AIEEE 2005

If radius of the \(\matrix{ {27} \cr {13} \cr }\) \(Al\) nucleus is estimated to be \(3.6\) fermi then the radius of \(\matrix{ {125} \cr {52} \cr } \,Te\) nucleus is estimated to be nearly

A nuclear transformation is denoted by \(X\left( {n,\alpha } \right)\matrix{ 7 \cr 3 \cr } Li.\) Which of the following is the nucleus of element \(X\) ?

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

The intensity of gamma radiation from a given source is \(L\). On passing through \(36\) \(mm\) of lead, it is reduced to \({{\rm I} \over 8}.\) The thickness of lead which will reduce the intensity to \({{\rm I} \over 2}\) will be

Starting with a sample of pure \({}^{66}Cu,{7 \over 8}\) of it decays into \(Zn\) in \(15\) minutes. The corresponding half life is

A parallel plate capacitor is made by stacking \(n\) equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is \('C'\) then the resultant capacitance is

A fully charged capacitor has a capacitance \('C'\). It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity \('s'\) and mass \('m'.\) If the temperature of the block is rai...

A body \(A\) of mass \(M\) while falling vertically downloads under gravity breaks into two-parts; a body \(B\) of mass \({1 \over 3}\) \(M\) and a body \(C\) of mass \({2 \over 3}\) \(M.\) The center of mass of bodies \(B\) and \(C\) taken...

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force \('\,\,\overrightarrow F \,\,'\) is applied at the point \(P\) parallel to \(AB,\) such that the object has only the translational motion without rot...

The block of mass \(M\) moving on the frictionless horizontal surface collides with the spring of spring constant \(k\) and compresses it by length \(L.\) The maximum momentum of the block after collision is

A mass \('m'\) moves with a velocity \('v'\) and collides inelastically with another identical mass. After collision the \({1^{st}}\) mass moves with velocity \({v \over {\sqrt 3 }}\) in a direction perpendicular to the initial direction of...

Two voltmeters, one of copper and another of silver, are joined in parallel. When a total charge \(q\) flows through the voltmeters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are \({Z_1}\)...

An energy source will supply a constant current into the load if its internal resistance is

In a potentiometer experiment the balancing with a cell is at length \(240\) \(cm.\) On shunting the cell with a resistance of \(2\Omega ,\) the balancing length becomes \(120\) \(cm\). The internal resistance of the cell is

In the circuit, the galvanometer \(G\) shows zero deflection. If the batteries \(A\) and \(B\) have negligible internal resistance, the value of the resistor \(R\) will be -

The resistance of hot tungsten filament is about \(10\) times the cold resistance. What will be resistance of \(100\) \(W\) and \(200\) \(V\) lamp when not in use ?

A moving coil galvanometer has \(150\) equal divisions. Its current sensitivity is \(10\)- divisions per milliampere and voltage sensitivity is \(2\) divisions per millivolt. In order that each division reads \(1\) volt, the resistance in $...

Two sources of equal \(emf\) are connected to an external resistance \(R.\) The internal resistance of the two sources are \({R_1}\) and \({R_2}\left( {{R_1} > {R_1}} \right).\) If the potential difference across the source having interna...

A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

A photocell is illuminated by a small bright source placed \(1\) \(m\) away. When the same source of light is placed \({1 \over 2}\) \(m\) away, the number of electrons emitted by photo-cathode would

If the kinetic energy of a free electron doubles, it's deBroglie wavelength changes by the factor

A coil of inductance \(300\) \(mH\) and resistance \(2\,\Omega\) is connected to a source of voltage \(2\) \(V\). The current reaches half of its steady state value in

One conducting \(U\) tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field \(B\) is perpendicular to the plane of the figure. If each tube moves towards the other at a consta...

In a full wave rectifier circuit operating from \(50\) \(Hz\) mains frequency, the fundamental frequency in the ripple would be

In a common base amplifier, the phase difference between the input signal voltage and output voltage is

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than \(2480\) \(nm\) is incident on it. The band gap in \((eV)\) for the semiconductor is

Two thin wire rings each having a radius \(R\) are placed at a distance \(d\) apart with their axes coinciding. The charges on the two rings are \(+q\) and \(-q.\) The potential difference between the centres of the two rings is

A charged ball \(B\) hangs from a silk thread \(S,\) which makes angle \(\theta\) with a large charged conducting sheet \(P,\) as shown in the figure. The surface charge density \(\sigma\) of the sheet is proportional to
f

Two point charges \(+8q\) and \(-2q\) are located at \(x=0\) and \(x=L\) respectively. The location of a point on the \(x\) axis at which the net electric field due to these two point charges is zero is

A thin glass (refractive index \(1.5\)) lens has optical power of \(-5\) \(D\) in air. Its optical power in a liquid medium with refractive index \(1.6\) will be

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is \({4 \over 3}\) and the fish is \(12\) \(cm\) below the surface, the radius of this circle in \(cm\) is

Average density of the earth

The change in the value of \(g\) at a height \(h\) above the surface of the earth is the same as at a depth \(d\) below the surface of earth. When both \(d\) and \(h\) are much smaller than the radius of earth, then which one of the followi...

A particle of mass \(10\) \(g\) is kept on the surface of a uniform sphere of mass \(100\) \(kg\) and radius \(10\) \(cm.\) Find the work to be done against the gravitational force between them to take the particle far away from the sphere ...

A gaseous mixture consists of \(16\) \(g\) of helium and \(16\) \(g\) of oxygen. The ratio \({{Cp} \over {{C_v}}}\) of the mixture is

Which of the following is incorrect regarding the first law of thermodynamics?

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

A system goes from \(A\) to \(B\) via two processes \(I\) and \(II\) as shown in figure. If \(\Delta {U_1}\) and \(\Delta {U_2}\) are the changes in internal energies in the processes \(I\) and \(II\) respectively, then

The figure shows a system of two concentric spheres of radii \({r_1}\) and \({r_2}\) are kept at temperatures \({T_1}\) and \({T_2}\), respectively. The radial rate of flow of heat in a substance between the two concentric spheres is propor...

A particle of mass 0.3 kg subjected to a force \(F=-kx\) with \(k=15\) \(N/m\). What will be its initial acceleration if it is released from a point 20 cm away from the origin?

A block is kept on a frictionless inclined surface with angle of inclination \('\,\alpha \,'.\) The incline is given an acceleration \(a\) to keep the block stationary. Then \(a\) is equal to

Consider a car moving on a straight road with a speed of \(100\) \(m/s\). The distance at which car can be stopped is \(\left[ {{\mu _k} = 0.5} \right]\)

A smooth block is released at rest on a \({45^ \circ }\) incline and then slides a distance \('d'\). The time taken to slide is \('n'\) times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A magnetic needle is kept in a non-uniform magnetic field. It experiences :

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then

Two concentric coils each of radius equal to \(2\) \(\pi\) \(cm\) are placed at right angles to each other. \(3\) ampere and \(4\) ampere are the currents flowing in each coil respectively . The magnetic induction in Weber / \({m^2}\) at...

A charged particle of mass \(m\) and charge \(q\) travels on a circular path of radius \(r\) that is perpendicular to a magnetic field \(B.\) The time taken by the particle to complete one revolution is

Two thin, long, parallel wires, separated by a distance \('d'\) carry a current of \('i'\) \(A\) in the same direction. They will

A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity
changes to 5 m/s northwards. The average acceleration in this time is

A car starting from rest accelerates at the rate f through a distance S, then continues
at constant speed for time t and then decelerates at the rate \({f \over 2}\) to come to rest. If the
total distance traversed is 15 S, then