JEE Main 2025 Physics Paper: 7 Apr, Shift 2

An inductor of reactance $100\ \Omega$, a capacitor of reactance $50\ \Omega$, and a resistor of resistance $50\ \Omega$ are connected in series with an AC source of $10\text{ V}, 50\text{ Hz}$. Average power dissipated by the circuit is ___________ W.

A parallel plate capacitor has charge $5 \times 10^{-6}\text{ C}$. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $4 \times 10^{-6}\text{ C}$ then the dielectric constant of the slab is _______________.

A photoemissive substance is illuminated with a radiation of wavelength $\lambda_i$ so that it releases electrons with de-Broglie wavelength $\lambda_e$. The longest wavelength of radiation that can emit photoelectron is $\lambda_o$. Expression for de-Broglie wavelength is given by:

(m: mass of the electron, h: Planck's constant and c: speed of light)

The unit of $\sqrt{\frac{2I}{\varepsilon_0 c}}$ is:

(I = intensity of an electromagnetic wave, c = speed of light)

A dipole with two electric charges of 2 µC magnitude each, with separation distance 0.5 µm, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign in the direction due to a torque. The value of torque is:

The electric field in a region is given by $\vec{E} = (2\hat{i} + 4\hat{j} + 6\hat{k}) \times 10^{3}\text{ N/C}$. The flux of the field through a rectangular surface parallel to $x - z$ plane is $6.0\text{ N m}^2\text{C}^{-1}$. The area of the surface is _____________ $\text{cm}^2$.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The outer body of an aircraft is made of metal which protects persons sitting inside from lightning strikes.

Reason (R): The electric field inside the cavity enclosed by a conductor is zero. In the light of the above statements, choose the most$-$appropriate answer from the options given below:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.

Reason (R): For a central force field the angular momentum is a constant.

In the light of the above statements, choose the mostappropriate answer from the options given below:

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivities of these rods are: $\frac{L_A}{L_B} = \frac{1}{2},\ \frac{r_A}{r_B} = 2$ and $\frac{K_A}{K_B} = \frac{1}{2}$. The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of rods interface is ______________ $K$, when equilibrium is established.

An object with mass 500 g moves along x-axis with speed $v = 4\sqrt{x}$ m/s. The force acting on the object is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Magnetic monopoles do not exist.

Reason (R): Magnetic field lines are continuous and form closed loops.

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

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The density of the copper $\left({}_{29}^{64}\text{Cu}\right)$ nucleus is greater than that of the carbon $\left({}_{6}^{12}\text{C}\right)$ nucleus.

Reason (R): The nucleus of mass number A has a radius proportional to $A^{1/3}$.

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

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is:

(use acceleration due to gravity g = 10 m/s2 and neglect air resistance)

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Refractive index of glass is higher than that of air.

Reason (R): Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.

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

A mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between object and its image is 40 cm, then the focal length of the mirror is ________.

A transparent block A having refractive index $\mu = 1.25$ is surrounded by another medium of refractive index $\mu = 1.0$ as shown in the figure. A light ray is incident on the flat face of the block with incident angle $\theta$ as shown in the figure. What is the maximum value of $\theta$ for which light suffers total internal reflection at the top surface of the block?

Let M and R be the mass and radius of a disc. A small disc of radius $R/3$ is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis $AB$ passing through the centre $O$ and perpendicular to the plane of disc is $\frac{4}{x}MR^2$. The value of $x$ is ____________.

Consider the following logic circuit.

The output is Y = 0 when:

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle ≈ 0°) with 30° inclined with the vertical. The length of water risen in the capillary is _______ cm. (Take $g = 9.8$ m/s${}^{2}$)

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is:

(Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

Match List - I with List - II.

Choose the correct answer from the options given below:

The dimension of $\sqrt{\frac{\mu_0}{\epsilon_0}}$ is equal to that of:

($\mu_0$ = Vacuum permeability and $\epsilon_0$ = Vacuum permittivity)

Match List - I with List - II.

Choose the correct answer from the options given below:

The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is:

Which one of the following forces cannot be expressed in terms of potential energy?