Class 10 Mathematics
Full Model Answers – Previous Years Question Paper
These answers are written exactly in the way a student should write in the Class 10 Board Examination.
Section A – MCQs
1. HCF of 306 and 657 = 9
2. α + β = 5/2
3. x-intercept
4. sin 30° = 1/2
5. Distance = 5 units
6. Number of tangents = 0
7. Area becomes 4 times
8. Mean = 5.5
9. Sum = n(n + 1)/2
10. tan 45° = 1
Section B – Very Short Answer Questions
11. Use Euclid’s Division Algorithm to find HCF of 135 and 225.
225 = 135 × 1 + 90
135 = 90 × 1 + 45
90 = 45 × 2 + 0
∴ HCF = 45
12. Find zeroes of x² − 7x + 10.
x² − 7x + 10 = 0
(x − 5)(x − 2) = 0
∴ Zeroes are 5 and 2.
13. sin 60° + cos 30°
= √3/2 + √3/2 = √3
14. Distance between (1, 2) and (4, 6)
= √[(4−1)² + (6−2)²]
= √(9 + 16) = √25 = 5
15. Midpoint of (2,2) and (6,6)
= ((2+6)/2 , (2+6)/2) = (4,4)
Section C – Short Answer Questions
21. Prove that √3 is irrational.
Assume √3 is rational.
√3 = a/b where a, b are co-prime.
Squaring both sides:
3 = a²/b² ⇒ a² = 3b²
a² divisible by 3 ⇒ a divisible by 3.
Let a = 3k.
9k² = 3b² ⇒ b² = 3k² ⇒ b divisible by 3.
This contradicts the assumption that a and b are co-prime.
∴ √3 is irrational.
22. Find quadratic equation whose zeroes are 3 and −2.
Sum = 3 + (−2) = 1
Product = −6
Required equation:
x² − (sum)x + product = 0
x² − x − 6 = 0
Section D – Long Answer Questions
31. Find HCF and LCM of 26 and 91.
26 = 2 × 13
91 = 7 × 13
HCF = 13
LCM = 2 × 7 × 13 = 182
LCM × HCF = 182 × 13 = 2366
26 × 91 = 2366
∴ Verified.
32. Solve x² − 5x − 6 = 0
x² − 6x + x − 6 = 0
(x − 6)(x + 1) = 0
x = 6 or x = −1
Shaktimatha CBSE Learning
Class 10 Mathematics – Full Model Answers
⬅️ 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
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