JEE Main 2023 Physics Paper: 1 Feb, Shift 1

Match List - I with List - II:

Choose the correct answer from the options given below:

A series LCR circuit is connected to an ac source of $220\text{ V}, 50\text{ Hz}$. The circuit contain a resistance $R = 100\ \Omega$ and an inductor of inductive reactance $X_L = 79.6\ \Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _________ $\mu\text{F}$.

A light of energy $12.75\text{ eV}$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{\pi} \times 10^{-17}\text{ eVs}$. The value of $x$ is ___________ (use $h = 4.14 \times 10^{-15}\text{ eVs},\ c = 3 \times 10^{8}\text{ ms}^{-1}$ ).

The equivalent resistance between $A$ and $B$ of the network shown in figure;

In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf $1.5\text{ V}$ is found to be $60\text{ cm}$. If this cell is replaced by another cell of emf E, the length-of null point increases by $40\text{ cm}$. The value of $E$ is $\frac{x}{10}\text{ V}$. The value of $x$ is ____________.

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$. An alpha particle having certain kinetic energy has the same de-Broglie wavelength $\lambda$. The ratio of kinetic energy of proton and that of alpha particle is:

Match List I with List II:

Choose the correct answer from the options given below:

Two equal positive point charges are separated by a distance $2a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $\frac{a}{\sqrt{x}}$. The value of $x$ is __________.

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different regions $E_{I}, E_{II}$ and $E_{III}$ are:

A certain pressure '$P$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $0.01\%$ whereas the liquid gets compressed to $0.03\%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ is ____________.

Given below are two statements:

Statement I: Acceleration due to gravity is different at different places on the surface of earth. Statement II: Acceleration due to gravity increases as we go down below the earth's surface. In the light of the above statements, choose the correct answer from the options given below

If earth has a mass nine times and radius twice to that of a planet P. Then $\frac{v_e}{3}\sqrt{x}\text{ m s}^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of $P$, where $v_e$ is escape velocity on earth. The value of $x$ is

The average kinetic energy of a molecule of the gas is

A block of mass $5\text{ kg}$ is placed at rest on a table of rough surface. Now, if a force of $30\text{ N}$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50\text{ m}$ in an interval of time $10\text{ s}$. Coefficient of kinetic friction is (given, $g = 10\text{ ms}^{-2}$):

A certain pressure '$\text{P}$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $0.01\%$ whereas the liquid gets compressed to $0.03\%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ is ____________.

An object moves with speed $v_1, v_2$ and $v_3$ along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:

Find the magnetic field at the point $\text{P}$ in figure. The curved portion is a semicircle connected to two long straight wires.

A charge particle of $2\ \mu\text{C}$ accelerated by a potential difference of $100\text{ V}$ enters a region of uniform magnetic field of magnitude $4\text{ mT}$ at right angle to the direction of field. The charge particle completes semicircle of radius $3\text{ cm}$ inside magnetic field. The mass of the charge particle is __________ $\times 10^{-18}\text{ kg}$

The mass of proton, neutron and helium nucleus are respectively $1.0073\,u, 1.0087\,u$ and $4.0015\,u$. The binding energy of helium nucleus is:

The amplitude of a particle executing SHM is $3\text{ cm}$. The displacement at which its kinetic energy will be $25\%$ more than the potential energy is: __________ $\text{cm}$

A child stands on the edge of the cliff $10\text{ m}$ above the ground and throws a stone horizontally with an initial speed of $5\text{ m s}^{-1}$. Neglecting the air resistance, the speed with which the stone hits the ground will be ________ $\text{m s}^{-1}$ (given, $g = 10\text{ m s}^{-2}$ ).

A thin cylindrical rod of length $10\text{ cm}$ is placed horizontally on the principal axis of a concave mirror of focal length $20\text{ cm}$. The rod is placed in such a way that mid point of the rod is at $40\text{ cm}$ from the pole of mirror. The length of the image formed by the mirror will be $\frac{x}{3}\text{ cm}$. The value of $x$ is _____________.

A solid cylinder is released from rest from the top of an inclined plane of inclination $30^\circ$ and length $60\text{ cm}$. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is __________ $\text{ms}^{-1}$. (Given $g = 10\text{ ms}^{-2}$)

Match List I with List II:

Choose the correct answer from the options given below:

A mercury drop of radius $10^{-3}\text{ m}$ is broken into 125 equal size droplets. Surface tension of mercury is $0.45\text{ N m}^{-1}$. The gain in surface energy is:

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $\left(\text{given, } \gamma = \frac{3}{2}\right)$:

$\left(P + \frac{a}{V^2}\right)(V - b) = RT$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be:

A steel wire with mass per unit length $7.0 \times 10^{-3}\text{ kg m}^{-1}$ is under tension of $70\text{ N}$. The speed of transverse waves in the wire will be:

'$n$' polarizing sheets are arranged such that each makes an angle $45^\circ$ with the preceding sheet. An unpolarized light of intensity I is incident into this arrangement. The output intensity is found to be $I/64$. The value of $n$ will be:

A small particle moves to position $5\hat{i} - 2\hat{j} + \hat{k}$ from its initial position $2\hat{i} + 3\hat{j} - 4\hat{k}$ under the action of force $5\hat{i} + 2\hat{j} + 7\hat{k}\text{ N}$. The value of work done will be __________ J.