JEE Main 2019 Question Paper (10-Apr-2019) (Shift 1)

Question 1

A message signal of frequency $100\quad \mathrm{MHz}$ and peak voltage $100\quad \mathrm{V}$ is used to execute amplitude modulation on a carrier wave of frequency $300\quad \mathrm{GHz}$ and peak voltage $400\quad \mathrm{V}$. The modulation index and difference between the two sideband frequencies are:

Accepted Answer

$0.25; 2 	imes 10^{8} \, \mathrm{Hz}$

Answer

$4.2 	imes 10^{8} \ \mathrm{Hz}$

Answer

$\quad 4.1 	imes 10^{8} \mathrm{\ Hz}$

Answer

$ \quad 0.25; 1 	imes 10^{8} \, \mathrm{Hz} $

Question 2

A current of $5\,\mathrm{A}$ passes through a copper conductor (resistivity $=1.7 	imes 10^{-8}\,\Omega\,\mathrm{m}$) of radius of cross-section $5\,\mathrm{mm}$. Find the mobility of the charges if their drift velocity is $1.1 	imes 10^{-3}\,\mathrm{m\,s}^{-1}$.

Accepted Answer

$1.0\quad \mathrm{m}^{2}\,\mathrm{V}^{-1}\,\mathrm{s}^{-1}$

Answer

$1.5\quad \mathrm{m}^{2}\,\mathrm{V}^{-1}\,\mathrm{s}^{-1}$

Answer

$1.8\quad \mathrm{m}^{2}\,\mathrm{V}^{-1}\,\mathrm{s}^{-1}$

Answer

$1.3\quad \mathrm{m}^{2}\,\mathrm{V}^{-1}\,\mathrm{s}^{-1}$

Question 3

$n$ moles of an ideal gas with constant volume heat capacity $C_{v}$ undergo an isobaric expansion by a certain volume. The ratio of the work done in the process to the heat supplied is:

Accepted Answer

$\frac{nR}{C_v + nR}$

Answer

$ \frac{4 n R}{C_{v} + n R} $

Answer

$ \frac{4 n R}{C_v - n R} $

Answer

$ \frac{nR}{C_v - nR} $

Question 4

A particle of mass $m$ is moving along a trajectory given by $ x = x_0 + a \cos \omega_1 t $ $ y = y_0 + b \sin \omega_2 t $ The torque, acting on the particle about the origin, at $t = 0$ is:

Accepted Answer

$+\mathrm{m} y_{0} \mathrm{a} \omega_{1}^{2} \widehat{\mathrm{k}}$

Answer

$ -m\left(x_{0} b \omega_{2}^{2} - y_{0} a \omega_{1}^{2}\right) \widehat{\mathbf{k}} $

Answer

Zero

Answer

$ m\left(-x_{0}b + y_{0}a\right) \omega_{1}^{2} \widehat{k} $

Question 5

In the given circuit, an ideal voltmeter connected across the $10\ \mathrm{\Omega}$ resistance reads $2\ \mathrm{V}$. The internal resistance $r$ of each cell is:

Accepted Answer

$0.5\ \Omega$

Answer

$0 \quad \mathrm{\Omega}$

Answer

$1.5 \quad \Omega$

Answer

$1 \quad \mathrm{\Omega}$