JEE Main 2019 Question Paper (08-Apr-2019) (Shift 2)

Question 1

In the circuit shown, a four-wire potentiometer is made of a $400\mathrm{cm}$ long wire, which extends between $\mathrm{A}$ and $\mathrm{B}$. The resistance per unit length of the potentiometer wire is $r = 0.01\Omega/\mathrm{cm}$. If an ideal voltmeter is connected as shown with jockey $\mathrm{J}$ at $50\mathrm{cm}$ from end $\mathrm{A}$, the expected reading of the voltmeter will be:

Accepted Answer

$0.25 \mathrm{V}$

Answer

$0.50 \mathrm{V}$

Answer

$0.75 \mathrm{V}$

Answer

$0.20 \mathrm{V}$

Question 2

Two very long, straight, and insulated wires are kept at $90^\circ$ angle from each other in the $xy$ plane as shown in the figure. These wires carry currents of equal magnitude $I$, whose directions are shown in the figure. The net magnetic field at point $P$ will be:

Accepted Answer

Zero

Answer

$-\frac{\mu_0 I}{2 \pi d} \left( \widehat{\mathrm{x}} + \widehat{\mathrm{y}} \right)$

Answer

$ \frac{+\mu_{0} I}{\pi d} \left( \widehat{\mathrm{z}} \right) \, $

Answer

$\frac{\mu_0 I}{2 \pi d} \left( \widehat{x} + \widehat{y} \right)$

Question 3

A positive point charge is released from rest at a distance $r_0$ from a positive line charge with uniform charge density. The speed $\left(v\right)$ of the point charge, as a function of instantaneous distance $r$ from the line charge, is proportional to

Accepted Answer

$ \mathrm{v} \propto \sqrt{\ln\left(\frac{\mathrm{r}}{\mathrm{r}_0}\right)} $

Answer

$ \mathrm{v} \propto \left(\frac{\mathrm{r}}{\mathrm{r}_0}\right)$

Answer

$ \mathrm{v} \propto \ln\left(\frac{\mathrm{r}}{\mathrm{r}_0}\right)$

Answer

$ \mathrm{v} \propto e^{\frac{+r}{r_0}} $

Question 4

The ratio of mass densities of nuclei of $^{40}\mathrm{Ca}$ and $^{16}\mathrm{O}$ is close to:

Accepted Answer

$1$

Answer

$0.1$

Answer

$2$

Answer

$5$

Question 5

A damped harmonic oscillator has a frequency of $5$ oscillations per second. The amplitude drops to half its value for every $10$ oscillations. The time it will take to drop to $\frac{1}{1000}$ of the original amplitude is close to:

Accepted Answer

$20 \mathrm{s}$

Answer

$50 \mathrm{s}$

Answer

$100 \mathrm{s}$

Answer

$10 \mathrm{s}$