Period of a Function

Q. The fundamental period of the function $f\left(x\right)=2cos\frac{1}{3}(x-\pi )$ is

1. $6\pi$
2. $4\pi$
3. $2\pi$
4. $\pi$

Q. If f (x) +f (x+a) + f(x+2a) +....+ f (x+na) = constant; $\forall x$ $ϵR$ and $a>0$ and f(x) is periodic, then period of f(x), is

1. (n+1) a
2. $e^{n+1}a$
3. na
4. $e^{na}$

Q. The period of the function sin 3x + {x} (where {.} is fractional part of x)

1. $\frac{2\pi }{3}$
2. $2\pi$
3. $\frac{\pi }{6}$
4. Does not exist