NDA/NA SOLVED PAPER 2015-II (MATHEMATICS)

Total Questions: 120

11. If A = {x ∈ IR : (x²) + 6x - 7 0} , then which of the following is/are correct?

1. (A cap B)= (- 2, 1)
2. (A backslash B)= (- 7, - 2)

Select the correct answer using the code given below:

Correct Answer: (a) 1 only
Solution:

12. A, B, C and D are four sets such that A cap B = C cap D = phi Consider the following:

1. A ∪ C and B ∪ D are always disjoint.
2. A ∩ C and B ∩ D always disjoint

Which of the above statements is/are correct?

Correct Answer: (b) 2 only
Solution:

13. If A is an invertible matrix of order n and k is any positive real number, then the value of [det (kA)]⁻¹ det A is

Correct Answer: (a) k⁻ⁿ
Solution:

14. Solve the following equation

Correct Answer: (b) 36
Solution:

15. If the roots of the equation x² - nx + m = 0, differ by 1, then

Correct Answer: (a) n² - 4m - 1 = 0
Solution:

16. If different words are formed with all the letters of the word 'AGAIN' and are arranged alphabetically among themselves as in a dictionary, the word at the 50th place will be

Correct Answer: (b) NAAIG
Solution:

17. The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is

Correct Answer: (c) 1001
Solution:

18. Solve the following equation

Correct Answer: (a) 5
Solution:

19. The value of sin² 5° + sin² 10° + sin² 15° + sin² 20° +.... sin² 90° is

Correct Answer: (d) 19/2
Solution:

20. Solve the following equation

Correct Answer: (d) 3
Solution: