JEE Main 2022 Question Paper (25-Jul-2022) (Shift 1)

Question 1

If momentum $\left[P\right]$, area $\left[A\right]$ and time $\left[T\right]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is

Accepted Answer

$ \left[ \mathrm{PA}^{-1} \mathrm{T}^{0} \right] $

Answer

$ \left[\mathrm{PAT}^{-1}\right]$

Answer

$ \left[ \mathrm{PA}^{-1} \mathrm{T} \right] $

Answer

$\left[\mathrm{PA}^{-1}\mathrm{T}^{-1}\right]$

Question 2

Which of the following physical quantities have the same dimensions?

Accepted Answer

Electric displacement $\left(\overrightarrow{D}\right)$ and surface charge density

Answer

Displacement current and electric field

Answer

Current density and surface charge density

Answer

Electric potential and energy

Question 3

A person moved from $ A $ to $ B $ on a circular path as shown in the figure. If the distance travelled by him is $ 60  \mathrm{m} $, then the magnitude of displacement would be: (Given $ \cos 135^\circ = -0.7 $)

Accepted Answer

$47 \quad \mathrm{m}$

Answer

$42 \quad \mathrm{m}$

Answer

$19 \quad \mathrm{m}$

Answer

$40 \quad \mathrm{m}$

Question 4

A body of mass $0.5  \mathrm{kg}$ travels on a straight line path with velocity $v = \left(3x^{2} + 4\right)  \mathrm{m}  \mathrm{s}^{-1}$. The net work done by the force during its displacement from $x = 0$ to $x = 2  \mathrm{m}$ is

Accepted Answer

$60 \quad \mathrm{J}$

Answer

$64 \quad \mathrm{J}$

Answer

$120 \quad \mathrm{J}$

Answer

$128 \quad \mathrm{J}$

Question 5

A solid cylinder and a solid sphere, having the same mass $ M $ and radius $ R $, roll down the same inclined plane from the top without slipping. They start from rest. The ratio of the velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be

Accepted Answer

$\sqrt{\frac{14}{15}}$

Answer

$\sqrt{\frac{5}{3}}$

Answer

$\sqrt{\frac{4}{5}}$

Answer

$\sqrt{\frac{3}{5}}$