JEE Main 2021 26th February Morning Shift Question Paper with Solutions

Given, forward resistance, R₁ = 50 $\Omega$

Reverse resistance, R₂ = infinity

Battery voltage = 6V

According to circuit diagram,

In this case, diode D₁ is forward biased, whereas diode D₂ is reverse biased.

So, D₂ will act as open circuit.

$6 - 50I - 130I - 120I = 0$

$\Rightarrow 6 = 300I$

$\Rightarrow I = {6 \over {300}} = {1 \over {50}}$

$= {2 \over {100}} = 0.02$ A = 20 mA

Hence, current through 120 $\Omega$ = 20 mA

Given, charge passing through circuit, q = 20 C

Potential difference between two plates,

V = 15 V

Let W be the amount of work done by battery.

$\therefore$ W = qV = 20 $\times$ 15 = 300 J

The apparent weight $W_{\text{app}}$ of a person in an elevator moving with acceleration is given by:

$W_{\text{app}} = m(g - a)$

where:

• $W_{\text{app}}$ is the apparent weight,
• $m$ is the mass of the person,
• $g$ is the acceleration due to gravity,
• $a$ is the acceleration of the elevator.

Given that the person's mass is 60 kg, the acceleration due to gravity is 10 m/s², and the acceleration of the lift is 1.8 m/s², we can substitute these values into the formula:

$W_{\text{app}} = 60 \, \text{kg} \times (10 \, \text{m/s}^2 - 1.8 \, \text{m/s}^2) = 60 \, \text{kg} \times 8.2 \, \text{m/s}^2 = 492 \, \text{N}$

So, the apparent weight of the person when the lift descends with a uniform downward acceleration of 1.8 m/s² will be 492 N.

According to Kepler’s second law of planetary motion, areal velocity of every planet moving around the sun should remain constant in elliptical orbit.

Given all resistances have same resistance R.

Now, we can redraw the circuit as below

Let resistances be R₁, R₂, R₃ and R₄.

$\because$ ${{{R_1}} \over {{R_3}}} = {{{R_2}} \over {{R_4}}}$

So, circuit will behave as a Wheatstone bridge and no current will flow through middle resistor.

$\therefore$ ${R_{eq}} = {{({R_1} + {R_2})({R_3} + {R_4})} \over {({R_1} + {R_2}) + ({R_3} + {R_4})}}$

$= {{(R + R)(R + R)} \over {(R + R) + (R + R)}}$

$= R$