Class 10 Mathematics
Previous Board Examination Question Paper
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 405 and 504 is:
a) 9 b) 18 c) 36 d) 72
2. The zeroes of the polynomial x² − 9x + 14 are:
a) 2, 7 b) −2, −7 c) 1, 14 d) 3, 6
3. The value of cos 60° is:
a) 1 b) √3/2 c) 1/2 d) 0
4. Distance between the points (−2, 3) and (2, 3) is:
a) 2 b) 4 c) 5 d) 6
5. Number of tangents that can be drawn from an external point to a circle is:
a) 1 b) 2 c) 3 d) 0
6. Curved surface area of a cone is:
a) πr² b) πrl c) 2πr d) πr²h
7. Mean of first 20 natural numbers is:
a) 10 b) 10.5 c) 11 d) 20
8. Probability of getting a tail when a coin is tossed is:
a) 0 b) 1 c) 1/2 d) 2
9. The graph of y = mx + c is a:
a) Curve b) Circle c) Straight line d) Parabola
10. The value of tan 30° is:
a) 1 b) 1/√3 c) √3 d) 0
Section B – Very Short Answer
(2 × 10 = 20 Marks)
11. Use Euclid’s Division Algorithm to find the HCF of 405 and 504.
12. Find the zeroes of the polynomial x² − 9x + 14.
13. Find the value of sin 60° + cos 30°.
14. Find the distance between the points (1, −2) and (4, 2).
15. Find the midpoint of the line joining (−2, 4) and (6, 0).
16. Find the radius of a circle whose circumference is 88 cm.
17. Find the value of tan 45° − sin 30°.
18. Find the mean of first 10 natural numbers.
19. Write the formula for the volume of a sphere.
20. Find the probability of getting an odd number on a die.
Section C – Short Answer
(3 × 10 = 30 Marks)
21. Prove that √2 is irrational.
22. Find the quadratic equation whose zeroes are 5 and −3.
23. Solve the pair of linear equations:
2x + y = 11
x − y = 1
24. Find the area of a triangle whose vertices are (2, 1), (4, 5) and (6, 3).
25. Find the ratio in which the point (1, 2) divides the line joining A(3, 6) and B(−1, −2).
26. Find the curved surface area of a cylinder of radius 7 cm and height 10 cm.
27. Evaluate: sin 30° / cos 60°.
28. Find the mode of the data:
2, 4, 6, 8, 6, 4, 6, 10
29. Find the probability of getting a multiple of 3 when a number from 1 to 10 is chosen.
30. Find the sum of first 25 natural numbers.
Section D – Long Answer
(4 × 5 = 20 Marks)
31. Find the HCF and LCM of 26 and 91 and verify that:
LCM × HCF = Product of the numbers.
32. Solve the quadratic equation by factorisation:
x² − 7x + 10 = 0.
33. Find the area of a sector of a circle of radius 14 cm and angle 90°.
34. Find the mean using step deviation method:
| x | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| f | 4 | 6 | 10 | 8 | 2 |
35. Find the probability of getting a prime number when a die is thrown.
Shaktimatha CBSE Learning
Class 10 Mathematics – Previous Board Exam Question Paper
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