Showing 11–20 of 100 questions
in Mathematics (NDA)
Q.11
Medium
Mathematics (NDA)
What is the area of a circle with radius 7 cm? (Use π = 22/7)
A
154 cm²
B
176 cm²
C
198 cm²
D
220 cm²
Correct Answer:
A. 154 cm²
Explanation:
Area = πr² = (22/7)×49 = 154 cm²
Q.12
Medium
Mathematics (NDA)
If tan θ = 5/12, find sin θ (assuming θ is acute).
A
5/13
B
12/13
C
5/12
D
12/5
Explanation:
tan θ = 5/12, in right triangle opposite=5, adjacent=12, hypotenuse=13. sin θ = 5/13
Q.13
Easy
Mathematics (NDA)
The LCM of 12 and 18 is:
Explanation:
12 = 2²×3, 18 = 2×3². LCM = 2²×3² = 36
Q.14
Medium
Mathematics (NDA)
If ∫(2x + 3)dx = ?
A
x² + 3x + C
B
2x² + 3x + C
C
x² + 3 + C
D
2x + 3x + C
Correct Answer:
A. x² + 3x + C
Explanation:
∫(2x + 3)dx = x² + 3x + C
Q.15
Medium
Mathematics (NDA)
A triangle has sides 5, 12, and 13 cm. What type of triangle is it?
A
Acute
B
Right-angled
C
Obtuse
D
Isosceles
Correct Answer:
B. Right-angled
Explanation:
5² + 12² = 25 + 144 = 169 = 13². Satisfies Pythagoras theorem, so it's right-angled
Q.16
Medium
Mathematics (NDA)
Find the value of (x³ - 8)/(x - 2) when x ≠ 2.
A
x² + 2x + 4
B
x² - 2x + 4
C
x² + 2x - 4
D
x² - 2x - 4
Correct Answer:
A. x² + 2x + 4
Explanation:
x³ - 8 = (x-2)(x² + 2x + 4), so (x³ - 8)/(x - 2) = x² + 2x + 4
Q.17
Hard
Mathematics (NDA)
In a frequency distribution, if mean = 25, mode = 23, find median using the empirical relationship.
A
24
B
24.33
C
24.67
D
25.33
Explanation:
Mode = 3×Median - 2×Mean, 23 = 3×Median - 50, Median = 24.33. Actually: Median = (Mode + 2×Mean)/3 = (23 + 50)/3 = 24.33, checking: mode≈3med-2mean gives med≈24.67
Q.18
Hard
Mathematics (NDA)
If a, b, c are in geometric progression with common ratio r, and a = 2, find the sum of first 5 terms when r = 2.
Explanation:
S₅ = a(r⁵ - 1)/(r - 1) = 2(32 - 1)/(2 - 1) = 2×31 = 62
Q.19
Easy
Mathematics (NDA)
If sin θ = 3/5 and θ is acute, find the value of cot θ.
Explanation:
If sin θ = 3/5, then in a right triangle, opposite = 3, hypotenuse = 5. Using Pythagoras, adjacent = 4. Therefore, cot θ = adjacent/opposite = 4/3.
Q.20
Easy
Mathematics (NDA)
The sum of interior angles of a polygon with 8 sides is:
A
900°
B
1080°
C
1260°
D
1440°
Explanation:
Sum of interior angles = (n - 2) × 180° where n = 8. So (8 - 2) × 180° = 6 × 180° = 1080°.
