An LCR circuit contains resistance of 110$$\Omega$$ and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45$$^\circ$$. If on the other hand, only inductor is removed the current leads by 45$$^\circ$$ with the applied voltage. The rms current flowing in the circuit will be :

An electron with kinetic energy K₁ enters between parallel plates of a capacitor at an angle '$$\alpha$$' with the plates. It leaves the plates at angle '$$\beta$$' with kinetic energy K₂. Then the ratio of kinetic energies K₁ : K₂ will be :

A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v₀. It encounters an inclined plane at angle $$\theta$$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

An electron of mass m_e and a proton of mass m_p = 1836 m_e are moving with the same speed. The ratio of their de Broglie wavelength $${{{}^\lambda electron} \over {{}^\lambda proton}}$$ will be :

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1 $$\mu$$m. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that:

In a ferromagnetic material, below the curie temperature, a domain is defined as :

Given below are two statements :

Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.

Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.

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

Match List I with List II.

	List I		List II
(a)	Rectifier	(i)	Used either for stepping up or stepping down the a.c. voltage
(b)	Stabilizer	(ii)	Used to convert a.c. voltage into d.c. voltage
(c)	Transformer	(iii)	Used to remove any ripple in the rectified output voltage
(d)	Filter	(iv)	Used for constant output voltage even when the input voltage or load current change

Choose the correct answer from the options given below :

A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $$\overrightarrow E $$ through the shaded area is :

Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V₂ = 2V₁ then the ratio of temperature T₂/T₁ is :

The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is :

Y = A sin($$\omega$$t + $$\phi$$₀) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is $$Y = {A \over 2}$$ and it is moving along negative x-direction. Then the initial phase angle $$\phi$$₀ will be:

Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :

The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30$$^\circ$$ in 0.1 s. The perpendicular projection 'P' from 'A' on the diameter MN represents the simple harmonic motion of 'P'. The restoration force per unit mass when P touches M will be :

If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $${1 \over {4\pi {\varepsilon _0}}}{{|e{|^2}} \over {hc}}$$ has dimensions of :

For extrinsic semiconductors; when doping level is increased;

The truth table for the following logic circuit is :

A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is :

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is :

If $$\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P $$, the angle between $$\overrightarrow P $$ and $$\overrightarrow Q $$ is $$\theta$$(0$$^\circ$$ < $$\theta$$ < 360$$^\circ$$). The value of '$$\theta$$' will be ___________$$^\circ$$.

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be __________%.

The initial velocity v_i required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity v_e such that $${v_i} = \sqrt {{x \over y}} \times {v_e}$$. The value of x will be ____________.

The peak electric field produced by the radiation coming from the 8W bulb at a distance of 10 m is $${x \over {10}}\sqrt {{{{\mu _0}c} \over \pi }} {V \over m}$$. The efficiency of the bulb is 10% and it is a point source. The value of x is ___________.

Two identical conducting spheres with negligible volume have 2.1 nC and $$-$$0.1 nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is __________ $$\times$$ 10^$$-$$9 N.

[Given : $$4\pi {\varepsilon _0} = {1 \over {9 \times {{10}^9}}}$$ SI unit]

The wavelength of an X-ray beam is 10$$\mathop A\limits^o $$. The mass of a fictitious particle having the same energy as that of the X-ray photons is $${x \over 3}h$$ kg. The value of x is __________. (h = Planck's constant)

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is $${a \over {21}} \times {10^{ - 8}}$$C. The value of 'a' will be ___________. [Given g = 10 ms^$$-$$2]

Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be ___________.

A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 2$$\Omega$$ each and leaves by the corner R. The currents i₁ in ampere is _________.