### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2012

A spectrometer gives the following reading when used to measure the angle of a prism.
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data
A
58.59 degree
B
58.77 degree
C
58.65 degree
D
59 degree

## Explanation

30 vernier scale divisions coincide with 29 main scale divisions.

Therefore 1 V.S.D = ${{29} \over {30}}$ M.S.D

Least count = 1 M.S.D - 1 V.S.D

= 1 M.S.D - ${{29} \over {30}}$ M.S.D

= ${{1} \over {30}}$ M.S.D

= ${{1} \over {30}}$ $\times$ 0.5o

Reading of Vernier = Main Scale Reading + Vernier scale reading $\times$ Least count

Given that,

Vernier scale reading = 09 division

$\therefore$ Reading of Vernier = 58.5o + 9 $\times$ ${{0.5^\circ } \over {30}}$

= 58.65o
2

### AIEEE 2011

A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.
The diameter of wire from the above date is:
A
0.052 cm
B
0.026 cm
C
0.005 cm
D
0.52 cm

## Explanation

Least count of screw gauge

= ${{Pitch} \over {Number\,of\,division\,on\,circular\,scale}}$

= ${1 \over {100}}mm$

= 0.01 mm

Diameter of the wire = M.S.R + C.S.R $\times$ L.C

= 0 + 52 $\times$ 0.01

= 0.52 mm

= 0.052 cm
3

### AIEEE 2009

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and the image distance $v,$ from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of ${45^ \circ }$ with the $x$-axis meets the experimental curve at $P.$ The coordinates of $P$ will be :
A
$\left( {{f \over 2},{f \over 2}} \right)$
B
$\left( {f,f} \right)$
C
$\left( {4f,4f} \right)$
D
$\left( {2f,2f} \right)$

## Explanation

Here $u = - 2f,v = 2f$

As $|u|$ increases, $v$ decreases for $|u| > f.$ The graph between $|v|$ and $|u|$ is shown in the figure. A straight line passing through the origin and making an angle of ${45^ \circ }$ with the $x$-axis meets the experimental curve at $P\left( {2f,2f} \right).$
4

### AIEEE 2009

In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a degree(=$0.5^\circ$), then the least count of the instrument is:
A
one minute
B
half minute
C
one degree
D
half degree

## Explanation

30 vernier scale divisions coincide with 29 main scale divisions.

Therefore 1 V.S.D = ${{29} \over {30}}$ M.S.D

Least count = 1 M.S.D - 1 V.S.D

= 1 M.S.D - ${{29} \over {30}}$ M.S.D

= ${{1} \over {30}}$ M.S.D

= ${{1} \over {30}}$ $\times$ 0.5o

= ${{1} \over {30}}$ $\times$ ${1 \over 2}$o

= ${1 \over {60}}$o

= 1 min