AIEEE 2003

In the nuclear fusion reaction
\(${}_1^2H + {}_1^3H \to {}_2^4He + n\)$
given that the repulsive potential energy between the two nuclei is \(\sim 7.7 \times {10^{ - 14}}J\), the temperature at which the gases must be heated to initiate t...

If the binding energy of the electron in a hydrogen atom is \(13.6eV,\) the energy required to remove the electron from the first excited state of \(L{i^{ + + }}\) is

A nucleus with \(Z=92\) emits the following in a sequence:
\($\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,{\beta ^ + },{\beta ^ + },\alpha\)$
Then \(Z\) of the resulting nucl...

Which of the following cannot be emitted by radioactive substances during their decay ?

The work done in placing a charge of \(8 \times {10^{ - 18}}\) coulomb on a condenser of capacity \(100\) micro-farad is

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor

Consider the following two statements :
\(A.\) Linear momentum of a system of particles is zero
\(B.\) Kinetic energy of a system of particles is zero.
then

Consider telecommunication through optical fibres. Which of the following statements is not true?

A \(220\) volt, \(1000\) watt bulb is connected across a \(110\) \(volt\) mains supply. The power consumed will be

The nagative \(Zn\) pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by \(0.13g\) in \(30\) minutes. If the electrochemical equivalent of \(Zn\) and \(Cu\) are \(32.5\) and \(31.5\) respectively, the i...

The length of a given cylindrical wire is increased by \(100\%\). Due to the consequent decrease in diameter the change in the resistance of the wire will be

A \(3\) volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current \({\rm I}\), in the circuit will be

The length of a wire of a potentiometer is \(100\) \(cm\), and the \(e.\) \(m.\) \(f.\) of its standard cell is \(E\) volt. It is employed to measure the \(e.m.f.\) of a battery whose internal resistance in \(0.5\Omega .\) If the balance po...

The thermo \(e.m.f.\) of a thermo -couple is \(25\) \(\mu V/{}^ \circ C\) at room temperature. A galvanometer of \(40\) \(ohm\) resistance, capable of detecting current as low as \({10^{ - 5}}\,A,\) is connected with the thermo couple. The ...

An ammeter reads upto \(1\) ampere. Its internal resistance is \(0.81\) \(ohm\). To increase the range to \(10\) \(A\) the value of the required shunt is

Two identical photo-cathodes receive light of frequencies \({f_1}\) and \({f_2}\). If the velocities of the photo electrons (of mass \(m\) ) coming out are respectively \({v_1}\) and \({v_2},\) then

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

When the current changes from \(+ 2A\) to \(-2A\) in \(0.05\) second, an \(e.m.f.\) of \(8\) \(V\) is inducted in a coil. The coefficient of self- induction of the coil is

In the middle of the depletion layer of a reverse- biased \(p\)-\(n\) junction, the

The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the

A strip of copper and another of germanium are cooled from room temperature to \(80K.\) The resistance of

Three charges \(- {q_1}, + {q_2}\) and \(- {q_3}\) are placed as shown in the figure. The \(x\)-component of the force on \(- {q_1}\) is proportional to

A thin spherical conducting shell of radius \(R\) has a charge \(q.\) Another charge \(Q\) is placed at the center of the shell. The electrostatic potential at a point \(P\) a distance \({R \over 2}\) from the center of the shell is

If the electric flux entering and leaving an enclosed surface respectively is \({\phi _1}\) and \({\phi _2},\) the electric charge inside the surface will be

To get three images of a single object, one should have two plane mirrors at an angle of

The image formed by an objective of a compound microscope is

The time period of satellite of earth is \(5\) hours. If the separation between the earth and the satellite is increased to \(4\) times the previous value, the new time period will become

Two spherical bodies of mass \(M\) and \(5M\) & radii \(R\) & \(2R\) respectively are released in free space with initial separation between their centers equal to \(12R\). If they attract each other due to gravitational force only, then th...

The escape velocity for a body projected vertically upwards from the surface of earth is \(11\) \(km/s.\) If the body is projected at an angle of \({45^ \circ }\) with the vertical, the escape velocity will be

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio \({C_p}/{C_V}\) for the gas is

''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or consequence of :

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

A carnot engine takes \(3 \times {10^6}\) cal. of heat from a reservoir at \({627^ \circ }C,\) and gives it to a sink at \({27^ \circ }C\). The work done by the engine is

Which of the following parameters does not characterize the thermodynamic state of mattter?

A horizontal force of \(10\) \(N\) is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is \(0.2\). The weight of the block is

A rocket with a lift-off mass \(3.5 \times {10^4}\,\,kg\) is blasted upwards with an initial acceleration of \(10m/{s^2}.\) Then the initial thrust of the blast is

A light spring balance hangs from the hook of the other light spring balance and a block of mass \(M\) \(kg\) hangs from the former one. Then the true statement about the scale reading is

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads \(49\) \(N,\) when the lift is stationary. If the lift moves downward with an acceleration of \(5 m/{s^2}\), the reading of the sp...

Three forces start acting simultaneously on a particle moving with velocity, \(\overrightarrow v \,\,.\) These forces are represented in magnitude and direction by the three sides of a triangle \(ABC\). The particle will now move with veloc...

A marble block of mass \(2\) \(kg\) lying on ice when given a velocity of \(6\) \(m/s\) is stopped by friction in \(10\) \(s.\) Then the coefficient of friction is

A block of mass \(M\) is pulled along a horizontal frictionless surface by a rope of mass \(m.\) If a force \(P\) is applied at the free end of the rope, the force exerted by the rope on the block is

The magnetic lines of force inside a bar magnet

A thin rectangular magnet suspended freely has a period of oscillation equal to \(T.\) Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its peri...

A magnetic needle lying parallel to a magnetic field requires \(W\) units of work to turn it through \({60^ \circ }.\) The torque needed to maintain the needle in this position will be :

A particle of charge \(- 16 \times {10^{ - 18}}\) coulomb moving with velocity \(10m{s^{ - 1}}\) along the \(x\)-axis enters a region where a magnetic field of induction \(B\) is along the \(y\)-axis, and an electric field of magnitude $${...

A particle of mass \(M\) and charge \(Q\) moving with velocity \(\overrightarrow v\) describe a circular path of radius \(R\) when subjected to a uniform transverse magnetic field of induction \(B.\) The network done by the field when the ...

A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an
angle of \(30^\circ\) with the horizontal. How far from the throwing point will the ball be at the height
of 10 m from the ground?
$$\left[ {g = 1...

A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the
same car is moving at a speed of 100 km/hr, the minimum stopping distance is

The co-ordinates of a moving particle at any time 't' are given by x = \(\alpha\)t3 and y = βt3. The speed to the particle at time 't' is given by

According to Newton's law of cooling, the rate of cooling of a body is proportional to \({\left( {\Delta \theta } \right)^n},\) where \({\Delta \theta }\) is the difference of the temperature of the body and the surrounding, and \(n\) is e...