AIPMT 2012 Mains

The instantaneous values of alternating current and voltage in a circuit are given as
\(i = {1 \over {\sqrt 2 }}\) sin (100 \(\pi\)t) ampere
\(e = {1 \over {\sqrt 2 }}\sin \left( {100\pi t + {\pi \over 3}} \right)\) Volt
The average powe...

The half life of a radioactive nucleus is 50 days. The time invertal (t2 \(-\) t1) between the time t2 when \({2 \over 3}\) of it has decayed and the time t1 when \({1 \over 3}\) of it had decayed is

The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

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

Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70cm. The distance of the centre of mass from the orgin is :

The power dissipated in the circuit shown in the figure is 30 watts. The value of R is

A cell having an emf \(\varepsilon\) and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by

Two radiations of photons energies 1 eV and 2.5 eV, successively illuminate a photosensitive metallic surface of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons is

If the momentum of an electron is changed by P, then the de Broglie wavelength associated with changes by 0.5%. The initial momentum of electron will be

In a coil of resistance 10 \(\Omega\), the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in weber is

The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagatting in vacuum is equal to

Two metallic spheres of radii 1 cm and 3 cm are given charges of \(-\)1 \(\times\) 10\(-\)2 C and 5 \(\times\) 10\(-\)2 C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index.

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its enf closer to the pole is 20 cm away from the mirror. The length of the image is

If \({v_e}\) is escape velocity and \({v_o}\) is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by

Which one of the following plots represents the variation of gravitiational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)

An ideal gas goes from state A to state B via three different processes as indicated in the P-V diagram.

If Q1, Q2, Q3 indicate the heat absorbed by the gas along the three processes and \(\Delta\)U1, \(\Delta\)U2, \(\Delta\)U3 indicat...

A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

A magnetic needle suspended parallel to a magnetic field requires \(\sqrt 3 J\) of work to turn it through 60o. The torque needed to maintain the needle in this position will be

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. What should be the energy of an \(\alpha\)-particle to describe a circle of same radius in the same field?

A slab of stone of area 0.36 m2 and thickness 0.1 m is exposed on the lower surface to steam at 100oC. A block of ice at 0oC rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. The thermal conductivity of slab is
(G...

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the e...

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through

A car of mass m is moving on a level circular track of radius R. If \(\mu\)s represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by

To get an output Y= 1 in given circuit which of the following input will be correct ?

The input resistance of a silicon transistor is 100 \(\Omega\). Base current is changed by 40 \(\mu\)A which results in a change in collector current by 2 mA. This transistor is used as a common emitter amplifier with a load resistance of...

The dimensions of \({\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}\) are

A train moving at a speed of 220 m s\(-\)1 towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver ...

The equation of a simple harmonic wave is given by
y = 3 sin\({\pi \over 2}\)(50t \(-\) x),
where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this car is proportional to