AIPMT 2012 Prelims

In an electrical circuit R, L, C and a.c. voltage source are all connected in series. When L is removed from the circuit, the phase difference between the voltage and the current in the circuit is If instead, C is removed from the circuit, ...

The current \((I)\) in the inductance is varying with time according to the plot shown in figure.

Which one of the following is the correct variation of voltage with time in the coil ?

Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths \(\lambda\)1 : \(\lambda\)2 emitted in the two cases is

An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be

If the nuclear radius of 27Al is 3.6 fermi, the approximate nuclear radius of 64Cu in fermi is

A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A1 and 160 g of A2. The amount of the two in the mixture will become equal after

Two spheres A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity \({v \over 2}\) in a direction perpendicular to the original direction. The ...

Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weights 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre ...

A ring is made of a wire having a resistance R0 = 12 \(\Omega\). Find the points A and B, as shown in the figure, at which a current carrying conductor should be connected so that the resistance R of the sub circuit between these point is ...

In the circuit shown the cells A and B have negligible resistances. For VA = 12 V, R1 = 500 \(\Omega\) and R = 100 \(\Omega\) the galvanometer (G) shows no deflection. The value of Vs is

If voltage across a bulb rated 220 volt-100 watt drops by 2.5% of its rated value, the percentage of the rated value by which the power would decrease is

Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited to the ground state irradiates a photosensitive material. The stopping potential is measured to be 3.57 V. The threshold frequency of the material is

A 200 W sodium street lamp emits yellow light of wavelength 0.6 \(\mu\)m. Assuming it to be 25% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is

An \(\alpha\)-particle moves in a circular path of radius 0.83 cm in the presence of a magnetic field of 0.25 Wb/m2. The de Broglie wavelength associated with the particle will be

A coil of resistance 400 \(\Omega\) is placed in a magnetic field. If the magnetic flux \(\phi\) (Wb) linked with the coil varies with time t (sec) as \(\phi = 50{t^2} + 4\).
The current in the coil at t = 2 sec is

The electric field associated with an em wave in vacuum is given by
E = \(\widehat i\) 40 cos (kz \(-\) 6 \(\times\) 108 t) where E, z and t are in volt/m, meter and seconds respectively. The value of wave vector k is

What is the flux through a cube of side \(a\) if a point charge of q is at one of its corner?

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of ...

Four point charges \(-\)Q, \(-\)q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is

A concave mirror of focal length \(f\)1 is placed at a distance of d from a convex lens of focal length \(f\)2. A beam of light coming from infinity and falling on this convex lens \(-\) concave mirror combination returns to infinity. The d...

When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index

The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20 cm. The focal length of lenses are

A ray of light is incident at an angle of incidence i, on one face of a prism of angle A (assumed to be small ) and emerges normally from the opposite face. If the refractive index of the prism is \(\mu\). the angle of incidence i, is near...

A geostationary satellite is orbiting the earth at a height of 5R above the surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is

A spherical planet has a mass MP and diameter DP. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

The height at which the weight of a body becomes \({\left( {{1 \over {16}}} \right)^{th}}\), its weight on the surface of earth (radius R), is

A thermodynamic system is taken through the cycle ABCD as shown in figure. Heat rejected by the gas during the cycle is

One mole of an ideal gas goes from an initial state A to final state B via two processes : It first undergoes isothermal expansion from volume V to 3V and then its volume is reduced from 3V to V at constant pressure. The correct P-V diagram...

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It

A particle has initial velocity \(\left( {2\overrightarrow i + 3\overrightarrow j } \right)\) and acceleration \(\left( {0.3\overrightarrow i + 0.2\overrightarrow j } \right)\). The magnitude of velocity after 10 seconds will be

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

The motion of a particle along a straight line is described by equation x = 8 + 12t \(-\) t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

An alternating electric field, of frequency \(v\), is applied across the does (radius = R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K)...

A milli voltmeter of 25 milli volt range is to be converted into an ammeter of 25 ampare range. The value (in ohm) of neccessary shunt will be

Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\) and 2\(I\), respectively. The resultant magnetic field induction at the centre will be

Liquid oxygen at 50 K is heated to 300 K at constant pressure of 1 atm. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time ?

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?

ABC is an equilateral triangle with O as its centre. \({\overrightarrow F _1},{\overrightarrow F _2}\) and \({\overrightarrow F _3}\) represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is z...

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45o, the speed of the car is

Two ideal diodes are connected to a battery as shown in the circuit. The current supplied by the battery is

C and Si both have same lattice structure; having 4 bonding electrons in each. However, C is insulator where as Si is intrinsic semiconductor. This is because

Transfer characteristics [output voltage (V0) vs input voltage (Vi)] for a base biased transistor in CE configuration is as shown in the figure. For using transistor as a switch, it is used

The figure shows a logic circuit with two inputs A and B and the output C. The voltage wave forms across A, B and C are as given. The logic circuit gate is

In a CE transistor amplifier, the audio signal voltage across the collector resistance of 2 k\(\Omega\) is 2 V. If the base resistance is 1 k\(\Omega\) and the current amplification of the transistor is 100, the input signal voltage is

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

When a string is divided into three segments of length \(l\)1, \(l\)2 and \(l\)3 the fundamental frequencies of these three segments are \({\upsilon _1},{\upsilon _2}\) and \({\upsilon _3}\) respectively. The original fundamental frequency ...

Two sources of sound placed close to each other, are emitting progressive waves given by
y1 = 4sin600\(\pi\)t and y2 = 5sin608\(\pi\)t
An observer located near these two sources of sound will hear

The potential energy of a particle in a force field is \(U = {A \over {{r^2}}} - {B \over r}\) where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the ...

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s\(-\)1. It collides with a horizontal spring of force constant 200 N m\(-\)1. The maximum compression produced in the spring will be