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Water of mass \( m \) gram is slowly heated to increase the temperature from \( T_1 \) to \( T_2 \). The change in entropy of the water, given specific heat of water is \( 1 \,\mathrm{J\,kg^{-1}\,K^{-1}} \), is:

Two point charges \( -4 \,\mu\mathrm{C} \) and \( 4 \,\mu\mathrm{C} \), constituting an electric dipole, are placed at \( (-9, 0, 0) \,\mathrm{cm} \) and \( (9, 0, 0) \,\mathrm{cm} \) in a uniform electric field of strength \( 10^4 \,\mathrm{N\,C^{-1}} \). The work done on the dipole in rotating it from the equilibrium through \( 180^\circ \) is:

A ball having kinetic energy \( KE \), is projected at an angle of \( 60^\circ \) from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

A concave mirror of focal length \( f \) in air is dipped in a liquid of refractive index \( \mu \). Its focal length in the liquid will be:

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is \( 2.14 \, \text{eV} \) and stopping potential is \( 2 \, \text{V} \), what is the wavelength of the em-wave?
(Given \( hc = 1242 \, \text{eV}\,\text{nm} \) where \( h \) is the Planck’s constant and \( c \) is the speed of light in vacuum.)

A massless spring gets elongated by amount \( x_{1} \) under a tension of \( 5 \, \text{N} \). Its elongation is \( x_{2} \) under the tension of \( 7 \, \text{N} \). For the elongation of \( (5x_{1}-2x_{2}) \), the tension in the spring will be:

A circular disk of radius \( R \) meter and mass \( M \) kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that \( \theta(t) = 5t^{2} - 8t \) where \( \theta(t) \) is the angular position of the rotating disc as a function of time \( t \).

A galvanometer having a coil of resistance \( 30 \, \Omega \) need \( 20 \, \text{mA} \) of current for full-scale deflection. If a maximum current of \( 3 \, \text{A} \) is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be \( \dfrac{30}{X} \, \Omega \), where \( X \) is:

Match List-I with List-II.

Choose the correct answer from the options given below:

A plane electromagnetic wave of frequency \( 20 \, \text{MHz} \) travels in free space along the \( +x \) direction. At a particular point in space and time, the electric field vector of the wave is \( E_y = 9.3 \, \text{V m}^{-1} \). Then, the magnetic field vector of the wave at that point is:

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is \( P_1 \). The reading of the pressure gauge falls to \( P_2 \) when the valve is opened. The speed of water flowing in the pipe is proportional to:

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The binding energy per nucleon is found to be practically independent of the atomic number \( A \), for nuclei with mass numbers between \( 30 \) and \( 170 \).
Reason (R): Nuclear force is long range.
In the light of the above statements, choose the correct answer from the options given below:

What is the current through the battery in the circuit shown below?

The refractive index of the material of a glass prism is \( \sqrt{3} \). The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

The width of one of the two slits in Young’s double slit experiment is \( d \) while that of the other slit is \( x d \). If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is \( 9 : 4 \) then what is the value of \( x \)?
(Assume that the field strength varies according to the slit width.)

Using the given \( P-\!V \) diagram, the work done by an ideal gas along the path \( ABCD \) is:

If a satellite orbiting the Earth is \( 9 \) times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon \( = 27 \, \text{days} \) and gravitational attraction between the satellite and the moon is neglected.

The equation of a transverse wave travelling along a string is \( y(x,t) = 4.0 \sin \big( 20 \times 10^{-3} x + 600 t \big) \, \text{mm} \), where \( x \) is in \( \text{mm} \) and \( t \) is in second. The velocity of the wave is:

Two charges \( 7 \,\mu \text{C} \) and \( -4 \,\mu \text{C} \) are placed at \( (-7 \, \text{cm}, 0, 0) \) and \( (7 \, \text{cm}, 0, 0) \) respectively. Given, \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \, \text{N}^{-1} \, \text{m}^{-2} \), the electrostatic potential energy of the charge configuration is:

The energy of a system is given as \( E(t) = \alpha^{3} e^{-\beta t} \), where \( t \) is the time and \( \beta = 0.3 \, \text{s}^{-1} \). The errors in the measurement of \( \alpha \) and \( t \) are \( 1.2\% \) and \( 1.6\% \), respectively. At \( t = 5 \, \text{s} \), maximum percentage error in the energy is:

An air bubble of radius \( 1.0 \, \text{mm} \) is observed at a depth of \( 20 \, \text{cm} \) below the free surface of a liquid having surface tension \( 0.095 \, \text{J/m}^{2} \) and density \( 10^{3} \, \text{kg/m}^{3} \). The difference between pressure inside the bubble and atmospheric pressure is ________ \( \text{N/m}^{2} \). (Take \( g = 10 \, \text{m/s}^{2} \))

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance \( 2.5 \, \mu\text{F} \). The dielectric constant of the medium between the capacitor plates is \( 1 \). It produces an instantaneous displacement current of \( 0.25 \, \text{mA} \) in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be __________ \( \text{V}\,\text{s}^{-1} \).

At steady state the charge on the capacitor, as shown in the circuit below, is __________ \( \mu\text{C} \).

In a series LCR circuit, a resistor of \( 300 \, \Omega \), a capacitor of \( 25 \, \text{nF} \) and an inductor of \( 100 \, \text{mH} \) are used. For maximum current in the circuit, the angular frequency of the ac source is __________ \( \times 10^{4} \) radians \( \text{s}^{-1} \).

A satellite of mass \( \dfrac{M}{2} \) is revolving around earth in a circular orbit at a height of \( \dfrac{R}{3} \) from earth surface. The angular momentum of the satellite is \( M \sqrt{\dfrac{GMR}{x}} \). The value of \( x \) is __________, where \( M \) and \( R \) are the mass and radius of earth, respectively. \( (G \) is the gravitational constant).

JEE Main 2025 23rd Jan Evening Shift

Mathematics Physics Chemistry

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The refractive index of the material of a glass prism is \( \sqrt{3} \). The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?