The general solution of the equation $(\sqrt{3} - 1)\sin \theta + (\sqrt{3} + 1)\cos \theta = 2$ is

An ice ball melts at a rate proportional to the amount of ice present at that instant. Half the quantity of ice melts in $20 \text{ minutes}$. Let $x_0$ be the initial quantity of ice. If after $40 \text{ minutes}$ the amount of ice left is $k x_0$,then the value of $k$ is:

Given below are $2$ statements:
Statement $I$: The number of species among $BF_4^-$,$SiF_4$,$XeF_4$ and $SF_4$,that have unequal $E-F$ bond lengths is $2$. Here,$E$ is the central atom.
Statement $II$: Among $O_2^-$,$O_2^{2-}$,$F_2$ and $O_2^+$,$O_2^-$ has the highest bond order.
In the light of the above statements,choose the correct answer from the options given below

$A$ monoatomic ideal gas initially at temperature $T_1$ is enclosed in a cylinder fitted with a massless,frictionless piston. By releasing the piston suddenly,the gas is allowed to expand adiabatically to a temperature $T_2$. If $L_1$ and $L_2$ are the lengths of the gas columns before and after expansion respectively,then $\frac{T_2}{T_1}$ is

The minimum deviation produced by a hollow prism filled with a certain liquid is found to be $30^o$. The angle of refraction is also found to be $30^o$. The refractive index of the liquid is

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is