Top 20 NDA Maths Questions with Solutions

1. If x+1x=2x + \frac{1}{x} = 2x+x1​=2, then the value of x2+1x2x^2 + \frac{1}{x^2}x2+x21​ is:

A) 0
B) 2
C) 4
D) 6

Answer: C) 4
Solution:
(x+1/x)2=x2+1/x2+2(x + 1/x)^2 = x^2 + 1/x^2 + 2(x+1/x)2=x2+1/x2+2
⇒ 22=x2+1/x2+22^2 = x^2 + 1/x^2 + 222=x2+1/x2+2
⇒ 4=x2+1/x2+24 = x^2 + 1/x^2 + 24=x2+1/x2+2
⇒ x2+1/x2=2x^2 + 1/x^2 = 2x2+1/x2=2

2. If sin A = 3/5 and A is acute, find cos A.

A) 4/5
B) 5/3
C) 3/4
D) 1

Answer: A) 4/5
Solution:
cos⁡A=1−sin⁡2A=1−9/25=16/25=4/5\cos A = \sqrt{1 – \sin^2 A} = \sqrt{1 – 9/25} = \sqrt{16/25} = 4/5cosA=1−sin2A​=1−9/25​=16/25​=4/5

3. The value of tan⁡45∘+cot⁡45∘\tan 45^\circ + \cot 45^\circtan45∘+cot45∘ is:

A) 0
B) 1
C) 2
D) 4

Answer: C) 2
Solution: tan⁡45∘=1\tan 45^\circ = 1tan45∘=1, cot⁡45∘=1\cot 45^\circ = 1cot45∘=1, so sum = 2

4. If x2−5x+6=0x^2 – 5x + 6 = 0x2−5x+6=0, then the value of $x$ is:

A) 2 and 3
B) 1 and 6
C) 3 and 4
D) 0 and 6

Answer: A) 2 and 3
Solution: Factor: $(x-2)(x-3)=0$

5. If A=[2345]A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}A=[24​35​], find det(A)

A) 10
B) -2
C) -2
D) 2

Answer: C) -2
Solution:
Determinant = (2×5) – (3×4) = 10 – 12 = -2

6. log⁡28\log_2 8log2​8 is equal to:

A) 2
B) 3
C) 4
D) 1

Answer: B) 3
Solution:
23=8⇒log⁡28=32^3 = 8 \Rightarrow \log_2 8 = 323=8⇒log2​8=3

7. Area of a triangle with base = 6 cm and height = 8 cm is:

A) 48 cm²
B) 24 cm²
C) 30 cm²
D) 12 cm²

Answer: B) 24 cm²
Solution:
Area = (1/2) × base × height = (1/2) × 6 × 8 = 24 cm²

8. What is the sum of first 50 natural numbers?

A) 1225
B) 1275
C) 1325
D) 1000

Answer: B) 1275
Solution:
Sum = $n(n+1)/2=50\times 51/2=1275$

9. If sin⁡θ=513\sin \theta = \frac{5}{13}sinθ=135​, and $\theta$ is acute, find $\cos \theta$

A) 12/13
B) 5/13
C) 1/2
D) 13/5

Answer: A) 12/13
Solution:
Using identity: cos⁡θ=1−sin⁡2θ=1−25/169=144/169=12/13\cos \theta = \sqrt{1 – \sin^2 \theta} = \sqrt{1 – 25/169} = \sqrt{144/169} = 12/13cosθ=1−sin2θ​=1−25/169​=144/169​=12/13

10. What is the value of (a+b)2−(a−b)2(a + b)^2 – (a – b)^2(a+b)2−(a−b)2?

A) $4ab$
B) a2−b2a^2 – b^2a2−b2
C) $2ab$
D) $a+b$

Answer: A) 4ab
Solution:
(a+b)2−(a−b)2=a2+2ab+b2−(a2−2ab+b2)=4ab(a + b)^2 – (a – b)^2 = a^2 + 2ab + b^2 – (a^2 – 2ab + b^2) = 4ab(a+b)2−(a−b)2=a2+2ab+b2−(a2−2ab+b2)=4ab

11. The derivative of x2x^2x2 is:

A) 1
B) x
C) 2x
D) x^2

Answer: C) 2x

12. Solve: 1x+1x+1=1\frac{1}{x} + \frac{1}{x+1} = 1x1​+x+11​=1

A) x = 1
B) x = -1
C) x = 2
D) x = 0

Answer: A) x = 1
Solution:
Take LCM: $(x+1+x)/(x(x+1))=1$ ⇒ $2x+1=x(x+1)$ ⇒ Solve to get x = 1

13. The angle between hour and minute hand at 3:00 is:

A) 90°
B) 60°
C) 75°
D) 45°

Answer: A) 90°
Solution:
Each hour = 30°; 3 hours = 90°

14. A train moves at 60 km/hr. How far will it travel in 30 minutes?

A) 15 km
B) 20 km
C) 30 km
D) 25 km

Answer: B) 30 km
Solution:
Time = 0.5 hours ⇒ Distance = Speed × Time = 60 × 0.5 = 30 km

15. The LCM of 12 and 18 is:

A) 36
B) 6
C) 72
D) 24

Answer: A) 36

16. Solve: $(x-1)(x+2)=0$

A) x = 1 or -2
B) x = 2 or 1
C) x = -1 or 2
D) x = 0 or 2

Answer: A) x = 1 or -2
Solution: Solve each factor.

17. If a circle has radius 7 cm, its area is:

A) 154 cm²
B) 44 cm²
C) 49 cm²
D) 21 cm²

Answer: A) 154 cm²
Solution:
Area = πr² = (22/7)×7×7 = 154 cm²

18. If the roots of a quadratic are equal, then the discriminant is:

A) > 0
B) < 0
C) = 0
D) Can’t be found

Answer: C) = 0
Solution:
D = b² – 4ac ⇒ Equal roots means D = 0

19. Find the value of cos⁡230∘+sin⁡230∘\cos^2 30^\circ + \sin^2 30^\circcos230∘+sin230∘

A) 1
B) 0
C) 2
D) 1/2

Answer: A) 1
Solution: Always true: cos⁡2θ+sin⁡2θ=1\cos^2 \theta + \sin^2 \theta = 1cos2θ+sin2θ=1

20. Simplify: (a2−b2)(a−b)\frac{(a^2 – b^2)}{(a – b)}(a−b)(a2−b2)​

A) $a+b$
B) $a-b$
C) a2+b2a^2 + b^2a2+b2
D) $a$

Answer: A) $a+b$
Solution:
Difference of squares: $(a-b)(a+b)/(a-b)=a+b$