JEE Main 2022 Question Paper (29-Jul-2022) (Shift 1)

Question 1

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension $ S $. If the density of the liquid is $ \rho $ and the radius of the drop is $ r $, then $ T = K \sqrt{\frac{\rho r^{3}}{S^{\frac{3}{2}}}} $ is dimensionally correct, where $ K $ is dimensionless. Reason (R) : Using dimensional analysis, we get the R.H.S. having different dimension than that of the time period. In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

(A) is false but (R) is true

Answer

Both (A) and (R) are true and (R) is the correct explanation of (A).

Answer

Both (A) and (R) are true but (R) is not the correct explanation of (A)

Answer

(A) is true but (R) is false

Question 2

A ball is thrown up vertically with a certain velocity so that it reaches a maximum height $ h $. Find the ratio of the times in which it is at height $ \frac{h}{3} $ while going up and coming down respectively.

Accepted Answer

$\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$

Answer

$\frac{\sqrt{2} - 1}{\sqrt{2} + 1}$

Answer

$\frac{\sqrt{3} - 1}{\sqrt{3} + 1}$

Answer

$\frac{1}{3}$

Question 3

If $ t = \sqrt{x} + 4 $, then $\left(\frac{\mathrm{d}x}{\mathrm{d}t}\right)_{t=4}$ is:

Accepted Answer

Zero

Answer

$4$

Answer

$8$

Answer

$16$

Question 4

A smooth circular groove has a smooth vertical wall as shown in the figure. A block of mass $ m $ moves against the wall with a speed $ v $. Which of the following curves represents the correct relation between the normal reaction on the block by the wall $ \left(N\right) $ and the speed of the block $ \left(v\right) $?

Accepted Answer

""

Answer

Given the function $ f(x) = \frac{1}{x} $, we want to find the values of $ x $ for which $ f(x) > 0 $ and $ f(x) 0 $: $ \frac{1}{x} > 0 $ This inequality holds when $ x > 0 $. 2. For \( f(x) 0 \quad \text{for} \quad x > 0, $ and $ f(x)

Answer

Answer

Question 5

A ball is projected with kinetic energy $ E $, at an angle of $ 60^\circ $ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :

Accepted Answer

$\frac{E}{4}$

Answer

Zero

Answer

$ \frac{E}{2} $

Answer

$E$