JEE Main 2022 Question Paper (27-Jun-2022) (Shift 1)

Question 1

A projectile is launched at an angle $ \alpha $ with the horizontal with a velocity $ 20 \ \mathrm{m} \ \mathrm{s}^{-1} $. After $ 10 \ \mathrm{s} $, its inclination with the horizontal is $ \beta $. The value of $ \tan \beta $ will be: $\left( g = 10 \ \mathrm{m} \ \mathrm{s}^{-2} \right)$.

Accepted Answer

$ 	an \alpha - 5 \sec \alpha $

Answer

$ 	an \alpha + 5 \sec \alpha $

Answer

$2 	an \alpha - 5 \sec \alpha$

Answer

$2 	an \alpha + 5 \sec \alpha$

Question 2

A girl standing on the road holds her umbrella at $45^\circ$ with the vertical to keep the rain away. If she starts running without the umbrella with a speed of $15\sqrt{2} \ \mathrm{km} \ \mathrm{h}^{-1}$, the raindrops hit her head vertically. The speed of the raindrops with respect to the moving girl is

Accepted Answer

$ \frac{30}{\sqrt{2}} \quad \mathrm{km} \quad \mathrm{h}^{-1} $

Answer

$30 \quad \mathrm{km} \quad \mathrm{h}^{-1}$

Answer

$\frac{25}{\sqrt{2}} \quad \mathrm{km} \quad \mathrm{h}^{-1}$

Answer

$25\quad \mathrm{km} \quad \mathrm{h}^{-1}$

Question 3

A silver wire has a mass $ (0.6 \pm 0.006) \, \mathrm{g} $, radius $ (0.5 \pm 0.005) \, \mathrm{mm} $, and length $ (4 \pm 0.04) \, \mathrm{cm} $. The maximum percentage error in the measurement of its density will be

Accepted Answer

$4\%$

Answer

$7\%$

Answer

$3\%$

Answer

$6\%$

Question 4

A system of two blocks of masses $ m = 2 \ \mathrm{kg} $ and $ M = 8 \ \mathrm{kg} $ is placed on a smooth table as shown in the figure. The coefficient of static friction between the two blocks is $ 0.5 $. The maximum horizontal force $ F $ that can be applied to the block of mass $ M $ so that the blocks move together will be (taking $ g = 9.8 \ \mathrm{m} \ \mathrm{s}^{-2} $):

Accepted Answer

$49 \quad \mathrm{N}$

Answer

$9.8 \quad \mathrm{N}$

Answer

$39.2 \quad \mathrm{N}$

Answer

$78.4 \quad \mathrm{N}$

Question 5

Two blocks of masses $10 \ \mathrm{kg}$ and $30 \ \mathrm{kg}$ are placed on the same straight line with coordinates $\left(0,0\right) \mathrm{cm}$ and $\left(x,0\right) \mathrm{cm}$ respectively. The block of $10 \ \mathrm{kg}$ is moved on the same line through a distance of $6 \ \mathrm{cm}$ towards the other block. The distance through which the block of $30 \ \mathrm{kg}$ must be moved to keep the position of centre of mass of the system unchanged is

Accepted Answer

$2 \quad \mathrm{cm}$ towards the $10 \quad \mathrm{kg}$ block

Answer

$4 \quad \mathrm{cm}$ towards the $10 \quad \mathrm{kg}$ block

Answer

$2 \quad \mathrm{cm}$ away from the $10 \quad \mathrm{kg}$ block

Answer

$4 \quad \mathrm{cm}$ away from the $10 \quad \mathrm{kg}$ block