AIPMT 2008

In an a.c. circuit the e.m.f. (\(\varepsilon\)) and the current
(i)  at any instant are given respectively by
\(\varepsilon\) = E0sin\(\omega\)t,   \(i\) = \(I\)0sin(\(\omega\)t \(-\) \(\phi\))
The average power in the circuit over o...

Two radioactive materials X1 and X2 have decay constants \(5\lambda\) and \(\lambda\) respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that X2 will be 1/e after a time

The ground state energy of hydrogen atom is \(-\) 13.6 eV. When its electron is in the first excited state, its excitation energy is

Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be

If M(A; Z), Mp and Mn denote the masses of the nucleus \({}_Z^AX,\) proton and neutron respectively in units of u (1 u = 931.5 MeV/c2) and BE represents its bonding energy in MeV, then

A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is :

A particle of mass m is projected with velocity v making an angle of 45o with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be :

In the circuit shown, the current through the 4 \(\Omega\) resistor is 1 amp when the points P and M are connected to a d.c. voltage source. The potential difference betwen the points M and N is

A current of 3 amp. flows through the 2 \(\Omega\) resistor shown in the circuit. The power dissipated in the 5 \(\Omega\) resistor is

An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from temperature 20oC ? The temperature of boiling water is 100oC

A cell can be balanced against 110 cm and 100 cm of potentiometer wire, respectively with and without being short circuited through a resistance of 10 \(\Omega\). Its internal resistance is

A wire of a certain material is stretched slowly by ten percent. Its new resistance and specific resistance become respectively

The work function of a surface of a photosensitive material is 6.2 eV. The wavelength of the incident radiation for which the stopping potential is 5 V lies in the

In the phenomenon of electric discharge through gases at low pressure, the coloured glow in the tube appears as a result of

A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of 3 \(\times\) 106 m s\(-\)1. The velocity of the particle is

A long solenoid has 500 turns. When a current of 2 ampere is passed through it, the resulting magnetic flux linked with each turn of the solenoid is 4 \(\times\) 10\(-\)3 Wb. The self-inductance of the solenoid is

A circular disc of radius 0.2 meter is placed in a uniform magnetic field of induction \({1 \over \pi }\left( {{{Wb} \over {{m^2}}}} \right)\) in such a way that its axis makes an angle of 60o with \(\overrightarrow B .\) The magnetic flux ...

The velocity of electromagnetic radiation in a medium of permittivity \(\varepsilon\)0 and permeability \(\mu\)0 is given by

A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is

The electric potential at a point in free space due to charge Q coulomb is Q \(\times\) 1011 volts. The electric field at that point is

Two thin lenses of focal lengths f1 and f2 are in contact and coaxial. The power of the combination is

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is 1.39 \(\times\) 109 m and its mean distance from the earth is 1.5 \(\times\) 1011 m. Wh...

At 10oC the value of the density of a fixed mass of an ideal gas divided by it pressure is x. At 110oC this ratio is

If Q, E and W denote respectively the heat added, change in internal energy and the work done in a closed cyclic process, then

A roller coaster is designed such that riders experience ''weightlessness'' as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

Sand is being dropped on a conveyer belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of \(\upsilon\) m/s will be :

Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

Curie temperature above which

A particle shows distance - time curve as given in this figure. The maximum instaneous velocity of the particle is around the point

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms\(-\)1 to 20 ms\(-\)1 while passing through a distance 135 m in t second. The value of t is

The distance travelled by a particle starting from rest and moving with an acceleration \({4 \over 3}\)m s\(-\)2, in the third second is

A galvanometer of resistance 50 \(\Omega\) is connected to a battery of 3 V along with a resistance of 2950 \(\Omega\) in series. A full scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection ...

A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RQ are F1, F2 and F3 respectively and are in the plane of the paper and along the directions shown, the force on the ...

A particle of mass m, charge Q and kinetic energy T enters a transverse uniform magnetic field of induction \(\overrightarrow B\). After 3 seconds the kinetic energy of the particle will be

Two simple harmonic motions of angular frequency 100 and 1000 rad s\(-\)1 have the same displacement amplitude. The ratio of their maximum acceleration is

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39oW and 239oW respectively. What will be the temperature on the new scale, corresponding to a temperature of 39oC on the ...

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90o. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defin...

The voltage gain of an amplifier with 9% negative feedback is 10. The voltage gain without feedback will be

A p-n photodiode is made of a material with a band gap of 2.0 eV. The minimum frequency of the radiation that can be absorbed by the material is nearly

If the lattice parameter for a crystalline structure is 3.6 \(\mathop A\limits^ \circ\), then the atomic radius in fcc crystal is

If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be

Which two of the following five physical parameters have the same dimensions ?
1.  Energy density
2.  Refractive index
3.  Dielectric constant
4.  Young's modulus
5.  Magnetic field

The wave described by y = 0.25 sin(10\(\pi\)x \(-\) 2\(\pi\)t), where x and y are in metres and t in seconds, is a wave travelling along the

A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin(\(\omega\)t + \(\pi\)/6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of it...

Two periodic waves of intensities \(I\)1 and \(I\)2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine ? (g = 10 m/s2)