 JEE Mains Previous Years Questions with Solutions

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1

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.
2

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 $A.$ $20$
3

AIEEE 2008

The speed of sound in oxygen $\left( {{O_2}} \right)$ at a certain temperature is $460\,\,m{s^{ - 1}}.$ The speed of sound in helium $(He)$ at the same temperature will be (assume both gases to be ideal)
A
$1421\,\,m{s^{ - 1}}$
B
$500\,\,m{s^{ - 1}}$
C
$650\,\,m{s^{ - 1}}$
D
$300\,\,m{s^{ - 1}}$

Explanation

The speed of sound in a gas is given by $v = \sqrt {{{\gamma RT} \over M}}$
$\therefore$ ${{{v_{{O_2}}}} \over {{v_{He}}}} = \sqrt {{{{\gamma _{{O_2}}}} \over {{M_{{O_2}}}}} \times {{{M_{He}}} \over {{\gamma _{He}}}}}$
$= \sqrt {{{1.4} \over {32}} \times {4 \over {1.67}}} = 0.3237$
$\therefore$ ${v_{He}} = {{{v_{{O_2}}}} \over {0.3237}}$
$= {{460} \over {0.3237}}$
$= 1421\,m/s$
4

AIEEE 2007

One end of a thermally insulated rod is kept at a temperature ${T_1}$ and the other at ${T_2}$. The rod is composed of two sections of length ${L_1}$ and ${L_2}$ and thermal conductivities ${K_1}$ and ${K_2}$ respectively. The temperature at the interface of the two section is A
${{\left( {{K_1}{L_1}{T_1} + {K_2}{L_2}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}$
B
${{\left( {{K_2}{L_2}{T_1} + {K_1}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_1} + {K_2}{L_2}} \right)}}$
C
${{\left( {{K_2}{L_1}{T_1} + {K_1}{L_2}{T_2}} \right)} \over {\left( {{K_2}{L_1} + {K_1}{L_2}} \right)}}$
D
${{\left( {{K_1}{L_2}{T_1} + {K_2}{L_1}{T_2}} \right)} \over {\left( {{K_1}{L_2} + {K_2}{L_1}} \right)}}$

Explanation ${{{K_1}A\left( {{T_1} - T} \right)} \over {{\ell _1}}} = {{{K_2}A\left( {T - {T_2}} \right)} \over {{\ell _2}}}$
$\therefore$ $T = {{{K_1}{T_1}{\ell _2} + {K_2}{T_2}{\ell _1}} \over {{K_2}{\ell _1} + {K_1}{\ell _2}}}$
$= {{{K_1}{\ell _2}{T_1} + {K_2}{\ell _1}{T_2}} \over {{K_1}{\ell _2} + {K_2}{\ell _1}}}$