Match the statements of Column I with values of Column II.
Column-I | Column-II |
(i) Let X = {a1, a2,….., a6} and Y = {b1, b2, b3}. The number of functions f from X to Y such that it is onto and there are exactly three elements x in X such that f(x) = b1, is greater than | [A] 2 |
(ii) The number of real solutions for x, y if y = |sin x| and y = sin–1(sin x) where x ∈ [–2π, 2π], is | [B] 5 |
(iii) If a, b and c are distinct positive real numbers such that a + b + c = 1, then can be | [C] 120 |
(iv) The period of the function [6x + 7] + cos πx – 6x, where denotes the greatest integer function, is | [D] 80 |
Text Solution
Verified by Experts(i) [A]; (ii) [B]; (iii) [C]; (iv) [A]; (iv) [6x]
Ans.
(i) [A], [B], [D]
(ii) [B]
(iii) [C], [D]
(iv) [A]
Sol. (i) Required no. of functions
= 6 C 3 (2 3 – 2) = 120.
(ii)
From figure it is clear that no. of solutions are 5.
(iii) a = 1 – b – c
⇒ 1 + a = (1 – b) + (1 – c) > 2 
Similarly, 1 + b > 2 
and 1 + c > 2 
Required expression > 8.
(iv) [6x] + 7 + cos π x – 6x ⇒ {6x} + cos π x
Period of {6x} is 
and period of cos π x is 2.
Hence, LCM of 
, 2 is 2.
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