In $Anthoceros$,vegetative reproduction occurs by which of the following?

If $x y \neq 0, x+y \neq 0$ and $x^m y^n=(x+y)^{m+n}$,where $m, n \notin N$,then $\frac{d y}{d x}$ is equal to

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ and $l^2 = m^2 + n^2$ is

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively,then $T_1/T_2$ is given by

$A$ $200\, W$ sodium street lamp emits yellow light of wavelength $0.6\, \mu m$. Assuming it to be $50\%$ efficient in converting electrical energy to light,the number of photons of yellow light it emits per second is:

$A$ uniform rope of mass $0.1 ~kg$ and length $2.45 ~m$ hangs from a rigid support. The time taken by the transverse wave formed in the rope to travel through the full length of the rope is (Assume $g=9.8 ~m/s^2$) (in $~s$)