NDA/NA SOLVED PAPER 2016-II (MATHEMATICS)

Total Questions: 120

11. What is the number of distinct solutions of the equation z² + |z| =0( where z is a complex number)?

Correct Answer: (c) Three
Solution:


12. How many geometric progressions is/are possible containing 27, 8 and 12 as three of its/their terms?

Correct Answer: (d) Infinitely many
Solution:

13. Let R be a relation from A = {1, 2, 3, 4} to B = {1, 3, 5} such that R=[ (a, b) : a < b where a ∈ A and b ∈ B ] . What is RoR⁻¹ equal to?

Correct Answer: (c) {(3, 3), (3, 5), (5, 3), (5, 5)}
Solution:R = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
R⁻¹ = {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}
RoR⁻¹={(3, 3), (3, 5), (5, 3), (5, 5)}.

14. A five-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3 and 4 without repetition of digits. What is the number of ways this can be done?

Correct Answer: (d) No number can be formed
Solution:Since sum of digits = 10 (which is not divisible by 3)
∴ No numbers can be formed.

15. Solve the following equation

Correct Answer: (a)
Solution:

16. What is the value of ab?

Let a, x, y, z, b be in AP, where x + y + z = 15 . Let a, p, q, r, b be in HP, where p⁻¹ + q⁻¹ + r⁻¹ = 5/3

Correct Answer: (b) 9
Solution:

17. What is the value of xyz?

Let a, x, y, z, b be in AP, where x + y + z = 15 . Let a, p, q, r, b be in HP, where p⁻¹ + q⁻¹ + r⁻¹ = 5/3

Correct Answer: (b) 105
Solution:

18. What is the value of pqr?

Let a, x, y, z, b be in AP, where x + y + z = 15 . Let a, p, q, r, b be in HP, where p⁻¹ + q⁻¹ + r⁻¹ = 5/3

Correct Answer: (c) 243/35
Solution:

19. What is the common difference of the AP so that the product of the first, fourth and fifth terms is greatest?

The sixth term of an AP is 2 and its common difference is greater than 1.

Correct Answer: (a) 8/5
Solution:

20. What is the first term of the AP so that the product of the first, fourth and fifth terms is greatest?

The sixth term of an AP is 2 and its common difference is greater than 1.

Correct Answer: (b) -6
Solution:Since, a = 2 - 5x ⇒ a = 2 - 5(8/5) ⇒ a = - 6