(Mathematics) NDA/NA SOLVED PAPER 2024 – I (01 to 50)

Total Questions: 50

1. What is the value?

Correct Answer: (d) 1
Solution:

2. What is value?

Correct Answer: (b) 4
Solution:Since that iz³ + z² - z + i = put z = i

i⁴ + i² - i + i = 0 ⇒ 1 - 1 - i + i = 0

satisfied then, (|z| + 1)² = [ |i| + 1]² = 4

3. What is the sum of all four digit numbers formed by using all digits 0, 1, 4, 5 without repetition of digits?

Correct Answer: (d) 64440
Solution:

4. If x, y and z are the cube roots of unity, then what is the value of xy + yz + zx ?

Correct Answer: (a) 0
Solution:Considering that -x, y and z are the cube roots of unity

Assume x = 1, y = ω and z = ω²

So, xy + yz + zx = ω + ω³ + ω²

= ω + 1 + ω² = 0 ( ω³ = 1)

5. A man has 7 relatives (4 women and 3 men). His wife also has 7 relatives (3 women and 4 men). In how many ways can they invite 3 women and 3 men so that 3 of them are man's relatives and 3 of them are his wife's relatives?

Correct Answer: (c) 485
Solution:

6. A triangle PQR is such that 3 points lie on the side PQ, 4 points on QR and 5 points on RP respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?

Correct Answer: (a) 205
Solution:

7. equal to?

Correct Answer: (a) bd²f³
Solution:

8. Which one is correct?

Correct Answer: (c) a₀ = 6, a₃ = 0
Solution:

9. equal to?

Correct Answer: (c) 1
Solution:

10. If 26! = n8ᵏ , where k and n are positive integers, then what is the maximum value of k?

Correct Answer: (b) 7
Solution: