Class 10 Mathematics
Previous Board Examination – Full Solved Answers
The following solutions are written exactly in the way a Class 10 student should write answers in the Board Examination to score full marks.
Section A – MCQs
1. HCF of 405 and 504 = 9
2. Zeroes are 2 and 7
3. cos 60° = 1/2
4. Distance = 4 units
5. Number of tangents = 2
6. Curved surface area of cone = πrl
7. Mean = 10.5
8. Probability = 1/2
9. Graph is a straight line
10. tan 30° = 1/√3
Section B – Very Short Answer Questions
11. Use Euclid’s Division Algorithm to find the HCF of 405 and 504.
504 = 405 × 1 + 99
405 = 99 × 4 + 9
99 = 9 × 11 + 0
∴ HCF = 9
12. Find the zeroes of x² − 9x + 14.
x² − 9x + 14 = 0
(x − 7)(x − 2) = 0
∴ Zeroes are 2 and 7.
13. sin 60° + cos 30°
= √3/2 + √3/2 = √3
14. Distance between (1, −2) and (4, 2)
= √[(4−1)² + (2+2)²]
= √(9 + 16) = 5 units
15. Midpoint of (−2,4) and (6,0)
= ((−2+6)/2 , (4+0)/2) = (2,2)
16. Radius when circumference = 88 cm
2πr = 88 ⇒ r = 14 cm
17. tan 45° − sin 30°
= 1 − 1/2 = 1/2
18. Mean of first 10 natural numbers
Mean = (1+2+…+10)/10 = 55/10 = 5.5
19. Formula for volume of a sphere
4/3 πr³
20. Probability of getting an odd number on a die
Odd numbers: 1,3,5 → 3 outcomes
Probability = 3/6 = 1/2
Section C – Short Answer Questions
21. Prove that √2 is irrational.
Assume √2 is rational.
Let √2 = a/b, where a and b are co-prime integers.
Squaring both sides:
2 = a²/b² ⇒ a² = 2b²
So, a is divisible by 2 ⇒ let a = 2k.
Substituting: 4k² = 2b² ⇒ b² = 2k² ⇒ b divisible by 2.
This contradicts the assumption that a and b are co-prime.
∴ √2 is irrational.
22. Quadratic equation whose zeroes are 5 and −3
Sum = 2, Product = −15
Required equation:
x² − 2x − 15 = 0
23. Solve: 2x + y = 11, x − y = 1
Adding equations:
3x = 12 ⇒ x = 4
Substitute in x − y = 1 ⇒ y = 3
∴ Solution is (4,3)
Section D – Long Answer Questions
31. Find HCF and LCM of 26 and 91
26 = 2 × 13
91 = 7 × 13
HCF = 13
LCM = 182
LCM × HCF = 182 × 13 = 2366
26 × 91 = 2366
∴ Verified.
32. Solve x² − 7x + 10 = 0
(x − 5)(x − 2) = 0
x = 5 or 2
33. Area of sector (r = 14 cm, θ = 90°)
Area = (90/360) × π × 14²
= 1/4 × 22/7 × 196 = 154 cm²
34. Mean by step deviation method
Mean = 30
35. Probability of getting a prime number on a die
Prime numbers: 2,3,5
Probability = 3/6 = 1/2
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Class 10 Mathematics – Previous Board Exam Full Answers
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📘 Class 10 Mathematics – Previous Board Question Papers & Model Answers
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📝 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
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- Full Answers – Set 6
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