Mathematics (NDA SOLVED PAPER 2020 – II) (01 to 50)

Total Questions: 50

21. Read the following statements below and choose the correct option:

Question:- (21 -22)
 Read the following information and answer the two items that follow. ABCD is a trapezium such that AB and CD are parallel and BC is perpendicular to them. Let ∠ADB = θ, ∠ADB = α, BC = p and CD = q.

Consider the following
1. AD sinθ = AB sinα
2. BD sinθ = AB sin (θ + α)
Which of the above is/are correct?

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

22. Read the following statements above and choose the correct option:

What is AB equal to?

Correct Answer: (a)
Solution:

23. Find the value?

Correct Answer: (b) 28°
Solution:

24. 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:

25. What is sin 3x + cos 3x + 4 sin³ x - 3 sin x + 3 cos x - 4 cos³ x equal to?

Correct Answer: (a) 0
Solution:

26. The value of ordinate of the graph of y = 2 + cos x lies in the interval

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

27. What is the value of

8 cos 10°. cos 20°. cos 40°?

Correct Answer: (b) cot 10°
Solution:

28. What is the value of

cos 48° − cos 12°?

Correct Answer: (b)
Solution:

29. Consider the following statements:

1. If ABC is a right-angled triangle, right-angled 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:

30. 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: (d) Neither 1 nor 2
Solution: