Column I Column II A Let f(x)=√ log ( cos [ x ]), then f(x) is P Even and Periodic function B Let f :(-1,1) arrow R be defined as f ( x )= displaystyle∑ r =1100[ x 2 r ], then f(x) is Q Bounded C Let f(x)= cos -1([ e x ]-1)+ sin -1([ e x ]), then f(x) is R Domain contains at least one integer and at most 3 integers S Both many one and odd function [Note: [y] and y denote greatest integer and fractional part function of y respectively.]

Question

Column I Column II A Let f(x)=√ log ( cos [ x ]), then f(x) is P Even and Periodic function B Let f :(-1,1) arrow R be defined as f ( x )= displaystyle∑ r =1100[ x 2 r ], then f(x) is Q Bounded C Let f(x)= cos -1([ e x ]-1)+ sin -1([ e x ]), then f(x) is R Domain contains at least one integer and at most 3 integers S Both many one and odd function [Note: [y] and y denote greatest integer and fractional part function of y respectively.] (A) (A) P, Q, S; (B) P, Q, R, P; (C) Q (B) (A) P, Q, S; (B) P, Q, R, Q; (C) Q (C) (A) P, Q, S; (B) P, Q, R, R; (C) Q (D) (A) P, Q, S; (B) P, Q, R, S; (C) Q

Tardigrade Admin · Accepted Answer

Correct answer is (d) (A) P, Q, S; (B) P, Q, R, S; (C) Q

Column I		Column II
A	Let $f (x) = lo g (cos [{x}])$ , then $f (x)$ is	P	Even and Periodic function
B	Let $f : (- 1, 1) \to R$ be defined as $f (x) = r = 1 \sum 100 [x^{2 r}]$ , then $f (x)$ is	Q	Bounded
C	Let $f (x) = cos^{- 1} ([e^{x}] - 1) + sin^{- 1} ([e^{x}])$ , then $f (x)$ is	R	Domain contains at least one integer and at most 3 integers
		S	Both many one and odd function