 JEE Mains Previous Years Questions with Solutions

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1

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.
2

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

$\therefore$ $f = - \left( {{1 \over {10}} \times 100} \right)cm = - 10\,cm.$
3

AIEEE 2007

In a Young's double slit experiment the intensity at a point where the path difference is ${\lambda \over 6}$ ( $\lambda$ being the wavelength of light used ) is $I$. If ${I_0}$ denotes the maximum intensity, ${I \over {{I_0}}}$ is equal to
A
${3 \over 4}$
B
${1 \over {\sqrt 2 }}$
C
${{\sqrt 3 } \over 2}$
D
${1 \over 2}$

Explanation

The intensity of light at any point of the screen where the phase difference due to light coming from the two slits is $\phi$ is given by

$I = {I_0}{\cos ^2}\left( {{\phi \over 2}} \right)\,\,$ where ${I_0}$ is the maximum intensity.

NOTE : This formula is applicable when ${I_1} = {I_2}.$

Here $\phi = {\raise0.5ex\hbox{\pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{3}}$

$\therefore$ ${I \over {{I_0}}} = {\cos ^2}{\pi \over 6} = {\left( {{{\sqrt 3 } \over 2}} \right)^2} = {3 \over 4}$
4

AIEEE 2006

The refractive index of a glass is $1.520$ for red light and $1.525$ for blue light. Let ${D_1}$ and ${D_2}$ be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then,
A
${D_1} < {D_2}$
B
${D_1} = {D_2}$
C
${D_1}$ can be less than or greater than ${D_2}$ depending upon the angle of prism
D
${D_1} > {D_2}$

Explanation

For a thin prism, $D = \left( {\mu - 1} \right)A$

Since ${\lambda _b} < {\lambda _r} \Rightarrow {\mu _r} < {\mu _b} \Rightarrow {D_1} < {D_2}$