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 $e^{f(x)}=\frac{10+x}{10-x}, x \in(-10,10)$ and $f(x)=k f\left(\frac{200 x}{100+x^2}\right)$,then $k$ is equal to

Force acting on a particle moving in a straight line varies with the velocity of the particle as $F = \frac{K}{v}$. Here $K$ is a constant. The work done by this force in time $t$ is

$\left|\begin{array}{ccc}x+2 & x+3 & x+5 \\ x+4 & x+6 & x+9 \\ x+8 & x+11 & x+15\end{array}\right|$ is equal to

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. Fresnel's diffraction pattern occurs when the source of light or the screen on which the diffraction pattern is seen,or when both,are at a finite distance from the aperture.
$B$. Diffracted light can be used to estimate the helical structure of nucleic acids.

Which of the following expressions is correct in case of a $CsCl$ unit cell (edge length,$a$)?