Class 10 Mathematics
Previous Board Examination Question Paper – Set 2
Time: 3 Hours Maximum Marks: 80
General Instructions:
- All questions are compulsory.
- The question paper consists of Sections A, B, C and D.
- Use of calculator is not permitted.
- Draw neat diagrams wherever required.
Section A – MCQs
(1 × 10 = 10 Marks)
1. The HCF of 867 and 255 is:
a) 51 b) 17 c) 9 d) 3
2. The zeroes of the polynomial x² − 11x + 30 are:
a) 5, 6 b) −5, −6 c) 3, 10 d) 2, 15
3. The value of sin 45° is:
a) 1 b) 1/2 c) √3/2 d) 1/√2
4. Distance between points (−1, −2) and (2, 2) is:
a) 3 b) 4 c) 5 d) √13
5. The number of tangents that can be drawn to a circle from a point on the circle is:
a) 0 b) 1 c) 2 d) Infinite
6. The total surface area of a sphere depends on:
a) Radius b) Diameter c) Radius² d) Radius³
7. Mean of first 50 natural numbers is:
a) 25 b) 25.5 c) 26 d) 50
8. Probability of getting a number greater than 4 when a die is thrown is:
a) 1/6 b) 1/3 c) 1/2 d) 2/3
9. The graph of a quadratic polynomial is a:
a) Straight line b) Circle c) Parabola d) Triangle
10. The value of cos 30° is:
a) 1/2 b) 1/√3 c) √3/2 d) 1
Section B – Very Short Answer
(2 × 10 = 20 Marks)
11. Use Euclid’s Division Algorithm to find the HCF of 867 and 255.
12. Find the zeroes of the polynomial x² − 11x + 30.
13. Evaluate: sin 45° + cos 45°.
14. Find the distance between points (1, 1) and (4, 5).
15. Find the midpoint of the line joining (−4, 2) and (2, −6).
16. Find the radius of a sphere whose diameter is 14 cm.
17. Find the value of tan 45° − cos 60°.
18. Find the mean of first 20 natural numbers.
19. Write the formula for curved surface area of a cylinder.
20. Find the probability of getting a prime number on a die.
Section C – Short Answer
(3 × 10 = 30 Marks)
21. Prove that √7 is irrational.
22. Find the quadratic equation whose zeroes are 6 and 5.
23. Solve the pair of linear equations:
3x − y = 5
2x + y = 11
24. Find the area of a triangle whose vertices are (−2,1), (1,4) and (4,1).
25. Find the ratio in which the point (0,2) divides the line joining A(−2,4) and B(4,−2).
26. Find the curved surface area of a cone of radius 7 cm and slant height 24 cm.
27. Evaluate: sin 60° / cos 30°.
28. Find the mode of the data:
4, 6, 8, 6, 10, 6, 12
29. Find the probability of getting a number less than 3 from numbers 1 to 10.
30. Find the sum of first 40 natural numbers.
Section D – Long Answer
(4 × 5 = 20 Marks)
31. Find the HCF and LCM of 68 and 204 using prime factorisation.
32. Solve the quadratic equation by quadratic formula:
x² − 4x − 5 = 0.
33. Find the area of a sector of a circle of radius 21 cm and angle 60°.
34. Find the mean using step deviation method:
| x | 5 | 15 | 25 | 35 | 45 |
|---|---|---|---|---|---|
| f | 6 | 10 | 14 | 8 | 2 |
35. Find the probability of getting a number divisible by 4 when a die is thrown.
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Class 10 Mathematics – Previous Board Exam Paper (Set 2)
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