MATHEMATICS (NDA/NA SOLVED PAPER 2022-I) (01 to 50)

Total Questions: 50

11. How many terms are there in the expansion of

Correct Answer: (b) 10
Solution:

12. Consider the following statements in respect of the expansion of (x + y)¹⁰:

1. Among coefficients of the terms, the coefficient of the 6th term has the highest value
2. The coefficient of the 3rd term is equal to coefficient of the 9th term
Which of the above statements is/are correct?

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

13. If C(3n, 2n) = C(3n, 2n - 7) then what is the value of C(n, n - 5)?

Correct Answer: (d) 21
Solution:

14. What is the value of C(51,21) - C(51,22) + C(51,23) - C(51,24) + C(51,25) - C(51,26) + C(51,27) - C(51,28) + C(51,29) - C(51,30)?

Correct Answer: (c) C(51,51) - C(51, 0)
Solution:

15. How many odd numbers between 300 and 400 are there in which none of the digits is repeated?

Correct Answer: (a) 32
Solution:

16. How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even positions?

Correct Answer: (b) 36
Solution:

17. Let α and β be the roots of the equation x² + px + q = 0. If α³ and β³ are the roots of the equation x²+ mx + n = 0, then what is the value of m +n?

Correct Answer: (d) p³ + q³ - 3pq
Solution:

18. Let α and β be the roots of the equation

x² - ax - bx + ab - c = 0 What is the quadratic equation whose roots are a and b?

Correct Answer: (a) x² - αx - βx + αβ + c = 0
Solution:

19. If the roots of the equation

x² -ax - bx - cx + bc + ca = 0 are equal, then which one of the following is correct?

Correct Answer: (c) a + b - c = 0
Solution:

20. Let a and β(α > β) be the roots of the equation

x² - 8x + q = 0. If α² - β² = 16, then what is the value of q?

Correct Answer: (d) 15
Solution: