A) \[f(x)=x\cos x\]
B) \[f(x)=|\cos x|\]
C) \[f(x)=\sin x\]
D) \[f(x)=[x+\pi ]\] Where \[[x]\] means the greater integer not greater than \[x.\]
Correct Answer: B
Solution :
(a)\[f(x)=x\cos x\] It is not periodic for any period (b) \[f(x)=\,|\cos x|\] It is periodic for the period \[\pi \] (c) \[f(x)=\sin x\] It is periodic for the period \[2\,\pi \] \[f(x)=[x+\pi ]\] It is not periodic with period \[\pi \] \[\therefore \]Option (b) is correct.
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