JEE Main 2024 Physics Paper: 30 Jan, Shift 1

Primary coil of a transformer is connected to $220\text{ V}$ ac. Primary and secondary turns of the transformer are 100 and 10 respectively. Secondary coil of transformer is connected to two series resistances shown in figure. The output voltage $(V_0)$ is:

A series L.R circuit connected with an ac source $E = (25\sin 1000t)\text{ V}$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $E = (20\sin 2000t)\text{ V}$, the new power factor of the circuit will be:

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is:

An electron of hydrogen atom in an excited state is having energy $E_n = -0.85\text{ eV}$. The maximum number of allowed transitions to lower energy level is _________.

A capacitor of capacitance $C$ and potential $V$ has energy $E$. It is connected to another capacitor of capacitance $2C$ and potential $2V$. Then the loss of energy is $\frac{x}{3}E$, where $x$ is _______.

Two cells are connected in opposition as shown. Cell $E_1$ is of $8\text{ V}$ emf and $2\ \Omega$ internal resistance; the cell $E_2$ is of $2\text{ V}$ emf and $4\ \Omega$ internal resistance. The terminal potential difference of cell $E_2$ is __________ V.

A potential divider circuit is shown in figure. The output voltage V$0$ is:

An electric toaster has resistance of $60\ \Omega$ at room temperature $(27^\circ\text{C})$. The toaster is connected to a $220\text{ V}$ supply. If the current flowing through it reaches $2.75\text{ A}$, the temperature attained by toaster is around: ( if $\alpha = 2 \times 10^{-4}/^\circ\text{C}$)

The work function of a substance is $3.0\text{ eV}$. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately;

A ceiling fan having 3 blades of length $80\text{ cm}$ each is rotating with an angular velocity of 1200 $\text{rpm}$. The magnetic field of earth in that region is $0.5\text{ G}$ and angle of dip is $30^\circ$. The emf induced across the blades is $N\pi \times 10^{-5}\text{ V}$. The value of $N$ is _________.

The electric field of an electromagnetic wave in free space is represented as $\vec{E} = E_0\cos(\omega t - kz)\hat{i}$. The corresponding magnetic induction vector will be:

The electrostatic potential due to an electric dipole at a distance '$r$' varies as:

The gravitational potential at a point above the surface of earth is $-5.12 \times 10^{7}\text{ J/kg}$ and the acceleration due to gravity at that point is $6.4\text{ m/s}^2$. Assume that the mean radius of earth to be $6400\text{ km}$. The height of this point above the earth's surface is:

At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^\circ\text{C}$?

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $2\text{ kg}$ is:

Each of three blocks $P, Q$ and$R$ shown in figure has a mass of $3\text{ kg}$. Each of the wires $A$ and $B$ has cross-sectional area $0.005\text{ cm}^2$ and Young's modulus $2 \times 10^{11}\text{ N m}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is ________ $\times 10^{-4}$. (Take $g = 10\text{ m/s}^2$)

Young's modulus of material of a wire of length '$L$' and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and cross-sectional area is halved then Young's modulus will be:

The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $(t+1)\text{ s}$ are $125\text{ m}$ and $50\text{ m/s}$, respectively. The distance travelled by the particle in $(t+2)^{\text{th}}\text{ s}$ is _________ m.

Two insulated circular loops A and B of radius '$a$' carrying a current of '$I$' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be:

The horizontal component of earth's magnetic field at a place is $3.5 \times 10^{-5}\text{ T}$. A very long straight conductor carrying current of $\sqrt{2}\text{ A}$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is __________ $\times 10^{-6}\text{ N/m}$.

The distance between object and its two times magnified real image as produced by a convex lens is $45\text{ cm}$. The focal length of the lens used is _______ cm.

A particle of mass $\mathrm{m}$ is projected with a velocity '$\mathrm{u}$' making an angle of $30^\circ$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $\mathrm{h}$ is:

Consider a Disc of mass $5\text{ kg}$, radius $2\text{ m}$, rotating with angular velocity of $10\text{ rad/s}$ about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is ________ J.

A Zener diode of breakdown voltage $10\text{ V}$ is used as a voltage regulator as shown in the figure. The current through the Zener diode is:

Two thermodynamical processes are shown in the figure. The molar heat capacity for process A and B are $C_A$ and $C_B$. The molar heat capacity at constant pressure and constant volume are represented by $C_P$ and $C_V$, respectively. Choose the correct statement.

Match List I with List II.

Choose the correct answer from the options given below:

In a closed organ pipe, the frequency of fundamental note is $30\text{ Hz}$. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to $110\text{ Hz}$. If the organ pipe has a cross-sectional area of $2\text{ cm}^{2}$, the amount of water poured in the organ tube is __________ g. (Take speed of sound in air is $330\text{ m/s}$)

The diffraction pattern of a light of wavelength $400\text{ nm}$ diffracting from a slit of width $0.2\text{ mm}$ is focused on the focal plane of a convex lens of focal length $100\text{ cm}$. The width of the $1$st secondary maxima will be:

A particle is placed at the point $A$ of a frictionless track $ABC$ as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is:

(Take $g = 10\text{ m/s}^2$).