JEE Main 2024 Physics Paper: 8 Apr, Shift 1

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5 \times 10^{-14}\text{ m}$. If target nucleus has atomic number 80, then maximum velocity of $\alpha$-particle is __________ $\times 10^{5}\text{ m/s}$ approximately.

( $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ SI}$ unit, mass of $\alpha$ particle $= 6.72 \times 10^{-27}\text{ kg}$)

A uniform thin metal plate of mass $10\text{ kg}$ with dimensions is shown. The ratio of $x$ and y coordinates of center of mass of plate is $\frac{n}{9}$. The value of $n$ is ________.

A clock has $75\text{ cm}, 60\text{ cm}$ long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi = 3.14$):

In the given circuit, the terminal potential difference of the cell is:

Resistance of a wire at $0^\circ\text{C}, 100^\circ\text{C}$ and $t^\circ\text{C}$ is found to be $10\ \Omega, 10.2\ \Omega$ and $10.95\ \Omega$ respectively. The temperature $t$ in Kelvin scale is _________.

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is:

(Assume h = 6.63 $\times 10^{-34}\text{ J s},\ \mathrm{m_e} = 9.0 \times 10^{-31}\text{ kg}$ and $\mathrm{m_p} = 1836$ times $\mathrm{m_e}$)

Average force exerted on a non-reflecting surface at normal incidence is $2.4 \times 10^{-4}\text{ N}$. If $360\text{ W/cm}^2$ is the light energy flux during span of 1 hour 30 minutes, then the area of the surface is:

An electric field, $\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$ passes through the surface of $4\text{ m}^2$ area having unit vector $\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is _________ $\text{V m}$.

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

Correct Bernoulli's equation is (symbols have their usual meaning):

Two planets $A$ and $B$ having masses $m_1$ and $m_2$ move around the sun in circular orbits of $r_1$ and $r_2$ radii respectively. If angular momentum of $A$ is $L$ and that of $B$ is $3$ $L$, the ratio of time period $\left(\frac{T_A}{T_B}\right)$ is:

A player caught a cricket ball of mass $150\text{ g}$ moving at a speed of $20\text{ m/s}$. If the catching process is completed in $0.1\text{ s}$, the magnitude of force exerted by the ball on the hand of the player is:

Paramagnetic substances:

A. align themselves along the directions of external magnetic field.

B. attract strongly towards external magnetic field.

C. has susceptibility little more than zero.

D. move from a region of strong magnetic field to weak magnetic field.

Choose the most appropriate answer from the options given below:

Young's modulus is determined by the equation given by $\text{Y} = 49000\frac{\text{m}}{\text{l}}\,\frac{\text{dyne}}{\text{cm}^2}$ where $M$ is the mass and $l$ is the extension of wire used in the experiment. Now error in Young modules $(Y)$ is estimated by taking data from $M - l$ plot in graph paper. The smallest scale divisions are $5\text{ g}$ and $0.02\text{ cm}$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $500\text{ g}$ and $2\text{ cm}$ respectively then percentage error of $Y$ is:

An electron with kinetic energy $5\text{ eV}$ enters a region of uniform magnetic field of 3 $\mu\text{T}$ perpendicular to its direction. An electric field $E$ is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is __________ $\text{NC}^{-1}$. (Given, mass of electron $= 9 \times 10^{-31}\text{ kg}$, electric charge $= 1.6 \times 10^{-19}\text{ C}$)

A square loop PQRS having 10 turns, area $3.6 \times 10^{-3}\text{ m}^2$ and resistance $100\ \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $B = 0.5\text{ T}$ as shown. Work done in pulling the loop out of the field in $1.0\text{ s}$ is _________ $\times 10^{-6}\text{ J}$.

Binding energy of a certain nucleus is $18 \times 10^{8}\text{ J}$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

Critical angle of incidence for a pair of optical media is $45^\circ$. The refractive indices of first and second media are in the ratio:

The output $\mathrm{Y}$ of following circuit for given inputs is:

A liquid column of height $0.04\text{ cm}$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $8 \times 10^3\text{ kg m}^{-3}$ and surface tension of soap is $0.28\text{ N m}^{-1}$, then diameter of the soap bubble is __________ $\text{cm}$. (if $g = 10\text{ m s}^{-2}$)

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $(27^\circ\text{C})$. The ratio of specific heat of gases at constant volume respectively is:

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $1\text{ mm}$. The main scale reading is $2\text{ cm}$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 $g$, the density of the sphere is:

In an expression $a \times 10^{b}$:

Three vectors $\overrightarrow{OP}, \overrightarrow{OQ}$ and $\overrightarrow{OR}$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A\sqrt{x}$. The value of $x$ is _________.

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of $a$ is _________.

A parallel beam of monochromatic light of wavelength $600\text{ nm}$ passes through single slit of $0.4\text{ mm}$ width. Angular divergence corresponding to second order minima would be _________ $\times 10^{-3}\text{ rad}$.

Three bodies A, B and C have equal kinetic energies and their masses are $400\text{ g}, 1.2\text{ kg}$ and $1.6\text{ kg}$ respectively. The ratio of their linear momenta is: