 JEE Mains Previous Years Questions with Solutions

4.5
star star star star star
1

JEE Main 2013 (Offline)

The graph between angle of deviation $\left( \delta \right)$ and angle of incidence $(i)$ for a triangular prism is represented by
A B C D Explanation

For the prism as the angle of incidence $(i)$ increase, the angle of deviation $\left( \delta \right)$ first decreases goes to minimum value and then increases.
2

JEE Main 2013 (Offline)

Two coherent point sources ${S_1}$ and ${S_2}$ are separated by a small distance $'d'$ as shown. The fringes obtained on the screen will be A
points
B
straight lines
C
semi-circles
D
concentric circles

Explanation

It will be concentric circles.
3

JEE Main 2013 (Offline)

Diameter of a plano-convex lens is $6$ $cm$ and thickness at the center is $3mm$. If speed of light in material of lens is $2 \times {10^8}\,m/s,$ the focal length of the lens is
A
$15$ $cm$
B
$20$ $cm$
C
$30$ $cm$
D
$10$ $cm$

Explanation $\therefore$ $n = {{Velocity\,\,of\,\,light\,\,in\,\,vacuum} \over {Velocity\,\,of\,\,light\,\,in\,\,medium}}$

$\therefore$ $n = {3 \over 2}$

${3^2} + {\left( {R - 3mm} \right)^2} = {R^2}$

$\Rightarrow {3^2} + {R^2} - 2R\left( {3mm} \right) + {\left( {3mm} \right)^2} = {R^2}$

$\Rightarrow R \approx 15\,cm$

${1 \over f} = \left( {{3 \over 2} - 1} \right)\left( {{1 \over {15}}} \right) \Rightarrow f = 30\,cm$
4

JEE Main 2013 (Offline)

A beam of unpolarised light of intensity ${{\rm I}_0}$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of ${45^ \circ }$ relative to that of $A$. The intensity of the emergent light is
A
${{\rm I}_0}$
B
${{\rm I}_0}/2$
C
${{\rm I}_0}/4$
D
${{\rm I}_0}/8$

Explanation

Relation between intensities ${{\rm I}_r} = \left( {{{{{\rm I}_0}} \over 2}} \right){\cos ^2}\left( {{{45}^ \circ }} \right) = {{{{\rm I}_0}} \over 2} \times {1 \over 2} = {{{{\rm I}_0}} \over 4}$