A capacitor is made of two square plates each of side 'a' making a very small angle $$\alpha $$ between them, as shown in figure. The capacitance will be close to :

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the mirror (x) is correctly given by :
(Graphs are drawn schematically and are not to scale)

A particle moves such that its position vector $$\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \omega t\widehat j$$ where $$\omega $$ is a constant and t is time. Then which of the following statements is true for the velocity $$\overrightarrow v \left( t \right)$$ and acceleration $$\overrightarrow a \left( t \right)$$ of the particle :

Consider two charged metallic spheres S₁ and S₂ of radii R₁ and R₂, respectively. The electric fields E₁ (on S₁) and E₂ (on S₂) on their surfaces are such that E₁/E₂ = R₁/R₂. Then the ratio V₁ (on S₁) / V₂ (on S₂) of the electrostatic potentials on each sphere is :

An electron (mass m) with initial velocity $$\overrightarrow v = {v_0}\widehat i + {v_0}\widehat j$$ is in an electric field $$\overrightarrow E = - {E_0}\widehat k$$. If $$\lambda _0$$ is initial de-Broglie wavelength of electron, its de-Broglie wave length at time t is given by :

A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is :

Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its C_P/C_V value will be :

A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $$\sqrt {2gh} $$. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $$\sqrt {{h \over g}} $$ is :

A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to circular turn at N and D. Magnetic field at the centre of circle is :

In the given circuit, value of Y is :

A shown in the figure, a battery of emf $$\varepsilon $$ is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and t = t_c (t_c is the time constant of the circuit) is :

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 10⁴ N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :

Two liquids of densities $${\rho _1}$$ an $${\rho _2}$$ ($${\rho _2}$$ = 2$${\rho _1}$$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing)

A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

A simple pendulum is being used to determine th value of gravitational acceleration g at a certain place. Th length of the pendulum is 25.0 cm and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is :

A galvanometer having a coil resistance 100 $$\Omega $$ gives a full scale deflection when a current of 1 mA is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of 10 V?

A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by $$\overrightarrow B = 5 \times {10^{ - 8}}\widehat jT$$. The corresponding electric field $$\overrightarrow E $$ is (speed of light c = 3 × 10⁸ ms^–1)

In a double slit experiment, at a certain point on the screen the path difference between the two interfering waves is $${1 \over 8}$$th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is :

As shown in figure, when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centered at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, on the surface of the cavity. R can be detemined by the equation :

The series combination of two batteries, both of the same emf 10 V, but different internal resistance of 20$$\Omega $$ and 5$$\Omega $$, is connected to the parallel combination of two resistors 30$$\Omega $$ and R $$\Omega $$. The voltage difference across the battery of internal resistance 20$$\Omega $$ is zero, the value of R (in $$\Omega $$) is : _______

An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s) ? Give your answer to the nearest integer in kilometer/s _____.

The first member of the Balmer series of hydrogen atom has a wavelength of 6561 Å. The wavelength of the second member of the Balmer series (in nm) is:

A ball is dropped from the top of a 100 m high tower on a planet. In the last $${1 \over 2}s$$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in ms^–2) near the surface on that planet is _____.

Three containers C₁, C₂ and C₃ have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) The value of $$\theta $$ (in °C to the nearest integer) is ..........