 JEE Mains Previous Years Questions with Solutions

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1

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 $(a).$
2

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

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

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.
4

AIEEE 2008

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume ${V_1}$ and contains ideal gas at pressure ${P_1}$ and temperature ${T_1}$. The other chamber has volume ${V_2}$ and contains ideal gas at pressure ${P_2}$ and temperature ${T_2}$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be
A
${{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}}}$
B
${{{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \over {{P_1}{V_1} + {P_2}{V_2}}}$
C
${{{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \over {{P_1}{V_1} + {P_2}{V_2}}}$
D
${{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}}}$

Explanation

Same as $A.$ $20$