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

Question 1

If $ Z = \frac{A^{2} B^{3}}{C^{4}} $, then the relative error in $ Z $ will be

Accepted Answer

$\left(\frac{2\Delta A}{A} + \frac{3\Delta B}{B} + \frac{4\Delta C}{C}\right)$

Answer

$\left(\frac{\Delta A}{A} + \frac{\Delta B}{B} + \frac{\Delta C}{C}\right)$

Answer

$\left(\frac{2\Delta A}{A} + \frac{3\Delta B}{B} - \frac{4\Delta C}{C}\right)$

Answer

$\left(\frac{\Delta A}{A} + \frac{\Delta B}{B} - \frac{\Delta C}{C}\right)$

Question 2

$ \overrightarrow{A} $ is a vector quantity such that $ \left| \overrightarrow{A} \right| = $ non-zero constant. Which of the following expressions is true for $ \overrightarrow{A} $?

Accepted Answer

$ \overrightarrow{A} 	imes \overrightarrow{A} = 0 $

Answer

$ \overrightarrow{A} \cdot \overrightarrow{A} = 0 $

Answer

$ \overrightarrow{A} 	imes \overrightarrow{A} < 0 $

Answer

$ \overrightarrow{A} 	imes \overrightarrow{A} > 0 $

Question 3

Which of the following relations is true for two unit vectors $ \hat{A} $ and $ \hat{B} $ making an angle $ \theta $ with each other?

Accepted Answer

$ \left|\hat{A} - \hat{B}ight| = \left|\hat{A} + \hat{B}ight| \frac{	an 	heta}{2} $

Answer

$ \left|\hat{A} + \hat{B}ight| = \left|\hat{A} - \hat{B}ight| \frac{	an 	heta}{2} $

Answer

$ \left|\hat{A} + \hat{B}ight| = \left|\hat{A} - \hat{B}ight| \frac{\cos 	heta}{2} $

Answer

$ \left|\hat{A} - \hat{B}ight| = \left|\hat{A} + \hat{B}ight| \frac{\cos 	heta}{2} $

Question 4

If force $\overrightarrow{F} = 3\hat{\mathrm{i}} + 4\hat{\mathrm{j}} - 2\hat{\mathrm{k}}$ acts on a particle having position vector $2\hat{\mathrm{i}} + \hat{\mathrm{j}} + 2\hat{\mathrm{k}}$, then the torque about the origin will be:

Accepted Answer

$-10\hat{\imath} + 10\hat{\jmath} + 5\hat{k}$

Answer

$3\hat{\imath} + 4\hat{\jmath} - 2\hat{k}$

Answer

$10\hat{\imath} + 5\hat{\jmath} - 10\hat{k}$

Answer

$10\hat{\imath} + \hat{\jmath} - 5\hat{k}$

Question 5

The height of any point $ P $ above the surface of the Earth is equal to the diameter of the Earth. The value of acceleration due to gravity at point $ P $ will be: (Given $ g = $ acceleration due to gravity at the surface of the Earth).

Accepted Answer

$\frac{g}{9}$

Answer

$\frac{g}{2}$

Answer

$ \frac{g}{4} $

Answer

$\frac{g}{3}$