Showing 21–30 of 100 questions
Q.21
Easy
Mathematics (NDA)
If 3x - 7 = 2, what is the value of x?
Explanation:
3x - 7 = 2 → 3x = 9 → x = 3.
Q.22
Easy
Mathematics (NDA)
What is the value of 4³ × 2⁻² ?
Explanation:
4³ = 64, 2⁻² = 1/4. Therefore, 64 × 1/4 = 16.
Q.23
Easy
Mathematics (NDA)
The HCF of 48 and 64 is:
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.
Q.24
Medium
Mathematics (NDA)
If the ratio of two numbers is 3:5 and their sum is 64, find the larger number.
Explanation:
Let numbers be 3x and 5x. 3x + 5x = 64 → 8x = 64 → x = 8. Larger number = 5 × 8 = 40.
Q.25
Medium
Mathematics (NDA)
If a quadratic equation has roots α and β, and α + β = 7, αβ = 10, what is the equation?
A
x² - 7x + 10 = 0
B
x² + 7x + 10 = 0
C
x² - 7x - 10 = 0
D
x² + 7x - 10 = 0
Correct Answer:
A. x² - 7x + 10 = 0
Explanation:
Quadratic equation is x² - (sum of roots)x + (product of roots) = 0, which gives x² - 7x + 10 = 0.
Q.26
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.27
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.28
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.29
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.30
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.
