JEE Main 2021 Question Paper (24-Feb-2021) (Shift 1)

Question 1

Consider two satellites $S_{1}$ and $S_{2}$ with periods of revolution $1\,\mathrm{hr}$ and $8\,\mathrm{hr}$ respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite $S_{1}$ to the angular velocity of satellite $S_{2}$ is:

Accepted Answer

$8:1$

Answer

$2:1$

Answer

$1:4$

Answer

$1:8$

Question 2

Moment of inertia $\left(\mathrm{M}.\mathrm{I}.ight)$ of four bodies, having the same mass and radius, are reported as: $ I_{1} = 	ext{M.I. of thin circular ring about its diameter}, $ $ I_{2} = 	ext{M.I. of circular disc about an axis perpendicular to the disc and going through the centre}, $ $ I_{3} = 	ext{M.I. of solid cylinder about its axis}, $ $ I_{4} = 	ext{M.I. of solid sphere about its diameter}. $ Then:

Accepted Answer

${I}_{1} = {I}_{2} = {I}_{3} > {I}_{4}$

Answer

${I}_{1} + {I}_{2} = {I}_{3} + \frac{5}{2} {I}_{4}$.

Answer

${I}_{1} + {I}_{3} < {I}_{2} + {I}_{4}$

Answer

${I}_{1} = {I}_{2} = {I}_{3} < {I}_{4}$

Question 3

A cube of side $a$ has point charges $+\mathrm{Q}$ located at each of its vertices except at the origin where the charge is $-\mathrm{Q}$. The electric field at the centre of the cube is:

Accepted Answer

$ \frac{-2Q}{3\sqrt{3}\pi \epsilon_0 a^2} \left( \hat{x} + \hat{y} + \hat{z} \right) $

Answer

$ \frac{-Q}{3\sqrt{3}\pi \epsilon_0 a^2} \left( \hat{x} + \hat{y} + \hat{z} \right) $

Answer

$ \frac{Q}{3\sqrt{3}\pi \epsilon_0 a^2} \left( \hat{x} + \hat{y} + \hat{z} \right) $

Answer

$ \frac{2Q}{3\sqrt{3}\pi \epsilon_0 a^2} \left( \hat{x} + \hat{y} + \hat{z} \right) $

Question 4

If the velocity-time graph has the shape $\mathrm{AMB}$, what would be the shape of the corresponding acceleration-time graph?

Accepted Answer

""

Answer

Answer

Answer

Question 5

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

Accepted Answer

$1:4$

Answer

$1:2$

Answer

$4:1$

Answer

$2:1$