Period of a Function

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

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

Q.

What does $e$ mean in math?

Q.

If $f\left(x\right)+f(x+4)=f(x+2)+f(x+6)\forall xϵRanda>0$ and and f(5)=10, then ∑r=1100​f(5+8r) equal to

1. 1000
2. 100
3. 10000
4. 10

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

1. 
2. 
3. Does not exist
4. 

Q.

Given f(x) defined on f: R $\to$ R is a periodic function with the fundamental period 2 then f(3) is not equal to -

1. f(2)

2. f(9)

3. f(5)

4. f(-1)

Q. The period of the function f(x) = sin 3x is

1. 
2. 
3. 
4. 

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. na
3. 
4. e^{na}

Q. If f(x)is an odd periodic function with period 2, then f(4) equals

1. 0
2. 2
3. 4
4. -4

Q. The period of the function $|sinx|+|cosx|$ is

1. $\frac{\pi }{2}$
2. $2\pi$
3. $4\pi$
4. $\pi$

Q. If f(x)is an odd periodic function with period 2, then f(4) equals

1. 0
2. 2
3. 4
4. -4

Q.

Period of a function is always a positive integer.

1. True

2. False