Mathematics NDA/NA SOLVED PAPER 2021-II (01 to 50)

Total Questions: 50

11. Let ABC be a triangle. If cos 2A + cos 2B + cos 2C = - 1 then which one of the following is correct?

Correct Answer: (d) cos A cos cos C = 0
Solution:

12. What is the value of the following determinant?

Correct Answer: (b) 0
Solution:cos C (tan A. sin B) - tan A (sin B . cos C) = 0.

13. Suppose set A consists of first 250 natural numbers that are multiples of 3 and set B consists of first 200 even natural numbers. How many elements does A ∪ B have?

Correct Answer: (c) 384
Solution:

14. Let Sₖ denote the sum of first k terms of an AP. What is S₃₀/ S₂₀ - S₁₀ equal to?

Correct Answer: (c) 3
Solution:

15. If the roots of the equation 4x²- (5k + 1)x + 5k = 0 differ by unity, then which one of the following is a possible value of k?

Correct Answer: (c) - 1/5
Solution:

16. x² + x + 1 = 0 then what is the value of x¹⁹⁹ + x²⁰⁰ + x²⁰¹?

Correct Answer: (b) 0
Solution:

17. If x, y, z are in GP, then which of the following is/are correct?

1. ln(3x), In (3y), In (3z) are in AP
2. xyz +ln(), xyz + ln(y), xyz + ln(z) are in HP
Select the correct answer using the code given below.

Correct Answer: (a) 1 only
Solution:

18. If log₁₀ 2, log₁₀(2ˣ - 1), log₁₀(2ˣ + 3) are in AP, then what is x equal to?

Correct Answer: (c) log₂ 5
Solution:

19. Let S = {2, 3, 4, 5, 6, 7, 9}. How many different 3-digit numbers (with all digits different) from S can be made which are less than 500?

Correct Answer: (c) 90
Solution:n(s) = 7
For 3 digit numbers less than 500 (recetion not allowed)
Numbers of digits choice for hundred place (2, 3, 4) = 3
Numbers of digits choice for tens place = 6
Numbers of digits choice for once place = 5
Total numbers of 3 digit numbers less than 500 = 3 × 6 × 5 = 90

20. If p =(1111.....up to n digits), then what is the value of 9p² + p

Correct Answer: (a) 10ⁿ p
Solution: