Match the column:
Column-IColumn-II(i) Domain of sin–1 [2x – 1] is (where [.] denotes greatest inte…

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Match the column:
Column-IColumn-II(i) Domain of sin–1 [2x – 1] is (where [.] denotes greatest integer function)[A] [0, 3/2](ii) Range of  is (where {.} represent fractional part function)[B] (– ∞, 0] or [1, ∞)(iii) Greatest interval, in which f(x) = 4x3 – 9x2 + 13 is decreasing, in[C] (– ∞ , 0) ∪ (1, ∞)(iv) An interval in which f '(x) = x(x – 2)2 (x – 1)79 (1 + sin2x) is strictly increasing[D] [0, 3/2)

CGP EDU Academic Team · Accepted Answer

The correct answer is (i) [D]; (ii) [C]; (iii) [A]; (iv) [B]. Ans.
(i) [D]
(ii) [C]
(iii) [A]
(iv) [B]
Sol.
(i) – 1 < 2x – 1 < 20 ≤ 2x < 30 ≤ x < 3/2
(ii) 0 ≤ {x} < 10 ≤ e {x} < e λ n0 ≤ λ n(e{x}) < λ ne ,– ∞ < λ n (e{x}) < 1– ∞ <  < 0 and 1 <  < ∞
(iii) f '(x) = 12x 2 – 18x for decreasing interval f '(x) ≤ 012 x (x – 3/2) ≤ 0 ⇒ x ∈ [0, 3/2]
(iv) For increasing f '(x) ≥ 0 x (x –1) ≥ 0 x ∈ (– ∞ , 0] ∪ [1, ∞ )

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Column-I	Column-II
(i) Domain of sin–1 [2x – 1] is (where [.] denotes greatest integer function)	[A] [0, 3/2]
(ii) Range of is (where {.} represent fractional part function)	[B] (– ∞, 0] or [1, ∞)
(iii) Greatest interval, in which f(x) = 4x3 – 9x2 + 13 is decreasing, in	[C] (– ∞ , 0) ∪ (1, ∞)
(iv) An interval in which f '(x) = x(x – 2)2 (x – 1)79 (1 + sin2x) is strictly increasing	[D] [0, 3/2)

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