JEE Main 2019 Question Paper (08-Apr-2019) (Shift 1)

Question 1

A boy’s catapult is made of rubber cord which is $42 \mathrm{cm}$ long, with $6 \mathrm{mm}$ diameter of cross-section and of negligible mass. The boy keeps a stone weighing $0.02 \mathrm{kg}$ on it and stretches the cord by $20 \mathrm{cm}$ by applying a constant force. When released, the stone flies off with a velocity of $20 \mathrm{m} \mathrm{s}^{-1}$. Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:

Accepted Answer

$10^{6} \, \mathrm{N} \, \mathrm{m}^{-2}$

Answer

$10^{4} \, \mathrm{N} \, \mathrm{m}^{-2}$

Answer

$10^{8} \mathrm{N} \mathrm{m}^{-2}$

Answer

$10^{3} \, \mathrm{N} \, \mathrm{m}^{-2}$

Question 2

A thermally insulated vessel contains $150\,\mathrm{g}$ of water at $0^\circ \mathrm{C}$. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at $0^\circ \mathrm{C}$ itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water $= 2.10 	imes 10^{6}\,\mathrm{J\,kg}^{-1}$ and Latent heat of fusion of water $= 3.36 	imes 10^{5}\,\mathrm{J\,kg}^{-1}$)

Accepted Answer

$20 \mathrm{g}$

Answer

$35 \mathrm{g}$

Answer

$130 \mathrm{g}$

Answer

$150 \mathrm{g}$

Question 3

A $20\, 	ext{H}$ inductor coil is connected to a $10\, \mathrm{\Omega}$ resistance in series as shown in the figure. The time at which the rate of dissipation of energy (Joule's heat) across the resistance is equal to the rate at which magnetic energy is stored in the inductor is:

Accepted Answer

$2 \ln 2$

Answer

$\frac{1}{2} \ln 2$

Answer

$\frac{2}{ln 2}$

Answer

$ \ln 2 $

Question 4

Radiation coming from transitions $ n=2 $ to $ n=1 $ of hydrogen atoms falls on $\mathrm{He}^+$ ions in $ n=1 $ and $ n=2 $ states. The possible transitions of helium ions as they absorb energy from the radiation are:

Accepted Answer

$n=2 	o n=4$

Answer

$ n=2 	o n=3 $

Answer

$n=2 	o n=5$

Answer

$n=1 	o n=4$

Question 5

Four identical particles of mass $ M $ are located at the corners of a square of side $ a $. What should be their speed if each of them revolves under the influence of the others' gravitational field in a circular orbit circumscribing the square?

Accepted Answer

$ \quad 1.16 \sqrt{\frac{GM}{a}}$

Answer

$1.35 \sqrt{\frac{GM}{a}}$

Answer

$\quad 1.21 \sqrt{\frac{GM}{a}}$

Answer

$1.41 \sqrt{\frac{GM}{a}}$