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Physics

From the combination of resistors with resistances values \( R_1=R_2=R_3=5\,\Omega \) and \( R_4=10\,\Omega \), which of the following combination is the best circuit to get an equivalent \( 6\,\Omega \)?

27.

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains \( 300 \) equal divisions equals to \( 15 \,\text{cm} \). The vernier scale attached to the microscope has \( 25 \) divisions equals to \( 24 \) divisions of main scale.
The least count (\( LC \)) of the travelling microscope is (in \( \text{cm} \)):

28.

A radioactive material \( P \) first decays into \( Q \) and then \( Q \) decays to non-radioactive material \( R \). Which of the following figure represents time dependent mass of \( P, Q \) and \( R \)?

29.

Consider a \( n \)-type semiconductor in which \( n_{e} \) and \( n_{h} \) are number of electrons and holes, respectively.
(A) Holes are minority carriers
(B) The dopant is a pentavalent atom
(C) \( n_{e} n_{h} \neq n_{i}^{2} \)
(where \( n_{i} \) is number of electrons or holes in semiconductor when it is intrinsic form)
(D) \( n_{e} n_{h} \ge n_{i}^{2} \)
(E) The holes are not generated due to the donors
Choose the correct answer from the options given below:

30.

A metallic ring is uniformly charged as shown in figure. \( AC \) and \( BD \) are two mutually perpendicular diameters. Electric field due to arc \( AB \) at \( 'O' \) is \( 'E' \) in magnitude. What would be the magnitude of electric field at \( 'O' \) due to arc \( ABC \)?

31.

There are '\( n \)' number of identical electric bulbs, each is designed to draw a power \( p \) independently from the mains supply. They are now joined in series across the mains supply. The total power drawn by the combination is:

32.

Three parallel plate capacitors \( C_1 \), \( C_2 \) and \( C_3 \) each of capacitance \( 5\,\mu \mathrm{F} \) are connected as shown in figure. The effective capacitance between points \( A \) and \( B \), when the space between the parallel plates of \( C_1 \) capacitor is filled with a dielectric medium having dielectric constant of \( 4 \), is:

33.

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is \( 8\,\text{m/s} \). The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be:

34.

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at \( 8\,\text{kPa} \) at \( 1000\,\text{K} \) while the smaller vessel contains the gas at \( 7\,\text{kPa} \) at \(500\,\text{K} \). If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at \( 600\,\text{K} \), at steady state the pressure in the vessels will be (in \( \text{kPa} \)).

35.

An object is kept at rest at a distance of \( 3R \) above the earth's surface where \( R \) is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is:
(Assume \( M \) = mass of earth, \( G \) = Universal gravitational constant)

36.

Displacement of a wave is expressed as \( x(t) = 5 \cos\!\left(628 t + \frac{\pi}{2}\right) \, \text{m} \). The wavelength of the wave when its velocity is \( 300 \, \text{m/s} \) is: \( (\pi = 3.14) \)

37.

A block of mass \( 25 \, \text{kg} \) is pulled along a horizontal surface by a force at an angle \( 45^\circ \) with the horizontal. The friction coefficient between the block and the surface is \( 0.25 \). The block travels at a uniform velocity. The workdone by the applied force during a displacement of \( 5 \, \text{m} \) of the block is:

38.

A cylindrical rod of length \( 1 \, \text{m} \) and radius \( 4 \, \text{cm} \) is mounted vertically. It is subjected to a shear force of \( 10^5 \, \text{N} \) at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement \( \theta \) of the rod axis from its original position would be:
(shear moduli, \( G = 10^{10} \, \text{N/m}^2 \) )

39.

Match List I with List - II.

List – I	List – II
(A) Isobaric	(I) \( \Delta Q = \Delta W \)
(B) Isochoric	(II) \( \Delta Q = \Delta U \)
(C) Adiabatic	(III) \( \Delta Q = \text{zero} \)
(D) Isothermal	(IV) \( \Delta Q = \Delta U + P \Delta V \)

\( \Delta Q = \text{Heat supplied} \)
\( \Delta W = \text{Work done by the system} \)
\( \Delta U = \text{Change in internal energy} \)
\( P = \text{Pressure of the system} \)
\( \Delta V = \text{Change in volume of the system} \)
Choose the correct answer from the options given below :

40.

Two polarisers \( P_1 \) and \( P_2 \) are placed in such a way that the intensity of the transmitted light will be zero. A third polariser \( P_3 \) is inserted in between \( P_1 \) and \( P_2 \), at particular angle between \( P_2 \) and \( P_3 \). The transmitted intensity of the light passing the through all three polarisers is maximum. The angle between the polarisers \( P_2 \) and \( P_3 \) is:

41.

Consider a rectangular sheet of solid material of length \( l = 9 \, \text{cm} \) and width \( d = 4 \, \text{cm} \). The coefficient of linear expansion is \( \alpha = 3.1 \times 10^{-5} \, \text{K}^{-1} \) at room temperature and one atmospheric pressure. The mass of sheet \( m = 0.1 \, \text{kg} \) and the specific heat capacity \( C_v = 900 \, \text{J\kg}^{-1}\text{K}^{-1} \). If the amount of heat supplied to the material is \( 8.1 \times 10^2 \, \text{J} \) then change in area of the rectangular sheet is:

42.

A finite size object is placed normal to the principal axis at a distance of \( 30 \, \text{cm} \) from a convex mirror of focal length \( 30 \, \text{cm} \). A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is:

43.

Given below are two statements:
Statement (I): The dimensions of Planck's constant and angular momentum are same.
Statement (II): In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.
In the light of the above statements, choose the most appropriate answer from the options given below:

44.

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of \( M^{P} L^{Q} T^{R} A^{S} \). The value of \( P \) and \( Q \) are:

45.

The displacement \( x \) versus time graph is shown below.

(A) The average velocity during \( 0 \) to \( 3 \, \text{s} \) is \( 10 \, \text{m/s} \)
(B) The average velocity during \( 3 \) to \( 5 \, \text{s} \) is \( 0 \, \text{m/s} \)
(C) The instantaneous velocity at \( t = 2 \, \text{s} \) is \( 5 \, \text{m/s} \)
(D) The average velocity during \( 5 \) to \( 7 \, \text{s} \) and instantaneous velocity at \( t = 6.5 \, \text{s} \) are equal
(E) The average velocity from \( t = 0 \) to \( t = 9 \, \text{s} \) is zero
Choose the correct answer from the options given below:

46.

A solid sphere with uniform density and radius \( R \) is rotating initially with constant angular velocity \( (\omega_{1}) \) about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become \( R/2 \) is \( x \omega_{1} \). The value of \( x \) is ________.

47.

An inductor of self inductance \( 1 \, \text{H} \) is connected in series with a resistor of \( 100\pi \, \Omega \) and an ac supply of \( 100\pi \, \text{V} \), \( 50 \, \text{Hz} \). Maximum current flowing in the circuit is ________ \( \text{A} \).

48.

If an optical medium possesses a relative permeability of \( \frac{10}{\pi} \) and relative permittivity of \( \frac{1}{0.0885} \), then the velocity of light is greater in vacuum than that in this medium by _______ times.
\( (\mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \;, \; \varepsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \;, \; c = 3 \times 10^{8} \, \text{m/s} )\)

49.

A particle of charge \( 1.6 \, \mu\text{C} \) and mass \( 16 \, \mu\text{g} \) is present in a strong magnetic field of \( 6.28 \, \text{T} \). The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is ________ \( \text{s} \). \( (\pi = 3.14) \)

50.

In a Young's double slit experiment, two slits are located \( 1.5 \, \text{mm} \) apart. The distance of screen from slits is \( 2 \, \text{m} \) and the wavelength of the source is \( 400 \, \text{nm} \). If the \( 20 \) maxima of the double slit pattern are contained within the central maximum of the single slit diffraction pattern, then the width of each slit is \( x \times 10^{-3} \) \( \text{cm} \), where x-value is _______.

JEE Main 2025 4th April Evening Shift

Mathematics Physics Chemistry

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