 JEE Mains Previous Years Questions with Solutions

4.5
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1

AIEEE 2009

A transparent solid cylindrical rod has a refractive index of ${2 \over {\sqrt 3 }}.$ It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is :

A
${\sin ^{ - 1}}\left( {{\raise0.5ex\hbox{{\sqrt 3 }} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{2}}} \right)$
B
${\sin ^{ - 1}}\left( {{\raise0.5ex\hbox{2} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{{\sqrt 3 }}}} \right)$
C
${\sin ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)$
D
${\sin ^{ - 1}}\left( {{\raise0.5ex\hbox{1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{2}}} \right)$

Explanation Applying Snell's law at $Q$

$n = {{\sin {{90}^ \circ }} \over {\sin C}} = {1 \over {\sin C}}$

$\therefore$ $\sin C = {1 \over n} = {{\sqrt 3 } \over 2}$

$\therefore$ $C = {60^ \circ }$

Applying Snell's Law at $P$

$n = {{\sin \theta } \over {\sin \left( {90 - C} \right)}}$

$\Rightarrow \sin \theta = n \times \sin \left( {90 - C} \right);$ from $(1)$

$\Rightarrow \sin \theta = n\,\cos$

$\therefore$ $\theta = {\sin ^{ - 1}}\left[ {{2 \over {\sqrt 3 }} \times \cos {{60}^0}} \right]$

or, $\theta = {\sin ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)$
2

AIEEE 2009

A mixture of light, consisting of wavelength $590$ $mm$ and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the $4$th bright fringe of the unknown light. From this data, the wavelength of the unknown light is :
A
$885.0$ $nm$
B
$442.5$ $nm$
C
$776.8$ $nm$
D
$393.4$ $nm$

Explanation

Third bright fringe of known light coincides with the 4th bright fringe of the unknown light.

$\therefore$ ${{3\left( {590} \right)D} \over d} = {{4\lambda D} \over d}$

$\Rightarrow \lambda = {3 \over 4} \times 590$

$= 442.5\,nm$
3

AIEEE 2008

A student measures the focal length of a convex lens by putting an object pin at a distance $'u'$ from the lens and measuring the distance $'v'$ of the image pin. The graph between $'u'$ and $'v'$ plotted by the student should look like
A B C D Explanation

This graph obeys the lens equation

${1 \over v} - {1 \over u} = {1 \over f}$

where $f$ is a positive constant for a given convex lens.
4

AIEEE 2007

Two lenses of power $-15$ $D$ and $+5$ $D$ are in contact with each other. The focal length of the combination is
A
$+ 10\,cm$
B
$- 20\,cm$
C
$- 10\,cm$
D
$+ 20\,cm$

Explanation

Power of combination is given by

$P = {P_1} + {P_2} = \left( { - 15 + 5} \right)D$ $\,\,\,\,\,\,\,\,\, = - 10D.$

Now, $P = {1 \over f} \Rightarrow f = {1 \over P} = {1 \over { - 10}}$ metre

$\therefore$ $f = - \left( {{1 \over {10}} \times 100} \right)cm = - 10\,cm.$