JEE Main 2023 Question Paper (29-Jan-2023) (Shift 2)

Question 1

Substance $A$ has atomic mass number $16$ and half-life of $1$ day. Another substance $B$ has atomic mass number $32$ and half-life of $\frac{1}{2}$ day. If both $A$ and $B$ simultaneously start undergoing radioactivity at the same time with initial mass $320  \mathrm{g}$ each, how many total atoms of $A$ and $B$ combined would be left after $2$ days?

Accepted Answer

$3.38 	imes 10^{24}$

Answer

$6.76 	imes 10^{24}$

Answer

$\quad 6.76 	imes 10^{23}$

Answer

$1.69 	imes 10^{24}$

Question 2

At $300 \quad K$, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha + 5}{\alpha}}$ times that of its average speed in the gas. Then, the value of $\alpha$ will be (use $\mathrm{\pi} = \frac{22}{7}$)

Accepted Answer

$28$

Answer

$32$

Answer

$24$

Answer

$27$

Question 3

The ratio of de-Broglie wavelength of an $\alpha$-particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{m}}$, the value of $m$ is:

Accepted Answer

$8$

Answer

$4$

Answer

$16$

Answer

$2$

Question 4

For the given logic gates combination, the correct truth table will be

Accepted Answer

A B X 0 0 0 0 1 1 1 0 1 1 1 0

Answer

ABX001010100110

Answer

ABX001010101110

Answer

A B X 0 0 0 0 1 1 1 0 1 1 1 1

Question 5

The time taken by an object to slide down a $45^\circ$ rough inclined plane is $n$ times the time it takes to slide down a perfectly smooth $45^\circ$ inclined plane. The coefficient of kinetic friction between the object and the inclined plane is:

Accepted Answer

$1 - \frac{1}{n^{2}}$

Answer

$\sqrt{\frac{1}{1 - n^{2}}}$

Answer

$ \sqrt{1 - \frac{1}{n^{2}}} $

Answer

$1 + \frac{1}{n^{2}}$