JEE Main 2019 Question Paper (10-Apr-2019) (Shift 2)

Question 1

In the formula $ \mathrm{X} = 5 \mathrm{Y} \mathrm{Z}^2 $, $ \mathrm{X} $ and $ \mathrm{Z} $ have dimensions of capacitance and magnetic field, respectively. What are the dimensions of $ \mathrm{Y} $ in SI units?

Accepted Answer

$\left[\mathrm{M}^{-3} \, \mathrm{L}^{-2} \, \mathrm{T}^{8} \, \mathrm{A}^{4}\right]$

Answer

$\left[\mathrm{M}^{-1} \mathrm{L}^{-2} \mathrm{T}^{4} \mathrm{A}^{2}\right]$

Answer

$\left[\mathrm{M}^{-2} \quad \mathrm{L}^{0} \quad \mathrm{T}^{-4} \quad \mathrm{A}^{-2}\right]$

Answer

$\left[\mathrm{M}^{-2} \, \mathrm{L}^{-2} \, \mathrm{T}^{6} \, \mathrm{A}^{3}\right]$

Question 2

Two blocks $\mathrm{A}$ and $\mathrm{B}$ of masses $m_{\mathrm{A}} = 1\,\mathrm{kg}$ and $m_{\mathrm{B}} = 3\,\mathrm{kg}$ are kept on the table as shown in the figure. The coefficient of friction between $\mathrm{A}$ and $\mathrm{B}$ is $0.2$ and between $\mathrm{B}$ and the surface of the table is also $0.2$. The maximum force $F$ that can be applied on $\mathrm{B}$ horizontally, so that the block $\mathrm{A}$ does not slide over the block $\mathrm{B}$ is: [Take $g = 10\,\mathrm{m/s}^2$]

Accepted Answer

$16\,\mathrm{N}$

Answer

$12\,\mathrm{N}$

Answer

$40\,\mathrm{N}$

Answer

$8\,\mathrm{N}$

Question 3

A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius $2R$. The second part is converted into a uniform solid sphere. Let $I_1$ be the moment of inertia of the disc about its axis and $I_2$ be the moment of inertia of the new sphere about its axis. The ratio $\frac{I_1}{I_2}$ is given by:

Accepted Answer

$140$

Answer

$185$

Answer

$65$

Answer

$285$

Question 4

One mole of an ideal gas passes through a process where pressure and volume obey the relation $ \mathrm{P} = {\mathrm{P}}_{\mathrm{o}} \left[ 1 - \frac{1}{2} \left( \frac{{\mathrm{V}}_{\mathrm{o}}}{\mathrm{V}} \right)^2 \right]. $ Here, ${\mathrm{P}}_{\mathrm{o}}$ and ${\mathrm{V}}_{\mathrm{o}}$ are constants. Calculate the change in the temperature of the gas if its volume changes from ${\mathrm{V}}_{\mathrm{o}}$ to $2{\mathrm{V}}_{\mathrm{o}}$.

Accepted Answer

$\frac{5}{4} \frac{P_0 V_0}{R}$

Answer

$\frac{1}{4} \frac{P_0 V_0}{R}$

Answer

$\frac{1}{2} \frac{P_0 V_0}{R}$

Answer

$\frac{3}{4} \frac{P_0 V_0}{R}$

Question 5

A square loop is carrying a steady current $ I $ and the magnitude of its magnetic dipole moment is $ m $. If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of the circular loop will be:

Accepted Answer

$\frac{4\mathrm{m}}{\pi}$

Answer

$\frac{3\mathrm{m}}{\pi}$

Answer

$\frac{2\mathrm{m}}{\pi}$

Answer

$\frac{m}{\pi}$