JEE Main 2021 Question Paper (26-Feb-2021) (Shift 1)

Question 1

Four identical solid spheres each of mass $ m $ and radius $ a $ are placed with their centres on the four corners of a square of side $ b $. The moment of inertia of the system about one side of the square, where the axis of rotation is parallel to the plane of the square, is:

Accepted Answer

$\frac{8}{5} m a^{2} + 2 m b^{2}$

Answer

$\frac{8}{5} m a^{2} + m b^{2}$

Answer

$\frac{4}{5} m a^{2} + 2 m b^{2}$

Answer

$ \frac{4}{5} m a^{2} $

Question 2

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : An electron microscope can achieve better resolving power than an optical microscope. Reason R : The de Broglie wavelength of the electrons emitted from an electron gun is much less than the wavelength of visible light. In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

Both $ A $ and $ R $ are true and $ R $ is the correct explanation of $ A $.

Answer

A is false but R is true.

Answer

Both A and R are true but R is NOT the correct explanation of A

Answer

A is true but R is false.

Question 3

LED is constructed from $Ga-As-P$ semiconducting material. The energy gap of this LED is $1.9  \mathrm{eV}$. Calculate the wavelength of light emitted and its colour. Given, $h = 6.63 	imes 10^{-34}  \mathrm{J \cdot s}$ and $c = 3 	imes 10^{8}  \mathrm{m \cdot s^{-1}}$.

Accepted Answer

$654  \mathrm{nm}$ and red colour

Answer

$654  \mathrm{nm}$ and orange colour

Answer

$1046  \mathrm{nm}$ and red colour

Answer

$1046  \mathrm{nm}$ and blue colour

Question 4

A planet revolving in an elliptical orbit has: A. a constant velocity of revolution. B. has the least velocity when it is nearest to the sun. C. its areal velocity is directly proportional to its velocity. D. areal velocity is inversely proportional to its velocity. E. to follow a trajectory such that the areal velocity is constant. Choose the correct answer from the options given below:

Accepted Answer

E only

Answer

A only

Answer

C only

Answer

D only

Question 5

If $\lambda_{1}$ and $\lambda_{2}$ are the wavelengths of the third member of the Lyman and the first member of the Paschen series respectively, then the value of $\lambda_{1} : \lambda_{2}$ is :

Accepted Answer

$7:135$

Answer

$1:9$

Answer

$1:3$

Answer

$7:108$