Mathematics NDA/NA SOLVED PAPER 2019 (II) (51 to 100)

Total Questions: 50

11. Find the answer of given question?

Correct Answer: (a) (a + b)²
Solution:

12. If the angles of a triangle ABC are in AP and b : c = √3 : √2, then what is the measure of angle A?

Correct Answer: (d) 75°
Solution:

13. If tanA - tan B = x and cot B - cot A = y, then what is the value of cot (A - B)?

Correct Answer: (a)
Solution:

14. What is sin (α + β) - 2 sin α cos β + sin (α - β) equal to?

Correct Answer: (a) 0
Solution:

15. If 2tan A = 3 tan B = 1, then what is tan (A - B ) equal to?

Correct Answer: (c) 1/7
Solution:

16. What is cos 80° + cos 40° − cos 20° equal to?

Correct Answer: (c) 0
Solution:

17. If angle C of a triangle ABC is a right angle, then what is tan A + tan B equal to?

Correct Answer: (d)
Solution:

18. What is cot (A/2) - tan (A/2) equal to?

Correct Answer: (d) 2 cot A
Solution:

19. What is cot A + cosec A equal to?

Correct Answer: (b)
Solution:

20. What is tan 25° tan 15° + tan 15° + tan 50° + tan 25° tan 50° equal to?

Correct Answer: (b) 1
Solution:

∵ tan 50° = tan (90° – 40°)
⇒ tan 50° = cot 40°
⇒ tan 50° = 1 / tan 40°
⇒ tan 50° = 1 / tan (25° + 15°)
⇒ tan 50° = (1 – tan 25° tan 15°) / (tan 25° + tan 15°)
⇒ tan 25° tan 50° + tan 15° tan 50° = 1 – tan 25° tan 15°
⇒ tan 25° tan 15° + tan 15° tan 50° + tan 25° tan 50° = 1