JEE Main 2021 Question Paper (25-Feb-2021) (Shift 2)

Question 1

Match List I with List II. List I List II (a) Rectifier (ii) Used to convert A.C. voltage into D.C. voltage (b) Stabilizer (iv) Used for constant output voltage even when the input voltage or load current change (c) Transformer (i) Used either for stepping up or stepping down the A.C. voltage (d) Filter (iii) Used to remove any ripple in the rectified output voltage Choose the correct answer from the options given below:

Accepted Answer

$(\mathrm{a}) - (\mathrm{ii}), \quad (\mathrm{b}) - (\mathrm{iv}), \quad (\mathrm{c}) - (\mathrm{i}), \quad (\mathrm{d}) - (\mathrm{iii})$

Answer

$(\mathrm{a}) - (\mathrm{ii}), \quad (\mathrm{b}) - (\mathrm{i}), \quad (\mathrm{c}) - (\mathrm{iv}), \quad (\mathrm{d}) - (\mathrm{iii})$

Answer

$(\mathrm{a}) - (\mathrm{ii}), \quad (\mathrm{b}) - (\mathrm{i}), \quad (\mathrm{c}) - (\mathrm{iii}), \quad (\mathrm{d}) - (\mathrm{iv})$

Answer

$(\mathrm{a}) - (\mathrm{iii}), \quad (\mathrm{b}) - (\mathrm{iv}), \quad (\mathrm{c}) - (\mathrm{i}), \quad (\mathrm{d}) - (\mathrm{ii})$

Question 2

Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed supports (see figure). When the mass is displaced from the equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is:

Accepted Answer

$ \pi \sqrt{\frac{m}{k}} $

Answer

$2\pi \sqrt{\frac{m}{2k}}$

Answer

$ \pi \sqrt{\frac{m}{2k}} $

Answer

$2\pi \sqrt{\frac{m}{k}}$

Question 3

A sphere of radius $ a $ and mass $ m $ rolls along a horizontal plane with constant speed $ v_0 $. It encounters an inclined plane at angle $ \theta $ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

Accepted Answer

$\frac{7 v_0^2}{10 g \sin \theta}$

Answer

$ \frac{2}{5} \frac{v_0^2}{g \sin 	heta} $

Answer

$\frac{v_0^2}{5g \sin \theta}$

Answer

$\frac{v_0^2}{2g \sin \theta}$

Question 4

An $L.C.R.$ circuit contains resistance of $110  \mathrm{\Omega}$ and a supply of $220  \mathrm{V}$ at $300  \mathrm{rad}  \mathrm{s}^{-1}$ angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by $45^\circ$. If, on the other hand, only the inductor is removed, the current leads by $45^\circ$ with the applied voltage. The $R.M.S.$ current flowing in the circuit will be:

Accepted Answer

$2  \mathrm{A}$

Answer

$2.5  \mathrm{A}$

Answer

$1 \mathrm{A}$

Answer

$1.5  \mathrm{A}$

Question 5

The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36  \mathrm{m}$ and covers $30^\circ$ in $0.1  \mathrm{s}$. The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple harmonic motion of $P$. The restoration force per unit mass when $P$ touches $M$ will be :

Accepted Answer

$9.87  \mathrm{N}$

Answer

$0.49 \mathrm{N}$

Answer

$50  \mathrm{N}$

Answer

$100 \mathrm{N}$

	List I		List II
(a)	Rectifier	(ii)	Used to convert A.C. voltage into D.C. voltage
(b)	Stabilizer	(iv)	Used for constant output voltage even when the input voltage or load current change
(c)	Transformer	(i)	Used either for stepping up or stepping down the A.C. voltage
(d)	Filter	(iii)	Used to remove any ripple in the rectified output voltage