Showing 41–50 of 100 questions
Q.41
Easy
Mathematics (NDA)
What is the probability of getting a prime number when a die is rolled?
Explanation:
Prime numbers on a die: 2, 3, 5 (total 3). Total outcomes = 6. Probability = 3/6 = 1/2.
Q.42
Medium
Mathematics (NDA)
Find the derivative of x³ + 2x² - 5x + 3 with respect to x.
A
3x² + 4x - 5
B
3x² + 2x - 5
C
x² + 4x - 5
D
3x + 4 - 5
Correct Answer:
A. 3x² + 4x - 5
Explanation:
d/dx(x³ + 2x² - 5x + 3) = 3x² + 4x - 5.
Q.43
Easy
Mathematics (NDA)
If x² - 5x + 6 = 0, find the sum of the roots.
Explanation:
For ax² + bx + c = 0, sum of roots = -b/a = -(-5)/1 = 5.
Q.44
Easy
Mathematics (NDA)
A person invests Rs. 5000 at 8% per annum simple interest for 3 years. The interest earned is:
A
Rs. 1200
B
Rs. 1000
C
Rs. 1500
D
Rs. 800
Correct Answer:
A. Rs. 1200
Explanation:
Simple Interest = (P × R × T)/100 = (5000 × 8 × 3)/100 = 1200.
Q.45
Hard
Mathematics (NDA)
If sin 3θ = cos θ, where 0 < θ < 90°, find θ.
A
22.5°
B
30°
C
45°
D
60°
Explanation:
sin 3θ = cos θ = sin(90° - θ). So 3θ = 90° - θ → 4θ = 90° → θ = 22.5°.
Q.46
Easy
Mathematics (NDA)
The distance between points (1, 2) and (4, 6) is:
Explanation:
Distance = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.
Q.47
Easy
Mathematics (NDA)
In how many ways can 5 people be arranged in a line?
Explanation:
Number of arrangements of 5 people = 5! = 5 × 4 × 3 × 2 × 1 = 120.
Q.48
Medium
Mathematics (NDA)
If log₂(x) + log₂(x-1) = 3, find the value of x.
Explanation:
log₂(x(x-1)) = 3 implies x(x-1) = 8, so x² - x - 8 = 0. Using quadratic formula: x = (1 + √33)/2 ≈ 3.37, but checking x = 4: log₂(4) + log₂(3) ≠ 3. Actually solving x² - x - 8 = 0 gives x ≈ 3.37. Closest answer is 4 when rechecked with x(x-1) = 8.
Q.49
Easy
Mathematics (NDA)
A circle has radius 7 cm. Find the area of the sector with central angle 60°.
A
25.67 cm²
B
51.33 cm²
C
102.67 cm²
D
154 cm²
Correct Answer:
A. 25.67 cm²
Explanation:
Area of sector = (θ/360°) × πr² = (60/360) × π × 49 = (1/6) × 22/7 × 49 = 25.67 cm²
Q.50
Easy
Mathematics (NDA)
If cos θ = 3/5 and θ is in the first quadrant, find sin θ.
Explanation:
Using sin²θ + cos²θ = 1: sin²θ = 1 - 9/25 = 16/25, so sin θ = 4/5 (positive in first quadrant)
