JEE Main 2019 Question Paper (09-Apr-2019) (Shift 1)

Question 1

A capacitor with capacitance $5\,\mu\mathrm{F}$ is charged to $5\,\mu\mathrm{C}$. If the plates are pulled apart to reduce the capacitance to $2\,\mu\mathrm{F}$, how much work is done?

Accepted Answer

$3.75 	imes 10^{-6} \, \mathrm{J}$

Answer

$6.25 	imes 10^{-6} \, \mathrm{J}$

Answer

$2.55 	imes 10^{-6} \, \mathrm{J}$

Answer

$2.16 	imes 10^{-6} \, \mathrm{J}$

Question 2

Taking the wavelength of the first Balmer line in the hydrogen spectrum $ (n=3 \to n=2) $ as $ 660 \, \mathrm{nm} $, the wavelength of the $ 2^{\mathrm{nd}} $ Balmer line $ (n=4 \to n=2) $ will be :

Accepted Answer

$488.9\,\mathrm{nm}$

Answer

$889.2\,\mathrm{nm}$

Answer

$388.9\,\mathrm{nm}$

Answer

$642.7	ext{\hspace{0.17em}nm}$

Question 3

A rigid square loop of side $a$ and carrying current $I_2$ is lying on a horizontal surface near a long current-carrying wire with current $I_1$ in the same plane as shown in the figure. The net force on the loop due to the wire will be:

Accepted Answer

Repulsive and equal to $\frac{\mu_0 I_1 I_2}{4 \pi}$

Answer

Attractive and equal to $\frac{\mu_0 I_1 I_2}{3 \pi}$

Answer

Repulsive and equal to $\frac{\mu_0 I_1 I_2}{2 \pi}$

Answer

Zero

Question 4

A body of mass $2\,\mathrm{kg}$ makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?

Accepted Answer

$1.2\,\mathrm{kg}$

Answer

$1.8\,\mathrm{kg}$

Answer

$1.0\ \mathrm{kg}$

Answer

$1.5\ \mathrm{kg}$

Question 5

A string is clamped at both ends and it is vibrating in its $4^{\mathrm{th}}$ harmonic. The equation of the stationary wave is \[ y = 0.3 \sin(0.157 x) \cos(200 \pi t). \] The length of the string is
(All quantities are in $\mathrm{SI}$ units.)

Accepted Answer

$80  \mathrm{m}$

Answer

$20 \mathrm{m}$

Answer

$60 \mathrm{m}$

Answer

$40 \mathrm{m}$