The CAT QA section requires speed and accuracy, along with a thorough understanding of the Geometry. This article provides a set of MCQs on Geometry to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT preparation.
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Geometry
1. Let ABCD be a parallelogram. The lengths of the side AD and the diagonal AC are 10 cm and 20 cm, respectively. If the angle \(∠ADC \) is equal to 30° then the area of the parallelogram, in sq. cm, is
A
\(\frac{25(\sqrt{3}+\sqrt{15})}{2}\)
B
\(25(\sqrt5+\sqrt{15})\)
C
\(\frac{25(\sqrt5+\sqrt{15})}{2}\)
D
\(25(\sqrt3+\sqrt{15})\)
2. The cost of fencing a rectangular plot is ₹ 200 per ft along one side, and ₹ 100 per ft along the three other sides. If the area of the rectangular plot is 60000 sq. ft, then the lowest possible cost of fencing all four sides, in INR, is
A
90000
B
160000
C
120000
D
100000
3. The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is [This Question was asked as TITA]
A
3 Square units
B
2 Square units
C
5 Square units
D
4 Square units
4. With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), is
A
3290
B
3920
C
3940
D
3950
5. Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is
A
8
B
9
C
10
D
7
6. If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is
A
\(4 \sqrt6\)
B
\(6 \sqrt6\)
C
\(2 \sqrt6\)
D
\(\sqrt6\)
7. In triangle PQR, PM is perpendicular to QR. If ‘T’ is a point in between ‘Q’ and ‘M’ such that PT = \(5\sqrt3\) cm, PM = \(\sqrt{39}\) cm then find the value of PQ such that QM : TM = 5 : 2.
A
\(3\sqrt{70}\) cm
B
\(5\sqrt{35}\) cm
C
\(2\sqrt{66}\) cm
D
\(3\sqrt{45}\) cm
8. In the given figure, AB is the chord of the circle with centre ‘O’. A tangent AT is drawn at point ‘A’ so that angle BAT = 48°, then measure of angle ADB is
A
112°
B
148°
C
132°
D
142°
9. In triangle PQR, the straight line parallel to side QR meets PQ and PR at points ‘A’ and ‘B’, respectively. If PA = BR, PQ = 36 cm and PB = 6 cm, then BR = ?
A
12 cm
B
10 cm
C
16 cm
D
8 cm
10. In triangle ABC, ‘D’ and ‘E’ are two points on sides AB and AC, respectively such that DE is parallel to BC. If AD=16 cm, BD=(5x-16) cm, AE=2x cm and EC=(25-2x) cm, then find the value of ‘x’.
A
\(2\sqrt10\)
B
\(3\sqrt5\)
C
\(4\sqrt5\)
D
\(3\sqrt10\)
11. PQRS is a rhombus such that length of its each side is 30 cm. If PR=36 cm and QS=\(4\sqrt{x}\) cm then the length of each side of the rhombus (in terms of ‘x’) is:
A
\((\sqrt{x }+ 18) cm\)
B
\(5\sqrt{x}\, cm\)
C
18 cm
D
30 cm
12. In the given figure, ‘O’ is the centre of the semi-circle and ∠MON =48°, Find ∠MRP.
A
60°
B
66°
C
54°
D
72°
13. The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is
A
1300
B
1340
C
1480
D
1520
14. The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
A
-5
B
-6
C
-7
D
-8
15. Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is
A
2 : 5
B
4 : 9
C
3 : 8
D
1 : 3
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