Match the column

Answer

`p to c; q to a; r to c; s to b`

Explanation

(p) `f(x)=sin^(3)x +cos^(4)x,`
` sin^(3)x` has period `2pi` and `cos^(4)x` has period `pi`, and L.C.M. of `pi` and `2pi` is `2pi`. Hence, period is `2pi`.
(q) ` f(x)=sin^(4)x+cos^(4)x,`
Both `sin^(4)x` and ` cos^(4)x` have the same period `pi`, and L.C.M. of `pi` and `pi` is `pi`.
But `f(x+pi//2)=f(x)`. Then period is `pi//2`.
(r) Both `sin^(3)x` and `cos^(3)x` have the same period `2pi,` and L.C.M. of `2pi` and `2pi` is `2 pi`.
Hence, period is `2pi, [(f(x+pi) ne f(x)].`
(s) `f(x)=cos^(4)x -sin^(4)x`
Both `sin^(4)x` and `cos^(4)x` have the same period `pi,` and L.C.M. of `pi` and `pi` is `pi`.
Hence, period is `pi,[f(x+pi//2) ne f(x)].`