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 75◦ 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 mid-points 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 &nbsp... 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 co-ordinates of the mid-point of a line segment PQ are (1,-2). If the co-ordinates 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 non-overlapping. 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 mid-point 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