Mathmatics NDA/NA Solved Paper 2020-I (1-50)

Total Questions: 50

41. The value of ordinate of the graph of y = 2 + cos𝓍 lies in the interval

Correct Answer: (d) [1, 3]
Solution:

42. What is the value of 8 cos 10°. cos 20° . cos 40° ?

Correct Answer: (b) cot 10°
Solution:


43. What is the value of cos 48° - cos 12° ?

Correct Answer: (b)
Solution:

44. Consider the following statements :

(1) If ABC is a right-angled triangle, rightangled at A and if sin B = 1/3 , then cosec C = 3.
(2) If b cos B = c cos C and if the triangle ABC is not right-angled, then ABC must be isosceles. Which of the above statements is/are correct ?

Correct Answer: (b) 2 only
Solution:



45. Consider the following statements :

(1) If in a triangle ABC, A = 2B and b = c, then it must be an obtuse-angled triangle.
(2) There exists no triangle ABC with A = 40°, B = 65° and a/c = sin 40° cosec 15°.
Which of the above statements is/are correct ?

Correct Answer: (b) 2 only
Solution:

Consider a right angle triangle ABC, right angle at A and B = C = 45º.
Then, b = c is also true.
Hence, for the given condition, △ABC must not be an obtuse-angled triangle.


Hence, △ABC is not possible.
Thus, statements (2) is correct.

46. Solve the following equation?


Which one of the following is correct ?

Correct Answer: (c)
Solution:

A square M matrix is said to be Hermitian (or self-adjoint) if it is equal to its. Own Hermitian conjugate, i.e.

47. Solve the following equation?

Correct Answer: (a) 180
Solution:

48. Solve the following equation?

Correct Answer: (b) 64
Solution:

49. If C(20, n + 2) = C(20, n - 2), then what is n equal to?

Correct Answer: (c) 10
Solution:

50. For how many values of k, is the matrix

Correct Answer: (d) Infinite
Solution:

For singular matrix,

Hence, for all values of K, given matrix is singular matrix.