Condition for Monotonically Increasing Function

Q.

if $x_r$=cos$\left(\frac{\pi }{2^r}\right)$+isin$\left(\frac{\pi }{2^r}\right)$ , then $x_r$, $x_r$, ......$\infty$ is

1. -3

2. -2

3. -1

4. 0

Q.

Which of the following function is a monotonically increasing function?

1. $f\left(x\right)=x^2+2x$

2. $f\left(x\right)=x^3+2x$

3. $f\left(x\right)=x^3+2x$

4. $f\left(x\right)=cosx$

Q. Find the fundamental period for $f\left(x\right)=\mid \cos x\mid$

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

Q. $f\left(x\right)=cos\left(\frac{\pi }{x}\right),x\ne 0$ increases in the interval

1. $(\frac{1}{2k+1},\frac{1}{2k})$
2. $(\frac{1}{2k}+2,\frac{1}{2k}+1)$
3. $(\frac{1}{2k}+1,\frac{1}{2k}+3)$
4. $(\frac{1}{2k+1},\frac{1}{2k}+3)$