Govt Exams
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Topics in NDA / CDS / AFCAT
If 2^(x+1) = 32, find the value of x.
Correct Answer:
B. 4
EXPLANATION
32 = 2⁵. So 2^(x+1) = 2⁵ → x + 1 = 5 → x = 4.
The HCF of 48 and 64 is:
Correct Answer:
C. 16
EXPLANATION
Factors of 48: 1,2,3,4,6,8,12,16,24,48. Factors of 64: 1,2,4,8,16,32,64. HCF = 16.
What is the value of 4³ × 2⁻² ?
Correct Answer:
B. 16
EXPLANATION
4³ = 64, 2⁻² = 1/4. Therefore, 64 × 1/4 = 16.
If 3x - 7 = 2, what is the value of x?
Correct Answer:
C. 3
EXPLANATION
3x - 7 = 2 → 3x = 9 → x = 3.
The sum of interior angles of a polygon with 8 sides is:
Correct Answer:
B. 1080°
EXPLANATION
Sum of interior angles = (n - 2) × 180° where n = 8. So (8 - 2) × 180° = 6 × 180° = 1080°.
If sin θ = 3/5 and θ is acute, find the value of cot θ.
Correct Answer:
A. 4/3
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.
The LCM of 12 and 18 is:
Correct Answer:
B. 36
EXPLANATION
12 = 2²×3, 18 = 2×3². LCM = 2²×3² = 36
The perimeter of a rectangle is 28 cm and its length is 8 cm. Find its breadth.
Correct Answer:
B. 6 cm
EXPLANATION
Perimeter = 2(l+b), 28 = 2(8+b), 14 = 8+b, b = 6 cm
Find the derivative of f(x) = 3x² + 2x + 1 with respect to x.
Correct Answer:
A. 6x + 2
EXPLANATION
f'(x) = d/dx(3x² + 2x + 1) = 6x + 2
If a + b = 10 and ab = 21, find a² + b².
Correct Answer:
A. 58
EXPLANATION
a² + b² = (a+b)² - 2ab = 100 - 42 = 58