### JEE Mains Previous Years Questions with Solutions

4.5
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1

### AIEEE 2004

If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on earth to what it was previously will be
A
$32$
B
$16$
C
$4$
D
$64$

## Explanation

$E = \sigma A{T^4};\,\,A \propto {R^2}$
$\therefore$ $E \propto {R^2}{T^4}$
$\therefore$ ${{{E_2}} \over {{E_1}}} = {{R_2^2T_2^4} \over {R_1^2T_1^4}}$
$\Rightarrow {{{E_2}} \over {{E_1}}}$
$= {{{{\left( {2R} \right)}^2}{{\left( {2T} \right)}^4}} \over {{R^2}{T^4}}}$
$= 64$
2

### 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

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

### 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
4

### 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

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