Class 10 Mathematics
Previous Board Examination – Full Solved Answers (Set 3)
The following answers are written in clear student style with proper steps, as expected by CBSE board examiners.
Section A – MCQs (Answers)
1. −4
2. 1/2
3. 6
4. 4
5. 1/√3
Section B – Very Short Answer
6. Find the zero of the polynomial x.
x = 0
7. Evaluate √196.
√196 = 14
8. Find the HCF of 16 and 24.
16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
HCF = 2 × 2 × 2 = 8
9. Write the value of sin 0°.
sin 0° = 0
10. Find the distance between (2,3) and (2,9).
Distance = √[(2−2)² + (9−3)²]
= √36
= 6 units
Section C – Short Answer
11. Find the zeros of the quadratic polynomial x² − 4x.
x² − 4x = 0
x(x − 4) = 0
x = 0 or x = 4
12. Solve: 5x − 10 = 0.
5x = 10
x = 2
13. Find HCF of 54 and 126 using Euclid’s Division Algorithm.
126 = 54 × 2 + 18
54 = 18 × 3 + 0
∴ HCF = 18
14. Prove: sec²A − tan²A = 1.
We know,
sec²A = 1 + tan²A
∴ sec²A − tan²A = 1
Hence proved.
15. Find the distance between (−1,2) and (5,2).
Distance = √[(5+1)² + (2−2)²]
= √36
= 6 units
16. Find the area of a circle of radius 21 cm.
Area = πr²
= 22/7 × 21 × 21
= 1386 cm²
Section D – Long Answer
17. Solve the quadratic equation x² − 7x + 10 = 0.
x² − 7x + 10 = 0
(x − 5)(x − 2) = 0
x = 5 or x = 2
18. Find the value of sin 60° / cos 30°.
sin 60° = √3/2
cos 30° = √3/2
Value = 1
19. Find the point dividing the line joining (−2,4) and (6,4) internally in the ratio 1:1.
Midpoint = ((−2+6)/2 , (4+4)/2)
= (2,4)
20. Find the area of a sector of radius 21 cm and angle 120°.
Area = (θ/360) × πr²
= (120/360) × 22/7 × 21 × 21
= 924 cm²
Section E – Case Study Based
21.
Length = 40 m, Breadth = 25 m
a) Perimeter = 2(l + b)
= 2(40 + 25) = 130 m
b) Area = l × b = 40 × 25 = 1000 m²
c) Fencing required = 130 m
Shaktimatha CBSE Learning
Class 10 Mathematics – Previous Board Exam Full Answers (Set 3)
⬅️ 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 ✨
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