Three moles of an ideal gas undergoes a cyclic process $A B C A$ as shown in the figure. The pressure, volume and absolute temperature at points $A, B$ and $C$ are respectively $\left(p_1, V_1, T_1\right),\left(p_2, 3 V_1, T_1\right)$ and $\left(p_2, V_1, T_2\right)$. Then, the total work done in the cycle $A B C A$ is ( $R=$ Universal gas constant).

The pressure of a mixture of 64 g of oxygen, 28 g of nitrogen and 132 g of carbon dioxide gases in a closed vessel is $p$. Under isothermal conditions if entire oxygen is removed from the vessel, the pressure of the mixture of remaining two gases is
A sound wave of frequency 210 Hz travels with a speed of $330 \mathrm{~ms}^{-1}$ along the positive $X$-axis. Each particle of the wave moves a distance of 10 cm between the two extreme points. The equation of the displacement function ( s ) of this wave is ( $x$ in metre, $t$ in second)
A string vibrates in its fundamental mode when a tension $T_1$ is applied to it. If the length of the string is decreased by $25 \%$ and the tension applied is changed to $T_2$, the fundamental frequency of the string increases by $100 \%$, then $\frac{T_2}{T_1}=$
(Linear density of the string is constant)
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