1 
A conical cup when completely filled with ice cream forms a hemispherical shape on its open end. Fin...
CAT
Quantitative Ability
Geometry
Mensuration

2 
A telephone company places round cables in round ducts. Assuming the diameter of a cable is 2 cm, wh...
CAT
Quantitative Ability
Geometry
Mensuration
Spheres and Hemispheres

3 
An equilateral triangle has a side of 12 cm. Find the area (in sq. cm) formed by the incentre, centr...
CAT
Quantitative Ability
Geometry
Mensuration

4 
A metallic solid cylinder of 14 cm diameter and 32 cm height is cast into 77 solid cubes of equal si...
CAT
Quantitative Ability
Geometry
Mensuration

5 
A right circular cone is cut parallel to its base at one third of its height from the top. Find the ...
CAT
Quantitative Ability
Geometry
Mensuration

6 
A circular sheet of paper of radius 6 cm is cut into six equal sectors. Each sector is formed i...
CAT
Quantitative Ability
Geometry
Mensuration

7 
A roller is 8 m long and has a diameter of 0.7 m. It takes exactly 1000 rotations of the roller to l...
CAT
Quantitative Ability
Geometry
Mensuration

8 
A cylindrical vessel of diameter 48 cm has water to a height of 10 cm. A metal cube of 14 cm edge is...
CAT
Quantitative Ability
Geometry
Mensuration

9 
Three balls are placed inside a cone such that each ball is in contact with the edge of the cone and...
CAT
Quantitative Ability
Geometry
Mensuration
Cones and Cylinders

10 
A rectangle and an equilateral triangle with equal area are inscribed in a circle with radius, 2. ...
CAT
Quantitative Ability
Geometry
Mensuration

11 
If one angle of a pentagon is 40o and all the other angles are equal, find the measure of each ...
CAT
Quantitative Ability
Geometry
Mensuration

12 
In the figure, where the two arcs are quarter circles, the area of the shaded region is Type...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Circles

13 
The diagram below shows a circle with centre O and AB parallel to CD. Given the angles 75â—¦ and ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Angles in a Circle

14 
In the figure below is a circle with centre O, and another circle with centre at the midpoint B...
CAT
Quantitative Ability
Geometry
Circles

15 
Two circles of radius 1 cm. touch at point P. A third circle is drawn through the points A, B, and C...
CAT
Quantitative Ability
Geometry
Circles

16 
In the given figure AMD, APQ and ASR are secants to the given circles. IF AM=4 cm, MD=6 cm and...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Chord

17 
In the figure, O and O’ are the centres of the bigger and smaller circles respectively and sma...
CAT
Quantitative Ability
Geometry
Circles

18 
PQRS is a square. SR is a tangent (at point S) to the circle with centre O and TR = OS. Then the rat...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents

19 
A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as sho...
CAT
Quantitative Ability
Geometry
Circles

20 
In the figure given below, O, Q, P, R are respective centres of circles of different radii and each ...
CAT
Quantitative Ability
Geometry
Circles

21 
A regular octagon is inscribed in a circle of radius 1 units. The product of the distances from a fi...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Other Polygons
Regular Polygons

22 
A string of length 24 inches is bent into in the form of a square named ABCD and then into the form ...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons

23 
A quadrilateral is obtained by joining the mid points of a rectangle. Further, a rectangle is obtain...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Rectangle

24 
ΔABC and ΔPQR are two similar triangles such that the ratio of the areas of ΔABC a...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

25 
The coordinates of the points which divides the line joining (1,7) and (4,3) in the ratio 2:3 is: ...
CAT
Quantitative Ability
Geometry
Coordinate Geometry
Section Formula

26 
In the figure given below, ABCD is a concave quadrilateral, and ∠BAD = 90°, BA = AD = 6 cm a...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals

27 
A vessel is in the form of an inverted cone.Its depth is 8 cm and the diameter of its top, which is ...
CAT
Quantitative Ability
Geometry
Mensuration

28 
The equation of the line passing through the point (1,3) and perpendicular to the line whose equatio...
CAT
Quantitative Ability
Geometry
Coordinate Geometry
Other Coordinate Geometry Concepts
Equation of a Line

29 
A rectangle is inscribed in a circle centre O as shown below, with AB = 5, BC = 12 and angle &a...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Angles in a Circle

30 
Two chords AB and CD of a circle intersect at E such that, AE = 2.4 cm, BE = 3.2 cm and CE = 1.6 cm....
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Chord

31 
In the given triangle, AD bisects A. The largest side among AB, BD and CD is: Type in your a...
CAT
Quantitative Ability
Geometry
Triangles
Properties of Triangles

32 
The perimeter of a regular hexagon is 108 m. Area of the hexagon is:
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Other Polygons
Regular Polygons

33 
Two circles touch each other externally. If the sum of their areas is 130 π cm2 and the distance...
CAT
Quantitative Ability
Geometry
Circles
Perimeter and Area of Circles and Sectors

34 
In the figure below, P, Q, and R are points on a circle with center O. The tangent to the circle at ...
CAT
Quantitative Ability
Geometry
Circles

35 
A swimming pool 150 m long and 50 m wide is 1 m deep at the shallow end and 6 m deep at the deep end...
CAT
Quantitative Ability
Geometry
Mensuration

36 
In the given figure, O is the center of the circle. AC, the diameter of the circle, measures 26 cm. ...
CAT
Quantitative Ability
Geometry
Triangles
Pythagoras Theorem
Circles

37 
In the given figure, PS is a tangent to a circle with radius 10 cm and centre at O. PQ = 9 cm and th...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Tangent

38 
Three cubes each of volume of 216 m3 are joined end to end. Find the surface area of the resulting f...
CAT
Quantitative Ability
Geometry
Mensuration

39 
In the given ABC, BCA=BAC. What can be the perimeter of ADC, if all sides have i...
CAT
Quantitative Ability
Geometry
Triangles
Properties of Triangles

40 
In the given figure, a circle is inscribed in the square such that it touches all four sides of the ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles

41 
The equation of the line passing through the points A(0,4) and B(6,2) is
CAT
Quantitative Ability
Geometry
Coordinate Geometry
Other Coordinate Geometry Concepts
Equation of a Line

42 
ABCD is a rectangle and E is a point on the line parallel to diagonal BD. BC is 4 cm and area o...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

43 
The areas of three adjacent faces of a cuboid are x, y, z. If the volume is V,then V2 will be equal ...
CAT
Quantitative Ability
Geometry
Mensuration

44 
A cuboid of dimension 24cm * 9 cm * 8cm is melted and smaller cubes are of side 3 cm is formed....
CAT
Quantitative Ability
Geometry
Mensuration

45 
The area of a circle inscribed in an equilateral triangle is 462 cm2. The perimeter of the triangle ...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

46 
The given figure shows a circle with centre O. AB is a chord on the circle such that AP=(11x+2) cm, ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Chord

47 
A chord AB of a circle of radius 5.25 cm makes an angle of 60 degree at the center of the c...
CAT
Quantitative Ability
Geometry
Circles

48 
What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of rad...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Chord

49 
In triangle ABC, AC is parallel to DE. AD:DB = 1:2. What is the length of BE? Type in your answer...
CAT
Quantitative Ability
Geometry
Triangles
Similarity of Triangles

50 
A rectangular plot with an area 600 m2 is fenced, the length of fencing being 100 m. The length of t...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Rectangle

51 
Four circular cardboard pieces, each of diameter 28 cm are placed in such a way that each piece touc...
CAT
Quantitative Ability
Geometry
Circles
Perimeter and Area of Circles and Sectors

52 
The measure of ADB is: Type in your answer as in Integer. For example, 62.3 to 62. ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Angles in a Circle

53 
If P(7,y), Q(2,4) and R(6,10) are three points such that PR=PQ, the value of y is:
CAT
Quantitative Ability
Geometry
Coordinate Geometry
Distance Formula

54 
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. The area of the tria...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

55 
If a wire is bent into the shape of a square, then the area of the square of 121 m2. If the wire is ...
CAT
Quantitative Ability
Geometry
Circles
Perimeter and Area of Circles and Sectors

56 
In the given figure, measure of BAC is Type in your answer as Integer. For example, 23.7 to 24. ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Angles in a Circle

57 
In the figure given below, O is the center of the center, MNO=20o, and NMP=60o, the measu...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Angles in a Circle

58 
In the given figure, O as center the of the circle, AB = BC = radius of circle. Find the measurement...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Angles in a Circle

59 
A solid wood toy is in the shape of a right circular cone mounted on a hemisphere. If the radiu...
CAT
Quantitative Ability
Geometry
Mensuration

60 
A wire 66 cm long has been put in the form of a circle. Find the area of the circle so formed. Type...
CAT
Quantitative Ability
Geometry
Circles
Perimeter and Area of Circles and Sectors

61 
Two circles of radii 9 cm and 4 cm touch each other externally. Find the length of their direct comm...
CAT
Quantitative Ability
Geometry
Mensuration

62 
In the figure given below, AP and PB are tangents to the circle with radius 5 cm. Find the length of...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Tangent

63 
Which is the largest side of the following triangle? Type in your answer in a clockwise mann...
CAT
Quantitative Ability
Geometry
Triangles
Properties of Triangles

64 
ABCDEFGH is a regular octagon where the diagonals AC and BH intersect at O. what is the measure of &...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons

65 
AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If A...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents

66 
A closed wooden box measures externally 10 cm long, 8 cm board and 6 cm high. The thickness of wood ...
CAT
Quantitative Ability
Geometry

67 
In the given figure, AED = ABC. Find the value of x. Type in your answer as an integer. For examp...
CAT
Quantitative Ability
Geometry
Triangles
Similarity of Triangles

68 
In triangle ABC, CE and BF are medians to equal sides AB and AC respectively. Which of the following...
CAT
Quantitative Ability
Geometry
Triangles
Similarity of Triangles

69 
The area of a trapezium is 96 cm2. If its parallel sides are in ratio 3:5, and the perpendicular dis...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Trapezium

70 
An arc makes an angle of 72o at the centre of a circle of radius 10 cm. Length of the arc is ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Angles in a Circle

71 
Area of the triangle, two sides of which are 32 cm and 40 cm, and perimeter 96 cm, is: Type i...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle
Heron's Formulae

72 
In the given figure, ABCD is a square (all sides are equal and all internal angles are 90o) and DCE ...
CAT
Quantitative Ability
Geometry
Triangles
Properties of Triangles

73 
An order was placed for the supply of a rectangular carpet of breadth 3 m. The length of carpet was ...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Rectangle

74 
In the given figure, two circles with their centres O and O’ intersect each other at A and B. ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles

75 
If the area of an equilateral triangle is 24 3 m2, then its perimeter is ...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

76 
In the given figure, AD and BE are medians of ABC. If DF is parallel to BE, length of side EF is: ...
CAT
Quantitative Ability
Geometry
Triangles
Similarity of Triangles
Angle Bisector Theorem

77 
PR and QP are tangents to the bigger circle, PS and PR are tangents to the smaller circle. Length of...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Tangent

78 
ABCD is quadrilateral inscribed inside a circle with centre O such that AB is the diameter of the ci...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Angles in a Circle

79 
An isosceles PQR with base PQ = 6 cm, PR = RQ and RPQ = 30° is inscribed in a circle. A small ci...
CAT
Quantitative Ability
Geometry
Triangles
Circles

80 
In the figure given below, the measure of angle PRQ is 75o. QP and QR are tangents to the circle. Me...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Tangent

81 
In the given triangle ABC, DE is drawn parallel to BC such that AD:DB is 2:1 and DE is 14 cm. A circ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Tangent

82 
If the ratio of the perimeters of the two similar triangles is 3:1, then the ratio of their area is:...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

83 
In a regular hexagon of side a cm, the midpoints of the three alternate sides are joined in order t...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons

84 
For the figure given below, find the value of x Type in your answer as in integer. For e...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Secant

85 
A conical tent is to accommodate 10 persons. Each person must have 6 m2 space to sit and 3...
CAT
Quantitative Ability
Geometry
Mensuration

86 
The Centroid of a triangle having coordinates (2,4), (7,4) and (0,4) is
CAT
Quantitative Ability
Geometry
Coordinate Geometry
Section Formula

87 
The interior angles, in degrees of a polygon, are all distinct integers. If the greatest interior an...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons

88 
A circle is inscribed inside a square. The square is inscribed inside another circle. If the area of...
CAT
Quantitative Ability
Geometry
Circles

89 
If ABO = 20o and ACO =25o, then the measure of BOC is: Type in your answer as in Integer. For exa...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles

90 
In the given figure, AB measures 40 cm and BD measures 60 cm. BD is the angle bisector of both  ...
CAT
Quantitative Ability
Geometry
Triangles
Congruency of Triangles

91 
A cow is tied to a peg at one corner of an equilateral triangle shaped grass field by means of a 21 ...
CAT
Quantitative Ability
Geometry
Circles
Perimeter and Area of Circles and Sectors

92 
ABCDEF is a regular hexagon. Another hexagon PQRSTU is made by joining midpoints of each side. Ratio...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Other Polygons
Regular Polygons

93 
In the figure given below, ABCD is a rectangle. Area of triangle ABE = 15 cm2. If EC = 2.BE, then th...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Rectangle

94 
What would be the cost of building a 7 m wide garden around a circular field with a diameter of 280 ...
CAT
Quantitative Ability
Geometry
Circles
Perimeter and Area of Circles and Sectors

95 
In the square below, each vertex is joined to the midpoint of the opposite sides and a star shape is...
CAT
Quantitative Ability
Geometry
Mensuration

96 
For triangles ABD and CDB, AD = DC and AB = CB. Find (x + y) Type in your answer as an integer. F...
CAT
Quantitative Ability
Geometry
Triangles
Similarity of Triangles

97 
Triangle ABC is an equilateral triangle. The measure of BAD (in degrees) is Type in yo...
CAT
Quantitative Ability
Geometry
Triangles
Properties of Triangles

98 
The centroid of an isosceles triangle divides each median in the ratio:
CAT
Quantitative Ability
Geometry
Triangles

99 
The area of the largest triangle that can be inscribed in a semicircle with radius r is:
CAT
Quantitative Ability
Geometry
Circles
Perimeter and Area of Circles and Sectors

100 
In the given figure, AC = AE, AB = AD, and ∠BAD = ∠EAC. The length of side DE is: Type in...
CAT
Quantitative Ability
Geometry
Triangles
Similarity of Triangles

101 
Area of an equilateral triangle is 49√3 cm2. Radius of the circle circumscribing the triangle ...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

102 
For the given triangle, BE and AD are altitudes on sides AC and BC respectively. If BE = 20, AD = 16...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

103 
A boy with height 90 cm is standing parallel to the lamp post, which is 3.6 m away from the boy...
CAT
Quantitative Ability
Geometry
Triangles
Similarity of Triangles

104 
The perimeter of an isosceles triangle is 28 cm and the ratio of the length of the lateral...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

105 
The area of a rectangular field is 460 square metres. If the length is 15 percent more than the brea...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Rectangle

106 
The coordinates of the midpoint of a line segment PQ are (1,2). If the coordinates of P are (3,...
CAT
Quantitative Ability
Geometry
Coordinate Geometry
Section Formula

107 
The sides of a triangular plot are in the ratio of 3:5:4 and its perimeter is 36 m. Its area is: &n...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

108 
In the given figure, l is a line parallel to base BC. l intersects AB and AC at D and E respect...
CAT
Quantitative Ability
Geometry
Triangles
Similarity of Triangles

109 
For a triangle ABC right angled at A, AD is a perpendicular drawn on BC. Which of the foll...
CAT
Quantitative Ability
Geometry
Triangles
Similarity of Triangles

110 
Area of the triangle given in the figure below is: Type in your answer as an integer. For ex...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

111 
In the figure given below, AB is parallel to DC. The area of the trapezium is: Type in your answe...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Trapezium

112 
In a quadrilateral ABCD, AC and BD intersect at O such that AB = 16 cm, AO = 15 cm, OB = 5 cm, BC = ...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons

113 
The area of the four walls of a room is 660 m2 and its length is twice its breadth. If its height is...
CAT
Quantitative Ability
Geometry
Mensuration
Cubes and Cuboids

114 
The area of a rhombus each one of whose sides measures 10 cm and one diagonal is 12 cm is Type in y...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Rhombus

115 
ABCD is a trapezium in which AB is parallel DC, BD is a diagonal and E is the midpoint of AD. A line...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Trapezium

116 
In the given figure, ABHG and EFCD are two parallelograms. What is the measure of HXF? Type in yo...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Parallelogram

117 
In the given figure, AD=BA, BDA=54o, BC and CD are tangents to the circle with centre O. Measure of ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Tangent

118 
The ratio of the area of a square of side a cm and an equilateral triangle of side a cm is
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Square

119 
The length of a side of a rhombus is 5 m and one of its diagonals is of length 8 m. The ot...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Rhombus

120 
The angles of a quadrilateral are in the ratio 3:5:9:13. The largest angle of the quadrilateral is: ...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals

121 
Two concentric circles have radii 5 cm and 3 cm. The length of the chord of the larger circle which ...
CAT
Quantitative Ability
Geometry
Circles
Properties of Circles
Chords, Secants andTangents
Tangent

122 
In the figure given below, ‘a’ is the side of square ABCD and EFGH, IJKL, MNOP and QRST ...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
Rectangle

123 
In the adjoining figure all the circles are identical and nonoverlapping. The outer circle touch th...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons

124 
Find the volume of the largest sphere which can be cut from a cube having edges of 7 cm length. Appr...
CAT
Quantitative Ability
Geometry
Mensuration

125 
ΔABC and ΔDBF are equilateral triangles such that D is midpoint of BC. What is the rati...
CAT
Quantitative Ability
Geometry
Triangles
Area of Triangle

126 
ABCD is a quadrilateral. The diagonals of ABCD intersect at the point P. The area of the triangles A...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons

127 
In the figure shown below, what is the ratio of the area of the outer and the inner regular hexagon,...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons

128 
A cardboard piece was cut from a regular polygon, and thrown away. Tatenda picked up this ...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Other Polygons

129 
ABCD is a trapezium in which AD and BC are parallel. If the four sides AB, BC, CD and DA are re...
CAT
Quantitative Ability
Geometry
Quadrilaterals and Polygons
Quadrilaterals
