Which of the following is not a synthetic polymer?

The velocities of three particles of masses $20 \ g$,$30 \ g$,and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$,and $10 \hat{k}$ respectively. The velocity of the centre of mass of the three particles is:

The correct statements $(s)$ about intermolecular forces is$(are)$
$(A)$ The potential energy between two point charges approaches zero more rapidly than the potential energy between a point dipole and a point charge as the distance between them approaches infinity.
$(B)$ The average potential energy of two rotating polar molecules that are separated by a distance $r$ has $1 / r^3$ dependence.
$(C)$ The dipole-induced dipole average interaction energy is independent of temperature.
$(D)$ Nonpolar molecules attract one another even though neither has a permanent dipole moment.

$A$ square of side $3\;cm$ is placed at a distance of $25\;cm$ from a concave mirror of focal length $10\;cm$. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the square is $......\;cm^2$.

If $y = \sin(m \sin^{-1} x)$,then $(1 - x^2) y_2 - x y_1$ is equal to (Here,$y_n$ denotes $\frac{d^n y}{dx^n}$)

If the system of equations $x + 2y - 3z = 1$,$(k + 3)z = 3$,and $(2k + 1)x + z = 0$ is inconsistent,then the value of $k$ is: