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Physics

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

27.

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28.

Match List – I with List – II

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29.

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

30.

Given below are two statements: one is labelled as Assertion (A) and 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 most appropriate answer from the option given below:

31.

A dipole with two electric charges of \( 2 \, \mu \text{C} \) magnitude each, with separation distance \( 0.5 \, \mu \text{m} \), 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 \( 5 \, \text{V} \) is applied. Separation between the plates is \( 0.5 \, \text{mm} \). If the dipole is rotated by \( 30^\circ \) from the axis, it tends to realign in the direction due to a torque. The value of torque is:

32.

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 \(( {}^{64}_{29}\text{Cu} )\) nucleus is greater than that of the carbon \(( {}^{12}_{6}\text{C}) \) nucleus.
Reason (R) : The nucleus of mass number \( A \) has radius proportional to \( A^{1/3} \). In the light of the above statements, choose the most appropriate answer from the options given below :

33.

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 option given below;

34.

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

35.

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

36.

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

37.

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

38.

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 \( \lambda_0 \). Expression for de-Broglie wavelength is given by:
(\( m \) : mass of the electron, \( h \) : Planck’s constant and \( c \) : speed of light)

39.

A helicopter flying horizontally with a speed of \( 360 \, \text{km}/\text{h} \) at an altitude of \( 2 \, \text{km} \), drops an object at an instant. The object hits the ground at a point O, \( 20 \, \text{s} \) after it is dropped. Displacement of ‘O’ from the position of helicopter where the object was released is:
(use acceleration due to gravity \( g = 10 \, \text{m}/\text{s}^2 \) and neglect air resistance)

40.

Given below are two statements: one 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 most appropriate answer from the options given below:

41.

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 air craft is made of metal which protects person 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;

42.

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

43.

The unit of \( \sqrt{\dfrac{2I}{\epsilon_0 \, c}} \) is:
\( (I \) = intensity of an electromagnetic wave, \( c \) : speed of light\() \)

44.

Consider the following logic circuit.

The output \( Y = 0 \) when:

45.

The dimension of \( \sqrt{\dfrac{\mu_{0}}{\epsilon_{0}}} \) is equal to that of: \( (\mu_{0} = \text{Vacuum permeability and } \epsilon_{0} = \text{Vacuum permittivity}) \)

46.

\( M \) and \( R \) be the mass and radius of a disc. A small disc of radius \( \frac{R}{3} \) 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 \( \frac{4}{x} \, M R^{2} \). The value of \( x \) is _______.

47.

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 _____ \( \text{W} \).

48.

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 \( 400 \, \text{K} \), \( 200 \, \text{K} \), respectively. The temperature of rods interface is ___ \( \text{K} \), when equilibrium is established.

49.

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 _______.

50.

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 ______ \( \text{cm}^{2} \).

JEE Main 2025 7th April Evening Shift

Mathematics Physics Chemistry

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