Identify $A$ and $B$ in the following reactions:

For a ray of light,the critical angle is minimum when it travels from

$A$ circle $C_1$ of radius $2$ touches both $x$-axis and $y$-axis. Another circle $C_2$ whose radius is greater than $2$ touches circle $C_1$ and both the axes. Then the radius of circle $C_2$ is-

If the sum of two of the roots of $x^3+p x^2-q x+r=0$ is zero,then $p q$ is equal to

$A$ rectangular glass slab $ABCD,$ of refractive index $n_1,$ is immersed in water of refractive index $n_2$ $(n_1 > n_2)$. $A$ ray of light is incident at the surface $AB$ of the slab as shown. The maximum value of the angle of incidence $\alpha_{\max},$ such that the ray comes out only from the other surface $CD,$ is given by:

$A$ 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 $\frac{T_1}{T_2}$ is given by: