JEE Main 2023 Question Paper (30-Jan-2023) (Shift 1)

Question 1

The charge flowing in a conductor changes with time as $ Q(t) = \alpha t - \beta t^{2} + \gamma t^{3} $, where $ \alpha,  \beta $ and $ \gamma $ are constants. The minimum value of current is:

Accepted Answer

$ \alpha - \frac{\beta^{2}}{3\gamma} $

Answer

$ \alpha - \frac{3 \beta^{2}}{\gamma} $

Answer

$ \alpha - \frac{\gamma^{2}}{3\beta} $

Answer

$ \beta - \frac{\alpha^{2}}{3\gamma} $

Question 2

The pressure $ \left(P\right) $ and temperature $ \left(T\right) $ relationship of an ideal gas obeys the equation $ P T^{2} = $ constant. The volume expansion coefficient of the gas will be :

Accepted Answer

$\frac{3}{T}$

Answer

$3T^{2}$

Answer

$\frac{3}{{T}^{2}}$

Answer

$\frac{3}{{T}^{3}}$

Question 3

A person has been using spectacles of power $-1.0$ diopter for distant vision and a separate reading glass of power $2.0$ diopters. What is the least distance of distinct vision for this person:

Accepted Answer

$50 \quad \mathrm{cm}$

Answer

$\quad 10 \quad \mathrm{cm}$

Answer

$40 \quad \mathrm{cm}$

Answer

$30 \quad \mathrm{cm}$

Question 4

As per the given figure, a small ball $ P $ slides down the quadrant of a circle and hits the other ball $ Q $ of equal mass which is initially at rest. Neglecting the effect of friction and assuming the collision to be elastic, the velocity of ball $ Q $ after collision will be: $\left( g = 10 \ \mathrm{m} \ \mathrm{s}^{-2} \right)$.

Accepted Answer

$2 \quad \mathrm{m} \quad \mathrm{s}^{-1}$

Answer

$0$

Answer

$0.25 \quad \mathrm{m} \quad \mathrm{s}^{-1}$

Answer

$4 \quad \mathrm{m} \quad \mathrm{s}^{-1}$

Question 5

Choose the correct relationship between Poisson ratio $ \left(\sigma \right) $, bulk modulus $ \left(K\right) $, and modulus of rigidity $ \left(\eta \right) $ of a given solid object:

Accepted Answer

$ \sigma = \frac{3K - 2\eta}{6K + 2\eta} $

Answer

$$ \sigma = \frac{6K + 2\eta}{3K - 2\eta} $$

Answer

$ \sigma = \frac{3K + 2\eta}{6K + 2\eta} $

Answer

$$ \sigma = \frac{6K - 2\eta}{3K - 2\eta} $$