Class 10 Mathematics (NCERT)

1. All circles are always:

• A. Congruent
• B. Similar
• C. Equal in area
• D. Neither similar nor congruent

2. All squares are:

• A. Congruent
• B. Similar
• C. Equal in perimeter
• D. None of these

3. All _______ triangles are similar.

• A. Isosceles
• B. Scalene
• C. Equilateral
• D. Right-angled

4. Basic Proportionality Theorem is also known as:

• A. Pythagoras Theorem
• B. Thales Theorem
• C. Euclid's Lemma
• D. Apollonius Theorem

5. In ΔABC, DE || BC such that AD = 1.5 cm, DB = 3 cm, and AE = 1 cm. What is EC?

• A. 1.5 cm
• B. 2 cm
• C. 2.5 cm
• D. 3 cm

6. If two triangles are similar, then their corresponding sides are:

• A. Equal
• B. Proportional
• C. Parallel
• D. Perpendicular

7. If ΔABC ~ ΔPQR, then which of the following is true?

• A. AB/PQ = BC/QR = AC/PR
• B. AB/QR = BC/PR = AC/PQ
• C. AB/PR = BC/PQ = AC/QR
• D. AB = PQ

8. Which of the following is NOT a criterion for similarity of two triangles?

• A. AAA
• B. SAS
• C. SSS
• D. RHS

9. In ΔABC, DE || BC. If AD/DB = 3/5 and AC = 5.6 cm, then AE is equal to:

• A. 2.1 cm
• B. 3.1 cm
• C. 1.8 cm
• D. 2.4 cm

10. If ΔABC ~ ΔDEF such that AB = 1.2 cm and DE = 1.4 cm, the ratio of areas of ΔABC and ΔDEF is:

• A. 6 : 7
• B. 36 : 49
• C. 16 : 25
• D. 9 : 16

11. In a right triangle ABC, right angled at B, if AC = 10 cm and AB = 6 cm, then BC is:

• A. 8 cm
• B. 7 cm
• C. 9 cm
• D. 4 cm

12. The length of hypotenuse of an isosceles right-angled triangle whose one side is 4 cm long is:

• A. 4 cm
• B. 4√2 cm
• C. 8 cm
• D. 2√2 cm

13. In ΔABC, AB = 6√3 cm, AC = 12 cm, and BC = 6 cm. The angle B is:

• A. 120°
• B. 60°
• C. 90°
• D. 45°

14. The line segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to ____ of it.

• A. Double
• B. Half
• C. One-third
• D. Equal

15. Diagonals of a trapezium ABCD with AB || DC intersect each other at O. If AB = 2 CD, then ratio of areas of ΔAOB and ΔCOD is:

• A. 1 : 4
• B. 4 : 1
• C. 2 : 1
• D. 1 : 2

16. If a vertical pole of length 6 m casts a shadow 4 m long on ground, and at the same time a tower casts a shadow 28 m long, height of tower is:

• A. 40 m
• B. 42 m
• C. 38 m
• D. 50 m

17. Altitude of an equilateral triangle of side 8 cm is:

• A. 4√3 cm
• B. 2√3 cm
• C. 8√3 cm
• D. 4 cm

18. Areas of two similar triangles are in the ratio 9 : 25. The ratio of their corresponding sides is:

• A. 81 : 625
• B. 3 : 5
• C. 5 : 3
• D. 9 : 25

19. In ΔABC, ∠A = 90° and AD ⊥ BC. Then AD² is equal to:

• A. BD × CD
• B. AB × AC
• C. BC × CD
• D. AB × BD

20. Two triangles are similar if their corresponding angles are:

• A. Equal
• B. Unequal
• C. Complementary
• D. Supplementary

21. If side of an equilateral triangle is 'a', its area is given by:

• A. (√3/4) a²
• B. (√3/2) a²
• C. (1/2) a²
• D. √3 a²

22. Perimeters of two similar triangles ΔABC and ΔPQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then AB is:

• A. 15 cm
• B. 12 cm
• C. 18 cm
• D. 20 cm

23. In a square ABCD, length of diagonal AC is 10 cm. The side of square is:

• A. 5 cm
• B. 5√2 cm
• C. 10√2 cm
• D. 5/2 cm

24. If ΔABC ~ ΔDEF and ∠A = 47°, ∠E = 83°, then ∠C is equal to:

• A. 50°
• B. 60°
• C. 70°
• D. 80°

25. A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to other end. How far from base of pole should stake be driven?

• A. 6√7 m
• B. 12 m
• C. 6√5 m
• D. 18 m

26. Corresponding medians of two similar triangles are in ratio 4 : 9. Ratio of areas of these triangles is:

• A. 2 : 3
• B. 16 : 81
• C. 81 : 16
• D. 4 : 9

27. In a rhombus ABCD, side AB = 10 cm and diagonal AC = 12 cm. Length of other diagonal BD is:

• A. 16 cm
• B. 8 cm
• C. 20 cm
• D. 12 cm

28. If a line divides any two sides of a triangle in the same ratio, then the line is _____ to the third side.

• A. Perpendicular
• B. Parallel
• C. Equal
• D. Coincident

29. In ΔABC, D and E are points on AB and AC such that DE || BC. If AD = x, DB = x - 2, AE = x + 2, EC = x - 1, then x =

• A. 4
• B. 3
• C. 2
• D. 1

30. Triangle ABC is an isosceles triangle right-angled at C. Then AB² is equal to:

• A. 2 AC²
• B. AC²
• C. 3 AC²
• D. 4 AC²