If $\int \frac{e^x-1}{e^x+1} d x=f(x)+c$,then $f(x)$ is equal to

Consider the following reactions:
$C_2H_2 \xrightarrow[500^{\circ}C]{\text{red hot iron tube}} A$
$A \xrightarrow[70^{\circ}C]{\text{conc. } HNO_3, \text{conc. } H_2SO_4} B$
$B \xrightarrow{LiAlH_4} C_6H_5-N=N-C_6H_5$
$A$ and $B$ are:

If $x_n = \cos \frac{\pi}{2^n} + i \sin \frac{\pi}{2^n}$,then $\prod_{n=1}^{\infty} x_n$ is equal to

The path length of oscillation of a simple pendulum of length $1 \ m$ is $16 \ cm$. Its maximum velocity is $(g = \pi^2 \ m/s^2)$

If $f(x) = \sin^2 \left( \frac{\pi}{8} + \frac{x}{2} \right) - \sin^2 \left( \frac{\pi}{8} - \frac{x}{2} \right)$,then the period of $f$ is

The coefficient of $x^k$ in the expansion of $\frac{1-2x-x^2}{e^{-x}}$ is