Class 10 Mathematics
Previous Board Examination – Full Solved Answers (Set 4)
All answers are written in clear student exam-writing style with proper steps, as required for CBSE board valuation.
Section A – MCQs (Answers)
1. 2
2. 1
3. 14
4. 4
5. √3
Section B – Very Short Answer
6. Find the zero of the polynomial x − 9.
x − 9 = 0
x = 9
7. Evaluate √225.
√225 = 15
8. Find the LCM of 8 and 12.
8 = 2 × 2 × 2
12 = 2 × 2 × 3
LCM = 2 × 2 × 2 × 3 = 24
9. Write the value of tan 45°.
tan 45° = 1
10. Find the distance between (3,2) and (3,7).
Distance = √[(3−3)² + (7−2)²]
= √25
= 5 units
Section C – Short Answer
11. Find the zeros of the quadratic polynomial x² − 5x.
x² − 5x = 0
x(x − 5) = 0
x = 0 or x = 5
12. Solve: 4x + 8 = 0.
4x = −8
x = −2
13. Find HCF of 72 and 120 using Euclid’s Division Algorithm.
120 = 72 × 1 + 48
72 = 48 × 1 + 24
48 = 24 × 2 + 0
∴ HCF = 24
14. Prove: cosec²A − cot²A = 1.
We know,
cosec²A = 1 + cot²A
∴ cosec²A − cot²A = 1
Hence proved.
15. Find the distance between (0,−3) and (6,−3).
Distance = √[(6−0)² + (−3+3)²]
= √36
= 6 units
16. Find the area of a circle of radius 7 cm.
Area = πr²
= 22/7 × 7 × 7
= 154 cm²
Section D – Long Answer
17. Solve the quadratic equation x² − 3x − 10 = 0.
x² − 3x − 10 = 0
(x − 5)(x + 2) = 0
x = 5 or x = −2
18. Find the value of sin 30° / cos 60°.
sin 30° = 1/2
cos 60° = 1/2
Value = 1
19. Find the point dividing the line joining (1,3) and (7,3) internally in the ratio 1:1.
Midpoint = ((1+7)/2 , (3+3)/2)
= (4,3)
20. Find the area of a sector of a circle of radius 14 cm and angle 60°.
Area = (θ/360) × πr²
= (60/360) × 22/7 × 14 × 14
= 308/3 cm²
Section E – Case Study Based
21.
Side = 35 m
a) Perimeter = 4 × side = 4 × 35 = 140 m
b) Area = side² = 35 × 35 = 1225 m²
c) Fencing required = 140 m
Shaktimatha CBSE Learning
Class 10 Mathematics – Previous Board Exam Full Answers (Set 4)
⬅️ 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
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