 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2003

A $220$ volt, $1000$ watt bulb is connected across a $110$ $volt$ mains supply. The power consumed will be
A
$750$ watt
B
$500$ watt
C
$250$ watt
D
$1000$ watt

Explanation

We know that $R = {{V_{rated}^2} \over {{P_{rated}}}} = {{{{\left( {220} \right)}^2}} \over {1000}}$

When this bulb is connected to $110$ volt mains supply we get

$P = {{{V^2}} \over R} = {{{{\left( {110} \right)}^2} \times 1000} \over {{{\left( {220} \right)}^2}}} = {{1000} \over 4} = 250W$
2

AIEEE 2003

A $3$ volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current ${\rm I}$, in the circuit will be A
$1$ $A$
B
$1.5$ $A$
C
$2$ $A$
D
$1/3$ $A$

Explanation ${R_p} = {{3 \times 6} \over {3 + 6}} = {{18} \over 9} = 2\Omega$

$\therefore$ $V = IR$

$\Rightarrow I = {V \over R} = {3 \over 2} = 1.5A$
3

AIEEE 2003

The nagative $Zn$ pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by $0.13g$ in $30$ minutes. If the electrochemical equivalent of $Zn$ and $Cu$ are $32.5$ and $31.5$ respectively, the increase in the mass of the positive $Cu$ pole in this time is
A
$0.180$ $g$
B
$0.141$ $g$
C
$0.126$ $g$
D
$0.242$ $g$

Explanation

According to Faraday's first law of electrolysis $m = z \times q$

For same $q,$ $\,\,\,\,\,\,\,\,\,$ $m \propto Z$

$\therefore$ ${{{m_{Cn}}} \over {{m_{Zn}}}} = {{{Z_{Cu}}} \over {{Z_{Zn}}}}$

$\Rightarrow {m_{Cu}} = {{{Z_{Cu}}} \over {{Z_{Zn}}}} \times {m_{Zn}}$

$= {{31.5} \over {32.5}} \times 0.13 = 0.126\,g$
4

AIEEE 2003

An ammeter reads upto $1$ ampere. Its internal resistance is $0.81$ $ohm$. To increase the range to $10$ $A$ the value of the required shunt is
A
$0.03\,\Omega$
B
$0.3\,\Omega$
C
$0.9\,\Omega$
D
$0.09\,\Omega$

Explanation

${i_g} \times G = \left( {i - {i_g}} \right)S$

$\therefore$ $S = {{{i_g} \times G} \over {i - {i_g}}} = {{1 \times 0.81} \over {10 - 1}} = 0.09\Omega$