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

Total Questions: 50

21. The equation sin⁻¹x - cos⁻¹x = π/6 has

Correct Answer: (b) unique solution
Solution:

22. What is the value of the following?

(sin 24° + cos 66°) (sin 24°- cos 66°)

Correct Answer: (b) 0
Solution:

23. A chord subtends an angle 120° at the centre of a unit circle. What is the length of the chord?

Correct Answer: (d) √3 units
Solution:

24. What is 1 + cot θ - cosecθ ) (1+ tan θ + sec θ) equal to?

Correct Answer: (b) 2
Solution:

25. equal to?

Correct Answer: (b) 1
Solution:

26. What is the interior angle of a regular octagon of side length 2 cm?

Correct Answer: (b) 3π/4
Solution:

27. If 7 sin θ+ 24 cos θ = 25, then what is the value of (sin θ + cos θ)?

Correct Answer: (d) 31/25
Solution:

28. A ladder 6 m long reaches a point 6 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the top of the flagstaff is 75°. What is the height of the flagstaff?

Correct Answer: (d) (6 + 3√3) m
Solution:Let AC is a flagstaff of length h m and BD is a ladder of length 6 m. Point B is below the top of the flagstaff, such that AB = 6m.
Then, <ADCn= 75°.
Hence, height of flagstaff = (6 + 3√3) m.

29. The shadow of a tower is found to be x metre longer, when the angle of elevation of the sun changes from 60° to 45°. If the height of the tower is 5 (3 + √3) m, then what is x equal to?

Correct Answer: (b) 10m
Solution:Shadow length when elevation of sun is 60° = BC

30. If 3 cos θ = 4sin θ, then what is the value of tan( 45° + θ)?

Correct Answer: (b) 7
Solution: