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JEE Mains Previous Years Questions with Solutions

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1

JEE Main 2015 (Offline)

MCQ (Single Correct Answer)
Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $${V^q},$$ where $$V$$ is the volume of the gas. The value of $$q$$ is: $$\left( {\gamma = {{{C_p}} \over {{C_v}}}} \right)$$
A
$${{\gamma + 1} \over 2}$$
B
$${{\gamma - 1} \over 2}$$
C
$${{3\gamma + 5} \over 6}$$
D
$${{3\gamma - 5} \over 6}$$

Explanation

$$\tau = {1 \over {\sqrt 2 \pi {d^2}\left( {{N \over V}} \right)\sqrt {{{3RT} \over M}} }}$$
$$\tau \propto {V \over {\sqrt T }}$$
As, $$\,\,\,\,T{V^{\gamma - 1}} = K$$
So, $$\,\,\,\,\tau \propto {V^{\gamma + 1/2}}$$
Therefore, $$q = {{\gamma + 1} \over 2}$$
2

JEE Main 2015 (Offline)

MCQ (Single Correct Answer)
A solid body of constant heat capacity $$1$$ $$J/{}^ \circ C$$ is being heated by keeping it in contact with reservoirs in two ways:
$$(i)$$ Sequentially keeping in contact with $$2$$ reservoirs such that each reservoir
$$\,\,\,\,\,\,\,\,$$supplies same amount of heat.
$$(ii)$$ Sequentially keeping in contact with $$8$$ reservoirs such that each reservoir
$$\,\,\,\,\,\,\,\,\,\,$$supplies same amount of heat.
In both the cases body is brought from initial temperature $${100^ \circ }C$$ to final temperature $${200^ \circ }C$$. Entropy change of the body in the two cases respectively is :
A
$$ln2, 2ln2$$
B
$$2ln2, 8ln2$$
C
$$ln2, 4ln2$$
D
$$ln2, ln2$$

Explanation

The entropy change of the body in the two cases is same as entropy is a state function.
3

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)
There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $${d_1}$$ and $${d_2}$$ are filled in the tube. Each liquid subtends $${90^ \circ }$$ angle at center. Radius joining their interface makes an angle $$\alpha $$ with vertical. Radio $${{{d_1}} \over {{d_2}}}$$ is :
A
$${{1 + \sin \,\alpha } \over {1 - \sin \,\alpha }}$$
B
$${{1 + \cos \,\alpha } \over {1 - \cos \,\alpha }}$$
C
$${{1 + \tan \,\alpha } \over {1 - \tan \,\alpha }}$$
D
$${{1 + \sin \,\alpha } \over {1 - \cos \,\alpha }}$$

Explanation

Pressure at interface A must be same from both the sides to be in equilibrium.

$$\therefore$$ $$\left( {R\cos \alpha + R\sin \alpha } \right){d_2}g = \left( {R\cos \alpha - R\sin \alpha } \right){d_1}g$$
$$ \Rightarrow {{{d_1}} \over {{d_2}}} = {{\cos \alpha + \sin \alpha } \over {\cos \alpha - \sin \alpha }} = {{1 + \tan \alpha } \over {1 - \tan \alpha }}$$
4

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)
One mole of a diatomic ideal gas undergoes a cyclic process $$ABC$$ as shown in figure. The process $$BC$$ is adiabatic. The temperatures at $$A, B$$ and $$C$$ are $$400$$ $$K$$, $$800$$ $$K$$ and $$600$$ $$K$$ respectively. Choose the correct statement :
A
The change in internal energy in whole cyclic process is $$250$$ $$R.$$
B
The change in internal energy in the process $$CA$$ is $$700$$ $$R$$.
C
The change in internal energy in the process $$AB$$ is - $$350$$ $$R.$$
D
The change in internal energy in the process $$BC$$ is - $$500$$ $$R.$$

Explanation

In cyclic process, change in total internal energy is zero.
$$\Delta {U_{cyclic}} = 0$$
$$\Delta {U_{BC}} = n{C_v}\Delta T = 1 \times {{5R} \over 2}\Delta T$$

where, $${C_v} = $$ molar specific heat at constant volume.
For $$BC,$$ $$\Delta T = - 200\,K$$
$$\therefore$$ $$\Delta {U_{BC}} = - 500R$$

Questions Asked from Heat and Thermodynamics

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