Mathematics (NDA/NA SOLVED PAPER 2023-I) (01 to 50)

Total Questions: 50

21. How many real numbers satisfy the equation |x - 4| + |x - 7| = 15 ?

Correct Answer: (b) Only two
Solution:

22. equal to?

Correct Answer: (d)
Solution:

23. α and β are distinct real roots of the quadratic equation x²+ ax + b = 0. Which of the following statements is/are sufficient to find α?

1. α + β = 0, α² + β² = 2
2. αβ² = -1, a= 0
Select the correct answer using the code given below:

Correct Answer: (b) 2 only
Solution:x² + ax + b = 0
(i) α + β = 0 ⇒ β = -α
α² + β² = 2
(α + β)² - 2 αβ = 2
αβ = -1 ⇒ α . (-α) = -1 ⇒ α²  = 1
In statement (1), finding the value of α is completely Independent of the given equation x² + ax + b = 0
Hence it is not correct.

(ii) αβ² = -1
a = 0 ⇒ α + β = 0 ⇒ β = -α
α(-α)² = -1 ⇒ a³ = -1 ⇒ α = -1
Only 2 is sufficient.

24. Find the value?

Correct Answer: (d) 10
Solution:

25. How many terms are there in the expansion of (3x - y)⁴ (x + 3y)⁴ ?

Correct Answer: (a) 9
Solution:

26. p, q, r and s are in AP such that p + s = 8 and qr = 15. What is the difference between largest and smallest numbers?

Correct Answer: (a) 6
Solution:

27. Consider the following statements for a fixed natural number n:

1. C(n,r) is greatest if n = 2r
2. C(n,r) is greatest if n = 2r - 1 and n = 2r + 1
Which of the statements given above is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:

28. m parallel lines cut n parallel lines giving rise to 60 parallelograms. What is the value of (m + n)?

Correct Answer: (d) 9
Solution:

29. Let x be the number of permutations of the word "PERMUTATIONS' and y be the number of permutations of the word 'COMBINATIONS'. Which one of the following is correct?

Correct Answer: (c) x = 4y
Solution:

30. 5- digit numbers are formed using the digits 0, 1, 2, 4, 5 without repetition. What is the percentage of numbers which are greater than 50,000?

Correct Answer: (b) 25%
Solution: