The dimension of mutual inductance is :

In the arrangement shown in figure a₁, a₂, a₃ and a₄ are the accelerations of masses m₁, m₂, m₃ and m₄ respectively. Which of the following relation is true for this arrangement?

Arrange the four graphs in descending order of total work done; where W₁, W₂, W₃ and W₄ are the work done corresponding to figure a, b, c and d respectively.

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is

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

Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.

Reason R : At equator, the direction of acceleration due to the gravity is towards the center of earth.

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

If p is the density and $$\eta$$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number R_e is :

A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27$$^\circ$$C. The ratio of their average kinetic energy per molecule respectively will be :

The charge on capacitor of capacitance 15$$\mu$$F in the figure given below is :

A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 $$\mu$$F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure) will be :

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 $$\mu$$C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :

The equivalent resistance between points A and B in the given network is :

A bar magnet having a magnetic moment of 2.0 $$\times$$ 10⁵ JT^$$-$$1, is placed along the direction of uniform magnetic field of magnitude B = 14 $$\times$$ 10^$$-$$5 T. The work done in rotating the magnet slowly through 60$$^\circ$$ from the direction of field is :

Two coils of self inductance L₁ and L₂ are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :

A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s^$$-$$1. If the horizontal component of earth's magnetic field is 0.2 $$\times$$ 10^$$-$$4 T, then emf induced between the two ends of the conductor is :

Which is the correct ascending order of wavelengths?

For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 nm. The value of v is :

A metal surface is illuminated by a radiation of wavelength 4500 $$\mathop A\limits^o $$. The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90$$^\circ$$ with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of the metal is approximately :

A ball is projected vertically upward with an initial velocity of 50 ms^$$-$$1 at t = 0s. At t = 2s, another ball is projected vertically upward with same velocity. At t = __________ s, second ball will meet the first ball (g = 10 ms^$$-$$2).

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms^$$-$$1. The impulse imparted to the ball is ___________ Ns.

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7^th and 8^th ball is __________ N when 6^th ball just leaves the table.

A geyser heats water flowing at a rate of 2.0 kg per minute from 30$$^\circ$$C to 70$$^\circ$$C. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min^$$-$$1.

[Heat of combustion = 8 $$\times$$ 10³ Jg^$$-$$1, Specific heat of water = 4.2 Jg^$$-$$1 $$^\circ$$C^$$-$$1]

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _________ Hz.

Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of 10^$$-$$5 N, then separation between the wires is ____________ cm.

A small bulb is placed at the bottom of a tank containing water to a depth of $$\sqrt7$$ m. The refractive index of water is $${4 \over 3}$$. The area of the surface of water through which light from the bulb can emerge out is x$$\pi$$ m². The value of x is __________.

A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is __________ $$\times$$ 10^$$-$$6 m.

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 $$\mathop A\limits^o $$ is 0.42 V. If the threshold frequency is x $$\times$$ 10¹³ /s, where x is _________ (nearest integer).

(Given, speed light = 3 $$\times$$ 10⁸ m/s, Planck's constant = 6.63 $$\times$$ 10^$$-$$34 Js)