JEE Mains Previous Years Questions with Solutions

4.5
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1

AIEEE 2004

Time taken by a $836$ $W$ heater to heat one litre of water from $10{}^ \circ C$ to $40{}^ \circ C$ is
A
$150$ $s$
B
$100$ $s$
C
$50$ $s$
D
$200$ $s$

Explanation

$\Delta Q = mC \times \Delta T$

$= 1 \times 4180 \times \left( {40 - 10} \right) = 80 \times 30$

( $\therefore$ $\Delta Q =$ heat supplied in time $t$ for heating $1L$ water from ${10^ \circ }C$ to ${40^ \circ }C$ )

also $\Delta Q = 836 \times t \Rightarrow t = {{4180 \times 30} \over {836}} = 150\,s$
2

AIEEE 2004

The total current supplied to the circuit by the battery is
A
$4A$
B
$2A$
C
$1A$
D
$6A$

Explanation

hence ${{\mathop{\rm R}\nolimits} _{eq}} = 3/2;$

$\therefore$ $I = {6 \over {3/2}} = 4A$
3

AIEEE 2004

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of ${4 \over 3}$ and ${2 \over 3}$, then the ratio of the current passing through the wires will be
A
$8/9$
B
$1/3$
C
$3$
D
$2$

Explanation

${i_1}{R_1} = {i_2}{R_2}\,\,\,\,\,\,\,\,\,\,$ (same potential difference)

V = I1R1 = I1$\times $${{\rho {l_1}} \over {\pi r_1^2}} Also V = I2R2 = I2 \times$${{\rho {l_2}} \over {\pi r_2^2}}$

$\therefore$ I1$\times $${{\rho {l_1}} \over {\pi r_1^2}} = I2 \times$${{\rho {l_2}} \over {\pi r_2^2}}$

$\Rightarrow$ ${{{I_1}} \over {{I_2}}} = {{{\ell _1}} \over {{\ell _2}}} \times {{r_1^2} \over {r_2^2}}$

$= {3 \over 4} \times {4 \over 9} = {1 \over 3}\,\,$
4

AIEEE 2004

The resistance of the series combination of two resistances is $S.$ When they are jointed in parallel the total resistance is $P.$ If $S = nP$ then the Minimum possible value of $n$ is
A
$2$
B
$3$
C
$4$
D
$1$

Explanation

$S = {R_1} + {R_2}$ and $P = {{{R_1}{R_2}} \over {{R_1} + {R_2}}}$

$S = nP \Rightarrow {R_1} + {R_2} = {{n\left( {{R_1}{R_2}} \right)} \over {\left( {{R_1} + {R_2}} \right)}}$

$\Rightarrow {\left( {{R_1} + {R_2}} \right)^2} = n{R_1}{R_2}$

$\Rightarrow n = {{R_1^1 + R_2^2 + {R_1}{R_2}} \over {{R_1}{R_2}}}$

$n = {{{R_1}} \over {{R_2}}} + {{{R_2}} \over {{R_1}}} + 2$

Arithmetic mean $>$ Geometric mean

Minimum value of $n$ is $4$