Solved papers for JEE Main & Advanced AIEEE Solved Paper-2003
done AIEEE Solved Paper-2003 Total Questions - 74
question_answer1) A particle of mass M and charge Q moving with velocity v describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circle is
AIEEE Solved Paper-2003
question_answer2) A particle of charge \[-16\times {{10}^{-18}}C\] 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 \[{{10}^{4}}\] V/m is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is
AIEEE Solved Paper-2003
question_answer3) 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 period of oscillation is T', the ratio T'/T is
AIEEE Solved Paper-2003
question_answer4) A magnetic needle lying parallel to a magnetic field requires W unit of work to turn it through \[{{60}^{o}}\]. The torque needed to maintain the needle in this position will be
AIEEE Solved Paper-2003
question_answer7) 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 spring balance will be
AIEEE Solved Paper-2003
question_answer8) The length of a wire of a potentiometer is 100 cm and the emf of its stand and cell is. E volt. It is employed to measure the emf of a battery whose internal resistance is \[0.5\,\,\Omega \]. If the balance point is obtained at \[1=30\] cm from the positive end, the emf of the battery is
AIEEE Solved Paper-2003
A)
\[\frac{30\,E}{100.5}\]
doneclear
B)
\[\frac{30\,E}{100-05}\]
doneclear
C)
\[\frac{30\,(E-0.5i)}{100}\], where \[i\] is the current in the potentiometer wire
question_answer11) The thermo-emf of a thermocouple is \[25\mu V{{/}^{o}}C\] at room temperature. A galvanometer of \[40\,\Omega \]. resistance, capable of detecting current as low as \[{{10}^{-5}}\] A, is connected with the thermocouple. The smallest temperature difference that can be detected by this system is
AIEEE Solved Paper-2003
question_answer12) The negative Zn-pole of Daniell cell, sending a constant current through a circuit, decreases in mass by \[0.13\]g in 30 min. If the electrochemical equivalent of Zn and Cu are \[32.5\] and \[31.5\] respectively, the increase in the mass of the positive Cu-pole in this time is
AIEEE Solved Paper-2003
question_answer14) A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then, the relation between the moment of inertia \[{{I}_{X}}\] and \[{{I}_{Y}}\] is
question_answer15) The time period of a satellite of earth is 5 h. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become
AIEEE Solved Paper-2003
question_answer16) A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is
AIEEE Solved Paper-2003
question_answer18) When \[{{U}^{238}}\] nucleus originally at rest, decays by emitting an alpha particle having a speed u, the recoil speed of the residual nucleus is
AIEEE Solved Paper-2003
question_answer19) Two spherical bodies of mass M and 5 M and radii R and 2 R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
question_answer20) The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the
AIEEE Solved Paper-2003
A)
crystal structure
doneclear
B)
variation of the number of charge carriers with temperature
doneclear
C)
type of bonding
doneclear
D)
variation of scattering mechanism with temperature
question_answer21) A car moving with a speed of 50 km/h, can be stopped by brakes after atleast 6 m. If the same car is moving at a speed of 100 km/h, the minimum stopping distance is
AIEEE Solved Paper-2003
question_answer22) 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 \[{{30}^{o}}\] with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? \[[g=10\,m/{{s}^{2}},\sin {{30}^{o}}=1/2,\cos {{30}^{o}}=\sqrt{3}/2]\]
question_answer23) An ammeter reads upto 1 A. Its internal resistance is \[0.81\,\,\Omega \]. To increase the range to 10 A, the value of the required shunt is
AIEEE Solved Paper-2003
question_answer25) Three forces start acting C simultaneously on a particle moving with velocity v. These forces are represented in magnitude and direction by the three sides of a \[\Delta ABC\] (as shown). The particle will now move with velocity
AIEEE Solved Paper-2003
A)
less than v
doneclear
B)
greater than v
doneclear
C)
\[\left| v \right|\] in the direction of largest force BC
question_answer26) Resultant force is zero, as three forces acting on the particle can be represented in magnitude and direction by three sides of a triangle in same order. Hence, by Newton's 2nd law \[\left( F=m\frac{d\,\,v}{dt} \right)\], particle velocity (v) will be same. (\[\because \] if F = 0, v = constant) 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
AIEEE Solved Paper-2003
question_answer27) 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
AIEEE Solved Paper-2003
question_answer28) A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10s. Then, the coefficient of friction is
AIEEE Solved Paper-2003
question_answer29) 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,
AIEEE Solved Paper-2003
question_answer31) . 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
AIEEE Solved Paper-2003
question_answer32) 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
AIEEE Solved Paper-2003
A)
both the scales read M kg each
doneclear
B)
the scale of the lower one reads M kg and of the upper one zero
doneclear
C)
the reading of the two scales can be anything but the sum of the readings will be M kg
question_answer33) A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then, the elastic energy stored in the wire is
AIEEE Solved Paper-2003
question_answer34) 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 \[{{45}^{o}}\] with the vertical, the escape velocity will be
AIEEE Solved Paper-2003
question_answer35) A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes \[5T/3\], then the ratio of \[\frac{m}{M}\] is
AIEEE Solved Paper-2003
question_answer36) "Heat cannot be itself flow from a body at lower temperature to a body at higher temperature" is a statement or consequence of
AIEEE Solved Paper-2003
question_answer37) Two particles A and B of equal masses are suspended from two massless springs of spring constants \[{{k}_{1}}\] and \[{{k}_{2}}\], respectively. If the maximum velocities, during oscillations are equal, the ratio of amplitudes of A and B is
AIEEE Solved Paper-2003
question_answer38) The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is
AIEEE Solved Paper-2003
question_answer39) The displacement y of a wave travelling in the x-direction is given by \[y={{10}^{-4}}\sin \left( 600\,t-2x+\frac{\pi }{3} \right)\] metre where, \[x\] is expressed in metres and t in seconds. The speed of the wave motion, in \[m{{s}^{-1}}\] is
AIEEE Solved Paper-2003
question_answer40) When the current changes from \[+2\] A to \[-2\] A in \[0.05\] s, an emf of 8 V is induced in a coil. The coefficient of self-induction of the coil is
AIEEE Solved Paper-2003
question_answer41) In an oscillating LC circuit, the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is
AIEEE Solved Paper-2003
question_answer43) Let F be the force acting on a particle having position vector r and \[\tau \] be the torque of this force about the origin. Then,
AIEEE Solved Paper-2003
question_answer44) A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is
AIEEE Solved Paper-2003
question_answer45) A nucleus with \[Z=92\] emits the following in a sequence: \[\alpha ,\alpha ,{{\beta }^{-}},{{\beta }^{-}},\alpha ,\alpha ,\alpha ,\alpha ;{{\beta }^{-}},{{\beta }^{-}},\alpha ,{{\beta }^{+}},{{\beta }^{+}},\alpha \]. The Z of the resulting nucleus is
AIEEE Solved Paper-2003
question_answer47) A 3 V battery with negligible internal resistance is connected in a circuit as shown in the figure. The current I, in the circuit will be
AIEEE Solved Paper-2003
question_answer48) A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor
AIEEE Solved Paper-2003
question_answer49) The displacement of a particle varies according to the relation \[x=4\,(\cos \pi \,t+\sin \pi t)\]. The amplitude of the particle is
AIEEE Solved Paper-2003
question_answer50) A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point P at a distance R/2 from the centre of the shell is
AIEEE Solved Paper-2003
question_answer52) The coordinates of a moving particle at any time t are given by \[x=\alpha {{t}^{3}}\] and \[y=\beta {{t}^{3}}\]. The speed of the particle at time t is given by
AIEEE Solved Paper-2003
question_answer53) 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
AIEEE Solved Paper-2003
question_answer55) A Carnot engine takes \[3\times {{10}^{6}}\] cal of heat from a reservoir at \[{{627}^{o}}C\] and gives it to a sink at \[{{27}^{o}}C\]. The work done by the engine is
AIEEE Solved Paper-2003
question_answer56) A spring of spring constant \[5\times {{10}^{3}}\,N/m\] is stretched initially by 5 cm from the unstretched position. Then, the work required to stretch it further by another 5 cm is
AIEEE Solved Paper-2003
question_answer57) A metal wire of linear mass density of \[9.8\] g/m is stretched with a tension of 10 kg-wt between two rigid supports 1 m apart. The wire passes at its middle point between the poles of a permanent magnet and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n of the alternating source is
AIEEE Solved Paper-2003
question_answer58) A tuning fork of known frequency 256 Hz makes 5 beats/s with the vibrating string of a piano. The beat frequency decreases to 2 beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
AIEEE Solved Paper-2003
question_answer59) A body executes simple harmonic motion. The potential energy (PE), the kinetic energy (KE) and total energy (TE) are measured as function of displacement \[x\]. Which of the following statements is true?
AIEEE Solved Paper-2003
question_answer60) In the nuclear fusion reaction, \[_{1}^{2}H+_{1}^{3}H\to _{2}^{4}He+n\] given that the repulsive potential energy between the two nuclei is \[7.7\times {{10}^{-14}}\] J the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant \[k=1.38\times {{10}^{-23}}J/K\]]
AIEEE Solved Paper-2003
question_answer62) The wavelengths involved in the spectrum of deuterium \[\left( _{1}^{2}D \right)\] are slightly different from that of hydrogen spectrum, because
AIEEE Solved Paper-2003
A)
sizes of the two nuclei are different
doneclear
B)
nuclear forces are different in the two cases
doneclear
C)
masses of the two nuclei are different
doneclear
D)
attraction between the electron and the nucleus is different in the two cases
question_answer64) If the binding energy of the electron in a hydrogen atom is \[13.6\] eV, the energy required to remove the electron from the first excited state of \[L{{i}^{2+}}\] is
AIEEE Solved Paper-2003
question_answer65) A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to
AIEEE Solved Paper-2003
question_answer66) A rocket with a lift-off mass \[3.5\times {{10}^{4}}\] kg is blasted upwards with an initial acceleration of \[10\,m/{{s}^{2}}\] . Then, the initial thrust of the blast is
AIEEE Solved Paper-2003
question_answer68) 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
AIEEE Solved Paper-2003
question_answer73) According to Newton's law of cooling, the rate of cooling of a body is proportional to \[{{(\Delta \theta )}^{n}}\], where \[\Delta \theta \] is the difference of the temperature of the body and the surroundings and n is equal to
AIEEE Solved Paper-2003
question_answer74) 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
AIEEE Solved Paper-2003