 13
C) 3
D) 12
Answer:
B) 13

Question 66.
In an A.P. if common difference is 2, sum of n terms is 49,7th term is 13, then n = ………………
A) 7
B) 0
C) 13
D) 5
Answer:
A) 7

Question 67.
If the n^th term of an A.P, is 2n + 5, its first term is
A) 0
B) 7
C) 2
D) 4
Answer:
B) 7

Question 68.
How many numbers are divisible by 9 in between 1 and 1000 ?
A) 100
B) 101
C) 110
D) 111
Answer:
B) 101

Question 69.
The number of odd numbers between 1,100 that are divisible by 5 is
A) 15
B) 5
C) 10
D) 11
Answer:
C) 10

Question 70.
If the sum of three numbers which are in A.P is 27 and the product of first and last is 77, then the numbers are
A) 7, 10,11
B) 7, 9, 11
C) 6, 9, 12
D) 8, 9, 10
Answer:
B) 7, 9, 11

Question 71.
If the sum of three numbers which are in A.P is 15 and the sum of the squares of the extremes is 58, then those numbers are
A) 3, 6, 9
B) 3, 5, 7
C) 2, 5, 8
D) 2, 6, 7
Answer:
B) 3, 5, 7

Question 72.
If the sum of four numbers in A.P is 24 and the sum of their squares 164, then those numbers are
A) 3, 5, 7, 9
B) 3, 4, 5, 6
Q 1, 4, 7,11
D) 2, 4, 6,12
Answer:
A) 3, 5, 7, 9

Question 73.
If the sum of the series 24, 20, 16, …………… is 60, then the number of terms is
A) 13
B) 25
C) 3
D) 25
Answer:
C) 3

Question 74.
72 + 70 + 68 + ……………. + 40=
A) 952
B) 1852
C) 1052
D) 1252
Answer:
A) 952

Question 75.
If d = 2 and 8th term of an A.P is 15, then the sum of 15 terms is ………………
A) \(\frac{225}{2}\)
B) 0
C) 15
D) 225
Answer:
D) 225

Question 76.
If the sum of n terms of an A.P is 4n² + 5n, then common difference is
A) 8
B) 0
C) 4
D) 6
Answer:
A) 8

Question 77.
If 5^th term of a G.P is 32 and common ratio 2, then the sum of 14 terms is
A) 32, 766
B) 16, 388
C) 64, 432
D) 30,746
Answer:
A) 32, 766

Question 78.
The sum of even numbers between 100, 200 is
A) 7650
B) 6750
C) 5670
D) 7350
Answer:
D) 7350

Question 79.
Arithmetic mean of \(\frac{1}{2}\) and \(\frac{1}{3}\) is
A) \(\frac{12}{5}\)
B) \(\frac{6}{5}\)
C) \(\frac{5}{12}\)
D) \(\frac{5}{6}\)
Answer:
C) \(\frac{5}{12}\)

Question 80.
One of the four A.M’s between 3, 23 is ………………..
A) 15
B) 6
C) 21
D) 8
Answer:
A) 15

Question 81.
The product of two numbers is 91 and their arithmetic mean is 10 then the two numbers are
A) 14,6
B) 13, 7
C) 10, 10
D) 12, 8
Answer:
B) 13, 7

Question 82.
Sum of 10 arithmetic means between 3, 10 is
A) 65
B) 130
C) 0
D) 60
Answer:
A) 65

Question 83.
Sum of 4 arithmetic means between 3 and 23 is
A) 69
B) 48
C) 52
D) 50
Answer:
C) 52

Question 84.
Sum of first 100 odd numbers is
A) 10,000
B) 100
C) 1000
D) 1,00,000
Answer:
A) 10,000

Question 85.
1² + 2² + 3² + +100² = ……………….
A) (5050)²
B) 42925
C) 5050
D) 5500
Answer:
D) 5500

Question 86.
Sum to ‘n’ terms of 1, 8, 27, 64, ……………
A) \(\frac{n^{2}(n+1)}{4}\)
B) \(\frac{n^{2}(n+1)^{2}}{4}\)
C) \(\frac{n(n+1)}{2}\)
D) \(\frac{n(n+1)(2 n+1)}{6}\)
Answer:
B) \(\frac{n^{2}(n+1)^{2}}{4}\)

Question 87.
Sum to ‘n’ terms of 3.5 + 4.7 + 5.9 + …………………
A) \(\frac{n(n+1)(n-3)}{12}\)
B) \(\frac{n\left(4 n^{2}+27 n+59\right)}{6}\)
C) \(\frac{n\left(25 n^{2}+65 n+2\right)}{12}\)
D) \(\frac{n\left(25 n^{2}+65 n+2\right)}{6}\)
Answer:
B) \(\frac{n\left(4 n^{2}+27 n+59\right)}{6}\)

Question 88.
(1) + (1 + 3) + (1 + 3 + 5) + to ‘n’ terms = ……………….
A) \(\frac{n(n-1)(2 n-1)}{24}\)
B) \(\frac{n(n+1)(2 n-1)}{12}\)
C) \(\frac{n(n+1)(2 n+1)}{6}\)
D) \(\frac{n(n+1)(2 n+1)}{24}\)
Answer:
C) \(\frac{n(n+1)(2 n+1)}{6}\)

Question 89.
Which of the following geometric pro-gressions has the common ratio as 2?
A) \(\sqrt{2}, \sqrt{6}, \sqrt{18}\) , ……………….
B) \(\sqrt{3}, \sqrt{6}, \sqrt{12}\) , ……………….
C) \(\sqrt{5}, \sqrt{15}, \sqrt{45}\) , ……………….
D) \(\sqrt{7}, \sqrt{21}, \sqrt{63}\) , ……………….
Answer:
B) \(\sqrt{3}, \sqrt{6}, \sqrt{12}\) , ……………….

Question 90.
\(\frac{1^{2}}{3}+\frac{1^{2}+2^{2}}{5}+\frac{1^{2}+2^{2}+3^{2}}{7}\) + ………… n terms =
A) \(\frac{n(n+1)(n+2)}{12}\)
B) \(\frac{n(n+1)(n+2)}{24}\)
C) \(\frac{n(n+1)(n+2)}{6}\)
D) \(\frac{n(n+1)(n+2)}{18}\)
Answer:
D) \(\frac{n(n+1)(n+2)}{18}\)

Question 91.
Sum of first n terms of 1.4 + 4.7 + 7.10 + 10.13 + ……………… is
A) Σn² – 4Σn + n
B) 9Σn² – 3Σn – 2n
C) Σn² – 3Σn + 4
D) 9Σn² – 3Σn – 2
Answer:
B) 9Σn² – 3Σn – 2n

Question 92.
The n^th term of the series 1.3 + 3.5 + 5.7 + …………….. is
A) 1 – 4n
B) n² + 4
C) 4n² – 1
D) 4n² + 1
Answer:
C) 4n² – 1

Question 93.
n^th \(\frac{5}{1.2}+\frac{7}{2.3} \cdot \frac{1}{3}+\frac{9}{3.4} \cdot \frac{1}{3^{2}}\) + \(\frac{11}{4.5} \cdot \frac{1}{3^{3}}\) term of the series
A) \(\frac{2 n+4}{n(n+1)} \cdot \frac{1}{3^{n}}\)
B) \(\frac{2 n+3}{n(n+1)} \cdot \frac{1}{3^{n+1}}\)
C) \(\frac{2 n+3}{n(n+1)} \cdot \frac{1}{3^{n}}\)
D) \(\frac{2 n+3}{n(n+1)} \cdot \frac{1}{3^{n-1}}\)
Answer:
D) \(\frac{2 n+3}{n(n+1)} \cdot \frac{1}{3^{n-1}}\)

Question 94.
Sum to n terms of 1.2.3 + 2.3.4 + 3.4.5 + ……………… is .
A) \(\frac{n(n+1)(n+2)(n+3)}{6}\)
B) \(\frac{n(n+1)(n+2)}{2}\)
C) \(\frac{n(n+1)(n+2)(n+3)}{4}\)
D) \(\frac{n(n+1)(n+2)(n+3)}{8}\)
Answer:
C) \(\frac{n(n+1)(n+2)(n+3)}{4}\)

Question 95.
\(\frac{1+2+3+\ldots \ldots+n}{1+3+5+\ldots \ldots+(2 n-1)}\) =
A) \(\frac{(\mathrm{n}+1)}{2 \mathrm{n}}\)
B) \(\frac{2}{\mathrm{n}}\)
C) \(\frac{\mathrm{n}}{2}\)
D) \(\frac{(\mathrm{n}-1)}{2}\)
Answer:
A) \(\frac{(\mathrm{n}+1)}{2 \mathrm{n}}\)

Question 96.
If the common difference of an A.P is 1 and 6th term is \(\frac{\left(4 \cos ^{2} \alpha+1\right)}{\cos ^{2} \alpha}\), then first term is
A) cot²α
B) cosec²α
C) tan²α
D) sec²α
Answer:
C) tan²α

Question 97.
Sum of n terms of + ……………. is
A) \(\frac{(2 n+1)}{n}\)
B) \(\frac{n}{(2 n+1)}\)
C) \(\frac{n+1}{n}\)
D) \(\frac{\mathrm{n}}{(\mathrm{n}+1)}\)
Answer:
D) \(\frac{\mathrm{n}}{(\mathrm{n}+1)}\)

Question 98.
Sum of n terms of 1 + 4 + 13 + 40 + ……………… is
A) \(\frac{\left(3^{n+1}+2 n-3\right)}{4}\)
B) \(\frac{\left(3^{n+1}-2 n-3\right)}{4}\)
C) \(\frac{\left(3^{n+1}-2 n+3\right)}{4}\)
D) \(\frac{\left(3^{n+1}+2 n+3\right)}{4}\)
Answer:
B) \(\frac{\left(3^{n+1}-2 n-3\right)}{4}\)

Question 99.
Sum of n terms of 2.3 + 3.4 + 4.5 + ………………. is
A) \(\frac{n\left(n^{2}+6 n+11\right)}{3}\)
B) \(\frac{n\left(n^{2}-6 n-11\right)}{3}\)
C) \(\frac{n\left(n^{2}-6 n+11\right)}{3}\)
D) \(\frac{n\left(n^{2}+6 n-11\right)}{3}\)
Answer:
A) \(\frac{n\left(n^{2}+6 n+11\right)}{3}\)

Question 100.
If 2nd term of a G.P is 24 and 5th term is 81, then first term is
A) 16
B) 20
C) \(\frac{3}{2}\)
D) 3
Answer:
A) 16

Question 101.
The common ratio of 2 + \(\frac{2}{3}+\frac{2}{9}+\frac{2}{27}\)+ …………….. is
A) \(\frac{1}{2}\)
B) 2
C) 3
D) \(\frac{1}{3}\)
Answer:
D) \(\frac{1}{3}\)

Question 102.
If the sum of three numbers in G.P is 21 and their product is 216, then the numbers are
A) 5, 7,9
B) 3, 6, 12
C) 2, 4, 8
D) 4, 8, 6
Answer:
B) 3, 6, 12

Question 103.
If the product of five numbers in G.P is 1024, then the middle number is
A) 2
B) 8
C) 4
D) 16
Answer:
C) 4

Question 104.
Sum of 20 terms of 3 + 6 + 12 + ……………. is
A) 3(2¹⁹ – 1)
B) 3(2²⁰ – 1)
C) 3(2¹⁹ -1)/2
D) \(\)
Answer:
B) 3(2²⁰ – 1)

Question 105.
1 + \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\) + ……………. n terms =
A) 3
B) 2
C) \(\frac{1}{2}\)
D) 1
Answer:
B) 2

Question 106.
1 + 2 + 2² + 2³ + …………. n terms =
A) 2ⁿ – 1
B) 1
C) 2^{n – 1} – 1
D) 2
Answer:
A) 2ⁿ – 1

Question 107.
If 5^th term of a G.P is 32 and common ratio 2, then the sum of 14 terms is
A) 64,432
B) 16,383
C) 32,766
D) 8,194
Answer:
C) 32,766

Question 108.
The value of 0.234 is
A) \(\frac{232}{990}\)
B) \(\frac{234}{1000}\)
C) \(\frac{232}{1000}\)
D) \(\frac{234}{990}\)
Answer:
A) \(\frac{232}{990}\)

Question 109.
The common ratio of the series 3 – 6 + 12 – 24 + 48 ……………. is
A) \(\frac{1}{2}\)
B) -2
C) -3
D) 3
Answer:
B) -2

Question 110.
If x, 2x + 2, 3x + 3 are in G.P. then 4^th term is
A) -27
B) 13.5
C) 27
D) -13.5
Answer:
D) -13.5

Question 111.
The 12th term of a G.P. whose first term is \(\frac{1}{8}\) and second term is \(\frac{1}{2}\) is
A) 4¹¹
B) 2 × 4¹¹
C) 2 × 4⁹
D) 2 × 4¹⁰
Answer:
C) 2 × 4⁹

Question 112.
The sum to n – terms of the series (1 – x) + (2 + x²) + (3 – x³) + ……………
A) \(\frac{n(n+1)}{2}+\frac{x\left(1-x^{n}\right)}{1-x}\)
B) \(\frac{2}{n(n+1)}-\frac{1-x}{x\left(1-x^{n}\right)}\)
C) \(\frac{n(n-1)}{2}-\frac{x\left(1-x^{n}\right)}{1-x}\)
D) \(\frac{n(n+1)}{2}-\frac{x\left(1-x^{n}\right)}{1-x}\)
Answer:
D) \(\frac{n(n+1)}{2}-\frac{x\left(1-x^{n}\right)}{1-x}\)

Question 113.
The seventh term in the sequence 1, \(\frac{-1}{2}, \frac{1}{4}\), ………………..
A) \(\frac{1}{64}\)
B) \(\frac{-1}{8}\)
C) \(\frac{1}{16}\)
D) \(\frac{-1}{32}\)
Answer:
A) \(\frac{1}{64}\)

Question 114.
If x, 2x + 2, 3x + 3, are in G.P. then the fourth term is ……………….
A) -13.5
B) -27
C) 27
D) 13.5
Answer:
A) -13.5

Question 115.
The common ratio of G.P.
1 – \(\frac{1}{3}+\frac{1}{9}-\frac{1}{27}\) + ……………. is
A) -3
B) \(\frac{-1}{3}\)
C) 3
D) \(\frac{1}{3}\)
Answer:
B) \(\frac{-1}{3}\)

Question 116.
1 + (0.04) + (0.04)² + ………………. ∞ =
A) \(\frac{24}{25}\)
B) 1
C) 0.04
D) \(\frac{25}{24}\)
Answer:
D) \(\frac{25}{24}\)

Question 117.
If |x| < 1,y = x – x² + x² – x? + ……………… ∞,then the value of x in terms of y is
A) \(\frac{1-y}{y}\)
B) \(\frac{y}{1-y}\)
C) \(\frac{y}{y+1}\)
D) \(\frac{\mathrm{y}}{\mathrm{y}-1}\)
Answer:
B) \(\frac{y}{1-y}\)

Question 118.
Coefficient of x² in (x + 1) (x + 2) (x + 3) (x + 4) (x + 5) is ………………..
A) 20
B) 6
C) 15
D) 12
Answer:
D) 12

Question 119.
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\) + ……………… = x,
\(\frac{1}{3}+\frac{1}{9}+\frac{1}{21}+\frac{1}{81}\) + y, then
A) x² = y
B) 2x + 4y = 4
C) x = y
D) x + y = 0
Answer:
B) 2x + 4y = 4

Question 120.
The sum to infinity of \(\frac{1}{7}+\frac{2}{7^{2}}+\frac{1}{7^{3}}+\frac{2}{7^{4}}\) + ……………. is
A) \(\frac{5}{48}\)
B) \(\frac{7}{24}\)
C) \(\frac{3}{16}\)
D) \(\frac{1}{5}\)
Answer:
C) \(\frac{3}{16}\)

Question 121.
The least value of n so that 1 + 3+ 3² + 3³ + ………….. n terms is greater than 2000 is …………….
A) 8
B) 7
C) 9
D) 6
Answer:
A) 8

Question 122.
The greatest value of n so that 1 + 5 + 5² + 5³ + …………. n terms is less than 4321 is ………………..
A) 7
B) 6
C) 9
D) 8
Answer:
B) 6

Question 123.
7 + 77 + 777 + ………………….. n terms =
A) \(\frac{7\left(10^{\mathrm{n}}-1\right)}{81}-\frac{7 \mathrm{n}}{9}\)
B) 7(10ⁿ – 1) – \(\frac{7 \mathrm{n}}{9}\)
C) \(\frac{70\left(10^{\mathrm{n}}-1\right)}{81}-\frac{7 \mathrm{n}}{9}\)
D) 70 (10ⁿ – 1) – \(\frac{7 \mathrm{n}}{9}\)
Answer:
C) \(\frac{70\left(10^{\mathrm{n}}-1\right)}{81}-\frac{7 \mathrm{n}}{9}\)

Question 124.
The sum to n terms of the series 0.5 + 0.55 + 0.555 + …………………… is
A) \(\frac{5 n}{9}-\frac{5}{81}\left(1-\frac{1}{10^{n}}\right)\)
B) \(\frac{5 n}{9}+\frac{5}{81}\left(1+\frac{1}{10^{n}}\right)\)
C) \(\frac{5 n}{9}-\frac{5}{81}\left(\frac{1}{10^{n}}-1\right)\)
D) \(\frac{5 n}{9}+\frac{5}{81}\left(1-\frac{1}{10^{n}}\right)\)
Answer:
A) \(\frac{5 n}{9}-\frac{5}{81}\left(1-\frac{1}{10^{n}}\right)\)

Question 125.
If the sum of the three numbers in a G.P is 26 and the sum of products taken two at a time is 156, then the numbers are
A) 1, 4, 16
B) 2, 6, 18
C) 1, 5, 25
D) 1, 8, 64
Answer:
B) 2, 6, 18

Question 126.
If the sum of three numbers in G.P is \(\frac{7}{64}\) and the product of the extremes is \(\frac{21}{1024}\) then the numbers are
A) \(\frac{1}{81}, \frac{1}{16}, \frac{1}{32}\)
B) 16, 32, 64
C) \(\frac{1}{64}, \frac{1}{32}, \frac{1}{16}\)
D) \(\frac{1}{16}, \frac{1}{64}, \frac{1}{32}\)
Answer:
C) \(\frac{1}{64}, \frac{1}{32}, \frac{1}{16}\)

Question 127.
If p^th,q^th,r^th terms of a G.Pare a, b, c then Σ(q – r) log a =
A) 0
B) 1
C) abc
D) pqr
Answer:
A) 0

Question 128.
If there are 3 geometric means between 4 and 64 then the common ratio is
A) 12
B) 15
C) 4
D) 16
Answer:
C) 4

Question 129.
Geometric mean of 6 and 24 is
A) 13
B) 30
C) 12
D) 15
Answer:
C) 12

Question 130.
One of the 5 geometric means 1 between \(\frac {1}{3}\) and 243 is
A) 81
B) 80
C) 79
D) 82
Answer:
A) 81

Question 131.
If the A.M and G.M of two numbers are 13 and 12 respectively then the two numbers are
A) 10, 18
B) 12, 18
C) 8, 18
D) 8, 12
Answer:
C) 8, 18

Question 132.
If the arithmetic mean of two numbers is 10 and geometric mean is 6, then the numbers are
A) 1, 19
B) 2, 18
C) 3, 17
D) 3, 18
Answer:
B) 2, 18

Question 133.
Which of the following series is an arithmetic progression ?
A) 2, 4, 6, 8,
B) 1, 2, 4, 8,
C) 4, 9, 16, 25,
D) 3, 9, 12, 18,
Answer:
D) 3, 9, 12, 18,

Question 134.
Which term of the A.P. 5, 2, -1, ……………….. is -22 ?
A) 11
B) 8
C) 9
D) 10
Answer:
D) 10

Question 135.
Which term of 7 + 11 +15 + ………………. is 67?
A) 20
B) 6
C) 16
D) 10
Answer:
B) 6

Question 136.
Which series is equal to \(\frac{n(n+1)}{2}\) ?
A) 1³ + 2³ + 3³ + + n³
B) 1.2 + 2.3 + 3.4 + + n(n + 1)
C) 1 + 2 + 3+ ……+ n
D) 1² + 2² + 3² + ……………… + n²
Answer:
C) 1 + 2 + 3+ ……+ n

Question 137.
Which term of 0.0004 + 0.02 + 0.1 + ……………… is 12 ?
A) 7
B) 5
C) 8
D) 6
Answer:
D) 6

Question 138.
Which term of 2 – \(\frac{1}{\sqrt{2}}+\frac{1}{4}\) – \(\frac{1}{32}\) ……………… is ?
A) 8
B) 7
C) 5
D) 6
Answer:
C) 5

Question 139.
n^th term of 4 + 9 + 14 + …………….. is
A) 5n +1
B) 4n – 1
C) 5n – 1
D) 4n + 1
Answer:
C) 5n – 1

Question 140.
If x, y, z are in A.P, then 2y =
A) \(\sqrt{\mathrm{XZ}}\)
B) xz
C) x + z
D) x – z
Answer:
C) x + z

Question 141.
The ratio of the sums of m arithmatic means and n arithmetic means between two numbers is
A) n : m
B) 2m – 1 : 2n – 1
C) m : n
D) 2m + 1, 2n + 1
Answer:
C) m : n

Question 142.
If the ratio of sum of n terms in two A.P is 2n : n + 1, then the ratio of 8th terms is …………….
A) 8 : 13
B) 15 : 8
C) 5 : 17
D) 8 : 17
Answer:
B) 15 : 8

Question 143.
Arithmetic mean of a and b is
A) \(\sqrt{a b}\)
B) \(\frac{2}{a+b}\)
C) \(\frac{a+b}{2}\)
D) a + b
Answer:
C) \(\frac{a+b}{2}\)

Question 144.
If S₁, S₂, S₃ are the sums of first n natural numbers, their squares and their cubes respectively, then S₃(1 + 8S₁) =
A) 9S₂²
B) S₂²
C) 9S₂
D) 9S²
Answer:
A) 9S₂²

Question 145.
If a, b, c are in G.P., then
A) c = ab
B) a = bc
C) b² = ac
D) b = ac
Answer:
C) b² = ac

Question 146.
The series (n – 1), (n – 2), (n – 3), ……………… is a type of
A) A.P
B) G.P
C) May be both
D) None
Answer:
A) A.P

Question 147.
If n^th term of a series is 3ⁿ, then the sum of n terms =
A) 3(3^{n – 1} – 1)
B) \(\frac{3\left(3^{n-1}-1\right)}{2}\)
C) 3(3ⁿ – 1)
D) \(\frac{3\left(3^{n}-1\right)}{2}\)
Answer:
D) \(\frac{3\left(3^{n}-1\right)}{2}\)

Question 148.
If n^th term of series is 2ⁿ + n, then sum of n terms =
A) \(\frac{2\left(2^{\mathrm{n}}-1\right)+\mathrm{n}(\mathrm{n}+1)}{2}\)
B) n(2ⁿ – 1) + n(n + 1)
C) \(\frac{2\left(2^{n}-1\right)}{2}+\frac{n(n+1)}{2}\)
D) n(2ⁿ + 1) + n(n – 1)
Answer:
A) \(\frac{2\left(2^{\mathrm{n}}-1\right)+\mathrm{n}(\mathrm{n}+1)}{2}\)

Question 149.
n^th term of -3 + 6 – 12 + 24 – 48 + …………… is
A) 2.3^{n – 1}
B) 3.2^{n + 1}
C) (-1)^{n – 1}. 3.2^{n – 1}
D) (-1)ⁿ. 3.2^{n – 1}
Answer:
C) (-1)^{n – 1}. 3.2^{n – 1}

Question 150.
If a, b, c are in geometric progression then \(\frac{a}{b}\) =
A) [late]\frac{c}{b}[/latex]
B) \(\frac{b}{c}\)
C) \(\frac{\mathrm{b}}{\mathrm{a}}\)
D) \(\frac{\mathrm{a}}{\mathrm{c}}\)
Answer:
B) \(\frac{b}{c}\)

Question 151.
\(\frac{x}{2}+\frac{x}{4}+\frac{x}{8}\) + ……………….. ∞ =
A) 2x
B) \(\frac{x}{2}\)
C) x
D) \(\frac{2 x}{2}\)
Answer:
C) x

Question 152.
If g₁, g₂, g₃ are three geometric means between two positive numbers a, b then g₁g₃ =
A) g₂
B) g₂²
C) 2g₂
D) 2g₂²
Answer:
B) g₂²

Question 153.
If g₁, g₂, g₃ are geometric means between m, n then
A) mn = g₃²
B) mn = g₁. g₂
C) mn = g₂²
D) mn = g₁²
Answer:
C) mn = g₂²

Question 154.
An employee got Rs. 200 per month in his 11th year service and got ₹495 per month in his 24th year service. If his monthly salary is in A.P., then what is his initial salary ? What is his incriment ?
A) ₹150, ₹ 20
B) ₹ 200, ₹ 10
C) ₹ 300,₹ 10
D) ₹ 150,₹ 15
Answer:
D) ₹ 150,₹ 15

Question 155.
If n arithmetic means are inserted between a and b, then the common difference is ……………….
A) \(\frac{a+b}{n+1}\)
B) \(\frac{n+1}{b+a}\)
C) \(\frac{n+1}{b-a}\)
D) \(\frac{b-a}{n+1}\)
Answer:
D) \(\frac{b-a}{n+1}\)

Question 156.
Sum of the terms 1, 2, 3, 4, ………….. n is
A) \(\frac{\mathrm{n}(\mathrm{n}+1)^{2}}{2}\)
B) \(\frac{n^{2}(n+1)}{2}\)
C) \(\frac{n(n+1)}{2}\)
D) \(\frac{\mathrm{n}(\mathrm{n}-1)}{2}\)
Answer:
C) \(\frac{n(n+1)}{2}\)

Question 157.
Sum to n terms of 1² + 3² + 5² + …………….. is
A) \(\frac{n\left(n^{2}-4\right)}{6}\)
B) \(\frac{\mathrm{n}(4 n-1)}{6}\)
C) \(\frac{n\left(n^{2}-4\right)}{3}\)
D) \(\frac{n\left(4 n^{2}-1\right)}{3}\)
Answer:
D) \(\frac{n\left(4 n^{2}-1\right)}{3}\)

Question 158.
1² + 1 + 2² + 2 + 3² + 3 + 4² + 4 + …………………… + n² + n =
A) \(\frac{n(n+1)(n+2)}{3}\)
B) \(\frac{n(n+1)}{2}\)
C) \(\frac{n(n+1)(n+2)(n+3)}{4}\)
D) \(\left[\frac{n(n+1)}{2}\right]^{2}\)
Answer:
A) \(\frac{n(n+1)(n+2)}{3}\)

Question 159.
1, 4, 9, 16, ………………. sum to ‘n’ terms =
A) \(\frac{n^{2}(n+1)^{2}}{4}\)
B) \(\frac{n(n+1)(2 n+1)}{6}\)
C) \(\frac{(\mathrm{n}+1)(2 \mathrm{n}+1)}{3}\)
D) \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
Answer:
B) \(\frac{n(n+1)(2 n+1)}{6}\)

Question 160.
Sum to ‘n’ terms of 2³ + 4³ + 6³ + ……………. is
A) 4n² (n + 1)²
B) 4n²(n – 1)²
C) 2n²(n + 1)²
D) n² (n + 1)²
Answer:
C) 2n²(n + 1)²

Question 161.
Sum to n terms of 1.2 + 2.3 + 3.4 + …………….. is
A) \(\frac{n(n-1)(n+2)}{3}\)
B) \(\frac{n(n+1)(n+2)}{3}\)
C) \(\frac{n(n+1)(n+2)}{2}\)
D) \(\frac{n(n-1)(n+2)}{6}\)
Answer:
B) \(\frac{n(n+1)(n+2)}{3}\)

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

AP State Syllabus 10th Class Maths Bits 5th Lesson Quadratic Equations with Answers

Question 1.
If sin α, cos α are roots of the equation ax2 + bx + c = 0, then ………………
A) a² + b² – 2ac = 0
B) (a + c)² = b² + c²
C) a² – b² + 2ac = 0
D) (a + c)² = b² – c²
Answer:
D) (a + c)² = b² – c²

Question 2.
If px² + qx + r = 0 has equal roots , then r = ……………….
A) \(\frac{\mathrm{q}^{2}}{2 \mathrm{p}}\)
B) \(\frac{\mathrm{q}}{2 \mathrm{p}}\)
C) \(\frac{-q^{2}}{4 p}\)
D) \(\frac{q^{2}}{4 p}\)
Answer:
D) \(\frac{q^{2}}{4 p}\)

Question 3.
If the equations x² + bx + c = 0, x² + cx + b = 0 [b ≠ c] have a common root, then …………………
A) b + c = 0
B) b + c = 1
C) b + c + 1 = 0
D) None of these
Answer:
C) b + c + 1 = 0

Question 4.
The roots of x – \(\frac{3}{x}\) = 2 are
A) 3, 2
B) 3,-2
C) 3, 1
D) 3, – 1
Answer:
D) 3, – 1

Question 5.
The roots of the quadratic equation 2x² -2√2x + 1 = 0 are ……………….
A) √2, \(\frac{1}{\sqrt{2}}\)
B) \(\frac{1}{2}, \frac{1}{2}\)
C) \(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\)
D) √2, √2
Answer:
C) \(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\)

Question 6.
If α, β are the roots of x² + 2x + 5 = 0 then \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) =
A) \(\frac{6}{5}\)
B) \(\frac{4}{5}\)
C) \(-\frac{6}{5}\)
D) \(-\frac{4}{5}\)
Answer:
C) \(-\frac{6}{5}\)

Question 7.
If the roots of a(b – c)x² + b(c – a) x + c(a – b) = 0 are equal, then a, b, c are in
A) AP
B) GP
C) HP
D) None
Answer:
C) HP

Question 8.
The roots of are \(\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}\)
A) -1, 2
B) 1, 2
C) 1, -2
D) -1, -2
Answer:
B) 1, 2

Question 9.
If A is the solution set of x² – 5x + 6 = 0 and B is the solution set of x – \(\sqrt{3 x-6}=\) = 2, then A ∩ B =
A) Φ
B) A
C) B
D) {2}
Answer:
D) {2}

Question 10.
If the sum of the squares of the roots of x² + px – 3 = 0 is 10, then p =
A) ± 2
B) ± 3
C) ± 5
D) ± 6
Answer:
A) ± 2

Question 11.
If one root of x² – 8x + 13 = 0 is 4 + √3,then the other root is …………….
A) 2 + √3
B) 2 – √3
C) -4 + √3
D) 4 – √3
Answer:
D) 4 – √3

Question 12.
If α and β are the roots of a quadratic a P equation x² – px + q = 0, then \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) =
A) \(\frac{p^{2}-2 q}{q}\)
B) \(\frac{p^{2}+2 q}{q}\)
C) \(\frac{p^{2}-q}{q}\)
D) \(\frac{p^{2}+q}{q}\)
Answer:
D) \(\frac{p^{2}+q}{q}\)

Question 13.
If x = \(\sqrt{3+\sqrt{3+\sqrt{3+\ldots \ldots \infty} \infty}}\) then
A) x² – x + 3 = 0
B) x² + x + 3 = 0
C) x² – x – 3 = 0
D) x² + x – 3 = 0
Answer:
C) x²– x – 3 = 0

Question 14.
If the difference of two numbers is 5 and their product is 84, then the numbers
A) 14, 6
B) 12, 7
C) 21, 4
D) 14, 9
Answer:
B) 12, 7

Question 15.
\(\sqrt{6+\sqrt{6+\sqrt{6+\ldots \ldots \infty} \infty}}\) =
A) 1
B) 2
C) 3
D) 4
Answer:
C) 3

Question 16.
If x + \(\frac{1}{x}\) = 2, then x² + \(\frac{1}{x^{2}}\) =
A) 0
B) 2
C) 4
D) 8
Answer:
B) 2

Question 17.
The discriminant of the quadratic equation ax² + bx + c = 0is
A) b² – 4ac
B) a² – 4bc
C) c² – 4ab
D) None
Answer:
A) b² – 4ac

Question 18.
A ball is thrown vertically upward from the ground. The distance s in t seconds is given by s = 4t² + t – 3. After how many seconds does the ball come to rest?
A) 2s
B) 1s
C) \(\frac{3}{4}\)s
D) \(\frac{4}{3}\)s
Answer:
A) 2s

Question 19.
The product of the roots of √2x² – 10x + 5√2 = 0 is
A) 5√2
B) 5
C) 2√5
D) 2
Answer:
A) 5√2

Question 20.
The discriminant of \(\sqrt{x^{2}-5 x-1}\) = 2 is
A) 21
B) 23
C) 27
D) 45
Answer:
C) 27

Question 21.
The equation x² + x + 1 = 0 has
A) real equal roots
B) no real roots
C) real and unequal roots
D) All of the above a
Answer:
B) no real roots

Question 22.
If \(\frac{\mathbf{x}}{\mathbf{a}-\mathbf{b}}=\frac{\mathbf{a}}{\mathbf{x}-\mathbf{b}}\) then x = …………….
A) (b – a), -a
B) (b – a), \(\frac{1}{a}\)
C) (a – b), b²
D) (b – a), a
Answer:
D) (b – a), a

Question 23.
The discriminant of the equation x² + 4x + 2 = 0 is ……………….
A) 8
B) -8
C) 10
D) 4
Answer:
A) 8

Question 24.
The discriminant of the equation px² + qx + r = 0 is …………………..
A) q² + 4pr
B) q² – 4pr
C) p² – 4qr
D) r² – 4pq
Answer:
B) q² – 4pr

Question 25.
The degree of a quadratic equation is
A) 1
B) 0
C) 2
D) 3
Answer:
C) 2

Question 26.
In a quadratic equation ax² + bx + c = 0, if b² – 4ac > 0, then the roots are ……………….
A) real arid distinct
B) real and equal
C) imaginary
D) none
Answer:
A) real arid distinct

Question 27.
A quadratic equation, whose roots are 2 + √3 and 2 – √3 = ……………….
A) x² – x – 4 = 0
B) x² – 4x + 1 = 0
C) x² + 4x + 3 = 0
D) x² + x – 3 = 0
Answer:
B) x² – 4x + 1 = 0

Question 28.
The adjacent diagram indicates …………………

A) b² – 4ac >0
B) b² – 4ac = 0
C) b² – 4ac < 0
D) None of the given
Answer:
A) b² – 4ac >0

Question 29.
If \(\sqrt{x}+\frac{58}{\sqrt{x}}\) = 31, then x =
A) 529
B) 933
C) 729
D) 841
Answer:
D) 841

Question 30.
Which one of the following figures shows the quadratic equation
ax² + bx + c = 0 (a ≠ 0) having distinct roots ?

Answer:

Question 31.
If 1 is a common root of ax² + ax + 2 = 0 and x² + x + b = 0, then a. b = ………………
A) 2
B) -2
C) 3
D) -3
Answer:
A) 2

Question 32.
Find the zeros of the quadratic polynomial x² – 5x – 14.
A) (+7,-2)
B) (-7,-2)
C) (-7, +2)
D) (7, 2)
Answer:
A) (+7,-2)

Question 33.
If one root of the quadratic equation x² – 4x + 1 = 0 is 2 + √3, then the other
root is ……………………
A) 7 + √3
B) 7 – 4√3
C) 1 + √3
D) 2 – √3
Answer:
D) 2 – √3

Question 34.
If α, β are the roots of x² – 10x + 9 = 0, then | α – β|=
A) 9
B) 8
C) -10
D) 10
Answer:
B) 8

Question 35.
The number of diagonals in a polygon having ‘n’ sides is ………………..
A) \(\frac{n(n+1)}{2}\)
B) \(\frac{n(n-1)}{2}\)
C) \(\frac{n(n-3)}{2}\)
D) \(\frac{n(n+3)}{2}\)
Answer:
C) \(\frac{n(n-3)}{2}\)

Question 36.
If x²– px + q = 0(p,q ∈ Rand p ≠ 0,q ≠ 0) has distinct real roots, then………………
A) p² < 4q
B) p² > 4q
C) p² = 4q
D) p² + 4q = 0
Answer:
B) p² > 4q

Question 37.
If 5 is a root of x² – (K – 1)x + 10 = 0, then the value of K is
A) -8
B) 7
C) 8
D) 12
Answer:
C) 8

Question 38.
Sum of the roots of x² – 16 = 0 is
A) \(\frac{1}{16}\)
B) 1
C) 0
D) 16
Answer:
C) 0

Question 39.
The sum of squares of the roots of x² + 8x + 15 = 0 is …………………
A) 30
B) 34
C) 40
D) 44
Answer:
B) 34

Question 40.
The value of \(\sqrt{2+\sqrt{2+\sqrt{2+\ldots \ldots \ldots}}}\) is……………….
A) 3
B) 4
C) 2
D) 8
Answer:
C) 2

Question 41.
The roots of (b – c) x² + (c – a) x + (a – b) = 0 are equal and kb = a + c, then the value of k is………………..
A) 1
B) 2
C) 3
D) 4
Answer:
B) 2

Question 42.
The roots of x – \(\frac{3}{x}\) = 2 are
A) 1, 3
B) 3, -1
C) 2, 2
D) 1, 2
Answer:
B) 3, -1

Question 43.
If one root of 3x² + 2x + k = 0 is the reciprocal of the other, then the value of
k is
A) 3
B) -3
C) 2
D) 6
Answer:
A) 3

Question 44.
If the roots of 2x² + kx + 3 = 0 are real and equal, then the value of k is
A) ± 2√6
B) ± 6√2
C) ± 4
D) ± 5
Answer:
C) ± 4

Question 45.
The quadratic equation px² + qx + r = 0 has imaginary roots, if ………………
A) q² > 4 pr
B) q² < 4 pr
C) q² = 4 pr
D) p = q + r
Answer:
B) q² < 4 pr

Question 46.
Which of the following is a quadratic equation ?
A) x³ – 6x² + 2x -1 = 0
B) x² + \(\frac{1}{x^{2}}\) = 2
C) x + \(\frac{1}{x}\) = 3
D) (x + 1) (x + 2) (x + 3) = 0
Answer:
C) x + \(\frac{1}{x}\) = 3

Question 47.
The roots of the quadratic equation x² – 5x + 6 = 0 are ………………..
A) -2, 3
B) -2, -3
C) 2, -3
D) 2, 3
Answer:
D) 2, 3

Question 48.
The roots of the quadratic equation x² – 2x + 1 = 0 are
A) -1, -1
B) 1, -1
C) 1, 1
D) 2, 2
Answer:
C) 1, 1

Question 49.
The roots of the quadratic equation 3(x + 3)² = 48 are
A) 1, 7
B) 1, -7
C) -1, 7
D) -1, -7
Answer:
B) 1, -7

Question 50.
The roots of x² – 2x – (r² – 1) = 0 are
A) 1 – r, r + 1
B) 1, r
C) 1 – r, r
D) 1 – r, -r – 1
Answer:
A) 1 – r, r + 1

Question 51.
If 3 is a solution of 3x² + (k -1) x + 9 = 0, then k =
A) 13
B) 11
C) -11
D) -13
Answer:
C) -11

Question 52.
The roots of the quadratic equation \(\frac{x^{2}-8}{x^{2}+20}=\frac{1}{2}\) are ………………….
A) ± 2
B) ± 4
C) ± 3
D) ± 6
Answer:
D) ± 6

Question 53.
If x² + 2kx + 4 = 0 has a root x = 2, then ‘ the value of k is
A) 2
B) -2
C) -1
D) -4
Answer:
B) -2

Question 54.
The roots of the quadratic equation (3x – 2) (2x + 1) = 0 are
A) \(\frac{2}{3}, \frac{-1}{2}\)
B) \(\frac{-2}{3}, \frac{-1}{2}\)
C) \(\frac{-2}{3}, \frac{1}{2}\)
D) \(\frac{2}{3}, \frac{1}{2}\)
Answer:
A) \(\frac{2}{3}, \frac{-1}{2}\)

Question 55.
The roots of the quadratic equation (√3x – √2) (√3x – √2) = 0 are
A) \(\frac{\sqrt{2}}{\sqrt{3}}, \frac{\sqrt{2}}{\sqrt{3}}\)
B) \(\frac{-\sqrt{2}}{\sqrt{3}}, \frac{-\sqrt{2}}{\sqrt{3}}\)
C) \(\frac{\sqrt{2}}{\sqrt{3}}, \frac{-\sqrt{2}}{\sqrt{3}}\)
D) \(\frac{-\sqrt{2}}{\sqrt{3}}, \frac{\sqrt{2}}{\sqrt{3}}\)
Answer:
A) \(\frac{\sqrt{2}}{\sqrt{3}}, \frac{\sqrt{2}}{\sqrt{3}}\)

Question 56.
If \(\frac {1}{2}\) is a root of the equation x2 + kx – \(\frac {5}{4}\) = 0 then the value of k is
A) \(\frac {1}{2}\)
B) \(\frac {1}{4}\)
C) 2
D) -2
Answer:
C) 2

Question 57.
The roots of the quadratic equation \(\frac{x}{a}=\frac{a}{x}\) are
A) a, – a
B) -a², a²
C) -a, -a
D) a, a
Answer:
A) a, – a

Question 58.
The roots of the quadratic equation \(\frac{x^{2}}{a^{2}-b^{2}}=\frac{a+b}{a-b}\) are
A) ± a
B) a, b
C) ± (a + b)
D) ± b
Answer:
C) ± (a + b)

Question 59.
The roots of the quadratic equation \(\frac{11}{3+x}\) = 4(3 – x)are
A) ± 2
B) ± \(\frac{5}{2}\)
C)± \(\frac{1}{5}\)
D) ± 5
Answer:
A) ± 2

Question 60.
The roots of the quadratic equation \(\frac{9}{x^{2}-27}=\frac{25}{x^{2}-11}\) are
A) ± 6
C) ± 3
B) ± 4
D) ± 5
Answer:
A) ± 6

Question 61.
The roots of the quadratic equation x² + 7x = 0 are
A) 0, 7
B) 7, -7
C) -7, -7
D) 0, -7
Answer:
D) 0, -7

Question 62.
If (x + 4) (x – 4) = 9, then the values of x are
A) ± \(\frac {1}{2}\)
B) ± 5
C) \(\frac{1}{5}, \frac{1}{5}\)
D) 5, 5
Answer:
B) ± 5

Question 63.
The roots of the quadratic equation (2x + b + a) (2x + b – a) = 0 are
A) \(\frac{a-b}{2}, \frac{a-b}{2}\)
B) \(\frac{a+b}{2}, \frac{a+b}{2}\)
C) \(-\frac{a+b}{2}, \frac{a-b}{2}\)
D) \(\frac{a+b}{2}, \frac{a-b}{2}\)
Answer:
C) \(-\frac{a+b}{2}, \frac{a-b}{2}\)

Question 64.
The roots of the equation \(\sqrt{2 x^{2}+9}\) = 9 are
A) x = 0
B) x = ± 6
C) x = 6
D) x = -6
Answer:
B) x = ± 6

Question 65.
The value of k for which 3 is a root of the equation kx² – 7x + 3 = 0 is
A) -3
B) 3
C) 2
D) -2
Answer:
C) 2

Question 66.
The two roots of a quadratic equation are 2 and – 1. The equation is
A) x² + x + 2 = 0
B) x² – 2x + 2 = 0
C) x² + 2x – 2 = 0
D) x² – x – 2 = 0
Answer:
D) x² – x – 2 = 0

Question 67.
Which constant must be added and subtracted to solve the quadratic equation 9x² + 3x – 8 = 0 by the method of completing the square ?
A) \(\frac {1}{36}\)
B) \(\frac {9}{64}\)
C) \(\frac {1}{3}\)
D) \(\frac {1}{4}\)
Answer:
D) \(\frac {1}{4}\)

Question 68.
If the sum of the roots of the quadratic equation 3x² + (2k + 1) x – (k + 5) = 0 is equal to the product of the roots, then the value of k is
A) 3
B) 5
C) 4
D) 2
Answer:
C) 4

Question 69.
The quadratic equation whose one root is 3 + √5 is
A) x² – 6x – 4 = 0
B)x² + 6x + 4 = 0
C) x² – 6x + 4 = 0
D) x² + 6x + 5 = 0
Answer:
C) x² – 6x + 4 = 0

Question 70.
If the two roots of the two quadratic equations x² + mx + 1 = 0 and ax² + bx + a = 0 are common, then the value of m is
A) \(\frac{a}{b}\)
B) b
C) \(\frac{b}{a}\)
D) ab
Answer:
C) \(\frac{b}{a}\)

Question 71.
The roots of the quadratic equation x² + 8x + 7 = 0 are
A) 1, 7
B) -1, -7
C) -1, 7
D) 1, -7
Answer:
B) -1, -7

Question 72.
The value of k for which roots of the quadratic equation kx² + 2x + 3 = 0 are equal is …………………..
A) \(\frac{1}{3}\)
B) -3
C) \(\frac{-1}{3}\)
D) 3
Answer:
A) \(\frac{1}{3}\)

Question 73.
If the roots of the equation 12x² + mx + 5 = 0 are real and equal then m is equal to
A) 4\(\sqrt{15}\)
B) 2\(\sqrt{15}\)
C) 8\(\sqrt{15}\)
D) 10√5
Answer:
A) 4\(\sqrt{15}\)

Question 74.
If the roots of the quadratic equation x² + px + 16 = 0 are equal then the value of pis
A) ± 7
B) ± 6
C) ± 8
D) ± 9
Answer:
C) ± 8

Question 75.
Which of the following equations has the equal roots ?
A) 6x² – x – 2 = 0
B) x² – 8x + 16 = 0
C) 10x – \(\frac{1}{x}\) = 3
D) x² + 6x + 5 = 0
Answer:
B) x² – 8x + 16 = 0

Question 76.
Discriminant of the quadratic equation 2x² + x – 8 = 0 is
A) 65
B) -15
C) -127
D) 15
Answer:
A) 65

Question 77.
The discriminant of x² + 5x + 5 = 0 is
A) \(\frac{-5}{2}\)
B) \(\frac{5}{2}\)
C) – 5
D) 5
Answer:
D) 5

Question 78.
The value (s) of k such that the equation kx² + 6x + k = 0 has equal roots is ………………..
A) ± 3
B) ± 6
C)-6 and 3
D) 9
Answer:
A) ± 3

Question 79.
If the discriminant of the equation 6x² – bx + 2 = 0 is 1, then the value of ‘b’ is
A) ± 7
B)± √7
C) -7
D) 7
Answer:
A) ± 7

Question 80.
The discriminant of the quadratic equation 7√3x² + 10x – √3 = 0 is :
A) \(\frac{-10}{7 \sqrt{3}}\)
B) 142
C) 184
D) 26
Answer:
C) 184

Question 81.
Discriminant of the quadratic equation 2x² + x – 8 = 0 is
A) -65
B) 65
C) -127
D) -15
Answer:
B) 65

Question 82.
The roots of (x² – 3x + 2) (x) (x – 4) = 0 are
A) 0 and 4
B) 0, 1, 2 and 4
C) 4
D) 1, 2 and 4
Answer:
B) 0, 1, 2 and 4

Question 83.
The difference of the roots of x² – 7x – 9 = 0 is
A) \(\sqrt{85}\)
B) 7
C) -9
D) 8
Answer:
A) \(\sqrt{85}\)

Question 84.
The equation \(\sqrt{x+10}-\frac{6}{\sqrt{x+10}}\) = 5 has
A) an extraneous root between -5 and -1
B) two extraneous roots
C) an extraneous root between -10 and -6
D) a real root between 20 and 25
Answer:
C) an extraneous root between -10 and -6

Question 85.
If log₁₀(x² – 3x + 6) = 1, then the value of x is
A) 4 or -1
B) 4 only
C) 10 or 2
D) 4 or -2
Answer:
A) 4 or -1

Question 86.
If y = x + \(\) then x⁴ + x³ – 4x² + x + 1 = 0 becomes
A) x²(y² + y – 6) = 0
B) x²(y² + y – 3) = 0
C) x²(y² + y – 4) = 0
D) x²(y² + y – 2) = 0
Answer:
A) x²(y² + y – 6) = 0

Question 87.
The roots of the equations \(2 \sqrt{x}+2 x^{\frac{1}{2}}\) = 5 can be found by solving
A) 4x² – 25x -4 = 0
B) 4x² – 17x + 4 = 0
C) 4x² – 25x + 4 = 0
D) 4x² – 17x -4 = 0
Answer:
B) 4x² – 17x + 4 = 0

Question 88.
The values of ’k’ for which the equation 2x² – kx + x + 8 = 0 will have real and
equal roots are …………………
A) 9 and -7
B)-9 and 7
C) only 9
D) only -7
Answer:
A) 9 and -7

Question 89.
Two numbers whose sum is 6 and the absolute value of whose difference is 8 are the roots of the equation
A) x² – 6x + 8 = 0
B) x² – 6x – 7 = 0
C) x² – 6x + 7 = 0
D) x² + 6x – 8 = 0
Answer:
B) x² – 6x – 7 = 0

Question 90.
If a and b are the roots of x² – px + q = 0, then a² + b² =…………………
A) p² + 2q
B) p² – q²
C) p² – 2q
D) p² + q²
Answer:
C) p² – 2q

Question 91.
The solution of \(\sqrt{5 x-1}+\sqrt{x-1}\) = 2 is
A) x = 2
B) x = 2, x = 1
C) x = 1
D) x = 1, x = 4
Answer:
C) x = 1

Question 92.
The’ roots of \(\frac{15}{x^{2}-4}-\frac{2}{x-2}\) = = 1 are………………
A) -3 and 5
B) 3 only
C) -5 and 3
D) -5 only
Answer:
C) -5 and 3

Question 93.
In the equation 2x² – hx + 2k = 0, the sum of the roots is 4 and the product of the roots is -3. Then h and k have the values ………………… respectively.
A) 8 and -3
B) 8 and 6
C) 4 and -3
D) -3 and 8
Answer:
A) 8 and -3

Question 94.
If \(\sqrt{x-1}-\sqrt{x+1}\) + 1 = 0, then 4x equal to
A) 0
B) 1 \(\frac{1}{4}\)
C) 5
D) 4\(\sqrt{-1}\)
Answer:
C) 5

Question 95.
The number of roots satisfying the equation \(\sqrt{5-x}=x \sqrt{5-x}\) – x is/are
A) 2
B) 3
C) 1
D) unlimited
Answer:
B) 3

Question 96.
If α and β are the roots of the quadratic equation x² + px + 12 = 0 with the condition α – β = 1, then the value of ‘p’ is
A) 7 or -7
B) 1
C) -7
D) 7
Answer:
A) 7 or -7

Question 97.
The coefficient of x in the quadratic equation x² + px + q = 0 was taken as 17 in the place of 13 and its roots were found to be-2 and-15. The roots of the original equation are
A) 3 or -10
B) -3 or 10
C) -3 or -10
D) 3 or 10
Answer:
C) -3 or -10

Question 98.
The roots of \(\sqrt{2 x-3}+\sqrt{3 x-5}-\sqrt{5 x-6}\) = 0 are
A) 2 or \(\frac{7}{6}\)
B) 2 only
C) \(\frac{7}{6}\) only
D) 2 and \(\frac{7}{6}\)
Answer:
A) 2 or \(\frac{7}{6}\)

Question 99.
If one of roots of x² + ax + 4 = 0 is twice the other root, then the value of ‘a’ is
A) 8√2
B) √2
C) -3√2
D) -2√2
Answer:
C) -3√2

Question 100.
If the roots of the equation
(a – b)x² + (b – c) x + (c – a) = 0 are equal, then
A) 2b = a + c
B) 2c = a + b
C) 2a = b + c
D) 2a = b – c
Answer:
C) 2a = b + c

Question 101.
If a = b = c, then the roots of the equa-tion (x – a) (x – b) + (x – b)(x – c) +
(x – c) (x – a) = 0 are
A) imaginary
B) real and equal
C) real and unequal
D) real
Answer:
B) real and equal

Question 102.
If the sum of the roots of the quadratic equation 3x² + (2k + 1) x – (k + 5) = 0 is equal to the product of the roots, then the value of ‘k’ is
A) 0
B) 1
C) -4
D) 4
Answer:
D) 4

Question 103.
For a quadratic equation, 3 + √5 is one root. The other root must be
A) 3 + √5
B) 3 – √5
C) 3 + 2√5
D) 3 – 2√5
Answer:
B) 3 – √5

Question 104.
If one root of the equation ax² + bx + c = 0 is three times the other, then …………………
A) b² = 16ac
B) 3b² = 16ac
C) 2b² = 9ac
D) b² = ac
Answer:
B) 3b² = 16ac

Question 105.
The root of the quadratic equation 3x² – kx + 14 = 0 are in the ratio 7 : 6 then k = ………………….
A) 12
B) -3
C) 1
D) 13
Answer:
D) 13

Question 106.
If α, β are the roots of the equation x² – px + q = 0, then the quadratic equation whose roots are \(\frac{\alpha}{\beta}\) and \(\frac{\boldsymbol{\beta}}{\alpha}\) is ……………………
A) qx² + (2q – p²) x + q = 0
B) qx² – px + 1 = 0
C) qx² + (p² – 2q) x + q = 0
D) qx² – px – 1 = 0
Answer:
A) qx² + (2q – p²) x + q = 0

Question 107.
Find the value of k, if the expression x² + kx + 1 is factorizable into two linear factors ………………
A) either k ≥ 2 or k ≤ -2
B) k ≥ 2
C) k ≤ -2
D) neither k ≥ 2 nor k ≤ – 2
Answer:
A) either k ≥ 2 or k ≤ -2

Question 108.
The product of two consecutive odd numbers is 143. The numbers are
A) 13 and 15
B) 11 and 13
C) -11 and 13
D) -13 and 15
Answer:
B) 11 and 13

Question 109.
The perimeter of a rectangular room is 34m and the length of a diagonal is 13m. The dimensions of the room are …………………..
A) 17m and 7m
B) 12m and 5m
C) 9m and 2m
D) 15m and 2m
Answer:
B) 12m and 5m

Question 110.
If x² + 4ax + 3 = 0 and 2x² + 3ax – 9 = 0 have a common root, then the value of ‘a’is ……………………
A) 1
B) ± 3
C) ± 1
D) -3
Answer:
C) ± 1

Question 111.
The product of two consecutive natural numbers is 600. The numbers are …………………….
A) 35, 36
B) 16, 25
C) 26, 25
D) 24, 25
Answer:
D) 24, 25

Question 112.
The roots of the quadratic equation x² – 5x + 6 = 0 are
A) 3, -2
B) -3, 2
C) 2, 3
D) -2, -3
Answer:
C) 2, 3

Question 113.
If the roots of a quadratic equation are equal, then
A) b² = 4ac
B) b² – 4ac < 0
C) b² – 4ac > 0
D) b² – 4ac = 0
Answer:
A) b² = 4ac

Question 114.
The roots of the quadratic equation abx² – (a + b) x + 1 are
A) a + b, a – b
B) \(\frac{1}{a}, \frac{1}{b}\)
C) a, b
D) \(\frac{1}{a+b}, \frac{1}{a-b}\)
Answer:
B) \(\frac{1}{a}, \frac{1}{b}\)

Question 115.
If α, β be the roots of the quadratic equation x² – 2x + 1 = 0, then the quadratic equation whose roots are α + β and αβ is ………………
A) x² – 2x – 1 = 0
B) x² + 2x + 1 = 0
C) x² + 2x -1 = 0
D) x² – 2x + 1 = 0
Answer:
D) x² – 2x + 1 = 0

Question 116.
The roots of the equation x + \(\) = 5\(\) are
A) 5, -5
B) 5, \(\frac{1}{5}\)
C) -5, -5
D) 5, 5
Answer:
B) 5, \(\frac{1}{5}\)

Question 117.
Which of the following is not a quadratic equation ?
A) x (2x + 3) = x² + 1
B) (x – 2)² + 1 = 2x – 3
C) x(x + 1) + 8 = (x + 2) (x – 2)
D) (x + 2)³ = x³ – 4
Answer:
C) x(x + 1) + 8 = (x + 2) (x – 2)

Question 118.
Is – √5x² + 6x + 3 = 0 a quadratic equation ?
A) Yes
B) No
C) can’t say
D) It is a linear equation
Answer:
A) Yes

Question 119.
Which of the following equation has \(\frac {1}{5}\) as a root ?
A) 2x² – 7x + 6 = 0
B) 35x² – 2x – 1 = 0
C) 35x² + 12x + 1 = 0
D) 10x² – 3x – 1 = 0
Answer:
B) 35x² – 2x – 1 = 0

Question 120.
If x = 1 is a common root of the equations ax² + ax + 3 = 0 and x² + x + b = 0, then the value of ab is :
A) 3
B) 6
C) 3.5
D) -3
Answer:
A) 3

Question 121.
Which of the following equations has the sum of roots as 3 ?
A) 2x² – 3x + 6 = 0
B) 3x² – 3x + 3 = 0
C) √2 x²–\(\frac{3}{\sqrt{2}}\)x + = 0
D) -x² + 3x – 3 = 0
Answer:
D) -x² + 3x – 3 = 0

Question 122.
Which constant should be added and substracted to solve the quadratic equation 4x² – √3x – 5 = 0 by the method of completing the square?
A) \(\frac{3}{16}\)
B) \(\frac{\sqrt{3}}{4}\)
C) \(\frac{9}{16}\)
D) \(\frac{3}{4}\)
Answer:
A) \(\frac{3}{16}\)

Question 123.
Which of the following equations has the product of its roots as 4 ?
A) x² + 4x – 4 = 0
B) x² + 4x + 4 = 0
C) x² + 4x – 24 = 0
D) -x² + 4x + 4 = 0
Answer:
B) x² + 4x + 4 = 0

Question 124.
ax² + bx + c = 0, a > 0,b = 0, c > 0 has;
A) Two equal roots
B) One real root
C) Two distinct real roots
D) No real roots
Answer:
D) No real roots

Question 125.
If the equation x² – 4x + a = 0 has no real roots, then
A) a ≤ 4
B) a < 2
C) a < 4 D) a > 4
Answer:
D) a > 4

Question 126.
If the discriminant of the quadratic equation ax² + bx + c = 0, then the roots of the equation
A) are irrational and equal
B) are rational and equal
C) do not exist and real
D) are real and equal
Answer:
D) are real and equal

Question 127.
The least value of ax² + bx + c (a > 0) is
A) \(\frac{-b}{2 a}\)
B) \(\frac{4 a^{2}-b^{2}}{4 a}\)
C) \(\frac{4 a^{2}+b^{2}}{4 a}\)
D) none of the above
Answer:
B) \(\frac{4 a^{2}-b^{2}}{4 a}\)

Question 128.
The equation x + \(\sqrt{x-2}\) = 4 has
A) two real roots
B) two imaginary roots
C) one real root
D) one real and one imaginary root
Answer:
C) one real root

Question 129.
If one root of the equation a(b – c) x² + b(c – a) x + c(a – b) = 0 is 1, then the other root is
A) \(\frac{a(b-c)}{c(a-b)}\)
B) \(\frac{a(b-c)}{b(c-a)}\)
C) \(\frac{c(a-b)}{a(b-c)}\)
D) \(\frac{b(c-a)}{a(b-c)}\)
Answer:
C) \(\frac{c(a-b)}{a(b-c)}\)

Question 130.
The roots of the equation x² + 2√3 x + 3 = 0 are
A) rational and equal
B) real and equal
C) rational and unequal
D) imaginary
Answer:
B) real and equal

Question 131.
The roots of the equation ax² + bx + c = 0 will be reciprocal if
A) a = bc
B) b = c
C) a = b
D) c = a
Answer:
D) c = a

Question 132.
The discriminant of ax² – 2√2 x + c = 0 with a, c and real constants is zero. The roots must be
A) rational and equal
B) real and equal
C) imaginary
D) equal and integral
Answer:
B) real and equal

Question 133.
The equation \(\sqrt{x+4}-\sqrt{x-3}\) + 1 = 0 has
A) one real root
B) two imaginary roots
C) no root
D) one real and one imaginary root
Answer:
C) no root

Question 134.
The sum of the reciprocals of the roots of the equation x² + px + q = 0 is
A) \(\frac{q}{p}\)
B) \(\frac{-\mathrm{p}}{\mathrm{q}}\)
C) \(\frac{-\mathrm{q}}{\mathrm{p}}\)
D) \(\frac{\mathrm{p}}{\mathrm{q}}\)
Answer:
D) \(\frac{\mathrm{p}}{\mathrm{q}}\)

Question 135.
The equation \(x-\frac{7}{x-3}=3-\frac{7}{x-3}\) has
A) no roots
B) infinitely many roots
C) one integral root
D) two real roots
Answer:
A) no roots

Question 136.
If \(\frac{b}{x-a}=\frac{x+a}{b}\) then the value of x in terms of a and b is
A) \(\sqrt{a^{2}+b^{2}}\)
B) \(\pm \sqrt{a^{2}+b^{2}}\)
C) \(-\sqrt{a^{2}+b^{2}}\)
D) \(\pm \sqrt{a^{2}-b^{2}}\)
Answer:
B) \(\pm \sqrt{a^{2}+b^{2}}\)

Question 137.
The standard form of a quadratic equation is
A) ax + b = 0, a ≠ 0
B) ax² + bx + c = 0, a ≠ 0
C) ax³ + bx² + cx + d = 0, a ≠ 0
D) ax⁴ + bx³ + cx² + dx + e = 0, a ≠ 0.
Answer:
B) ax² + bx + c = 0, a ≠ 0

Question 138.
Which of the following is a quadratic equation?
A) (x – 2) (x + 1) = (x – 1) (x + 3)
B) x⁴ – 1 = 0
C) (x + 1)² = 2(x – 3)
D) x² + 3x + 1 = (x – 2)²
Answer:
C) (x + 1)² = 2(x – 3)

Question 139.
A cottage industry produces a certain number of toys in a day. The cost of production of each toy was found to be 55 rupees. On a particular day, the total cost of production was ? 750. Represent this situation in the form of a quadratic equation.
A) x (55 – x) = 750
B) 55x = 750
C) x(x – 55) = 750
D) x (x + 55) = 750
Answer:
A) x (55 – x) = 750

Question 140.
The sum of the squares of two consecutive natural numbers is 25. Represent this situation in the form of a quadratic equation.
A) x² + (x + 1)² + 25 = 0
B) x² – (x + 1)² = 25
C) x² + (x + 1)² = 25
D) (x + 1)² – x² = 25
Answer:
C) x² + (x + 1)² = 25

Question 141.
If one root of the two quadratic equations x² + ax + b = 0 and x² + bx + a = 0 is common, then
A) a + b = -1
B) ab = -1
C) ab = 1
D) a + b = 1
Answer:
A) a + b = -1

Question 142.
The condition that both the roots of the two quadratic equations
a₁x2 + b₁x + c₁ = 0 and a₂x2 + b₂x + c₂ = 0 are common is
A) a₁a₂ + b₁b₂ + c₁c₂ = 0
B) a₁² + b₁² + c₁² = a₂² + b₂² + c₂²
C) \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)
D) a₁ + b₁ + c₁ = a₂ + b₂ + c₂
Answer:
C) \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)

Question 143.
If x = \(\sqrt{1+\sqrt{1+\sqrt{1+\ldots \ldots \ldots . .}}}\) , then
A) 1 < x < 2
B) x = 1
C) 0 < x < 1
D) x is infinite
Answer:
A) 1 < x < 2

Question 144.
If \(\) has roots which are numerically equal but of opposite signs, the value of ‘m’ must be
A) \(\frac{a+b}{a-b}\)
B) 0
C) 1
D) \(\frac{a-b}{a+b}\)
Answer:
D) \(\frac{a-b}{a+b}\)

Question 145.
Two consecutive positive integers differ by
A) 3
B) 4
C) 2
D) 1
Answer:
D) 1

Question 146.
The sum of a number and its reciprocal is \(\frac {5}{2}\) . Represent this, situation in the form of a quadratic equation.
A) x –\(\frac{1}{x}=\frac{5}{2}\)
B) x +\(\frac{1}{x}=\frac{5}{2}\)
C) x +\(\sqrt{x}=\frac{5}{2}\)
D) x²\(\frac{1}{x^{2}}=\frac{5}{2}\)
Answer:
B) x +\(\frac{1}{x}=\frac{5}{2}\)

Question 147.
Two consecutive even integers are
A) x, x + 1
B) x, 2x
C) x, x – 1
D) x, x + 2
Answer:
D) x, x + 2

Question 148.
Two consecutive positive integers are
A) x, x – 2
B) x, x + 1
C) x, x + 2
D) x, 2x
Answer:
B) x, x + 1

Question 149.
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each and the product of the number of marbles they have now is 124. Represent this situation in the form of quadratic equation.
A) (x – 5) (x – 40) = 124
B) (x + 5) (40 + x) + 124 = 0
C) (x – 5) (40 – x) = 124
D) (5 + x) (40 – x) = 124
Answer:
C) (x – 5) (40 – x) = 124

Question 150.
What is the condition that one root of the quadratic equation ax² + bx + c is reciprocal of the other ?
A) a = b
B) b = c
C) a = c
D) a + b + c = 0
Answer:
C) a = c

Question 151.
If the roots of the quadratic equation ax² + bx + c are sinα and cosα, then
A) a² + b² = c²
B) b² – 2ac = a²
C) b² + 2ac = a²
D) a²2 – 2bc = b²
Answer:
B) b² – 2ac = a²

Question 152.
If the difference of the roots of the quadratic equation x² – ax + b is 1, then
A) a² – 4b = -1
B) a² – 4b = 4
C) a² – 4b = 1
D) a² – 4b = 0
Answer:
C) a² – 4b = 1

Question 153.
The value of c for which the equation ax² + bx + c = 0 has equal roots is
A) \(\frac{\mathrm{b}^{2}}{4 \mathrm{a}}\)
B) \(\frac{a^{2}}{b}\)
C) \(\frac{a^{2}}{4 b}\)
D) \(\frac{\mathrm{b}^{2}}{\mathrm{a}}\)
Answer:
A) \(\frac{\mathrm{b}^{2}}{4 \mathrm{a}}\)

Question 154.
The roots of the equation x² – 2x = 0 can be obtained graphically by finding the abscissa of the points of intersection of each of the following pairs of equations except ………………….
A) y = x,y = x – 2
B) y = x² – 2x + 1, y = 1
C) y = x²,y = 2x
D) y = x² – 2x, y = 0
Answer:
A) y = x,y = x – 2

Question 155.
If in applying the quadratic f ormula to a quadratic equation f(x) = ax² + bx + c = 0 it happens that c = \(\). Then the graph of y = f(x) will certainly …………….
A) have a minimum
B) be a tangent to the Y – axis
C) have a maximum
D) be a tangent to X-axis
Answer:
D) be a tangent to X-axis

Question 156.
In the equation \(\) the roots are equal when
A) m = 0
B) m = \(\frac {1}{2}\)
C) m = –\(\frac {1}{2}\)
D) m = 1
Answer:
C) m = –\(\frac {1}{2}\)

Question 157.
If b² – 4ac > 0 the graph may be …………………

Answer:

Question 158.
If b² = 4ac then the graph may be

Answer:

Question 159.
The graph of a linear polynomial may be

Answer:

Question 160.
Identify parabola among the following graphs.

Answer:

Question 161.
If a quadratic equation have no real roots then the graph may be ………………

Answer:

Question 162.
If the graph of ax² + bx + c = 0, a ≠ 0 never intersects X axis then the number of real zeroes are ………………..
A) 2
B) 0
C) 3
D) 4
Answer:
B) 0

Question 163.
From the graph given below the nature of roots are ………………….

A) Real and equal
B) Real and not equal
C) Not real
D) 10, 11
Answer:
C) Not real

Practice the AP 10th Class Maths Bits with Answers Chapter 4 Pair of Linear Equations in Two Variables on a regular basis so that you can attempt exams with utmost confidence.

AP State Syllabus 10th Class Maths Bits 4th Lesson Pair of Linear Equations in Two Variables with Answers

Question 1.
The slope of the line passing through (2, 3) and (4, 7) is ………………….
A) 2
B) \(\frac{5}{6}\)
C) 4
D) 1
Answer:
A) 2

Question 2.
The value of P for which the pair of equations 2Px + 3y = 7, 2x + y = 6 has exactly one solution.
A) 3
B) Any real number except 3
C) Any real number
D) For no real P the system has solution
Answer:
B) Any real number except 3

Question 3.
If 2^x + 3^y = 17; 2^{x + 2} – 3^{y +1} = 5, then (x, y) is…………………..
A) (3, 2)
B) (2, 3)
C) (-2, 3)
D) (3, -2)
Answer:
A) (3, 2)

Question 4.
The value of k for which the system of equations (3k + 1) x + 3y – 2 = 0 and (k² + 1) x + (k – 2) y – 5 = 0 has no solution is…………………
A) 1
B) 2
C) -1
D) -2
Answer:
C) -1

Question 5.
The solution of the equations \(\frac{x+y}{x y}\) = 2 and \(\left\{2, \frac{-1}{4}\right\}\) = 6 is …………………..
A) \(\left\{\frac{-1}{2}, 4\right\}\)
B) \(\left\{2, \frac{-1}{4}\right\}\)
C) \(\left\{\frac{-1}{2}, \frac{-1}{4}\right\}\)
D) \(\left\{\frac{-1}{2}, \frac{1}{4}\right\}\)
Answer:
D) \(\left\{\frac{-1}{2}, \frac{1}{4}\right\}\)

Question 6.
The larger of two supplementary angles exceeds the smaller by 18°. The angles are ………………..
A) 80°, 100°
B) 81°, 99°
C) 82°, 98°
D) 83°, 97°
Answer:
B) 81°, 99°

Question 7.
If \(\) = 2 and \(\) = – 1,then ………………..
A) x = 2, y = 3
B) x = 4, y = 9
C) x = 2, y = 9
D) x = 4, y = 3
Answer:
B) x = 4, y = 9

Question 8.
The value of k for which the pair of equations 3x + 4y + 2 = 0 and 9x + 12y + k = 0 represent coincident lines is ……………..
A) 2
B) 3
C) 6
D) 12
Answer:
C) 6

Question 9.
If 2^x + 3^y = 31, 2^{x + 2} – 3^{y + 1} = 5, then …………………
A) x = 3, y = 2
B) x = 3,y = 4
C) x = 2, y = 3
D) x = 4, y = 3
Answer:
C) x = 2, y = 3

Question 10.
The point of intersection of the lines 2x + 3y – 5 = 0 and 3x – 4y + 1=0 lies in which quadrant ?
A) I
B) II
C) III
D) IV
Answer:
A) I

Question 11.
If the perimeter of a rectangular room is 34 and the length of the diagonal is 13, then the dimensions of the room are …………………
A) 7, 6
B) 11, 6
C) 12, 5
D) 12, 6
Answer:
C) 12, 5

Question 12.
If 9x + 11y = 51 and 11x + 9y = 49, then x = …………………….
A) -1
B) -2
C) 1
D) 2
Answer:
D) 2

Question 13.
If the pair of equations a₁x + b₁y + c₁= 0 and a₂ x + b₂y + c₂ = 0 has unique solution, then ………………
A) \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\)
B) \(\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}\)
C) \(\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\)
D) \(\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)
Answer:
B) \(\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}\)

Question 14.
The solution of the equations √3x – √7y = 0 and √8x + √3y = 0 is ……………………
A) x = 3, y = 7
B) x = 8, y = 3
C) x = 0, y = 1
D) x = 0, y = 0
Answer:
D) x = 0, y = 0

Question 15.
If twice the age of A is added to B’s age, the sum is 45 and if twice the age of B is added to A’s age, the sum is 30. Then the age of B is ………………
A) 20
B) 5
C) 10
D) 30
Answer:
B) 5

Question 16.
3 pens and 5 pencils together cost ₹ 35, whereas 5 pens and 3 pencils together cost ₹ 37. The cost of a pencil is …………………
A) ₹ 5
B) ₹ 3
C) ₹ 4
D) ₹ 6
Answer:
C) ₹ 4

Question 17.
Which of the following is a solution for the equation 2(x + 3) = 18 ?
A) 6
B) 5
C) 21
D) 13
Answer:
A) 6

Question 18.
If 3x + 4y – k = 0 and 6x + 8y – 4 = 0 are coincident lines, then the value of k is ………………
A) 3
B) 4
C) 6
D) 2
Answer:
D) 2

Question 19.
If y = 3, then the value of ‘x’ satisfying the equation \(\frac{5}{x}+\frac{3}{y}\) = 6 is ……………….
A) 3
B) \(\frac{1}{3}\)
C) \(-\frac{1}{3}\)
D) 1
Answer:
D) 1

Question 20.
Which one of the following is NOT a linear equation?
A) 5x + 4 = y + 3
B) x + 2y = y² – x
C) 3 – x = y² + 4
D) x + y = 0
Answer:
C) 3 – x = y² + 4

Question 21.
“Book” is an example of ……………….
A) prism
B) circle
C) cone
D) cuboid
Answer:
D) cuboid

Question 22.
The value of x which satisfies the equation 2x – (4 – x) = 5 – x is …………………..
A) 4.5
B) 3
C) 2.25
D) 0.5
Answer:
C) 2.25

Question 23.
If \(\frac{10}{x+y}+\frac{2}{x-y}\) = 4 and \(\frac{15}{x+y}-\frac{5}{x-y}\) = -2 then
A) x = 3, y = 2
B) x = 3, y = -2
C) x = -3, y = 2
D) x = -3, y = -2
Answer:
A) x = 3, y = 2

Question 24.
The point of intersection of the lines x = 2016 and y = 2017 is …………………
A) (2017, 2016)
B) (0, 2017)
C) (2016, 0)
D) (2016, 2017)
Answer:
D) (2016, 2017)

Question 25.
Which of the following equations has the solution of (2, -3) ?
A) 2x – 3y = 10
B) 2x + 3y = -13
C) 2x – 3y = 13
D) 2x + 3y = 13
Answer:
C) 2x – 3y = 13

Question 26.
The point of intersection of the line y = ax + b with X – axis is ……………………
A) \(\left(-\frac{b}{a}, 0\right)\)
B) \(\left(\frac{\mathrm{b}}{\mathrm{a}}, 0\right)\)
C) \(\left(0, \frac{\mathrm{b}}{\mathrm{a}}\right)\)
D) \(\left(0,-\frac{\mathrm{b}}{\mathrm{a}}\right)\)
Answer:
A) \(\left(-\frac{b}{a}, 0\right)\)

Question 27.
The value of x, which satisfies 2(x – 1) – (1 – x) = 2x + 3 is ………………..
A) 2
B) 4
C) 6
D) 8
Answer:
C) 6

Question 28.
The value of y when \(\frac{x+y}{x y}\) = 2, \(\frac{x-y}{x y}\) = 6 is …………………
A) \(\frac{1}{4}\)
B) \(\frac{-1}{2}\)
C) \(\frac{-1}{4}\)
D) \(\frac{1}{3}\)
Answer:
A) \(\frac{1}{4}\)

Question 29.
Which of the following is inconsistent equation to 2x + 3y – 5 = 0 ?
A) 4x – 6y – 11 = 0
B) 2x + y = 5
C) x + 3y = 5
D) 4x + 6y – 11 = 0
Answer:
D) 4x + 6y – 11 = 0

Question 30.
Which of the following is not a linear equation ?
A) 5 + 4x = y + 3
B) x + 2y = y – x
C) 3 – x = y² + 4
D) x + y = 0
Answer:
C) 3 – x = y² + 4

Question 31.
The solution set {x, y} of the system of equations x – 2y = 0 and 3x + 4y = 10 is
A) {2, 4}
B) {4, 2}
C) {1, 2}
D){2, 1}
Answer:
D){2, 1}

Question 32.
The two lines 3x + 2y – 80 = 0 and 4x + 3y -110 = 0 are
A) coincident lines
B) parallel lines
C) intersecting lines
D) None
Answer:
C) intersecting lines

Question 33.
The perimeter of a rectangular plot is 32 m. If the length l is increased by 2 m and the breadth b is decreased by 1m, the area of the plot remains the same. Then the values of l and b are respectively.
A) 6m, 10m
B) 10m, 6m
C) 10m, 10m
D) 6m, 6m
Answer:
B) 10m, 6m

Question 34.
Which of the following equations is a linear equation ?
A) 5 + 4x² = y + 3
B)x + 2y = y² – x
C) 3 – x = y + 4
D) x² + y = 0
Answer:
C) 3 – x = y + 4

Question 35.
4y² – 5y + 1 is ……………………
A) Linear polynomial.
B) Cubic polynomial.
C) Constant polynomial.
D) Quadratic polynomial.
Answer:
D) Quadratic polynomial.

Question 36.
Which of the following is a linear equation ?
A) 5 + 4x = y + 3
B) x + 2y = y – x²
C) 3 – x = y² + 4
D) x² + y = 0
Answer:
A) 5 + 4x = y + 3

Question 37.
Solution for the equations √8 x + √7 y = 0 and √6 x + √10 y = 0 is …………………
A) x = 3, y = 5
B) x = 7, y = 11
C) x = 1, y = 1
D) x = 0, y = 0
Answer:
D) x = 0, y = 0

Question 38.
If the system of equations 4x + py = 21 and px – 2y = 15 has unique solution, then which of the following could be the value of p ?
a) 103
b) 105
c) 192
d) 197
A) Both (a) and (b)
B) Both (c) and (d)
C) (a), (b) and (d)
D) All of the above
Answer:
D) All of the above

Question 39.
The semi perimeter of a triangle exceeds each of its side by 5, 3 and 2 respectively. What is the perimeter of the triangle?
A) 10
B) 20
C) 15
D) 12
Answer:
B) 20

Question 40.
For what value of k do the equation 3(k – 1) x + 4y = 24 and 15x + 20y = 8 (k + 13) have infinite solutions ?
A) 4
B) 2
C) 1
D) 3
Answer:
B) 2