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

Question 1

Two guns $A$ and $B$ can fire bullets at speeds $1\,\mathrm{km\,s}^{-1}$ and $2\,\mathrm{km\,s}^{-1}$ respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:

Accepted Answer

$1:16$

Answer

$1:2$

Answer

$1:4$

Answer

$1:8$

Question 2

To mop-clean a floor, a cleaning machine presses a circular mop of radius $R$ vertically down with a total force $F$ and rotates it with a constant angular speed about its axis. If the force $F$ is distributed uniformly over the mop and if the coefficient of friction between the mop and the floor is $\mu$, the torque applied by the machine on the mop is:

Accepted Answer

$2 \quad \mu \, 	ext{FR}/3$

Answer

$ \mu \frac{FR}{3} $

Answer

$ \mu \frac{FR}{6} $

Answer

$ \mu \frac{FR}{2} $

Question 3

A piece of wood of mass $0.03\,\mathrm{kg}$ is dropped from the top of a $100\,\mathrm{m}$ high building. At the same time, a bullet of mass $0.02\,\mathrm{kg}$ is fired vertically upward with a velocity of $100\,\mathrm{m\,s^{-1}}$ from the ground. The bullet gets embedded in the wood. Then, the maximum height to which the combined system reaches above the top of the building before falling below is: $\left(g=10\,\mathrm{m\,s^{-2}}\right)$

Accepted Answer

$40\,\mathrm{m}$

Answer

$20\,\mathrm{m}$

Answer

$10\ \mathrm{m}$

Answer

$30\,\mathrm{m}$

Question 4

A heat source at $ T = 10^{3}  \mathrm{K} $ is connected to another heat reservoir at $ T = 10^{2}  \mathrm{K} $ by a copper slab which is $ 1  \mathrm{m} $ thick. Given that the thermal conductivity of copper is $ 0.1  \mathrm{W}  \mathrm{K}^{-1}  \mathrm{m}^{-1} $, the energy flux through it in the steady-state is:

Accepted Answer

$90\,\mathrm{W} \, \mathrm{m}^{-2}$

Answer

$65\,\mathrm{W\,m}^{-2}$

Answer

$120\,\mathrm{W} \quad \mathrm{m}^{-2}$

Answer

$200\,\mathrm{W} \, \mathrm{m}^{-2}$

Question 5

A magnet of total magnetic moment $10^{-2} \, \hat{\mathrm{i}} \, \mathrm{A} \, \mathrm{m}^2$ is placed in a time-varying magnetic field, $B \hat{\mathrm{i}} \cos \omega t$, where $B = 1$ Tesla and $\omega = 0.125 \, \mathrm{rad} \, \mathrm{s}^{-1}$. The work done for reversing the direction of the magnetic moment at $t = 1$ second is:

Accepted Answer

$0.02 \quad \mathrm{J}$

Answer

$0.007 \quad \mathrm{J}$

Answer

$0.014\,\mathrm{J}$

Answer

$0.01 \quad \mathrm{J}$