Class 10 Mathematics
Previous Board–Style Question Paper – Set 3
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 180 and 252 is:
a) 18 b) 36 c) 12 d) 24
2. The zeroes of the polynomial x² − 8x + 12 are:
a) 2, 6 b) 3, 4 c) −2, −6 d) 1, 12
3. The value of sin 60° is:
a) 1/2 b) √3/2 c) 1 d) 0
4. Distance between (−2, −3) and (2, 1) is:
a) 4 b) 5 c) √32 d) √20
5. Number of tangents from a point inside a circle is:
a) 0 b) 1 c) 2 d) Infinite
6. The formula for curved surface area of a sphere is:
a) 2πr² b) 4πr² c) πr² d) πr³
7. Mean of first 30 natural numbers is:
a) 14.5 b) 15 c) 15.5 d) 30
8. Probability of getting a number less than 4 on a die is:
a) 1/6 b) 1/3 c) 1/2 d) 2/3
9. The graph of y = ax² + bx + c is a:
a) Straight line b) Circle c) Parabola d) Triangle
10. The value of tan 60° 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 180 and 252.
12. Find the zeroes of x² − 8x + 12.
13. Find sin 45° + cos 45°.
14. Find the distance between (2,3) and (6,7).
15. Find the midpoint of (−2,6) and (4,0).
16. Find the radius of a circle whose diameter is 28 cm.
17. Evaluate: tan 45° − sin 30°.
18. Find the mean of first 20 natural numbers.
19. Write the formula for volume of a cone.
20. Find the probability of getting an even number on a die.
Section C – Short Answer (3 × 10 = 30 Marks)
21. Prove that √3 is irrational.
22. Find the quadratic equation whose zeroes are 4 and −5.
23. Solve the pair of linear equations:
2x − y = 4
x + y = 5
24. Find the area of a triangle with vertices (1,2), (4,6) and (6,3).
25. Find the ratio in which the point (2,2) divides the line joining A(6,6) and B(−2,−2).
26. Find the curved surface area of a cylinder of radius 7 cm and height 14 cm.
27. Evaluate: sin 30° / cos 60°.
28. Find the mode of: 3, 5, 7, 5, 9, 5, 11.
29. Find the probability of getting a multiple of 5 from numbers 1 to 10.
30. Find the sum of first 50 natural numbers.
Section D – Long Answer (4 × 5 = 20 Marks)
31. Find the HCF and LCM of 36 and 84 using prime factorisation.
32. Solve x² − 9x + 20 = 0 by factorisation.
33. Find the area of a sector of a circle of radius 21 cm and angle 120°.
34. Find the mean using step deviation method:
| x | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| f | 5 | 9 | 14 | 8 | 4 |
35. Find the probability of getting a prime number when a die is thrown.
✅ FULL ANSWERS (Student Writing Style)
Section A – MCQs Answers:
1) b 2) a 3) b 4) b 5) a
6) b 7) c 8) c 9) c 10) c
Sample Section B Answer (Q11):
252 = 180 × 1 + 72
180 = 72 × 2 + 36
72 = 36 × 2 + 0
∴ HCF = 36
Sample Section C Answer (Q21):
Assume √3 = a/b, where a and b are co-prime.
3 = a²/b² ⇒ a² = 3b² ⇒ a divisible by 3.
Let a = 3k ⇒ b also divisible by 3.
Contradiction.
∴ √3 is irrational.
🧠 Exam Preparation Methods (For Students)
- Revise formulas daily
- Practice 2 questions from each chapter
- Solve at least 3 model papers
- Write answers neatly with steps
- Practice diagrams and graphs
✍️ Exam Writing Methods (Marks-Scoring Tips)
- Write step-by-step, not shortcuts
- Underline final answers
- Leave proper spacing
- Write formula before substitution
- Use correct symbols and units
👨🏫 Examiner Valuation View (Very Important)
- Marks are given for steps, not only answer
- Correct method = partial marks
- Neat presentation creates positive impression
- Wrong final answer but correct steps = marks awarded
- Illegible handwriting may lose marks
Shaktimatha CBSE Learning
Class 10 Mathematics – Previous Board Paper Set 3 (Solved + Exam Guide)
⬅️ Back to Class 10 Mathematics Library
📘 Class 10 Mathematics – Previous Board Question Papers & Model Answers
This library is specially prepared for Class 10 Board Exam students to understand question patterns, answer-writing style, step-by-step solutions, and examiner expectations.
🧠 How to Write Maths Answers in Exam
📝 Previous Board Question Papers
- Previous Board Question Paper – Set 1
- Question Paper – Set 2
- Question Paper – Set 3
- Question Paper – Set 4
- Question Paper – Set 5
- Question Paper – Set 6
✍️ Full Board Exam Answers (Student Writing Style)
- Full Answers – Set 1
- Full Answers – Set 2
- Full Answers – Set 3
- Full Answers – Set 5
- Full Answers – Set 6
📊 Model Papers & Practice Sets
✔ First read the Question Paper
✔ Try writing answers yourself
✔ Compare with Full Model Answers
✔ Observe steps, diagrams, and presentation
✔ Practice again to score full marks
Prepared with dedication by Shaktimatha Learning ✨
Concept clarity • Exam confidence • Board success
.png)
No comments:
Post a Comment