### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2005

Two point white dots are $1$ $mm$ apart on a black paper. They are viewed by eye of pupil diameter $3$ $mm.$ Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light $=500$ $nm$ ]
A
$1m$
B
$5m$
C
$3m$
D
$6m$

## Explanation

${y \over D} \ge 1.22{\lambda \over d}$

$\Rightarrow D \le {{yd} \over {\left( {1.22} \right)\lambda }}$

$= {{{{10}^{ - 3}} \times 3 \times {{10}^{ - 3}}} \over {\left( {1.22} \right) \times 5 \times {{10}^{ - 7}}}}$

$= {{30} \over {61}} \approx 5m$

$\therefore$ ${D_{\max }} = 5m$
2

### AIEEE 2005

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is ${4 \over 3}$ and the fish is $12$ $cm$ below the surface, the radius of this circle in $cm$ is
A
${{36} \over {\sqrt 7 }}$
B
${36\sqrt 7 }$
C
${4\sqrt 5 }$
D
${36\sqrt 5 }$

## Explanation

$\sin {\theta _c} = {1 \over \mu } = {3 \over 4}$

or $\tan {\theta _c} = {3 \over {\sqrt {16 - 9} }} = {3 \over {\sqrt 7 }} = {R \over {12}}$

$\Rightarrow R = {{36} \over {\sqrt 7 }}\,cm$
3

### AIEEE 2004

A light ray is incident perpendicularly to one face of a ${90^ \circ }$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is ${45^ \circ }$, we conclude that the refractive index $n$
A
$n > {1 \over {\sqrt 2 }}$
B
$n > \sqrt 2$
C
$n < {1 \over {\sqrt 2 }}$
D
$n < \sqrt 2$

## Explanation

The incident angle is ${45^ \circ }$

Incident angle $>$ critical angle, $i > {i_c}$

$\therefore$ $\sin i > \sin {i_c}$ or $\sin \,45\, > \sin \,{i_c},$ $\sin {i_c} = {1 \over n}$

$\therefore$ $\sin \,{45^ \circ } > {1 \over n}$ or ${1 \over {\sqrt 2 }} > {1 \over n} \Rightarrow n > \sqrt 2$
4

### AIEEE 2004

The maximum number of possible interference maximum for slit-separation equal to twice the wavelength in Young's double-slit experiment is
A
three
B
five
C
infinite
D
zero

## Explanation

For constructive interference $d\,\sin \theta = n\lambda$

given $d = 2\lambda \Rightarrow \sin \theta = {n \over 2}$

$n = 0,1, - 1,2, - 2$ hence five maxima are possible