AIEEE 2007

In an \(a.c.\) circuit the voltage applied is \(E = {E_0}\,\sin \,\omega t.\) The resulting current in the circuit is \(I = {I_0}\sin \left( {\omega t - {\pi \over 2}} \right).\) The power consumption in the circuit is given by

The half-life period of a ratio-active element \(X\) is same as the mean life time of another ratio-active element \(Y.\) Initially they have the same number of atoms. Then

If \({M_O}\) is the mass of an oxygen isotope \({}_8{O^{17}}\) , \({M_p}\) and \({M_N}\) are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is

Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

In gamma ray emission from a nucleus

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the batter...

A parallel plate condenser with a dielectric of dielectric constant \(K\) between the plates has a capacity \(C\) and is charged to a potential \(V\) volt. The dielectric slab is slowly removed from between the plates and then reinserted. T...

A circular disc of radius \(R\) is removed from a bigger circular disc of radius \(2R\) such that the circumferences of the discs coincide. The center of mass of the new disc is \(\alpha R\) form the center of the bigger disc. The value of ...

The resistance of a wire is \(5\) ohm at \({50^ \circ }C\) and \(6\) ohm at \({100^ \circ }C.\) The resistance of the wire at \({0^ \circ }C\) will be

Photon of frequency \(v\) has a momentum associated with it. If \(c\) is the velocity of light, the momentum is

An ideal coil of \(10H\) is connected in series with a resistance of \(5\Omega\) and a battery of \(5V\). \(2\) second after the connection is made, the current flowing in ampere in the circuit is

If in a \(p\)-\(n\) junction diode, a square input signal of \(10\) \(V\) is applied as shown

Then the output signal across \({R_L}\) will be

Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate ?

The potential at a point \(x\) (measured in \(\mu \,m\)) due to some charges situated on the \(x\)-axis is given by \(V\left( x \right) = 20/\left( {{x^2} - 4} \right)\) volt
The electric field \(E\) at \(x = 4\,\mu \,m\) is given by

An electric charge \({10^{ - 3}}\,\,\mu \,C\) is placed at the origin \((0,0)\) of \(X-Y\) co-ordinate system. Two points \(A\) and \(B\) are situated at \(\left( {\sqrt 2 ,\sqrt 2 } \right)\) and \(\left( {2,0} \right)\) respectively. The...

Charges are placed on the vertices of a square as shown. Let \(\overrightarrow E\) be the electric field and \(V\) the potential at the center. If the charges on \(A\) and \(B\) are interchanged with those on \(D\) and \(C\) respectively, ...

Two lenses of power \(-15\) \(D\) and \(+5\) \(D\) are in contact with each other. The focal length of the combination is

If \({g_E}\) and \({g_M}\) are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio
$${{electro\,\,ch...

If \({C_p}\) and \({C_v}\) denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

When a system is taken from state \(i\) to state \(f\) along the path iaf, it is found that \(Q=50\) cal and \(W=20\) \(cal\). Along the path \(ibf\) \(Q=36\) \(cal.\) \(W\) along the path \(ibf\) is

One end of a thermally insulated rod is kept at a temperature \({T_1}\) and the other at \({T_2}\). The rod is composed of two sections of length \({L_1}\) and \({L_2}\) and thermal conductivities \({K_1}\) and \({K_2}\) respectively. The t...

A Carnot engine, having an efficiency of \(\eta = 1/10\) as heat engine, is used as a refrigerator . If the work done on the system is \(10\) \(J\), the amount of energy absorbed from the reservoir at lower temperature is

A block of mass \(m\) is connected to another block of \(mass\) \(M\) by a spring (massless) of spring constant \(k.\) The block are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a c...

Two identical conducting wires \(AOB\) and \(COD\) are placed at right angles to each other. The wire \(AOB\) carries an electric current \({I_1}\) and \(COD\) carries a current \({I_2}\). The magnetic field on a point lying at a distance $...

A current \(I\) flows along the length of an infinitely long, straight, thin walled pipe. Then

A long straight wire of radius \(a\) carries a steady current \(i.\) The current is uniformly distributed across its cross section. The ratio of the magnetic field at \(a/2\) and \(2a\) is

A charged particle moves through a magnetic field perpendicular to its direction. Then

A charged particle with charge \(q\) enters a region of constant, uniform and mutually orthogonal fields \(\overrightarrow E\) and \(\overrightarrow B\) with a velocity \(\overrightarrow v\) perpendicular to both \(\overrightarrow E\) a...

The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

For the given uniform square lamina \(ABCD\), whose center is \(O,\)

A round uniform body of radius \(R,\) mass \(M\) and moment of inertia \(I\) rolls down (without slipping) an inclined plane making an angle \(\theta\) with the horizontal. Then its acceleration is

Angular momentum of the particle rotating with a central force is constant due to

The displacement of an object attached to a spring and executing simple harmonic motion is given by \(x = 2 \times {10^{ - 2}}\) \(cos\) \(\pi t\) metre. The time at which the maximum speed first occurs is

Two springs, of force constant \({k_1}\) and \({k_2}\) are connected to a mass \(m\) as shown. The frequency of oscillation of the mass is \(f.\) If both \({k_1}\) and \({k_2}\) are made four times their original values, the frequency of os...

A point mass oscillates along the \(x\)-axis according to the law \(x = {x_0}\,\cos \left( {\omega t - \pi /4} \right).\) If the acceleration of the particle is written as \(a = A\,\cos \left( {\omega t + \delta } \right),\) then

A particle of mass \(m\) executes simple harmonic motion with amplitude a and frequency \(v.\) The average kinetic energy during its motion from the position of equilibrium to the end is

In a Young's double slit experiment the intensity at a point where the path difference is \({\lambda \over 6}\) ( \(\lambda\) being the wavelength of light used ) is \(I\). If \({I_0}\) denotes the maximum intensity, \({I \over {{I_0}}}\)...

A sound absorber attenuates the sound level by \(20\) \(dB\). The intensity decreases by a factor of

A \(2\) \(kg\) block slides on a horizontal floor with a speed of \(4m/s.\) It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is \(15N\) and spring constant is \(10, 000\) \(N/m.\) Th...

A particle is projected at \(60^\circ\) to the horizontal with a kinetic energy K. The kinetic energy at the
highest point is