$A$ cylindrical conductor of radius $R$ carries a current $i$. The value of the magnetic field at a point which is $R/4$ distance inside from the surface is $10 \ T$. Find the value of the magnetic field at a point which is $4R$ distance outside from the surface.

Bottles containing $C_6H_5I$ and $C_6H_5CH_2I$ lost their original labels. They were labelled $A$ and $B$ for testing. $A$ and $B$ were separately taken in a test tube and boiled with $NaOH$ solution. The end solution in each tube was made acidic with dilute $HNO_3$ and then some $AgNO_3$ solution was added. Substance $B$ gave a yellow precipitate. Which one of the following statements is true for this experiment?

The potential difference between $A$ and $B$ in the figure is ................. $V$.

The value of $\cos 15^{\circ} \cos 7.5^{\circ} \sin 7.5^{\circ}$ is

The $pH$ of $0.05 \ M$ acetic acid is $(K_a = 2 \times 10^{-5})$

$A$ 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: