Take sectional tests or a full 40-question Geometry & Mensuration mock for CUET UG with timers, answer review, and detailed explanations.
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Use the sectional sessions to isolate lines and angles, triangle geometry, 2D mensuration, and 3D mensuration. Then switch to the full mixed mock to test recall under timer pressure.
One question at a time, 60 seconds per question, with score, accuracy, and subtopic insight at the end.
1. Two parallel lines are cut by a transversal. One pair of co-interior angles is in the ratio 2:3. Find the larger angle.
Explanation: Co-interior angles add up to 180deg. Let them be 2x and 3x. Then 5x = 180deg, so x = 36deg and the larger angle is 3x = 108deg.
2. Two adjacent angles are (4x + 10)deg and (2x + 50)deg. Find x.
Explanation: Adjacent angles on a straight line are supplementary. (4x + 10) + (2x + 50) = 180 gives 6x = 120, so x = 20.
3. What is the sum of interior angles of a hexagon?
Explanation: For an n-gon, sum of interior angles = (n - 2) x 180deg. For n = 6, the sum is 4 x 180deg = 720deg.
4. Each interior angle of a regular polygon is 135deg. How many sides does the polygon have?
Explanation: Exterior angle = 180deg - 135deg = 45deg. Number of sides = 360deg / 45deg = 8.
5. In triangle ABC, an exterior angle at A is 120deg. If angle B = 70deg, find angle C.
Explanation: Exterior angle equals the sum of the two opposite interior angles. So 120deg = 70deg + angle C, giving angle C = 50deg.
6. Three parallel lines are cut by two transversals. The intercepts on one transversal are 3 and 5. If the first intercept on the second transversal is 9, find the second intercept.
Explanation: Intercepts formed by parallel lines on transversals are proportional. So 3/5 = 9/x gives x = 15.
7. The ratio of an interior angle to an exterior angle of a regular polygon is 5:1. Find the number of sides.
Explanation: If interior : exterior = 5 : 1, let exterior = x and interior = 5x. Then 6x = 180deg, so x = 30deg. Number of sides = 360deg / 30deg = 12.
8. The angles of a triangle are xdeg, (x + 20)deg, and (x + 40)deg. Find the largest angle.
Explanation: x + (x + 20) + (x + 40) = 180 gives 3x = 120, so x = 40. The largest angle is x + 40 = 80deg.
9. The base angles of an isosceles triangle are each 40deg. Find the vertex angle.
Explanation: Sum of angles in a triangle is 180deg. The vertex angle is 180deg - 40deg - 40deg = 100deg.
10. If two lines are perpendicular to the same line, then the two lines are:
Explanation: Two lines that each make a right angle with the same line must run in the same direction, so they are parallel.
11. Two similar triangles have perimeters 30 cm and 45 cm. If a side of the smaller triangle is 8 cm, find the corresponding side of the larger triangle.
Explanation: For similar triangles, the ratio of corresponding sides equals the ratio of perimeters. So side ratio = 30:45 = 2:3, and the larger side is 8 x 3/2 = 12 cm.
12. Areas of two similar triangles are 81 cm^2 and 49 cm^2. If a side of the first is 9 cm, find the corresponding side of the second.
Explanation: Ratio of corresponding sides is the square root of the area ratio. sqrt(81/49) = 9/7, so the corresponding side is 7 cm.
13. In triangle PQR, ST is parallel to QR. If PS = 4, SQ = 6, and PT = 5, find TR.
Explanation: By BPT, PS/SQ = PT/TR. So 4/6 = 5/TR gives TR = 7.5.
14. G is the centroid of triangle ABC. If median AD = 15 cm, find AG.
Explanation: The centroid divides each median in the ratio 2:1 from the vertex. So AG = 2/3 of AD = 10 cm.
15. A triangle has sides 5, 12, and 13. What type of triangle is it?
Explanation: Since 5^2 + 12^2 = 13^2, the triangle satisfies Pythagoras and is right-angled.
16. In triangle ABC, M and N are midpoints of AB and AC. If BC = 20 cm, find MN.
Explanation: The segment joining the midpoints of two sides is half the third side. So MN = 20/2 = 10 cm.
17. In triangle ABC, AB = 6, AC = 8, and BC = 10. Find the median from A to BC.
Explanation: Since BC = 10, its midpoint splits it into 5 and 5. By Apollonius, 6^2 + 8^2 = 2(AD^2 + 5^2), giving AD^2 = 25 and AD = 5 cm.
18. Which of the following is NOT a valid congruency condition?
Explanation: SSA is not a standard congruency rule because it can produce more than one triangle.
19. Two triangles have angles 40deg, 60deg, 80deg and 40deg, 60deg, 80deg respectively. They are:
Explanation: Equal angles guarantee AA similarity, but not necessarily congruency.
20. In which triangle do centroid, incenter, circumcenter, and orthocenter coincide?
Explanation: In an equilateral triangle, all classical centers lie at the same point.
21. The circumference of a circle exceeds its diameter by 30 cm. Find the radius. Use pi = 22/7.
Explanation: 2pi r - 2r = 30. So 2r(pi - 1) = 30, and substituting pi = 22/7 gives r = 7 cm.
22. A sector has radius 14 cm and central angle 90deg. Find its area. Use pi = 22/7.
Explanation: Area of sector = (theta/360) x pi r^2. So (90/360) x (22/7) x 14^2 = 154 cm^2.
23. The diagonal of a rectangle is 13 cm and one side is 5 cm. Find its area.
Explanation: Use Pythagoras to get the other side: sqrt(13^2 - 5^2) = 12 cm. Area = 5 x 12 = 60 cm^2.
24. A trapezium has parallel sides 10 m and 14 m, and height 8 m. Find its area.
Explanation: Area of trapezium = 1/2 x (sum of parallel sides) x height. So area = 1/2 x 24 x 8 = 96 m^2.
25. An equilateral triangle has side 12 cm. Find its area.
Explanation: Area of an equilateral triangle = (sqrt(3)/4)a^2. With a = 12, the area is 36sqrt(3) cm^2.
26. The area of a circle is 616 cm^2. Find its circumference. Use pi = 22/7.
Explanation: From pi r^2 = 616, we get r^2 = 196 and r = 14. Circumference = 2pi r = 88 cm.
27. The diagonals of a rhombus are 16 cm and 12 cm. Find its area.
Explanation: Area of a rhombus = 1/2 x d1 x d2. So area = 1/2 x 16 x 12 = 96 cm^2.
28. A circular ring has outer radius 10 cm and inner radius 6 cm. Find the area of the ring. Use pi = 3.14.
Explanation: Area of annulus = pi(R^2 - r^2). So 3.14 x (100 - 36) = 200.96 cm^2.
29. A triangle has sides 9 cm, 12 cm, and 15 cm. Find its area using Heron's formula.
Explanation: Semi-perimeter s = (9 + 12 + 15)/2 = 18. Area = sqrt[18 x 9 x 6 x 3] = sqrt(2916) = 54 cm^2.
30. The perimeter of a square equals the perimeter of a rectangle with sides 8 cm and 6 cm. Find the area of the square.
Explanation: Perimeter of the rectangle = 2(8 + 6) = 28 cm. So the square has side 7 cm and area 49 cm^2.
31. Find the volume of a sphere with radius 21 cm. Use pi = 22/7.
Explanation: Volume of sphere = (4/3)pi r^3. Substituting r = 21 and pi = 22/7 gives 38808 cm^3.
32. A cylinder has diameter 14 cm and height 20 cm. Find its total surface area. Use pi = 22/7.
Explanation: Radius = 7 cm. TSA = 2pi r(r + h). So TSA = 2 x (22/7) x 7 x 27 = 1188 cm^2.
33. A cone has base radius 7 cm and slant height 25 cm. Find its lateral surface area. Use pi = 22/7.
Explanation: Lateral surface area of cone = pi r l. So (22/7) x 7 x 25 = 550 cm^2.
34. A cube has total surface area 384 cm^2. Find its volume.
Explanation: 6a^2 = 384 gives a^2 = 64, so a = 8 cm. Volume = a^3 = 512 cm^3.
35. How many small spheres of radius 1 cm can be formed from a solid sphere of radius 4 cm?
Explanation: Volume ratio equals the cube of the radius ratio. So the number of small spheres is (4/1)^3 = 64.
36. The height of a cylinder is halved while radius stays the same. By what factor does the volume change?
Explanation: Volume of a cylinder is pi r^2 h. If h is halved and r is unchanged, the volume also becomes half.
37. A cone and a cylinder have the same base and height. What is the ratio of their volumes?
Explanation: Volume of cone = (1/3)pi r^2 h, while volume of cylinder = pi r^2 h. So the ratio is 1:3.
38. A room measures 12 m x 9 m x 6 m. How many cubes of side 3 m fit exactly inside it?
Explanation: Fit count along each dimension: 12/3 = 4, 9/3 = 3, and 6/3 = 2. Total cubes = 4 x 3 x 2 = 24.
39. A hemispherical bowl has radius 10.5 cm. Find the outer curved surface area. Use pi = 22/7.
Explanation: Curved surface area of a hemisphere = 2pi r^2. With r = 10.5 cm, the area is 693 cm^2.
40. Two similar cylinders have radii 2 cm and 5 cm. What is the ratio of their curved surface areas?
Explanation: For similar solids, corresponding heights scale in the same ratio as radii, so curved surface area scales as the square of the linear ratio. Therefore the ratio is 2^2 : 5^2 = 4:25.