JEE Main 2024 Question Paper (04-Apr-2024) (Shift 1)

Question 1

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then:

Accepted Answer

The electron will continue to move with uniform velocity along the axis of the solenoid.

Answer

The electron will be accelerated along the axis.

Answer

The electron path will be circular about the axis.

Answer

The electron will experience a force at 45&deg; to the axis and execute a helical path.

Question 2

The electric field in an electromagnetic wave is given by $\overrightarrow{E} = \hat{i} \, 40 \cos \omega \left(t - \frac{z}{c}ight) \, 	ext{N C}^{-1}$. The magnetic field induction of this wave is (in SI unit):

Accepted Answer

$\overrightarrow{B} = \hat{j} \frac{40}{c} \cos \omega \left( t - \frac{z}{c} \right)$

Answer

$\overrightarrow{B} = \hat{i} \frac{40}{c} \cos \omega \left(t - \frac{z}{c}\right)$

Answer

$ \overrightarrow{B} = \hat{j} \, 40 \cos \omega \left(t - \frac{z}{c}\right)$

Answer

$$ \overrightarrow{B} = \hat{k} \frac{40}{c} \cos \omega \left( t - \frac{z}{c} \right) $$

Question 3

Which of the following nuclear fragments corresponding to nuclear fission between neutron $\left({}_{0}^{1}\mathrm{n}\right)$ and uranium isotope $\left({}_{92}^{235}\mathrm{U}\right)$ is correct:

Accepted Answer

$ {}_{56}^{144}\mathrm{Ba} \quad + \quad {}_{36}^{89}\mathrm{Kr} \quad + \quad {}_{0}^{1}\mathrm{n} $

Answer

$ {}_{56}^{140}\mathrm{Xe} \quad + \quad {}_{38}^{94}\mathrm{Sr} \quad + \quad 3\, {}_{0}^{1}\mathrm{n} $

Answer

$ {}_{51}^{153}\mathrm{Sb} \quad + \quad {}_{41}^{99}\mathrm{Nb} \quad + \quad 3\,{}_{0}^{1}\mathrm{n} $

Question 4

In an experiment to measure the focal length ($f$) of a convex lens, the least counts of the measuring scales for the position of the object ($u$) and for the position of the image ($v$) are $\Delta u$ and $\Delta v$, respectively. The error in the measurement of the focal length of the convex lens will be :

Accepted Answer

${f}^{2} \quad \left[ \frac{\Delta u}{u^{2}} \quad + \quad \frac{\Delta v}{v^{2}} \right]$

Answer

$ \frac{\Delta u}{u} \quad + \quad \frac{\Delta v}{v} $

Answer

$2f \quad \left[\frac{\Delta u}{u} \quad + \quad \frac{\Delta v}{v}\right]$

Answer

$ f\left[\frac{\Delta u}{u^{2}} \quad + \quad \frac{\Delta v}{v^{2}}\right]$

Question 5

Given below are two statements : Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $ P_1 - P_2 = \rho g (h_2 - h_1) $ Statement II : In venturi tube shown, $ 2gh = u_1^2 - u_2^2 $In the light of the above statements, choose the most appropriate answer from the options given below.

Accepted Answer

Statement I is correct but Statement II is incorrect.

Answer

Both Statement I and Statement II are correct.

Answer

Statement I is incorrect but Statement II is correct.

Answer

Both Statement I and Statement II are incorrect.