1
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 9th April Morning Slot

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P1 , P2 and P3 respectively, then :

A
P1 > P2 > P3
B
P1 > P3 > P2
C
P2 > P1 > P3
D
P3 > P2 > P1
2
MCQ (Single Correct Answer)

JEE Main 2018 (Offline)

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k$$\Omega $$. How much was the resistance on the left slot before interchanging the resistances?
A
910 $$\Omega $$
B
990 $$\Omega $$
C
505 $$\Omega $$
D
550 $$\Omega $$

Explanation



$${X \over l}$$ = $${{1000 - X} \over {100 - l}}$$ . . . . . (1)

When X and Y are interchanged.



$${{1000 - X} \over {l - 10}}$$ = $${X \over {100 - l + 10}}$$

$$ \Rightarrow $$$$\,\,\,$$ $${{1000 - X} \over {l - 10}}$$ = $${X \over {110 - l}}$$ . . . . . (2)

From (1) and (2) we get,

$${l \over {100 - l}}$$ = $${{110 - l} \over {l - 10}}$$

$$ \Rightarrow $$$$\,\,\,$$ $$l$$2 $$-$$ 10 = 11000 $$-$$ 100$$l$$ $$-$$ 110$$l$$ + $$l$$2

$$ \Rightarrow $$$$\,\,\,$$ 200$$l$$ = 11000

$$l$$ = 55 cm

Putting this value of $$l$$, in equation (1)

$${X \over {55}}$$ = $${{1000 - X} \over {100 - 55}}$$

$$ \Rightarrow $$$$\,\,\,$$ 45X = 55000 $$-$$ 55X

$$ \Rightarrow $$$$\,\,\,$$ 100X = 55000

$$ \Rightarrow $$$$\,\,\,$$ X = 550 $$\Omega $$
3
MCQ (Single Correct Answer)

JEE Main 2018 (Offline)

Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 $$\Omega $$. The internal resistances of the two batteries are 1 $$\Omega $$ and 2 $$\Omega $$ respectively. The voltage across the load lies between :
A
11.7 V and 11.8 V
B
11.6 V and 11.7 V
C
11.5 V and 11.6 V
D
11.4 V and 11.5 V

Explanation



Let potential at S, T, R = V and potential at P, Q, U, = 0

Using kirchhoff's law at P :

Current at P is ,

$${{V - 12} \over 1} + {{V - 13} \over 2} + {{V - 0} \over {10}} = 0$$

$$ \Rightarrow $$$$\,\,\,$$ $${V \over 1}$$ + $${V \over 2}$$ + $${V \over 10}$$ = 12 + $${{13} \over 2}$$

$$ \Rightarrow $$$$\,\,\,$$ $${{10V + 5V + V} \over {10}}$$ = $${{37} \over 2}$$

$$ \Rightarrow $$$$\,\,\,$$ $${{16V} \over {10}}$$ = $${{37} \over 2}$$

$$ \Rightarrow $$$$\,\,\,$$ V = 11.56 Volt.
4
MCQ (Single Correct Answer)

JEE Main 2018 (Online) 15th April Morning Slot


In a meter bridge, as shown in the figure, it is given that resistance $$Y = 12.5\,\,\Omega $$ and that the balance is obtained at a distance $$39.5$$ $$cm$$ from end $$A$$ (by Jockey J). After interchanging the resistances $$X$$ and $$Y$$, a new balance point is found at a distance $${l_2}$$ from end $$A.$$ What are the value of $$X$$ and $${l_2}$$ ?
A
$$8.16\,\,\Omega $$ and $$60.5$$ $$cm$$
B
$$19.15\,\,\Omega $$ and $$39.5$$ $$cm$$
C
$$8.16\,\,\Omega $$ and $$39.5$$ $$cm$$
D
$$19.15\,\,\Omega $$ and $$60.5$$ $$cm$$

Explanation

For balanced meter bridge,

$${X \over {39.5}}$$ = $${Y \over {\left( {100 - 39.5} \right)}}$$

$$ \Rightarrow $$$$\,\,\,\,$$ X = $${{12.5 \times 39.5} \over {60.5}}$$

= 8.16 $$\Omega $$

Now, when we interchange X and Y then

$${Y \over {{l_2}}} = {X \over {100 - {l_2}}}$$

$$ \Rightarrow $$ $${{12.5} \over {{l_2}}} = {{8.16} \over {100 - {l_2}}}$$

$$ \Rightarrow $$20.66 $${{l_2}}$$ = 1250

$$ \Rightarrow $$ $${{l_2}}$$ = 60.5 $$\Omega $$

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