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

Total Questions: 50

31. If the number of elements in Y and Z are in the ratio 4 : 5 then what is the value of b ?

Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in Z be denoted by n(Z) which is equal to 90.

Correct Answer: (c) 21
Solution:

32. What is the value of

n(X) + n(Y) + n(Z) - n(X ∩ Y) - n(Y ∩ Z) - n(X ∩ Z) + n(X ∩ Y ∩ Z) ?

Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in Z be denoted by n(Z) which is equal to 90.

Correct Answer: (d) a + b + 106
Solution:

33. If the number of elements belonging to neither X, nor Y, nor Z is equal to p, then what is the number of elements in the complement of X?

Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in Z be denoted by n(Z) which is equal to 90.

Correct Answer: (a) p + b + 60
Solution:

34. What is tan² A equal to?


Correct Answer: (b)
Solution:


35. For real values of tan A, K cannot lie between

Correct Answer: (e) None of the above
Solution:

36. Consider the following:

ABCD is a trapezium such that AB and CD are parallel and BC is perpendicular to them. Let ∠ADB = θ, ∠ABD = α, BC = p and CD = q.
(1) AD sin θ = AB sin α
(2) BD sin θ = AB sin (θ + α)
Which of the above is/are correct ?

Correct Answer: (c) Both 1 and 2
Solution:

37. What is AB equal to?

ABCD is a trapezium such that AB and CD are parallel and BC is perpendicular to them. Let ∠ADB = θ, ∠ABD = α, BC = p and CD = q.

Correct Answer: (a)
Solution:


38. Solve the following equation?

Correct Answer: (b) 28°
Solution:

39. A and B are positive acute angles such that cos 2B = 3 sin² A and 3 sin 2A = 2 sin 2B. What is the value of (A + 2B) ?

Correct Answer: (d) π/2
Solution:

40. What is sin 3𝓍 + cos 3𝓍 + 4 sin³𝓍 - 3 sin𝓍 + 3 cos𝓍 - 4 cos³𝓍 equal to?

Correct Answer: (a) 0
Solution: