A cube is placed inside an electric field, $$\overrightarrow E = 150{y^2}\widehat j$$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :

A square loop of side 20 cm and resistance 1$$\Omega$$ is moved towards right with a constant speed v₀. The right arm of the loop is in a uniform magnetic field of 5T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value 4$$\Omega$$. What should be the value of v₀ so that a steady current of 2 mA flows in the loop?

The temperature of an ideal gas in 3-dimensions is 300 K. The corresponding de-Broglie wavelength of the electron approximately at 300 K, is :

[m_e = mass of electron = 9 $$\times$$ 10^$$-$$31 kg, h = Planck constant = 6.6 $$\times$$ 6.6 $$\times$$ 10^$$-$$34 Js, k_B = Boltzmann constant = 1.38 $$\times$$ 10^$$-$$23 JK^$$-$$1]

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of 0.8$$\sqrt {gh} $$. The value of workdone by the air-friction is :

The ranges and heights for two projectiles projected with the same initial velocity at angles 42$$^\circ$$ and 48$$^\circ$$ with the horizontal are R₁, R₂ and H₁, H₂ respectively. Choose the correct option :

A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given m = 8 kg, M = 16 kg Assume all the surfaces shown in the figure to be frictionless.

Due to cold weather a 1 m water pipe of cross-sectional area 1 cm² is filled with ice at $$-$$10$$^\circ$$C. Resistive heating is used to melt the ice. Current of 0.5A is passed through 4 k$$\Omega$$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice = 3.33 $$\times$$ 10⁵ J kg^$$-$$1, specific heat of ice = 2 $$\times$$ 10³ J kg^$$-$$1 and density of ice = 10³ kg/m³

A student determined Young's Modulus of elasticity using the formula $$Y = {{Mg{L^3}} \over {4b{d^3}\delta }}$$. The value of g is taken to be 9.8 m/s², without any significant error, his observation are as following.

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass (M)	1 g	2 kg
Length of bar (L)	1 mm	1 m
Breadth of bar (b)	0.1 mm	4 cm
Thickness of bar (d)	0.01 mm	0.4 cm
Depression ($$\delta $$)	0.01 mm	5 mm

Then the fractional error in the measurement of Y is :

Two resistors R₁ = (4 $$\pm$$ 0.8) $$\Omega$$ and R₂ = (4 $$\pm$$ 0.4) $$\Omega$$ are connected in parallel. The equivalent resistance of their parallel combination will be :

Following plots show magnetization (M) vs magnetizing field (H) and magnetic susceptibility ($$\chi $$) vs temperature (T) graph :


Which of the following combination will be represented by a diamagnetic material?

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water ($$\mu$$ = 4/3) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

In the given figure, each diode has a forward bias resistance of 30$$\Omega$$ and infinite resistance in reverse bias. The current I₁ will be :

For the given circuit the current i through the battery when the key in closed and the steady state has been reached is __________.

An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following surface profile.


The correct applied force vs distance graph will be :

A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?

A capacitor is connected to a 20 V battery through a resistance of 10$$\Omega$$. It is found that the potential difference across the capacitor rises to 2 V in 1 $$\mu$$s. The capacitance of the capacitor is __________ $$\mu$$F. Given : $$\ln \left( {{{10} \over 9}} \right) = 0.105$$

Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is :

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by

E = 20cos(2 $$\times$$ 10¹⁰ t $$-$$ 200x) V/m. The dielectric constant of the medium is equal to : (Take $$\mu$$_r = 1)

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____________.

The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0$$^\circ$$C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $${x \over {10}}$$. Then the value of x (round off to the nearest integer) is ___________. (Given R = 8.31 J mol^$$-$$1 K^$$-$$1)

The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is x : 4 where x is ____________.

Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is 2 $$\times$$ 10³ km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $${\pi \over x}rad\,{h^{ - 1}}$$ where x is ____________.

When a body slides down from rest along a smooth inclined plane making an angle of 30$$^\circ$$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time $$\alpha$$T, where $$\alpha$$ is a constant greater than 1. The co-efficient of friction between the body and the rough plane is $${1 \over {\sqrt x }}\left( {{{{\alpha ^2} - 1} \over {{\alpha ^2}}}} \right)$$ where x = __________.

The average translational kinetic energy of N₂ gas molecules at .............$$^\circ$$C becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt. (Given k_B = 1.38 $$\times$$ 10^$$-$$23 J/K) (Fill the nearest integer).

A uniform heating wire of resistance 36$$\Omega$$ is connected across a potential difference of 240 V. The wire is then cut into half and potential difference of 240V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be 1 : x, where x is ____________

A steel rod with y = 2.0 $$\times$$ 10¹¹ Nm^$$-$$2 and $$\alpha$$ = 10^$$-$$5 $$^\circ$$C^$$-$$1 of length 4 m and area of cross-section 10 cm² is heated from 0$$^\circ$$C to 400$$^\circ$$C without being allowed to extend. The tension produced in the rod is x $$\times$$ 10⁵ N where the value of x is ____________.

A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity, ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is ____________ ms^$$-$$1. (Take g = 10 ms^$$-$$2)

An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of 72 kmh^$$-$$1 when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is ____________ $$\times$$ 10⁵ N/m.