Govt Exams
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Topics in NDA / CDS / AFCAT
A triangle has sides 5, 12, and 13 cm. What type of triangle is it?
Correct Answer:
B. Right-angled
EXPLANATION
5² + 12² = 25 + 144 = 169 = 13². Satisfies Pythagoras theorem, so it's right-angled
If ∫(2x + 3)dx = ?
Correct Answer:
A. x² + 3x + C
EXPLANATION
∫(2x + 3)dx = x² + 3x + C
If tan θ = 5/12, find sin θ (assuming θ is acute).
Correct Answer:
A. 5/13
EXPLANATION
tan θ = 5/12, in right triangle opposite=5, adjacent=12, hypotenuse=13. sin θ = 5/13
What is the area of a circle with radius 7 cm? (Use π = 22/7)
Correct Answer:
A. 154 cm²
EXPLANATION
Area = πr² = (22/7)×49 = 154 cm²
If 2x + 3y = 13 and 3x + 2y = 12, find x + y.
Correct Answer:
A. 5
EXPLANATION
Adding both equations: 5x + 5y = 25, so x + y = 5
A person walks 3 km north, then 4 km east. What is the shortest distance from the starting point?
Correct Answer:
A. 5 km
EXPLANATION
Using Pythagoras theorem: distance = √(3² + 4²) = √(9 + 16) = √25 = 5 km
If the roots of ax² + bx + c = 0 are α and β, then α + β = ?
Correct Answer:
A. -b/a
EXPLANATION
By Vieta's formulas, sum of roots = -b/a