Column Ι Column ΙI (A) The number of the possible values of k if fundamental period of sin^−1 (sin kx) is π/2, (p) 1

Question

Match the following:

Column Ι	Column ΙI
(A) The number of the possible values of k if fundamental period of sin−1 (sin kx) is π/2,	(p) 1
(B)  Numbers of the elements in the domain of  f(x) = tan-1x + sin -1 x + sec-1x is	(q) 2
(C)  Period of the function f(x) = sin(πx/2). cosec (πx/2) is	(r) 3
(D)  If the range of the function f(x) = cos-1[5x] is {a, b, c} and a + b + c = λπ/2, then λ is equal to  (where [⋅] denotes greatest integer)	(s) 4
	(t) 0

Answer 1

Correct option (A) → (q), (B) → (q), (C) → (q), (D) → (r)

(A) Fundamental period of sin^-1 (sin kx) is 2π/|k| = π/2.

That is,  |k| = 4

⇒ K =  ±4

(B) Domain of tan^–1 x is R, domain of sin^–1x is [–1, 1], domain of sec^–1x is (–∞, –1] ∪ [1, ∞). Therefore, domain of f(x) is {–1, 1}

(C)  π  is a period of sin x ⋅ cosec x

Therefore, π x 2/π  is a period of sin πx/2. cosec π x/2

That is, 2 is a period of sin πx/2 cosec πx/2