### JEE Mains Previous Years Questions with Solutions

4.5
star star star star star
1

### AIEEE 2009

Two moles of helium gas are taken over the cycle $ABCD,$ as shown in the $P$-$T$ diagram.

Assuming the gas to be ideal the work done on the gas in taking it from $A$ to $B$ is :

A
$300$ $R$
B
$400$ $R$
C
$500$ $R$
D
$200$ $R$

## Explanation

$A$ to $B$ is an isobaric process. The work done
$W = nR\left( {{T_2} - {T_1}} \right) = 2R\left( {500 - 300} \right) = 400R$
2

### AIEEE 2009

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figures?
A
B
C
D

## Explanation

The heat flow rate is given by

${{dQ} \over {dt}} = {{kA\left( {{\theta _1} - \theta } \right)} \over x}$

$\Rightarrow {\theta _1} - \theta$ $= {x \over {kA}}{{dQ} \over {dt}}$

$\Rightarrow \theta$ $= {\theta _1} - {x \over {kA}}{{dQ} \over {dt}}$

where ${\theta _1}$ is the temperature of hot end and $\theta$ is temperature at a distance $x$ from hot end.
The above equation can be graphically represented by option $(a).$
3

### AIEEE 2009

One $kg$ of a diatomic gas is at a pressure of $8 \times {10^4}\,N/{m^2}.$ The density of the gas is $4kg/{m^3}$. What is the energy of the gas due to its thermal motion ?
A
$5 \times {10^4}\,J$
B
$6 \times {10^4}\,J$
C
$7 \times {10^4}\,J$
D
$3 \times {10^4}\,J$

## Explanation

$Volume\,\, = \,\,{{mass} \over {density}} = {1 \over 4}{m^3}$
$K.E = {5 \over 2}PV$
$= {5 \over 2} \times 8 \times {10^4} \times {1 \over 4}$
$= 5 \times {10^4}J$
4

### AIEEE 2009

Statement - 1: The temperature dependence of resistance is usually given as $R = {R_0}\left( {1 + \alpha \,\Delta t} \right).$ The resistance of wire changes from $100\Omega$ to $150\Omega$ when its temperature is increased from ${27^ \circ }C$ to ${227^ \circ }C$. This implies that $\alpha = 2.5 \times {10^{ - 3}}/C.$

Statement - 2: $R = {R_0}\left( {1 + \alpha \,\Delta t} \right)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta T = \left( {R - {R_0}} \right) < < {R_0}.$

A
Statement - 1 is true, Statement - 2 is true; Statement - 2 is the correct explanation of Statement - 1
B
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not the correct explanation of Statement - 1
C
Statement - 1 is false, Statement - 2 is true
D
Statement - 1 is true, Statement - 2 is false

## Explanation

The relation $R = {R_0}\left( {1 + \alpha \,\Delta t} \right)$ is valid for small values of $\Delta t$ and ${R_0}$ is resistance at ${0^ \circ }C$ and also $\left( {R - {R_0}} \right)$ should be much smaller than ${R_0}.$ So, statement $(1)$ is wrong but statement $(2)$ is correct.