A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $$-$$Q. The electric field at the centre of cube is :

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillations will be :

A current through a wire depends on time as

i = $$\alpha$$₀t + $$\beta$$t²

where $$\alpha$$₀ = 20 A/s and $$\beta$$ = 8 As^$$-$$2. Find the charge crossed through a section of the wire in 15 s.

Match List I with List II.

	List I		List II
(a)	Isothermal	(i)	Pressure constant
(b)	Isochoric	(ii)	Temperature constant
(c)	Adiabatic	(iii)	Volume constant
(d)	Isobaric	(iv)	Heat content is constant

Choose the correct answer from the options given below :

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.

A $$ \to $$ B : Isothermal expansion at temperature T so that the volume is doubled from V₁ to V₂ = 2V₁ and pressure charges from P₁ to P₂

B $$ \to $$ C : Isobaric compression at pressure P₂ to initial volume V₁.

C $$ \to $$ A : Isochoric change leading to change of pressure from P₂ to P₁.

Total workdone in the complete cycle ABCA is :

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is '$$\alpha$$'. The metal sheet is heated uniformly, by a small temperature $$\Delta$$T, so that its new temperature is T + $$\Delta$$T. Calculate the increase in the volume of the metal box.

A cell E₁ of emf 6V and internal resistance 2$$\Omega$$ is connected with another cell E₂ of emf 4V and internal resistance 8$$\Omega$$ (as shown in the figure). The potential difference across points X and Y is :

The focal length f is related to the radius of curvature r of the spherical convex mirror by :

In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be :

Consider two satellites S₁ and S₂ with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S₁ to the angular velocity of satellite S₂ is :

If Y, K and $$\eta $$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.

The transitions A, B and C respectively represent :

The work done by a gas molecule in an isolated system is

given by, $$W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha kT}}}}$$, where x is the displacement, k is the Boltzmann constant and T is the temperature. $$\alpha$$ and $$\beta$$ are constants. Then the dimensions of $$\beta$$ will be :

Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :

Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as;

I₁ = M.I. of thin circular ring about its diameter,

I₂ = M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I₃ = M.I. of solid cylinder about its axis and

I₄ = M.I. of solid sphere about its diameter.

Then :

An unpolarised light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by 30$$^\circ$$ in clockwise direction, the intensity of emerging light will be _________ Lumens.

A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30$$^\circ$$ with the original direction. The ratio of velocities of the balls after collision is x : y, where x is __________.

An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is ____________ $$\times$$ 10⁷ m/s.

A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift ___________ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass 'm' on the smaller piston.

An inclined plane is bent in such a way that the vertical cross-section is given by $$y = {{{x^2}} \over 4}$$ where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $$\mu$$ = 0.5, the maximum height in cm at which a stationary block will not slip downward is _________ cm.

A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V (A.C.) on standard domestic A.C. supply. The number of turns of secondary coil are 24, then the number of turns of primary are ___________.

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be _________ N. [g = 10 ms^$$-$$2]

In connection with the circuit drawn below, the value of current flowing through 2 k$$\Omega$$ resistor is _________ $$\times$$ 10^$$-$$4 A.

Given below are two statements :

Statement I : Two photons having equal linear momenta have equal wavelengths.

Statement II : If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.

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