Showing 31–40 of 47 questions
Q.31
Medium
Mathematics (NDA)
Find the value of tan 75°.
A
2 + √3
B
√3 + 1
C
2 - √3
D
√3 - 1
Correct Answer:
A. 2 + √3
Explanation:
tan 75° = tan(45° + 30°) = (tan 45° + tan 30°)/(1 - tan 45° tan 30°) = (1 + 1/√3)/(1 - 1/√3) = (√3 + 1)/(√3 - 1) × (√3 + 1)/(√3 + 1) = (3 + 2√3 + 1)/(3 - 1) = (4 + 2√3)/2 = 2 + √3
Q.32
Medium
Mathematics (NDA)
A train 100 m long is moving at 60 km/h. How long does it take to cross a platform 200 m long?
A
18 seconds
B
20 seconds
C
15 seconds
D
25 seconds
Correct Answer:
A. 18 seconds
Explanation:
Total distance = 100 + 200 = 300 m. Speed = 60 km/h = 60 × 1000/3600 = 50/3 m/s. Time = 300 ÷ (50/3) = 300 × 3/50 = 18 seconds
Q.33
Medium
Mathematics (NDA)
If a:b = 3:4 and b:c = 5:6, find a:b:c.
A
3:4:4.8
B
15:20:24
C
3:5:6
D
9:12:15
Correct Answer:
B. 15:20:24
Explanation:
From a:b = 3:4, let a=3k, b=4k. From b:c = 5:6, let b=5m, c=6m. Since b=4k=5m, k/m = 5/4. So a:b:c = 15:20:24
Q.34
Medium
Mathematics (NDA)
Solve: 2x² - 7x + 3 = 0
A
x = 1/2 or x = 3
B
x = 1 or x = 3/2
C
x = 2 or x = 1/2
D
x = 3 or x = 1
Correct Answer:
A. x = 1/2 or x = 3
Explanation:
Using factorization: 2x² - 7x + 3 = (2x-1)(x-3) = 0, so x = 1/2 or x = 3
Q.35
Medium
Mathematics (NDA)
If log₁₀(x) = 2, find x.
Explanation:
log₁₀(x) = 2 means 10² = x, so x = 100
Q.36
Medium
Mathematics (NDA)
If cot θ = 12/5, find sin θ (where θ is acute).
A
5/13
B
12/13
C
5/12
D
13/5
Explanation:
cot θ = 12/5 means adjacent/opposite = 12/5. Hypotenuse = √(144+25) = 13. So sin θ = opposite/hypotenuse = 5/13
Q.37
Medium
Mathematics (NDA)
If A = {1,2,3} and B = {2,3,4}, find (A ∪ B) ∩ A.
A
{2,3}
B
{1,2,3}
C
{1,2,3,4}
D
{3,4}
Correct Answer:
B. {1,2,3}
Explanation:
A ∪ B = {1,2,3,4}. (A ∪ B) ∩ A = {1,2,3,4} ∩ {1,2,3} = {1,2,3}
Q.38
Medium
Mathematics (NDA)
A quadratic equation has roots 2 and -3. Find the equation.
A
x² - x - 6 = 0
B
x² + x - 6 = 0
C
x² - 5x + 6 = 0
D
x² + 5x - 6 = 0
Correct Answer:
B. x² + x - 6 = 0
Explanation:
If roots are α and β, equation is x² - (α+β)x + αβ = 0. Here (2-3)x + (2)(-3) = 0 gives x² + x - 6 = 0
Q.39
Medium
Mathematics (NDA)
If 3^x × 3^(x+1) = 243, find x.
Explanation:
3^x × 3^(x+1) = 3^(2x+1) = 243 = 3⁵. So 2x+1 = 5, thus x = 2
Q.40
Medium
Mathematics (NDA)
A man covers 120 km in 3 hours. What is his speed in m/s?
A
10 m/s
B
11.11 m/s
C
12.5 m/s
D
15 m/s
Correct Answer:
B. 11.11 m/s
Explanation:
Speed = 120/3 = 40 km/h = 40 × (5/18) = 11.11 m/s
