 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2004

One mole of ideal monatomic gas $\left( {\gamma = 5/3} \right)$ is mixed with one mole of diatomic gas $\left( {\gamma = 7/5} \right)$. What is $\gamma$ for the mixture? $\gamma$ Denotes the ratio of specific heat at constant pressure, to that at constant volume
A
$35/23$
B
$23/15$
C
$3/2$
D
$4/3$

Explanation

${{{n_1} + {n_2}} \over {\gamma - 1}} = {{{n_1}} \over {{\gamma _1} - 1}} + {{{n_2}} \over {{\gamma _2} - 1}}$
$\Rightarrow {{1 + 1} \over {\gamma - 1}}$
$= {1 \over {{5 \over 3} - 1}} + {1 \over {{7 \over 5} - 1}}$
$\Rightarrow \gamma = {3 \over 2}$
2

AIEEE 2003

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by
A
Rayleigh Jeans law
B
C
D
Wien's law

Explanation

Wein's law correctly explanations the spectrum
3

AIEEE 2003

According to Newton's law of cooling, the rate of cooling of a body is proportional to ${\left( {\Delta \theta } \right)^n},$ where ${\Delta \theta }$ is the difference of the temperature of the body and the surrounding, and $n$ is equal to
A
two
B
three
C
four
D
one

Explanation

$- {{dQ} \over {dt}} \propto \left( {\Delta \theta } \right)$
4

AIEEE 2003

A carnot engine takes $3 \times {10^6}$ cal. of heat from a reservoir at ${627^ \circ }C,$ and gives it to a sink at ${27^ \circ }C$. The work done by the engine is
A
$4.2 \times {10^6}J$
B
$8.4 \times {10^6}J$
C
$16.8 \times {10^6}J$
D
zero

Explanation

$\eta = 1 - {{{T_2}} \over {{T_1}}}$

$= 1 - {{\left( {273 + 27} \right)} \over {\left( {273 + 627} \right)}}$

$= 1 - {{300} \over {900}}$

$= 1 - {1 \over 3} = {2 \over 3}$

But $\eta = {W \over Q}$

$\therefore$ ${W \over Q} = {2 \over 3} \Rightarrow W$

$= {2 \over 3} \times Q$

$= {2 \over 3} \times 3 \times {10^6}$

$= 2 \times {10^6}cal$

$= 2 \times {10^6} \times 4.2\,J$

$= 8.4 \times {10^6}J$