JEE Main 2024 Physics Paper: 4 Apr, Shift 1

An alternating current at any instant is given by $i = [6 + \sqrt{56} \sin(100\pi t + \pi/3)]$ A. The rms value of the current is ______ A.

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to:

A. pure inductor.

B. pure capacitor.

C. pure resistor.

D. combination of an inductor and capacitor.

Choose the correct answer from the options given below:

A hydrogen atom changes its state from $n = 3$ to $n = 2$. Due to recoil, the percentage change in the wavelength of emitted light is approximately $1 \times 10^{-n}$. The value of $n$ is _______. [Given Rhc $= 13.6\text{ eV},\ hc = 1242\text{ eV nm},\ h = 6.6 \times 10^{-34}\text{ J s}$ mass of the hydrogen atom $= 1.6 \times 10^{-27}\text{ kg}$]

Twelve wires each having resistance $2\ \Omega$ are joined to form a cube. A battery of $6\text{ V}$ emf is joined across point $a$ and $c$. The voltage difference between $e$ and $f$ is ________ V.

To measure the internal resistance of a battery, potentiometer is used. For $R = 10\ \Omega$, the balance point is observed at $l = 500\text{ cm}$ and for $\mathrm{R} = 1\ \Omega$ the balance point is observed at $l = 400\text{ cm}$. The internal resistance of the battery is approximately:

Which figure shows the correct variation of applied potential difference (V) with photoelectric current (I) at two different intensities of light $(\mathrm{I_1} < \mathrm{I_2})$ of same wavelengths:

The electric field in an electromagnetic wave is given by $\vec{E} = \hat{i}\,40\cos\omega(t - z/c)\text{ NC}^{-1}$. The magnetic field induction of this wave is (in SI unit):

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s\text{ C/m}^{2}$ is placed on $x\text{-}y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e\text{ C/m}$ is placed at $z = 4\text{ m}$ plane and parallel to $y$-axis. If the magnitude values $|\sigma_s| = 2|\lambda_e|$ then at point $(0, 0, 2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi\sqrt{n} : 1$. The value of $n$ is _________.

An infinitely long positively charged straight thread has a linear charge density $\lambda\text{ C m}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is:

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 ventury tube shown $2gh = v_1^2 - v_2^2$

In the light of the above statements, choose the most appropriate answer from the options given below.

A metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $m$ is placed at the centre of the arc. The gravitational force on the particle by the wire is:

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $t$. Which of the following curve best describes acceleration of the block with time:

An elastic spring under tension of $3\text{ N}$ has a length $a$. Its length is $b$ under tension $2\text{ N}$. For its length $(3a - 2b)$, the value of tension will be _______ N.

A body travels $102.5\text{ m}$ in $n$th second and $115.0\text{ m}$ in $(n+2)$th second. The acceleration is:

The magnetic field existing in a region is given by $\vec{B} = 0.2(1 + 2x)\hat{k}$. A square loop of edge $50\text{ cm}$ carrying 0.5 A current is placed in $x\text{-}y$ plane with its edges parallel to the $x\text{-}y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is _________ $\text{mN}$.

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

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

The co-ordinates of a particle moving in $x\text{-}y$ plane are given by: $x = 2 + 4t,\ y = 3t + 8t^{2}$. The motion of the particle is:

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is $25\text{ D}$. Focal length of each of the convex lens is:

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reach upto maximum heights $h_1$ and $h_2$ respectively, above the initial level. The ratio $h_1 : h_2$ is $\frac{n}{10}$. The value of $n$ is __________.

The value of net resistance of the network as shown in the given figure is:

A soap bubble is blown to a diameter of $7\text{ cm}.\ 36960\text{ erg}$ of work is done in blowing it further. If surface tension of soap is 40 dyne/$\text{cm}$ then the new radius is ________ cm. Take $\left(\pi = \frac{22}{7}\right)$.

P-T diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct:

On Celsius scale the temperature of body increases by $40^\circ\text{C}$. The increase in temperature on Fahrenheit scale is:

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8\ \Omega$ and $10\ \Omega$ respectively. After inserting in a hot bath of temperature $400^\circ\text{C}$, the resistance of platinum wire is:

The equation of stationary wave is:

$y = 2\mathrm{a}\sin\left(\frac{2\pi\mathrm{nt}}{\lambda}\right)\cos\left(\frac{2\pi x}{\lambda}\right)$.

Which of the following is NOT correct:

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

Two forces$\overline{F}_1$ and$\overline{F}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec{F}_1$ and $\vec{F}_2$ is $\cos^{-1}\left(\frac{1}{n}\right)$. The value of $|n|$ is _______.

Two wavelengths $\lambda_1$ and $\lambda_2$ are used in Young's double slit experiment. $\lambda_1 = 450\text{ nm}$ and $\lambda_2 = 650\text{ nm}$. The minimum order of fringe produced by $\lambda_2$ which overlaps with the fringe produced by $\lambda_1$ is $n$. The value of $n$ is _______.

If a rubber ball falls from a height $h$ and rebounds upto the height of $h/2$. The percentage loss of total energy of the initial system as well as velocity of ball before it strikes the ground, respectively, are: