(Mathematics) NDA/NA Solved Paper 2017-I

Total Questions: 50

11. The modulus and principal argument of the complex number 1 + 2i/1-(1-i)² are respectively.

Correct Answer: (a) 1,0
Solution:

12. If the graph of a quadratic polynomial lies entirely above x-axis, then which one of the following is correct?

Correct Answer: (c) Both the roots are complex
Solution:

Since the graph is not meeting the x - axis at all, roots are Complex numbers.

13. If |z+5| ≤3, then the maximum value of | z+1 | is

Correct Answer: (c) 6
Solution:

14. The number of roots of the equation z² = 2z̅ is

Correct Answer: (c) 4
Solution:

15. If cot α and cot β are the roots of the equation x²+ bx + c=0 with b≠0, then the value of cot (α+ β) is

Correct Answer: (b) 1-c/b
Solution:

16. The sum of the roots of the equation x²+ bx + c= 0 (where band c are non-zero) is equal to the sum of the reciprocals of their squares. Then 1/c, b, c/a are in

Correct Answer: (c) HP
Solution:

17. The sum of the roots of the equation ax² + x + c= 0 (where a and c are non-zero) is equal to the sum of the reciprocals of their squares. Then a, ca², c² are in

Correct Answer: (a) AP
Solution:

18. The value of [C (7, 0) + C (7, 1)] + [C (7, 1)+ C (7, 2)] + ....... + [C (7, 6) + C (7, 7)] is

Correct Answer: (a) 254
Solution:

19. The number of different words (eight-letter words) ending and beginning with a consonant which can be made out of the letters of the word 'EQUATION' is

Correct Answer: (b) 4320
Solution:

EQUATION-8 letters.
Consonants -Q, T, N-3 letters.
first letter of 8-letter word can be any of 3 consonants
Last letter of 8- letter word can be remaining 2
consonants.
The middle 6- letters can be arranged in 6! ways.
So, number of different words = 3×2×6!
=6× 720 = 4320.

20. The fifth term of an AP of n terms, whose sum is n² -2n, is

Correct Answer: (b) 7
Solution:

Given, Sₙ =n²-2n.
We know, Tₙ =Sₙ - Sₙ₋₁
So, T₅, = S₅ - S₄
S₅ = 5²-  2 (5) = 25–10 = 15
S₄ = 4²-2 (4) = 16-8 = 8
So, T₅ = 15-8 = 7.