JEE Main 2019 Question Paper (09-Apr-2019) (Shift 2)

Question 1

Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of $20 \mathrm{m} \, \mathrm{s}^{-1}$ with respect to the ground. If an observer in car A detects a frequency of $2000 \mathrm{Hz}$ of the sound coming from car B, what is the natural frequency of the sound source in car B?
(speed of sound in air $= 340 \mathrm{m} \, \mathrm{s}^{-1}$)

Accepted Answer

$2250  \mathrm{Hz}$

Answer

$2150  \mathrm{Hz}$

Answer

$2300  \mathrm{Hz}$

Answer

$2060  \mathrm{Hz}$

Question 2

A particle of mass $m$ is moving with speed $2v$ and collides with a mass $2m$ moving with speed $v$ in the same direction. After the collision, the first mass is stopped completely while the second one splits into two particles each of mass $m$, which move at an angle $45^{\circ}$ with respect to the original direction. The speed of each of the moving particles will be

Accepted Answer

$2\sqrt{2}	ext{v}$

Answer

$ \sqrt{2} \, 	ext{v} $

Answer

$ \frac{v}{\sqrt{2}} $

Answer

$\frac{v}{2\sqrt{2}}$

Question 3

A convex lens of focal length $20\ \mathrm{cm}$ produces images of the same magnification 2 when an object is kept at two distances $x_1$ and $x_2$ ($x_1 > x_2$) from the lens. The ratio of $x_1$ and $x_2$ is:

Accepted Answer

$3:1$

Answer

$2:1$

Answer

$5:3$

Answer

$4:3$

Question 4

The parallel combination of two air-filled parallel plate capacitors of capacitance $C$ and $nC$ is connected to a battery of voltage $V$. When the capacitors are fully charged, the battery is removed, and after that, a dielectric material of dielectric constant $K$ is placed between the two plates of the first capacitor. The new potential difference of the combined system is:

Accepted Answer

$ \frac{(n+1)V}{K+n} $

Answer

$\frac{nV}{K+n}$

Answer

$ \frac{V}{K + n} $

Answer

$V$

Question 5

Two materials having coefficients of thermal conductivity $3K$ and $K$ and thickness $d$ and $3d$ respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are ${\theta}_{2}$ and ${\theta}_{1}$ respectively, $\left({\theta}_{2} > {\theta}_{1}\right)$. The temperature at the interface is

Accepted Answer

$\frac{\theta_1}{10} + \frac{9\theta_2}{10}$

Answer

$ \frac{\theta_{2} + \theta_{1}}{2} $

Answer

$ \frac{\theta_1}{6} + \frac{5 \theta_2}{6} $

Answer

$\frac{\theta_1}{3} + \frac{2\theta_2}{3}$