Mathematics

Problem

Match the statements of Column I with values of Column II.

Column I	Column II
(A) $f(x) = \sin^2 x + \sin^2 \left(x + \frac{\pi}{3}\right) + \cos x \cos \left(x + \frac{\pi}{3}\right)$ then $f(x)$ is	(p) Defined for all real 'x'
(B) $g(x) = \tan(e^{ x }) + [x + \alpha] - 5 - x$ where $[.]$ denotes the greatest integer less than or equal to $x$ , then $g(x)$ is	(q) Even function
(C) $h(x) = \frac{x}{5^x - 1} + \frac{x}{2} + 5$ then $h(x)$ is	(r) Odd function
(D) $k(x) = 2 \sin^2 x - \cos 2\alpha + 4 \sin \alpha \cdot \sin x \cos (x + \alpha) + \cos 2(x + \alpha), \alpha \in R$ , then $k(x)$ is	(s) Periodic function