(A) The maximum value of sec^-1[(7 - 5(x^2 + 3))/2(x^2 + 2)]

Question

Match the following:

Column I	Column II
(A) The maximum value of sec-1[(7 - 5(x2 + 3))/2(x2 + 2)]	(i) π/6
(B) The minimum value of cosec-1[3x2 + 5/4] + sec-1[3x2 + 1/4] (where [.] denotes the greatest integer function) is	(ii) 1/3
(C) The number of solution of equation sin-1(|x2 - 1|) + cos-1(|2x2 - 5|) = π/2 is	(iii) 2π/3
(D) If y = tan-1(1/2) + tan-1(b), (0 < b < 1) and 0 < y ≤  π/4, then the maximum value of b will be	(iv) 2

Answer 1

Correct option (A) →(iii); (B) →(i); (C)→(iv); (D) →(ii)

Explanation:

Therefore, the maximum value is sec^-1(-2) = 2π/3.

(B) Minimum value = cosec^-12 + sec^-11 = π/6, when