### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2004

A plano convex lens of refractive index $1.5$ and radius of curvature $30$ $cm$. Is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of size of the object
A
$60$ $cm$
B
$30$ $cm$
C
$20$ $cm$
D
$80$ $cm$

## Explanation

KEY CONCEPT : The focal length $\left( F \right)$ of the final mirror

is ${1 \over F} = {2 \over {f\ell }} + {1 \over {{f_m}}}$

Here ${1 \over {{f_\ell }}} = \left( {\mu - 1} \right)\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$

$= \left( {1.5 - 1} \right)\left[ {{1 \over \alpha } - {1 \over { - 30}}} \right] = {1 \over {60}}$

$\therefore$ ${1 \over F} = 2 \times {1 \over {60}} + {1 \over {30/2}} = {1 \over {10}}$

$\therefore$ $F=10cm$

The combination acts as a converging mirror. For the object to be of the same size of mirror,

$u = 2F = 20cm$
2

### AIEEE 2003

To get three images of a single object, one should have two plane mirrors at an angle of
A
${60^ \circ }$
B
${90^ \circ }$
C
${120^ \circ }$
D
${30^ \circ }$

## Explanation

When $\theta = {90^ \circ }$ then ${{360} \over \theta } = {{360} \over {90}} = 4$

is an even number. The number of images formed is given by

$n = {{360} \over \theta } - 1 = {{360} \over {90}} - 1 = 4 - 1 = 3$
3

### AIEEE 2003

The image formed by an objective of a compound microscope is
A
virtual and diminished
B
real an diminished
C
real and enlarged
D
virtual and enlarged

## Explanation

A real, inverted and enlarged image of the object is formed by the objective lens of a compound microscope.
4

### AIEEE 2003

To demonstrate the phenomenon of interference, we require two sources which emit radiation
A
of nearly the same frequency
B
of the same frequency
C
of different wavelengths
D
of the same frequency and having a definite phase relationship

## Explanation

For the phenomenon of interference we require two sources of light of same frequency and having a definite phase relationship (a phase relationship that does not change with time)