NDA/NA SOLVED PAPER 2016-II (MATHEMATICS)

Total Questions: 120

21. What is the value of c?

Correct Answer: (c) 35
Solution:

22. What is the value of a + b + c + d ?

Correct Answer: (b) 63
Solution:a + b + c + d = 63

23. How many possible values can n have?

The interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.

Correct Answer: (a) One
Solution:Here, a = 120 deg and d = 5 .
Sum of angles of polygon = (n - 2) 180°
⇒ n/2 [2a + (n - 1) d] = (n - 2) 180°

24. What is the largest interior angle of the polygon?

The interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°.

Correct Answer: (a) 160° only
Solution:

25. Solve the following equation

Correct Answer: (c) 1
Solution:

26. Solve the following equation

1. f(θ) × f(Φ) = f(θ + Φ)
2. The value of the determinant of the matrix f(θ) × f(Φ) is 1.
3. The determinant of f(x) is an even function.

Select the correct answer using the code given below:

Correct Answer: (d) 1, 2 and 3
Solution:

27. Which of the following are correct in respect of the system of equations x + y + z = 8 x - y + 2z = 6 and 3x - y + 5z = k ?

1. They have no solution. k = 15
2. They have infinitely many solutions, k = 20
3. They have unique solution, k = 25

Select the correct answer using the code given below:

Correct Answer: (a) 1 and 2 only
Solution:


28. Solve the following equation

1. AB(A⁻¹ B⁻¹) is a unit matrix.
2. (AB)⁻¹ = A⁻¹ B⁻¹

Select the correct answer using the code given below:

Correct Answer: (d) Neither 1 nor 2
Solution:

29. Solve the following equation

Correct Answer: (b)
Solution:

30. If the number 235 in decimal system is converted into binary system, then what is the resulting number ?

Correct Answer: (b) (11101011)₂
Solution: