 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2006

The resistance of bulb filmanet is $100\Omega$ at a temperature of ${100^ \circ }C.$ If its temperature coefficient of resistance be $0.005$ per $^ \circ C$, its resistance will become $200\,\Omega$ at a temperature of
A
${300^ \circ }C$
B
${400^ \circ }C$
C
${500^ \circ }C$
D
${200^ \circ }C$

Explanation

$R{}_1 = {R_0}\left[ {1 + \alpha \times 100} \right] = 100\,\,\,\,\,\,\,\,\,\,\,...\left( 1 \right)$

${R_2} = {R_0}\left[ {1 + \alpha \times T} \right] = 200\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( 2 \right)$

On dividing we get

${{200} \over {100}} = {{1 + \alpha T} \over {1 + 100\alpha }}$

$\Rightarrow 2 = {{1 + 0.005T} \over {1 + 100 \times 0.005}}$

$\Rightarrow T = {400^ \circ }C$

NOTE : We may use this expression as an approximation because the difference in the answers is appreciable. For accurate results one should use $R = {R_0}{e^{\alpha \Delta T}}$
2

AIEEE 2006

In a Wheatstone's bridge, three resistance $P, Q$ and $R$ connected in the three arms and the fourth arm is formed by two resistances ${S_1}$ and ${S_2}$ connected in parallel. The condition for the bridge to be balanced will be
A
${P \over Q} = {{2R} \over {{S_1} + {S_2}}}$
B
${P \over Q} = {{R\left( {{S_1} + {S_2}} \right)} \over {{S_1}{S_2}}}$
C
${P \over Q} = {{R\left( {{S_1} + {S_2}} \right)} \over {2{S_1}{S_2}}}$
D
${P \over Q} = {R \over {{S_1} + {S_2}}}$

Explanation

${P \over Q} = {R \over S}$ where $S = {{{S_1}{S_2}} \over {{S_1} + {S_2}}}$
3

AIEEE 2006

An electric bulb is rated $220$ volt - $100$ watt. The power consumed by it when operated on $110$ volt will be
A
$75$ watt
B
$40$ watt
C
$25$ Watt
D
$50$ Watt

Explanation

The resistance of the bulb is $R = {{{V^2}} \over P} = {{{{\left( {220} \right)}^2}} \over {100}}$

The power consumed when operated at $110$ $V$ is

$P = {{{{\left( {110} \right)}^2}} \over {{{\left( {220} \right)}^2}/100}} = {{100} \over 4} = 25\,W$
4

AIEEE 2006

A thermocouple is made from two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is kept cold, then, an electric current will
A
flow from Antimony to Bismuth at the hot junction
B
flow from Bismuth to Antimony at the cold junction
C
now flow through the thermocouple
D
flow from Antimony to Bismuth at the cold junction

Explanation

At cold junction, current flows from Antimony to Bismuth (because current flows from metal occurring later in the series to metal occurring earlier in the thermoelectric series).