### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2002

Capacitance (in $F$) of a spherical conductor with radius $1$ $m$ is
A
$1.1 \times {10^{ - 10}}$
B
${10^{ - 6}}$
C
$9 \times {10^{ - 9}}$
D
${10^{ - 3}}$

## Explanation

For an isolated sphere, the capacitance is given by

$C = 4\pi \,{ \in _0}\,r$

$= {1 \over {9 \times {{10}^9}}} \times 1$

$= 1.1 \times {10^{ - 10}}F$
2

### AIEEE 2002

If a charge $q$ is placed at the center of the line joining two equal charges $Q$ such that the system is in equilibrium then the value of $q$ is
A
$Q/2$
B
$- Q/2$
C
$Q/4$
D
$- Q/4$

## Explanation

For equilibrium of charge $Q$

$K{{Q \times Q} \over {{{\left( {2x} \right)}^2}}} + K{{Qq} \over {{x^2}}} = 0 \Rightarrow q = - {Q \over 4}$

3

### AIEEE 2002

A charged particle $q$ is placed at the centre $O$ of cube of length $L(ABCDEFGH).$ Another same charge $q$ is placed at a distance $L$ from $O$. Then the electric flux through $ABCD$ is
A
$q/4\,\pi \,{ \in _0}L$
B
zero
C
$q/2\,\pi \,{ \in _0}L$
D
$q/3\,\pi \,{ \in _0}L$

## Explanation

Both the charges are identical and placed symmetrically about $ABCD$. The flux crossing $ABCD$ due to each charge is ${1 \over 6}\left[ {{q \over {{ \in _0}}}} \right]$ but in opposite directions. Therefore the resultant is zero.
4

### AIEEE 2002

If there are $n$ capacitors in parallel connected to $V$ volt source, then the energy stored is equal to
A
$CV$
B
${1 \over 2}nC{V^2}$
C
$C{V^2}$
D
${1 \over {2n}}C{V^2}$

## Explanation

The equivalent capacitance of $n$ identical capacitors of capacitance $C$ is equal to $nC.$ Energy stored in this capacitor

$E = {1 \over 2}\left( {nC} \right){V^2} = {1 \over 2}nC{V^2}$