### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2006

Which of the following units denotes the dimension ${{M{L^2}} \over {{Q^2}}}$, where $Q$ denotes the electric charge?
A
$Wb/{m^2}$
B
Henry $(H)$
C
$H/{m^2}$
D
Weber $(Wb)$

## Explanation

Mutual inductance $= {\phi \over I} = {{BA} \over I}$

[Henry] $= {{\left[ {M{T^{ - 1}}{Q^{ - 1}}{L^2}} \right]} \over {\left[ {Q{T^{ - 1}}} \right]}} = M{L^2}{Q^{ - 2}}$
2

### AIEEE 2005

One conducting $U$ tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field $B$ is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed $v,$ then the $emf$ induced in the circuit in terms of $B,l$ and $v$ where $l$ is the width of each tube, will be
A
$-Blv$
B
$blv$
C
$2$ $Blv$
D
zero

## Explanation

Relative velocity $= v + v = 2v$

$\therefore$ $emf.$ $= B.l\left( {2v} \right)$
3

### AIEEE 2005

The phase difference between the alternating current and $emf$ is ${\pi \over 2}.$ Which of the following cannot be the constituent of the circuit?
A
$R,L$
B
$C$ alone
C
$L$ alone
D
$L, C$

## Explanation

The difference for $R$-$L$ circuit lies between $\left( {0,{\pi \over 2}} \right)$
4

### AIEEE 2005

A circuit has a resistance of $12$ $ohm$ and an impedance of $15$ $ohm$. The power factor of the circuit will be
A
$0.4$
B
$0.8$
C
$0.125$
D
$1.25$

## Explanation

Power factor $= \cos \phi = {R \over Z} = {{12} \over {15}} = {4 \over 5} = 0.8$