Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8 g cm^{-3}, the angle remains the same. If the density of the material of the sphere is 1.6 g cm^{-3}, what is the dielectric constant of the liquid?

A small particle of mass *m* is projected at an angle with the *x-axis* with an initial velocity *v _{0}* in the

*x-y plane*as shown in the figure.

At a time the angular momentum of the particle is

Note: are unit vectors along *x, y* and *z-axis* respectively.

For a particle in uniform circular motion, the acceleration at a point *P(R, )* on the circle of radius *R* is (Here is measured from the x-axis)

Two fixed frictionless inclined planes making an angle 30° and 60° with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?

The equation of a wave on a string of linear mass density of 0.04 kg m^{-1} is given by

What is the tension in the string?

A radioactive sample S1 having an activity of 5 m Ci has twice the number of nuclei as another sample S2 which has an activity of 10 m Ci. The half lives of S1 and S2 can be

Half life of a radioactive element is 10 days. The time during which quantity remains 10 of initial mass will be

The half life period of a radioactive substance is 5 min. The amount of substance decayed in 20 min will be

A reactor is generating 1000 kW of power and 200 MeV of energy may be obtained per fission of U235. The rate of nuclear fission in the reactor is

Fast neutrons can easily be slowed down by

Two nucleons are at a separation of 1 × 10–15 m. The net force between them is F1 if both are protons, F2 if both are neutrons and F3 if one is a proton and other is a neutron. In such a case

For a nucleus to be stable, the correct relation between neutron number N and proton number Z is

The average binding energy per nucleon in the nucleus of atom is approximately

Let C be the capacitance of a capacitor discharging through a resistor *R*. Suppose *t _{1}* is the time taken for the energy stored in the capacitor to reduce to half its initial value and

*t*is the time taken for the charge to reduce to one-fourth its initial value. Then what will be the ratio

_{2}*t*/

_{1}*t*?

_{2}

The masses of neutron and proton are 1.0087 amu and 1.0073 amu respectively. If a helium nucleus (alpha particles) of mass 4.0015 amu is formed by combining neutrons and protons. The binding energy of the helium nucleus will be (1 amu = 931 MeV)

Size of nucleus is in the order of

A particle is moving with velocity where *K* is a constant. The general equation for its path is

In the circuit shown below, the key K is closed at *t = 0*. What will be the current through the battery?

In a series *LCR* circuit *R = 200* and the voltage and the frequency of the main supply is *220 V* and *50 Hz* respectively. On taking out the capacitance from the circuit the current lags behind the voltage by *30°*. On taking out the inductor from the circuit the current leads the voltage by *30°*. The power dissipated in the LCR circuit is

Let there be a spherically symmetric charge distribution with charge density varying as upto *r = R*, and *r(r) = 0* for *r > R*, where *r* is the distance from the origin. The electric field at a distance *r (r < R)* from the origin is given by

0.067 molar aqueous solution of a binary electrolyte A+B– shows 2.46 atm osmotic pressure at 27°C. What fraction of A+B– remains unionised?

Osmotic pressure of a blood sample is 4.92 atm at 27°C. Which of the following is not isotonic with blood

sample?

Degree of dissociation of three binary electrolytes AB, CD and EF are 60%, 20% and 100% in the solution having same mole fraction of water. Ratio of lowering in vapour pressure of their solution is

20 g of non-electrolyte, non-volatile solute (CxH2xOx), when dissolved in 100 gm water at 100°C, lowers the vapour pressure of solution by 1/100 th of the vapour pressure of pure water at this temperature. What is formula of the compound?

A complex is written as M(en)y.xBr. Its 0.05 molar solution shows 2.46 atm osmotic pressure at 27°C.Assuming 100% ionisation and coordination number of metal (III) is six, complex may be

A water sample contains 9.5% MgCl2 and 11.7% NaCl (by weight). Assuming 80% ionisation of each salt.Boiling point of water will be approximately (Kb= 0.52)

2 millimolar solution of sodium ferrocyanide is 60% dissociated at 27°C. Osmotic pressure of the solution is

If a solute undergoes dimerisation and trimerisation, the minimum values of the van't Hoff factors are

The value of observed and calculated molecular weights of silver nitrate are 92.64 and 170 respectively. The degree of dissociation of silver nitrate is

A 0.2 molal aqueous solution of weak acid HX is 20% ionized. The freezing point of solution is(Kf=1.86)

When 20 g of napthanoic acid (C11H8O2) is dissolved in 50 g of benzene (K, = 1.72 K kg/mol) a freezing point

depression of 2 K is observed. The van't Hoff factor (i) is

A nucleus of mass *M + ∆m* is at rest and decays into two daughter nuclei of equal mass *M / 2* each. Speed of light is c.

The speed of daughter nuclei is

A nucleus of mass *M + ∆m* is at rest and decays into two daughter nuclei of equal mass *M / 2* each. Speed of light is c.

The binding energy per nucleon for the parent nucleus is *E _{1}* and that for the daughter nuclei is

*E*. Then

_{2}

An initially parallel cylindrical beam travels in a medium of refractive index where and are positive constants and *I* is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

What will be the initial shape of the wavefront of the beam?

An initially parallel cylindrical beam travels in a medium of refractive index where and are positive constants and *I* is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

What will be the speed of light in the medium?

An initially parallel cylindrical beam travels in a medium of refractive index where and are positive constants and *I* is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

As the beam enters the medium, it will

A transparent solid cylindrical rod has a refractive index of . It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure

The incident angle θ for which the light ray grazes along the wall of the rod is

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature θ along the length x of the bar from its hot end is best described by which of the figures?

A charge *Q* is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on *Q* is zero, then what will be the *Q/q* ?

Consider a rubber ball freely falling from a height *h* = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then what will be the velocity as a function of time and the height as function of time?

A motor cycle starts from rest and accelerates along a straight path at 2 m/s^{2}. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest? (Speed of sound = 330 ms^{-1}).

A particle has an initial velocity and an acceleration of . What will be its speed after 10 s?

The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (*hc* = 1240 eV nm)

Two moles of helium gas are taken over the cycle *ABCDA*, as shown in the P - T diagram

The net work done on the gas in the cycle *ABCDA* is

Two moles of helium gas are taken over the cycle *ABCDA*, as shown in the P - T diagram

The work done on the gas in taking it from *D to A* is

Two moles of helium gas are taken over the cycle *ABCDA*, as shown in the P - T diagram

Assuming the gas to be ideal the work done on the gas in taking it from A to B is

An inductor of inductance *L = 400 mH* and resistors of resistances *R _{1}* = 2 and

*R*= 2 are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch

_{2}*S*is closed at

*t = 0.*What will be the potential drop across

*L*as a function of time?

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree (= 0.5°), then the least count of the instrument will be

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area *A* and wire 2 has cross-sectional area *3A*. If the length of wire 1 increases by ∆x on applying force *F*, how much force is needed to stretch wire 2 by the same amount?

The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth is