SOLVED PAPER 2024 (CDS) (II) (Mathematics)

Total Questions: 100

11. What is the maximum value of 8sin θ - 4sin² θ ?

Correct Answer: (b) 4
Solution:

12. What is (1 + tanα tanβ)² + (tanα - tanβ)² equal to ?

Correct Answer: (b) sec²α sec²β
Solution:

13. Consider the following statements

I. tan 50° - cot 50° is positive,
II. cot 25° - tan 25° is negative

Which of the statements is/are correct?

Correct Answer: (a) Only I
Solution:

14. If 0 ≤ (α - β) ≤ (α + β) ≤ π/2,

tan(α + β) = √3 and
tan(α - β) = 1/√3,
then what is tanα cot 2β equal to!

Correct Answer: (c) √3
Solution:

15. What is the value of sin²θ cos²θ (sec²θ + cosec²θ) equal to

Correct Answer: (b) 1
Solution:

16. .

Correct Answer: (b) 2
Solution:

17. If cosecθ - cotθ = m and secθ - tanθ = n, then what is cosecθ + secθ equal to

Correct Answer: (a)
Solution:

18. From a Point X on a bridge across a river, the angles of depression of two Points the banks on opposite side of the river are a and beta respectively. If the Point X is at a height h above the surface of the river, what is the width of the river if a and beta are complementary?

Correct Answer: (d) h secα . cosecα
Solution:Let PQ be a river,
In ΔPOX,
tanα = h/OP
OP = hcotα

19. In a triangle ABC, ∠ABC = 60° and AD is the altitude. If AB = 6cm and BC = 8cm then what is the area of the triangle?

Correct Answer: (b) 12√cm²
Solution:

20. If p and q are the roots of the equation x² - sin² θx - cos² θ = 0 then what is the minimum value of p² + q² ?

Correct Answer: (b) 1
Solution: