Showing 11–20 of 47 questions
Q.11
Medium
Mathematics (NDA)
The volume of a cone with radius 5 cm and height 12 cm is: (use π = 22/7)
A
314.29 cm³
B
628.57 cm³
C
471.43 cm³
D
314.86 cm³
Correct Answer:
A. 314.29 cm³
Explanation:
Volume of cone = (1/3)πr²h = (1/3) × (22/7) × 25 × 12 = (1/3) × (22/7) × 300 = 314.29 cm³.
Q.12
Medium
Mathematics (NDA)
In a triangle, if one angle is 90° and the other two angles are in ratio 1:2, the angles are:
A
30°, 60°, 90°
B
45°, 45°, 90°
C
20°, 70°, 90°
D
40°, 50°, 90°
Correct Answer:
A. 30°, 60°, 90°
Explanation:
One angle = 90°. Other two in ratio 1:2. Let them be x and 2x. x + 2x + 90 = 180 → 3x = 90 → x = 30°. Angles are 30°, 60°, 90°.
Q.13
Medium
Mathematics (NDA)
If cos θ = 7/25 and θ is acute, find tan θ.
A
7/24
B
24/7
C
25/24
D
24/25
Explanation:
cos θ = 7/25 means adjacent = 7, hypotenuse = 25. Using Pythagoras, opposite = 24. tan θ = opposite/adjacent = 24/7.
Q.14
Medium
Mathematics (NDA)
The average of five numbers is 35. If one number is replaced by 50, the new average becomes 38. What was the original number?
Explanation:
Sum of 5 numbers = 35 × 5 = 175. New sum = 38 × 5 = 190. Difference = 190 - 175 = 15. Original number = 50 - 15 = 35.
Q.15
Medium
Mathematics (NDA)
If log₁₀ 2 = 0.301, find log₁₀ 200.
A
2.301
B
2.602
C
1.301
D
3.301
Explanation:
log₁₀ 200 = log₁₀(2 × 100) = log₁₀ 2 + log₁₀ 100 = 0.301 + 2 = 2.301.
Q.16
Medium
Mathematics (NDA)
If ABCD is a rhombus with diagonals 6 cm and 8 cm, find its area.
A
24 cm²
B
48 cm²
C
28 cm²
D
56 cm²
Correct Answer:
A. 24 cm²
Explanation:
Area of rhombus = (1/2) × d₁ × d₂ = (1/2) × 6 × 8 = 24 cm².
Q.17
Medium
Mathematics (NDA)
What is the compound interest on Rs. 8000 at 10% per annum for 2 years?
A
Rs. 1680
B
Rs. 1600
C
Rs. 1800
D
Rs. 1500
Correct Answer:
A. Rs. 1680
Explanation:
A = P(1 + r/100)ⁿ = 8000(1.1)² = 8000 × 1.21 = 9680. CI = 9680 - 8000 = 1680.
Q.18
Medium
Mathematics (NDA)
In an AP, if first term a = 5, common difference d = 3, find the 10th term.
Explanation:
nth term = a + (n-1)d = 5 + (10-1) × 3 = 5 + 27 = 32.
Q.19
Medium
Mathematics (NDA)
If |x - 3| = 5, what are the possible values of x?
A
2 and 8
B
2 and -8
C
-2 and 8
D
3 and 5
Correct Answer:
C. -2 and 8
Explanation:
|x - 3| = 5 means x - 3 = 5 or x - 3 = -5. So x = 8 or x = -2.
Q.20
Medium
Mathematics (NDA)
A ladder of length 13 m leans against a wall. If the foot of the ladder is 5 m away from the wall, find the height reached on the wall.
A
8 m
B
10 m
C
12 m
D
15 m
Explanation:
Using Pythagoras: h² + 5² = 13² → h² + 25 = 169 → h² = 144 → h = 12 m.
