Q.1

If the volumes of two right circular cones are in the ratio 1:4 and their diameters of bases in the ratio 4:5, then their heights will be in the ratio:

  • 1: 5
  • 4:25
  • 16:25
  • 25:64
Q.2

The radius of a hemisphere is 21 cm, what is its volume? (Take π = 22/7)

  • 38808 cubic cms
  • 9702 cubic cms
  • 19404 cubic cms
  • 29106 cubic cms
Q.3

The length, breadth and height of a cuboid are in the ratio 19 : 11 :If length is 30 cm more than height, then what is the volume (in cub.cm) of this cuboid?

  • 81510
  • 89665
  • 195300
  • 339625
Q.4

The ratio of total surface area and volume of a sphere is 1 :This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres?

  • 31276
  • 36194
  • 25182
  • 33264
Q.5

The least number of square tiles of side 41 cms required to pave the ceiling of a room of size 15m 17cm long and 9m 2 cm broad is:

  • 902
  • 656
  • 738
  • 814
Q.6

Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles?A. 154 square cmB. 308 square cmC. 462 square cmD. 616 square cm

  • 154 square cm
  • 308 square cm
  • 462 square cm
  • 616 square cm
Q.7

In a Rhombus ABCD, measure of angle CAB is 30°, what is the measure of angle ABC?

  • 60°
  • 120°
  • 90°
  • 150°
Q.8

Curved surface area of a cylinder is 1232 sq cm. If circumference of its base is 154 cm, then what will be the height of the cylinder? (Take π = 22/7)

  • 16 cm
  • 4 cm
  • 8 cm
  • 12 cm
Q.9

Sum of lengths of all edges of a cube is 84 cm, find its volume?

  • 686 cubic cms
  • 343 cubic cms
  • 171.5 cubic cms
  • 514.5 cubic cms
Q.10

Circum center of ΔABC is O. If ∡BAC = 75 and ∡BCA = 80 degrees,

 then what is the value of ∡OAC(in deg)?

  • 45
  • 65
  • 90
  • 95
Q.11

In ∆XYZ measure of angle Y is 90 deg. If sinX = 4/5, and XY = 6cm, then what is the length (in cm) of side YZ?

  • 10
  • 5
  • 8
  • 4
Q.12

The measure of the four successive angles of a quadrilateral are in the ratio 7 : 11 : 7 :The quadrilateral is a ______.

  • trapezium
  • rectangle
  • parallelogram
  • square
Q.13

The base of a prism is in the shape of an equilateral triangle. If the perimeter of the base is 18 cm and the height of the prism is 20 cm, then what is the volume (in cm3) of the prism?

  • 60√3
  • 30√6
  • 60√2
  • not know
Q.14

ABCD is a trapezium in which AB is parallel to CD and AB = 4(CD). The diagonals of the trapezium intersects at O. What is the ratio of area of triangle DCO to the area of the triangle ABO?

  • 1 : 4
  • 1 : 2
  • 1 : 8
  • 1 : 16
Q.15

A regular hexagonal base prism has height 8 cm and side of base is 4 cm. What is the total surface area (in cm2) of the prism?

  • 54(3 + √3)
  • 36(3 + √3)
  • 48(4 + √3)
  • 24(4 + √3)
Q.16

ΔABC is an equilateral triangle and D, E are midpoints of AB and BC respectively. Then the area of ΔABC : the area of the trapezium ADEC is

  • 5:3
  • 4:1
  • 8:5
  • 4:3
Q.17

10 identical solid spherical balls of radius 3 cm are melted to form a single sphere. In this process 20% of solid is wasted. What is the radius (in cm) of the bigger sphere?

  • 24
  • 12
  • 8
  • 6
Q.18

A cone of radius 3.5 cm and height 12 cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 7 cm. What will be the height of water in this vessel?

  • 2 cm
  • 0.33 cm
  • 0.5 cm
  • 1 cm
Q.19

The perimeter and the length of one of the diagonals of a rhombus is 34 cm and 8 cm respectively. Find the length of its other diagonal (in cm).

 

  • 7.5
  • 30
  • 22.5
  • 15
Q.20

An equilateral triangle ABC is inscribed in a circle of radius 20√
The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?

  • 15 cm
  • 20 cm
  • 20√3 cm
  • 30√3 cm
Q.21

An equilateral triangle of area 300 cm2 is cut from its three vertices to form a regular hexagon. Area of hexagon is what percent of the area of triangle?

  • 66.66%
  • 33.33%
  • 83.33%
  • 56.41%
Q.22

The two sides holding the right-angle in a right-angled triangle are 3 cm and 4 cm long. The area of its circumcircle will be in sq.cm:

  • 6.25pi
  • 6.75pi
  • 5pi
  • 7pi
Q.23

If the edge of a cube is increased by 3 cm, the volume will increase by 657 cub.cm. What then is the original length of each edge of the cube?

  • 9 cm
  • 6 cm
  • 8 cm
  • 7 cm
Q.24

Diameter of wheel of a cycle is 21 cm. The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. How many revolutions will the wheel make during the journey?

  • 12325
  • 18750
  • 21000
  • 24350
Q.25

ΔABC is similar to ΔPQR. Length of AB is 18 cm and length of the corresponding side PQ is 12 cm. If area of ΔABC is 324 sq cm, what is the area of ΔPQR?

  • 72 sq cm
  • 144 sq cm
  • 36 sq cm
  • 487.5 sq cm
Q.26

ABC is a right angled triangle in which ∠A = 90°, AB = 5 cm and AC = 12 cm. What is the approximate volume (in cm3) of the double cone formed by rotating the triangle about its hypotenuse?

  • 145
  • 290
  • 435
  • 580
Q.27

If a cone of radius 3.5 cm and height 9.6 cm is melted and constructed into a cylinder of the same radius, what will be the height of this cylinder? (Take π = 22/7)

  • 3.2 cm
  • 6.4 cm
  • 1.6 cm
  • 4.8 cm
Q.28

The total surface area of a hemisphere is 4158 cmFind its diameter (in cm).

  • 21
  • 84
  • 42
  • 63
Q.29

The diagonals do not form at least two congruent triangles in a _____.

  • Parallelogram
  • Rhombus
  • Trapezium
  • Kite
Q.30

The length of diagonal of a square is 9√2 cm. The square is reshaped to form a triangle. What is the area (in sq.cm) of largest in circle that can be formed in that triangle?

  • 6π
  • 9π
  • 12π
  • 15π
Q.31

Two circles touch externally. The sum of their areas is 130π sq.cm and the distance between their centers is 14 cm. The radius of the bigger circle is

  • 22 cm
  • 11 cm
  • 33 cm
  • 44 cm
Q.32

A cylindrical vessel of radius 7 cm is partially filled with water. By how much will the water level rise if a sphere of radius 6 cm is completely immersed in this water?

  • 11.76 cm
  • 17.64 cm
  • 23.52 cm
  • 5.88 cm
Q.33

If the diameter of a hemisphere is 21 cm, then what is the volume (in cub.cm) of hemisphere?

  • 2810
  • 1250.5
  • 1725.25
  • 2425.5
Q.34

A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?

  • 150
  • 200
  • 300
  • 250
Q.35

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

  • 1 cm or 7 cm
  • 2 cm or 14 cm
  • 3 cm or 21 cm
  • 4 cm or 28 cm
Q.36

A regular pyramid has a square base. The height of the pyramid is 22 cm and side of its base is 14 cm. Volume of pyramid is equal to the volume of a sphere. What is the radius (in cm) of the sphere?

  • 493
  • 7
  • 14
  • 983
Q.37

The ratio of the volume of two cylinders is 7 : 3 and the ratio of their heights is 7 :If the area of the base of the second cylinder is 154 sq. cm, then what will be the radius (in cm) of the first cylinder?

  • 6√2
  • 6√3
  • 7√2
  • 7√3
Q.38

Two spheres of equal radius are taken out by cutting from a solid cube of side (12 + 4√3) cm. What is the maximum volume (in cm3) of each sphere?

  • 1077.31
  • 905.14
  • 966.07
  • 1007.24
Q.39

What is the reflection of the point (-4, 3) in the line x = -2?

  • (-4 , -7)
  • (4 , 3)
  • (0 , 3)
  • (-4 , 7)
Q.40

If the curved surface area of a right circular cone is 3080 sq cm and its slant height is 35 cm, find its total surface area?

  • 11088 sq cm
  • 1848 sq cm
  • 5544 sq cm
  • 2772 sq cm
Q.41

In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 50°, then what is the value (in degrees) of ∠PBC?

  • 30
  • 45
  • 50
  • 60
Q.42

ABCD is a quadrilateral in which BD and AC are diagonals then

  • AB + BC + CD + AD< AC + BD
  • AB + BC + CD + DA>AC + BD
  • AB + BC + CD + DA=AC + BD
  • AB + BC + CD + DA>2(AC + BD)
Q.43

Find the total surface area (in cm2 ) of a hemisphere of diameter 42 cm.

  • 4158
  • 5782
  • 6321
  • 7782
Q.44

ΔXYZ is similar to ΔPQR. If ratio of Perimeter of ΔXYZ and Perimeter of ΔPQR is 4:9 and if PQ = 27 cm, then what is the length of XY (in cm)?

  • 9
  • 12
  • 16
  • 15
Q.45

In triangle ABC, AD, BE and CF are the medians intersecting at point G and area of triangle ABC is 156 sq.cm. What is the area (in sq.cm) of triangle FGE?

  • 13
  • 26
  • 39
  • 52
Q.46

The surface areas of three faces of a cuboid sharing a vertex are 20, 32 and 40 sq. mts. What is the volume of the cuboid in cub. m?

  • √3024
  • 184
  • 160
  • 92
Q.47

What is the value of Cot 60°- Cos 45°?

  • (9 - 2√3)/9
  • (2√6 - 1)/√3
  • (1 - 2√3)/2
  • (√2 - √3)/√6
Q.48

In ΔABC, ∠BAC = 90° and AD is drawn perpendicular to BC. If BD = 7 cm and CD = 28 cm, then what is the length (in cm) of AD?

  • 3.5
  • 7
  • 10.5
  • 14
Q.49

In an isosceles ΔABC, AD is the median to the unequal side meeting BC at D. DP is the angle disector of ∠ADB and PQ is drawn parallel to BC meeting AC at Q. Then the measure of ∠PDQ is

  • 130°
  • 90°
  • 180°
  • 45°
Q.50

A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. What is the total surface area (in cm2) of all the 8 parts?

  • 11750
  • 14100
  • 18800
  • 23500
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