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**JEE main Previous Year Topic Wise Questions of Physics with Solutions**

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*Simulator***Previous Years JEE Advanced Questions**

Q. A real gas behaves like an ideal gas if its ?
(A) pressure and temperature are both high
(B) pressure and temperature are both low
(C) pressure is high and temperature is low
(D) pressure is low and temperature is high

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**Sol.**(D) $\operatorname{High} \vec{P},$ Low $P$

Q. A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic
mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds $\left(\frac{v_{r m s}(\text {helium})}{v_{r m s}(\text {arg on})}\right)$ is ?
(A) 0.32 (B) 0.45 (C) 2.24 (D) 3.16

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**Sol.**(D) $v_{m s}=\sqrt{\frac{3 R T}{M}} ; \frac{\left(v_{m s}\right)_{H e}}{\left(v_{m s}\right)_{A r}}=\sqrt{\frac{M_{A r}}{M_{H e}}}=\sqrt{\frac{40}{4}}=\sqrt{10}=3.16$

Q. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is :-
(A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9

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**Sol.**(D) $\mathrm{P}=\frac{\rho}{\mathrm{M}} \mathrm{RT}$ $\Rightarrow \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}=\frac{\rho_{1} \mathrm{M}_{2}}{\rho_{2} \mathrm{M}_{1}}=\frac{4}{3} \Rightarrow \frac{\rho_{1}}{\rho_{2}}=\frac{4}{3} \times \frac{2}{3}=\frac{8}{9}$

Q. A container of fixed volume has a mixutre of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is (are) :-
(A) The average energy per mole of the gas mixture is 2RT.
(B) The ratio of speed of sound in the gas mixture to that in helium gas is $\sqrt{6 / 5}$.
(C) The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2.
(D) The ratio of the rms speed of helium atoms to that of hydrogen molecules is $1 / \sqrt{2}$.

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**Sol.**(A,B,D) $C_{V(\operatorname{mix})}=\frac{(1)\left(\frac{3}{2} R\right)+(1)\left(\frac{5}{2} R\right)}{2}=2 R$ $\mathrm{C}_{\mathrm{P}(\mathrm{mix})}=3 \mathrm{R} \quad \gamma_{\operatorname{mix}}=\frac{3}{2} \Rightarrow \mathrm{f}=4$ Average energy/mole $=\mathrm{f} \frac{1}{2} \mathrm{RT}=2 \mathrm{RT}$ $\frac{\left(\mathrm{V}_{\mathrm{sound}}\right)_{\mathrm{mixture}}}{\left(\mathrm{V}_{\mathrm{sound}}\right)_{\mathrm{He}}}=\frac{\sqrt{\frac{\mathrm{RT}}{2}}}{\sqrt{\frac{5 \mathrm{RT}}{12}}}=\sqrt{\frac{6}{5}}$ $\frac{\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{He}}}{\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}=\frac{\sqrt{\frac{3 \mathrm{RT}}{4}}}{\sqrt{\frac{3 \mathrm{RT}}{2}}}=\frac{1}{\sqrt{2}}$ $\therefore(\mathrm{A}, \mathrm{B}, \mathrm{D})$

Thanks

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