# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2003

### done AIEEE Solved Paper-2003 Total Questions - 224

• 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

A)
$\left( \frac{M{{v}^{2}}}{R} \right)2\pi R$

B)
zero

C)
BQ $2\pi R$

D)
BQv $2\pi R$

• 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

A)
${{10}^{3}}$ Wb / ${{m}^{2}}$

B)
${{10}^{5}}$ Wb/${{m}^{2}}$

C)
${{10}^{16}}$ Wb/${{m}^{2}}$

D)
${{10}^{-3}}$ Wb/${{m}^{2}}$

• 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

A)
$\frac{1}{2\sqrt{2}}$

B)
$\frac{1}{2}$

C)
2

D)
$\frac{1}{4}$

• 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

A)
$\sqrt{3}$ W

B)
W

C)
$(\sqrt{3}/2)$W

D)
2 W

• question_answer5) The magnetic lines of force inside a bar magnet     AIEEE  Solved  Paper-2003

A)
are from north-pole to south-pole of the magnet

B)
do not exist

C)
depend upon the area of cross-section of the bar magnet

D)
are from south-pole to north-pole of the magnet

• question_answer6) Curie temperature is the temperature above which     AIEEE  Solved  Paper-2003

A)
a ferromagnetic material becomes paramagnetic

B)
a paramagnetic material becomes  diamagnetic

C)
a ferromagnetic material becomes diamagnetic

D)
a paramagnetic material becomes ferromagnetic

• 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

A)
24 N

B)
74 N

C)
15 N

D)
49 N

• 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)
$\frac{30\,E}{100.5}$

B)
$\frac{30\,E}{100-05}$

C)
$\frac{30\,(E-0.5i)}{100}$, where $i$ is the current in the potentiometer wire

D)
$\frac{30\,E}{100}$

• question_answer9) A strip of copper and another of germanium are cooled from room temperature to 80 K. The resistance of   AIEEE  Solved  Paper-2003

A)
each of these decreases

B)
copper strip increases and that of germanium decreases

C)
copper strip decreases and that of germanium increases

D)
each of the above increases

• question_answer10) Consider telecommunication through optical fibres. Which of the following statements is not true?     AIEEE  Solved  Paper-2003

A)
Optical fibres can be of graded refractive index

B)
Optical fibres are subjected to electro- magnetic interference from outside

C)
Optical fibres have extremely low transmission loss

D)
Optical fibres may have homogeneous core with a suitable cladding

• 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

A)
${{16}^{o}}C$

B)
${{12}^{o}}C$

C)
${{8}^{o}}C$

D)
${{20}^{o}}C$

• 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

A)
$0.180$ g

B)
$0.141$ g

C)
$0.126$g

D)
$0.242$ g

• question_answer13) Dimensions of $\frac{1}{{{\mu }_{0}}\,{{\varepsilon }_{0}}}$, where symbols have their usual meaning, are     AIEEE  Solved  Paper-2003

A)
$[{{L}^{-1}}T]$

B)
$[{{L}^{2}}{{T}^{2}}]$

C)
$[{{L}^{2}}{{T}^{-2}}]$

D)
$[L{{T}^{-1}}]$

• 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

A)
${{l}_{Y}}=32\,{{l}_{X}}$

B)
${{l}_{Y}}=16\,{{l}_{X}}$

C)
${{l}_{Y}}=\,{{l}_{X}}$

D)
${{l}_{Y}}=\,64{{l}_{X}}$

• 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

A)
10 h

B)
80 h

C)
40 h

D)
20 h

• 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

A)
$\frac{L}{4}$

B)
2L

C)
4L

D)
$\frac{L}{2}$

• question_answer17) Which of the following radiations has the least wavelength?     AIEEE  Solved  Paper-2003

A)
$\gamma$-rays

B)
$\beta$-rays

C)
$\alpha$-rays

D)
$X$-rays

• 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

A)
$\frac{4\,u}{238}$

B)
$-\frac{4\,u}{238}$

C)
$\frac{4\,u}{234}$

D)
$-\frac{4\,u}{238}$

• 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

A)
$2.5$ R

B)
$4.5$ R

C)
$7.5$ R

D)
$1.5$ R

• 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

B)
variation of the number of charge carriers with temperature

C)
type of bonding

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

A)
12m

B)
18m

C)
24m

D)
6m

• 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?              $[g=10\,m/{{s}^{2}},\sin {{30}^{o}}=1/2,\cos {{30}^{o}}=\sqrt{3}/2]$

A)
$5.20$ m

B)
$4.33$ m

C)
$2.60$ m

D)
$8.66$ m

• 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

A)
$0.03\,\,\Omega$

B)
$0.3\,\,\Omega$

C)
$0.9\,\,\Omega$

D)
$0.09\,\,\Omega$

• question_answer24) The physical quantities not having same dimensions are     AIEEE  Solved  Paper-2003

A)
torque and work

B)
momentum and Planck's constant

C)
stress and Young's modulus

D)
speed and ${{({{\mu }_{0}}-{{\varepsilon }_{0}})}^{-1/2}}$

• 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

B)
greater than v

C)
$\left| v \right|$ in the direction of largest force BC

D)
v remain unchanged

• 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

A)
$({{\phi }_{2}}-{{\phi }_{1}}){{\varepsilon }_{0}}$

B)
$({{\phi }_{1}}+{{\phi }_{2}})/{{\varepsilon }_{0}}$

C)
$({{\phi }_{2}}-{{\phi }_{1}})/{{\varepsilon }_{0}}$

D)
$({{\phi }_{1}}+{{\phi }_{2}}){{\varepsilon }_{0}}$

• 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

A)
20 N

B)
50 N

C)
100 N

D)
2 N

• 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

A)
$0.02$

B)
$0.03$

C)
$0.06$

D)
$0.01$

• 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

A)
A does not imply B and B does not imply A

B)
A implies B but B does not imply A

C)
A does not imply B but B implies A

D)
A implies B and B implies A

• question_answer30) Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon     AIEEE  Solved  Paper-2003

A)
the rates at which currents are changing in the two coils

B)
relative position and orientation of the two coils

C)
time for which current is flown

D)
the currents in the two coils

• 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

A)
$\frac{P\,m}{M+m}$

B)
$\frac{P\,m}{M-m}$

C)
P

D)
$\frac{P\,M}{M+m}$

• 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

B)
the scale of the lower one reads M kg and of the upper one zero

C)
the reading of the two scales can be anything but the sum of the readings will be M kg

D)
both the scales read M/2 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

A)
$0.2$ J

B)
10 J

C)
20 J

D)
$0.1$J

• 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

A)
$11\sqrt{2}$ km/s

B)
22 km/s

C)
11 km/s

D)
$11\sqrt{2}$ m/s

• 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

A)
$\frac{3}{5}$

B)
$\frac{25}{9}$

C)
$\frac{16}{9}$

D)
$\frac{5}{3}$

• 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

A)
second law of thermodynamics

B)
conservation of momentum

C)
conservation of mass

D)
first law of thermodynamics

• 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

A)
$\sqrt{{{k}_{1}}/{{k}_{2}}}$

B)
${{k}_{1}}/{{k}_{2}}$

C)
$\sqrt{{{k}_{2}}/{{k}_{1}}}$

D)
${{k}_{2}}/{{k}_{1}}$ 

• 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

A)
$11%$

B)
$21%$

C)
$42%$

D)
$10.5%$

• 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

A)
300

B)
600

C)
1200

D)
200

• 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

A)
$0.2$ H

B)
$0.4$ H

C)
$0.8$ H

D)
$0.1$ H

• 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

A)
$Q/2$

B)
$Q/\sqrt{3}$

C)
$Q/\sqrt{2}$

D)
Q

• question_answer42) The core of any transformer is laminated so as to     AIEEE  Solved  Paper-2003

A)
reduce the energy loss due to eddy currents

B)
make it light weight

C)
make it robust and strong

D)
increase the secondary voltage

• 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

A)
$r\,.\,\tau =0$ and $F\,.\,\,\tau \ne 0$

B)
$r\,.\,\,\tau \ne 0$ and $F\,.\,\,\tau =0$

C)
$r\,.\,\,\tau \ne 0$ and $F\,.\,\,\tau \ne 0$

D)
$r\,.\,\,\tau =0$ and $F\,.\,\,\tau =0$

• 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

A)
$0.4\,ln\,2$

B)
$0.2\,\ln \,2$

C)
$0.1\,\ln \,2$

D)
$0.8\,\ln \,2$

• 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

A)
76

B)
78

C)
82

D)
74

• question_answer46) Which of the following cannot be emitted by radioactive substances during their decay?     AIEEE  Solved  Paper-2003

A)
Protons

B)
Neutrinos

C)
Helium nuclei

D)
Electrons

• 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

A)
1 A

B)
$1.5$ A

C)
2 A

D)
1 A

• 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

A)
decreases

B)
remains unchanged

C)
becomes infinite

D)
Increases

• 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

A)
$-4$

B)
4

C)
$4\sqrt{2}$

D)
8

• 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

A)
$\frac{2Q}{4\pi {{\varepsilon }_{0}}R}$

B)
$\frac{2Q}{4\pi {{\varepsilon }_{0}}R}-\frac{2q}{4\pi {{\varepsilon }_{0}}R}$

C)
$\frac{2Q}{4\pi {{\varepsilon }_{0}}R}+\frac{q}{4\pi {{\varepsilon }_{0}}R}$

D)
$\frac{(q+Q)}{4\pi {{\varepsilon }_{0}}R}\frac{2}{R}$

• question_answer51) The work done in placing a charge of $8\times {{10}^{-18}}C$ on a condenser of capacity $100\mu F$ is     AIEEE  Solved  Paper-2003

A)
$16\times {{10}^{-32}}$ J

B)
$3.1\times {{10}^{-26}}$ J

C)
$4\times {{10}^{-10}}$ J

D)
$32\times {{10}^{-32}}$ J

• 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

A)
$3t\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

B)
$3{{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

C)
${{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

D)
$\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

• 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

A)
4/3

B)
2

C)
5/3

D)
3/2

• question_answer54) Which of the following parameters does not characterise the thermodynamic state of matter?     AIEEE  Solved  Paper-2003

A)
Temperature

B)
Pressure

C)
Work

D)
Volume

• 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

A)
$42\times {{10}^{6}}$J

B)
$8.4\times {{10}^{6}}$J

C)
$16.8\times {{10}^{6}}$ J

D)
Zero

• 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

A)
$12.50$N-m

B)
$18.75$N-m

C)
$25.00$ N-m

D)
$6.25$ N-m

• 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

A)
50 Hz

B)
100 Hz

C)
200 Hz

D)
25 Hz

• 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

A)
(256 + 2) Hz

B)
(256 - 2) Hz

C)
(256 - 5) Hz

D)
(256 + 5) Hz

• 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

A)
KE is maximum when $x=0$

B)
TE is zero when $x=0$

C)
KE is maximum when $x$ is maximum

D)
PE is maximum when $x=0$

• 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

A)
${{10}^{7}}$ K

B)
${{10}^{5}}$ K

C)
${{10}^{3}}$ K

D)
${{10}^{9}}$ K

• question_answer61) Which of the following atoms has the lowest ionisation potential?     AIEEE  Solved  Paper-2003

A)
$_{7}^{14}N$

B)
$_{55}^{133}Cs$

C)
$_{18}^{40}Ar$

D)
$_{8}^{16}O$

• 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

B)
nuclear forces are different in the two cases

C)
masses of the two nuclei are different

D)
attraction between the electron and the nucleus is different in the two cases

• question_answer63) In the middle of the depletion layer of reverse biased p-n junction, the     AIEEE  Solved  Paper-2003

A)
electric field is zero

B)
potential is maximum

C)
electric field is maximum

D)
potential is zero

• 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

A)
$30.6$ eV

B)
$13.6$ eV

C)
$3.4$ eV

D)
$122.4$ eV

• 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

A)
${{t}^{3/4}}$

B)
${{t}^{3/2}}$

C)
${{t}^{1/4}}$

D)
${{t}^{1/2}}$

• 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

A)
$3.5\times {{10}^{5}}$ N

B)
$7.0\times {{10}^{5}}$ N

C)
$14.0\times {{10}^{5}}$ N

D)
$1.75\times {{10}^{5}}$ N

• question_answer67) To demonstrate the phenomenon of interference, we require two sources which emit radiations of     AIEEE  Solved  Paper-2003

A)
nearly the same frequency

B)
the same frequency

C)
different wavelength

D)
the same frequency and having a definite phase relationship

• 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

A)
$\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta$

B)
$\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta$

C)
$\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta$

D)
$\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta$

• question_answer69) A 220 V, 1000 W bulb is connected across a 110 V mains supply. The power consumed will be     AIEEE  Solved  Paper-2003

A)
750 W

B)
500 W

C)
250 W

D)
1000 W

• question_answer70) The image formed by an objective of a compound microscope is     AIEEE  Solved  Paper-2003

A)
virtual and diminished

B)
real and diminished

C)
real and enlarged

D)
virtual and enlarged

• question_answer71) The earth radiates in the infrared region of the spectrum. The spectrum is correctly given by     AIEEE  Solved  Paper-2003

A)
Rayleigh Jeans law

B)

C)

D)
Wien's law

• question_answer72) To get three images of a single object, one should have two plane mirrors at an angle of     AIEEE  Solved  Paper-2003

A)
${{60}^{o}}$

B)
${{90}^{o}}$

C)
${{120}^{o}}$

D)
${{30}^{o}}$

• 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

A)
2

B)
3

C)
4

D)
1

• 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

A)
$200%$

B)
$100%$

C)
$50%$

D)
$300%$

• question_answer75) In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inner-orbit jumps of the electron for Bohr orbits in an atom of hydrogen?     AIEEE  Solved  Paper-2003

A)
$3\to 2$

B)
$5\to 2$

C)
$4\to 1$

D)
$2\to 5$

• question_answer76) The de-Broglie wavelength of a tennis ball of mass 60g moving with a velocity of 10 m/s is approximately (Planck's constant, $h=6.63\times {{10}^{-34}}$ Js)     AIEEE  Solved  Paper-2003

A)
${{10}^{-33}}$ m

B)
${{10}^{-31}}$ m

C)
${{10}^{-16}}$m

D)
${{10}^{-25}}$ m

• question_answer77) The orbital angular momentum for an electron revolving in an orbit is given by $\sqrt{l(l+1)}\frac{h}{2\pi }$. This momentum for an s-electron will be given by

A)
$+\frac{1}{2}.\,\frac{h}{2\pi }$

B)
zero

C)
$\,\frac{h}{2\pi }$

D)
$\sqrt{2}\,.\,\frac{h}{2\pi }$

• question_answer78) How many unit cells are present in a cube shaped ideal crystal of $NaCl$ of mass $1.00$g? [At. masses Na $=23,\,\,Cl=35.5$]     AIEEE  Solved  Paper-2003

A)
$2.57\times {{10}^{21}}$

B)
$5.14\times {{10}^{21}}$

C)
$1.28\times {{10}^{21}}$

D)
$1.71\times {{10}^{21}}$

• question_answer79) Glass is a     AIEEE  Solved  Paper-2003

A)
micro-crystalline solid

B)
super-cooled liquid

C)
gel

D)
polymeric mixture

• question_answer80) Which one of the following statements is correct?     AIEEE  Solved  Paper-2003

A)
Manganese salts give a violet borax bead test in the reducing flame

B)
From a mixed precipitate of $AgCl$ and $Agl,$ ammonia solution dissolves only $AgCl$

C)
Ferric ions give a deep green precipitate on adding potassium ferrocyanide solution

D)
On boiling a solution having ${{K}^{+}},C{{a}^{2+}}$ and $HCO_{3}^{-}$ ions we get a precipitate ${{K}_{2}}Ca{{(C{{O}_{3}})}_{2}}$

• question_answer81) According to the periodic law of elements, the variation in properties of elements is related to their     AIEEE  Solved  Paper-2003

A)
atomic masses

B)
nuclear masses

C)
atomic numbers

D)
nuclear neutron-proton number ratio

• question_answer82) Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that graphite     AIEEE  Solved  Paper-2003

A)
is a non-crystalline substance

B)
is an allotropic form of diamond

C)
has molecules of variable molecular masses like polymers

D)
has carbon atoms arranged in large plates of rings of strongly bound carbon atoms with weak interplate bonds

• question_answer83) The IUPAC name of $C{{H}_{2}}COCH{{(C{{H}_{3}})}_{2}}$ is     AIEEE  Solved  Paper-2003

A)
isopropylmethyl ketone

B)
2-methyl-S-butanone

C)
4-methyli-sopropyl ketone

D)
3-methyl-2-butanone

• question_answer84) When $C{{H}_{2}}=CH-COOH$ is reduced with $LiAl{{H}_{4}}$, the compound obtained will be     AIEEE  Solved  Paper-2003

A)
$C{{H}_{3}}-C{{H}_{2}}-COOH$

B)
$C{{H}_{2}}=CH-C{{H}_{2}}OH$

C)
$C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}OH$

D)
$C{{H}_{3}}-C{{H}_{2}}-CHO$

• question_answer85) According to the kinetic theory of gases, in an ideal gas, between two successive collisions a gas molecule travels      AIEEE  Solved  Paper-2003

A)
in a circular path

B)
in a wavy path

C)
in a straight line path

D)
with an accelerated velocity

• question_answer86) Which of the following group of transition metals is called coinage metals?     AIEEE  Solved  Paper-2003

A)
Cu, Ag, Au

B)
Ru, Rh, Pd

C)
Fe, Co, Ni

D)
Os, Ir, Pt

• question_answer87) The general formula ${{C}_{n}}{{H}_{2n}}{{O}_{2}}$ could be for open chain     AIEEE  Solved  Paper-2003

A)
diketones

B)
carboxylic-acids

C)
diols

D)
dialdehydes

• question_answer88) An ether is more volatile than an alcohol having the same molecular formula. This is due to     AIEEE  Solved  Paper-2003

A)
dipolar character of ethers

B)
alcohols having resonance structures

C)
inter-molecular hydrogen bonding in ethers

D)
inter-molecular hydrogen bonding in alcohols

• question_answer89) Among the following four structures I to IV ${{C}_{2}}{{H}_{5}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ || \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{3}}{{H}_{7}}C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-\overset{\begin{smallmatrix} C{{H}_{3}} \\ || \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{2}}{{H}_{5}}$                                 (I)                           (II)              $H-\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{{{\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{C}}\,}^{\oplus }}}}\,$                         ${{C}_{2}}{{H}_{5}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,H-{{C}_{2}}{{H}_{5}}$                   (III)                                       (IV) it is true that     AIEEE  Solved  Paper-2003

A)
all four are chiral compounds

B)
only I and II are chiral compounds

C)
only III is a chiral compound

D)
only II and IV are chiral compounds

• question_answer90) Which one of the following processes will produce hard water?     AIEEE  Solved  Paper-2003

A)
Saturation of water with $CaC{{O}_{3}}$

B)
Saturation of water with $MgC{{O}_{3}}$

C)
Saturation of water with $CaS{{O}_{4}}$

D)
Addition of $N{{a}_{2}}S{{O}_{4}}$ to water

• question_answer91) Which one of the following compounds has the smallest bond angle in its molecule?     AIEEE  Solved  Paper-2003

A)
$S{{O}_{2}}$

B)
$O{{H}_{2}}$

C)
$S{{H}_{2}}$

D)
$N{{H}_{3}}$

• question_answer92) Which one of the following pairs of molecules will have permanent dipole moments for both members?     AIEEE  Solved  Paper-2003

A)
$Si{{F}_{4}}$ and $N{{O}_{2}}$

B)
$N{{O}_{2}}$ and $C{{O}_{2}}$

C)
$N{{O}_{2}}$ and ${{O}_{3}}$

D)
$Si{{F}_{4}}$ and $C{{O}_{2}}$

• question_answer93) Which one of the following group represents a collection of isoelectronic species? (At. no. Cs-55. Br-35)     AIEEE  Solved  Paper-2003

A)
$N{{a}^{+}},C{{a}^{2+}},M{{g}^{2+}}$

B)
${{N}^{3-}},{{F}^{-}},N{{a}^{+}}$

C)
Be, $A{{l}^{3+}},C{{l}^{-}}$

D)
$C{{a}^{2+}},C{{s}^{+}},Br$

• question_answer94) In the anion $HCO{{O}^{-}}$ the two carbon-oxygen bonds are found to be of equal length. What is the reason for it?     AIEEE  Solved  Paper-2003

A)
Electronic orbits of carbon atom are hybridized

B)
The $c=0$ bond is weaker than the C?O bond

C)
The anion $HCO{{O}^{-}}$ has two resonating structures

D)
The anion is obtained by the removal of a proton from the acid molecule

• question_answer95) The pair of species having identical shapes for molecules of both species is     AIEEE  Solved  Paper-2003

A)
$C{{F}_{4}},S{{F}_{4}}$

B)
$Xe{{F}_{2}},C{{O}_{2}}$

C)
$B{{r}_{3}},PC{{l}_{3}}$

D)
$P{{F}_{5}},l{{F}_{5}}$

• question_answer96) The atomic numbers of vanadium (V), chromium (Cr), manganese (Mn) and iron (Fe) are respectively 23, 24, 25 and 26. Which one of these may be expected to have the highest second ionisation enthalpy?     AIEEE  Solved  Paper-2003

A)
V

B)
Cr

C)
Mn

D)
Fe

• question_answer97) Consider the reaction equilibrium,              $2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g);$                                                 $\Delta {{H}^{o}}=-198\,k\,J$ On the basis of Le Chatelier's principle, the condition favourable for the forward reaction is     AIEEE  Solved  Paper-2003

A)
lowering of temperature as well as pressure

B)
increasing temperature as well as pressure

C)
lowering the temperature and increasing the pressure

D)
any value of temperature and pressure

• question_answer98) What volume of hydrogen gas, at 273K and 1 atm pressure will be consumed in obtaining $21.6$ g of elemental boron (atomic mass $=10.8$) from the reduction of boron trichloride by hydrogen?     AIEEE  Solved  Paper-2003

A)
$89.6$ L

B)
$67.2$ L

C)
$44.8$ L

D)
$22.4$ L

• question_answer99) For the reaction equilibrium,                 ${{N}_{2}}{{O}_{4}}(g)\overset{{}}{leftrightarrows}2NO(g)$ the concentrations of ${{N}_{2}}{{O}_{4}}$ and $N{{O}_{2}}$ at equilibrium    are   $4.8\times {{10}^{-2}}$ and $1.2\times {{10}^{-2}}mol\,{{L}^{-1}}$ respectively. The value of ${{K}_{c}}$ for the reaction is     AIEEE  Solved  Paper-2003

A)
$3.3\times {{10}^{2}}mol\,{{L}^{-1}}$

B)
$3\times {{10}^{-1}}mol\,{{L}^{-1}}$

C)
$3\times {{10}^{-3}}mol\,{{L}^{-1}}$

D)
$3\times {{10}^{3}}mol\,{{L}^{-1}}$

• question_answer100) The solubility in water of a sparingly soluble salt $A{{B}_{2}}$ is $1.0\times {{10}^{-5}}mol\,{{L}^{-1}}$ Its solubility product number will be     AIEEE  Solved  Paper-2003

A)
$4\times {{10}^{-15}}$

B)
$4\times {{10}^{-10}}$

C)
$1\times {{10}^{-15}}$

D)
$1\times {{10}^{-10}}$

• question_answer101) When during electrolysis of a solution of $AgN{{O}_{3}}$, 9650 coulombs of charge pass through the electroplating bath, the mass of silver deposited on the cathode will be     AIEEE  Solved  Paper-2003

A)
$1.08$ g

B)
$10.8$ g

C)
$21.6$ g

D)
108 g

• question_answer102) For the redox reaction, $Zn(s)+C{{u}^{2+}}(0.1M)\xrightarrow{{}}Z{{n}^{2+}}(1M)+Cu(s)$taking place in a cell, $E_{cell}^{o}$ is $1.10$ volt. ${{E}_{cell}}$ for the cell will be $\left( 2.303\frac{RT}{F}=0.0591 \right)$     AIEEE  Solved  Paper-2003

A)
$2.14$ V

B)
$1.80$ V

C)
$1.07$ V

D)
$0.82$ V

• question_answer103) In a $0.2$ molal aqueous solution of a weak acid HX, the degree of ionisation is $0.3$. Taking ${{K}_{f}}$ for water as $1.85$, the freezing point of the solution will be nearest to     AIEEE  Solved  Paper-2003

A)
$-{{0.480}^{o}}C$

B)
$-{{0.360}^{o}}C$

C)
$-{{0.260}^{o}}C$

D)
$+\,{{0.480}^{o}}C$

• question_answer104) The rate law for a reaction between the substances A and B is given by rate $=k\,{{[A]}^{n}}{{[B]}^{m}}$. On doubling   the concentration of A and halving the concentration of B, the ratio of the new rate to the earlier rate of the reaction will be as   AIEEE  Solved  Paper-2003

A)
$\frac{1}{{{2}^{m+n}}}$

B)
(m + n)

C)
(n - m)

D)
${{2}^{(n-m)}}$

• question_answer105) 25 mL of a solution of barium hydroxide on titration with $0.1$ molar solution of hydrochloric acid gave a titre value of 35 mL. The molarity of barium hydroxide solution was     AIEEE  Solved  Paper-2003

A)
$0.07$

B)
$0.14$

C)
$0.28$

D)
$0.35$

• question_answer106) The correct relationship between free energy change in a reaction and the corresponding equilibrium constant ${{K}_{c}}$ is     AIEEE  Solved  Paper-2003

A)
$\Delta G=RT\,\ln \,{{K}_{c}}$

B)
$-\Delta G=RT\,\ln \,{{K}_{c}}$

C)
$\Delta {{G}^{o}}=RT\,\ln \,{{K}_{c}}$

D)
$-\Delta {{G}^{o}}=RT\,\ln \,{{K}_{c}}$

• question_answer107) If at 298K the bond energies of $C-H,C-C,\,C=C$ and $H-H$ bonds are respectively 414, 347, 615 and 435 kJ $mo{{l}^{-1}}$, the value of enthalpy change for the reaction ${{H}_{2}}C=C{{H}_{2}}(g)+{{H}_{2}}(g)\xrightarrow{\,}\,{{H}_{3}}C-C{{H}_{3}}(g)$ at 298K will be     AIEEE  Solved  Paper-2003

A)
$+250$ kJ

B)
$-250$ kJ

C)
$+125$ kJ

D)
$-125$ kJ

• question_answer108) The enthalpy change for reaction does not depend upon the     AIEEE  Solved  Paper-2003

A)
physical state of reactants and products

B)
use of different reactants for the same product

C)
nature of intermediate reaction steps

D)
difference in initial or final temperatures of involved substances

• question_answer109) A pressure cooker reduces cooking time for food because     AIEEE  Solved  Paper-2003

A)
heat is more evenly distributed in the cooking space

B)
boiling point of water involved in cooking is increased

C)
the higher pressure inside the cooker crushes the food material

D)
cooking involves chemical changes helped by a rise in temperature

• question_answer110) If liquids A and B form an ideal solution, the     AIEEE  Solved  Paper-2003

A)
enthalpy of mixing is zero

B)
entropy of mixing is zero

C)
free energy of mixing is zero

D)
free energy as well as the entropy of mixing are each zero

• question_answer111) For the reaction system                 $2NO(g)+{{O}_{2}}(g)\xrightarrow{{}}2N{{O}_{2}}(g)$   volume is suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to ${{O}_{2}}$ and second order with respect to NO; the rate of reaction will     AIEEE  Solved  Paper-2003

A)
diminish to one-fourth of its initial value

B)
diminish to one-eighth of its initial value

C)
increase to eight times of its initial value

D)
increase to four times of its initial value

• question_answer112) For a cell reaction involving a two-electron change, the standard emf of the cell is found to be $0.295$ V at ${{25}^{o}}C$. The equilibrium constant of the reaction at ${{25}^{o}}C$ will be     AIEEE  Solved  Paper-2003

A)
$1\times {{10}^{-10}}$

B)
$29.5\times {{10}^{-2}}$

C)
10

D)
$1\times {{10}^{10}}$

• question_answer113) In an irreversible process taking place at constant T and p and in which only pressure-volume work is being done, the change in Gibbs free energy (dG) and change in entropy (dS), satisfy the criteria     AIEEE  Solved  Paper-2003

A)
${{(dS)}_{V,E}}<0,{{(dG)}_{T,P}}<0$

B)
${{(dS)}_{V,E}}>0,{{(dG)}_{T,P}}<0$

C)
${{(dS)}_{V,E}}=0,{{(dG)}_{T,P}}=0$

D)
${{(dS)}_{V,E}}=0,{{(dG)}_{T,P}}>0$

• question_answer114) Which one of the following characteristics is not correct for physical adsorption?     AIEEE  Solved  Paper-2003

A)

B)
Adsorption increases with increase in temperature

C)

D)
Both enthalpy and entropy of adsorption are negative

• question_answer115) In the respect of the equation $k=A{{e}^{-{{E}_{\alpha }}/RT}}$ in chemical kinetics, which one of the following statements is correct?     AIEEE  Solved  Paper-2003

A)
k is equilibrium constant

B)

C)
${{E}_{a}}$ is energy of activation

D)
R is Rydberg constant

• question_answer116) Standard reduction electrode potentials of three metals A, B and C are $+1.5$ V, $-3.0$ V and $-1.2$ V respectively. The reducing power of these metals are     AIEEE  Solved  Paper-2003

A)
$B>C>A$

B)
$A>B>C$

C)
$C>B>A$

D)
$A>C>B$

• question_answer117) Which one of the following substances has the highest proton affinity?   AIEEE  Solved  Paper-2003

A)
${{H}_{2}}O$

B)
${{H}_{2}}S$

C)
$N{{H}_{3}}$

D)
$P{{H}_{3}}$

• question_answer118) Which one of the following is an amphoteric oxide?     AIEEE  Solved  Paper-2003

A)
$ZnO$

B)
$N{{a}_{2}}O$

C)
$S{{O}_{2}}$

D)
${{B}_{2}}{{O}_{3}}$

• question_answer119) A red solid is insoluble in water. However, it becomes soluble if some KI is added to water. Heating the red solid in a test tube results in liberation of some violet coloured fumes and droplets of a metal appear on the cooler parts of the test tube. The red solid is     AIEEE  Solved  Paper-2003

A)
${{(N{{H}_{4}})}_{2}}C{{r}_{2}}{{O}_{7}}$

B)
$Hg{{l}_{2}}$

C)
$HgO$

D)
$P{{b}_{3}}{{O}_{4}}$

• question_answer120) Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The explanation for it is that     AIEEE  Solved  Paper-2003

A)
concentrated hydrochloric acid emits strongly smelling HCI gas all the time

B)
oxygen in air reacts with the emitted HCI gas to form a cloud of chlorine gas

C)
strong affinity of HCI gas for moisture in air results in forming of droplets of liquid solution which appears like a cloudy smoke

D)
due to strong affinity for water, concentrated hydrochloric acid pulls moisture of air towards itself. This moisture forms droplets of water and hence the cloud

• question_answer121) The substance used in Holmes signals of the ship is a mixture of     AIEEE  Solved  Paper-2003

A)
$Ca{{C}_{2}}+C{{a}_{3}}{{P}_{2}}$

B)
$C{{a}_{3}}{{(P{{O}_{4}})}_{2}}+P{{b}_{3}}{{O}_{4}}$

C)
${{H}_{3}}P{{O}_{4}}\,+CaC{{l}_{2}}$

D)
$N{{H}_{3}}+HOCl$

• question_answer122) The number of d-electrons retained in $F{{e}^{2+}}$ (At. no. $Fe=26$) ions is     AIEEE  Solved  Paper-2003

A)
3

B)
4

C)
5

D)
6

• question_answer123) What would happen when a solution of potassium chromate is treated with an excess of dilute nitric acid?     AIEEE  Solved  Paper-2003

A)
$C{{r}^{3+}}$ and $C{{r}_{2}}O_{7}^{2-}$ are formed

B)
$C{{r}_{2}}O_{7}^{2-}$ and ${{H}_{2}}O$ are formed

C)
$CrO_{4}^{2-}$ is reduced to $+3$ state of Cr

D)
None of the above

• question_answer124) In the coordination compound, ${{K}_{4}}[Ni{{(CN)}_{4}}]$, the oxidation state of nickel is     AIEEE  Solved  Paper-2003

A)
$-1$

B)
0

C)
$+1$

D)
$+2$

• question_answer125) Ammonia forms the complex ion ${{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}$ with copper ions in the alkaline solutions but not in acidic solutions. What is the reason for it?     AIEEE  Solved  Paper-2003

A)
In acidic solutions hydration protects copper ions

B)
In acidic solutions protons coordinate with ammonia molecules forming $NH_{4}^{+}$ ions and $N{{H}_{3}}$ molecules are not available

C)
In alkaline solutions insoluble $Cu{{(OH)}_{2}}$ is precipitated which is soluble in excess of any alkali

D)
Copper hydroxide is an amphoteric substance

• question_answer126) One mole of the complex compound $Co{{(N{{H}_{3}})}_{5}}C{{l}_{3}}$, gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with two moles of $AgN{{O}_{3}}$ solution to yield two moles of $AgCl$ (s). The structure of the complex is     AIEEE  Solved  Paper-2003

A)
$[Co{{(N{{H}_{3}})}_{5}}Cl]C{{l}_{2}}$

B)
$[Co{{(N{{H}_{3}})}_{3}}C{{l}_{2}}].2N{{H}_{3}}$

C)
$[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl.\,N{{H}_{3}}$

D)
$[Co{{(N{{H}_{3}})}_{4}}Cl]C{{l}_{2}}.N{{H}_{3}}$

• question_answer127) The radius of $L{{a}^{3+}}$ (atomic number of $La=57$) is $1.06\overset{o}{\mathop{A}}\,$. Which one of the following given values will be closest to the radius of $L{{u}^{3+}}$ (atomic number of $Lu=71$)?     AIEEE  Solved  Paper-2003

A)
$1.60\,\overset{o}{\mathop{A}}\,$

B)
$1.40\,\overset{o}{\mathop{A}}\,$

C)
$1.06\,\overset{o}{\mathop{A}}\,$

D)
$0.85\,\overset{o}{\mathop{A}}\,$

• question_answer128) The radionuclide $_{90}^{234}Th$ undergoes two successive $\beta$ -decays followed by one $\alpha$ -decay. The atomic number and the mass number respectively of the resulting radionuclide are     AIEEE  Solved  Paper-2003

A)
92 and 234

B)
94 and 230

C)
90 and 230

D)
92 and 230

• question_answer129) the half-life of a radioactive isotope is 3 h. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 h would be     AIEEE  Solved  Paper-2003

A)
$4.0$ g

B)
$8.0$ g

C)
$12.0$ g

D)
$16.0$ g

• question_answer130) Several blocks of magnesium are fixed to the bottom of a ship to     AIEEE  Solved  Paper-2003

A)
keep away the sharks

B)
make the ship lighter

C)
prevent action of water and salt

D)
prevent puncturing by under-sea rocks

• question_answer131) In curing cement plasters water is sprinkled from time to time. This helps in     AIEEE  Solved  Paper-2003

A)
keeping it cool

B)
developing interlocking needle-like crystals of hydrated silicates

C)
hydrating sand and gravel mixed with cement

D)
converting sand into silicic acid

• question_answer132) Which one of the following statements is not true?       AIEEE  Solved  Paper-2003

A)
The conjugate base of ${{H}_{2}}PO_{4}^{-}$ is $HPO_{4}^{2-}$

B)
$pH+pOH=14$ for all aqueous solutions

C)
The pH of $1\times {{10}^{-8}}M$HCl is 8

D)
96,500 coulombs of electricity when passed through a $CuS{{O}_{4}}$ solution deposit 1g equivalent of copper at the cathode

• question_answer133) The correct order of increasing basic nature for the bases $N{{H}_{3}},C{{H}_{3}}N{{H}_{2}}$ and ${{(C{{H}_{3}})}_{2}}NH$is      AIEEE  Solved  Paper-2003

A)
$C{{H}_{3}}N{{H}_{2}}<N{{H}_{3}}<{{(C{{H}_{3}})}_{2}}NH$

B)
${{(C{{H}_{3}})}_{2}}NH<N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}$

C)
$N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH$

D)
$C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH<N{{H}_{3}}$

• question_answer134) Butene-1 may be converted to butane by reaction with     AIEEE  Solved  Paper-2003

A)
$Zn-HCl$

B)
$Sn-HCl$

C)
$Zn-Hg$

D)
$Pd/{{H}_{2}}$

• question_answer135) The solubilities of carbonates decrease down the magnesium group due to a decrease in     AIEEE  Solved  Paper-2003

A)
lattice energies of solids

B)
hydration energies of cations

C)
inter-ionic attraction

D)
entropy of solution formation

• question_answer136) During dehydration of alcohols to alkenes by heating with concentrated ${{H}_{2}}S{{O}_{4}}$ the initiation step is     AIEEE  Solved  Paper-2003

A)
protonation of alcohol molecule

B)
formation of carbocation

C)
elimination of water

D)
formation of an ester

• question_answer137)     Which one of the following nitrates will leave behind a metal on strong heating?     AIEEE  Solved  Paper-2003

A)
Ferric nitrate

B)
Copper nitrate

C)
Manganese nitrate

D)
Silver nitrate

• question_answer138) When rain is accompanied by a thunderstorm, the collected rain water will have a pH value     AIEEE  Solved  Paper-2003

A)
slightly lower than that of rain water without thunderstorm

B)
slightly higher than that when the thunderstorm is not there

C)
uninfluenced by occurrence of thunderstorm

D)
which depends on the amount of dust in air

• question_answer139) Complete hydrolysis of cellulose gives     AIEEE  Solved  Paper-2003

A)
D-fructose

B)
D-ribose

C)
D-glucose

D)
L-glucose

• question_answer140) For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liquid metal which does not solidify before glass. The metal used can be     AIEEE  Solved  Paper-2003

A)
mercury

B)
tin

C)
sodium

D)
magnesium

• question_answer141) The substance not likely to contain $CaC{{O}_{3}}$ is     AIEEE  Solved  Paper-2003

A)
a marble statue

B)
calcined gypsum

C)
sea shells

D)
dolomite

• question_answer142) The reason for double helical structure of DNA is operation of     AIEEE  Solved  Paper-2003

A)
van der Waals' forces

B)
dipole-dipole interaction

C)
hydrogen bonding

D)
electrostatic attractions

• question_answer143) Bottles containing ${{C}_{6}}{{H}_{5}}I$ and ${{C}_{6}}{{H}_{5}}C{{H}_{2}}I$ lost their original labels. They were labelled A and B for testing. A and B were separately taken in a test tube and boiled with $NaOH$ solution. The end solution in each tube was made acidic with dilute $HN{{O}_{3}}$ and then some $AgN{{O}_{3}}$ solution was added. Substance B gave a yellow precipitate. Which one of the following statements is true for this experiment?     AIEEE  Solved  Paper-2003

A)
A was ${{C}_{6}}{{H}_{5}}l$

B)
A was ${{C}_{6}}{{H}_{5}}C{{H}_{2}}l$

C)
B was ${{C}_{6}}{{H}_{5}}l$

D)
Addition of $HN{{O}_{3}}$ was unnecessary

• question_answer144) Ethyl isocyanide on hydrolysis in acidic medium generates     AIEEE  Solved  Paper-2003

A)
ethylamine salt and methanoic acid

B)
propanoic acid and ammonium salt

C)
ethanoic acid and ammonium salt

D)
methylamine salt and ethanoic acid

• question_answer145) The internal energy change when a system goes from state A to B is 40 kJ/mol. If the system goes from A to B by a reversible path and returns to state A by an irreversible path, what would be the net change in internal energy?     AIEEE  Solved  Paper-2003

A)
40 kJ

B)
> 40 kJ

C)
< 40 kJ

D)
zero

• question_answer146) The reaction of chloroform with alcoholic KOH and p-toluidine form     AIEEE  Solved  Paper-2003

A)

B)

C)

D)

A)
polyvinyl polymer

B)
polyester polymer

C)
polyamide polymer

D)
polyethylene polymer

• question_answer148) On mixing a certain alkane with chlorine and irradiating it with Ultraviolet light, it forms only one monochloroalkane. This alkane could be     AIEEE  Solved  Paper-2003

A)
propane

B)
pentane

C)
isopentane

D)
neopentane

• question_answer149) Which of the following could act as a propellant for rockets?      AIEEE  Solved  Paper-2003

A)
Liquid hydrogen + liquid nitrogen

B)
Liquid oxygen + liquid argon

C)
Liquid hydrogen + liquid oxygen

D)
Liquid nitrogen + liquid oxygen

• question_answer150)              A function $f$ from the set of natural numbers to integers defined by             f(n)=\left\{ \begin{align} & \frac{n-1}{n},\text{ }when\text{ }n\text{ }is\text{ }odd \\ & \frac{-n}{2},\,\,when\text{ }n\text{ }is\text{ }even \\ \end{align} \right.  is     AIEEE  Solved  Paper-2003

A)
one-one but not onto

B)
onto but not one-one

C)
one-one and onto both

D)
neither one-one nor onto

• question_answer151) Let ${{z}_{1}}$ and ${{z}_{2}}$ be two roots of the equation ${{z}_{2}}+az+b=0,\,\,z$ being complex. Further, assume that the origin, ${{z}_{1}}$ and ${{z}_{2}}$ form an equilateral triangle. Then,     AIEEE  Solved  Paper-2003

A)
${{a}^{2}}=b$

B)
${{a}^{2}}=2b$

C)
${{a}^{2}}=3b$

D)
${{a}^{2}}=4b$

• question_answer152) If z and $\omega$ are two non-zero complex numbers  such  that  $\left| z\,\omega \right|=1$ and arg (z) - arg $(\omega )=\frac{\pi }{2}$, then $\overline{z}\omega$ is equal to     AIEEE  Solved  Paper-2003

A)
1

B)
-1

C)
$i$

D)
$-i$

• question_answer153) If ${{\left( \frac{1+i}{1-i} \right)}^{x}}=1$ , then             AIEEE  Solved  Paper-2003

A)
$x=4\,n$, where n is any positive integer

B)
$x=2\,n$, where n is any positive integer

C)
$x=4\,n+1$, where n is any positive integer

D)
$x=2\,n+1$, where n is any positive integer

• question_answer154) If $\left| \begin{matrix} a & {{a}^{2}} & 1+{{a}^{3}} \\ b & {{b}^{2}} & 1+{{b}^{3}} \\ c & {{c}^{2}} & 1+{{c}^{3}} \\ \end{matrix} \right|=0$ and vectors $(1,\,\,a,\,\,{{a}^{2}})$, $(1,\,\,a,\,\,{{a}^{2}})$ and $(1,\,\,c,\,\,{{c}^{2}})$ are non-coplanar, then the product abc equals     AIEEE  Solved  Paper-2003

A)
2

B)
-1

C)
1

D)
0

• question_answer155) If the system of linear equations                 $x+2$ ay $+\,az=0$                 $x+3$ by $+\,bz=0$ and        $x+4$ cy $+cz=0$ has a non-zero solution, then a, b, c     AIEEE  Solved  Paper-2003

A)
are in AP

B)
are in GP

C)
are in HP

D)
satisfy a+2b+3c=0

• question_answer156) If the sum of the roots of the quadratic equation $a{{x}^{2}}+bx+c=0$ is equal to the sum of the squares f their reciprocals, then $\frac{a}{c},\frac{b}{a}$, and $\frac{c}{b}$ are in     AIEEE  Solved  Paper-2003

A)
arithmetic progression

B)
geometric progression

C)
harmonic progression

D)
arithmetico-geometric progression

• question_answer157) The number of the real solutions of the equation ${{x}^{2}}-3\left| x \right|+2=0$ is

A)
2

B)
4

C)
1

D)
3

• question_answer158) The value of a for which one root of the quadratic equation             $({{a}^{2}}-5a+3)\,{{x}^{2}}+(3a-1)\,x+2=0$ is twice as large as the other, is     AIEEE  Solved  Paper-2003

A)
2/3

B)
-2/3

C)
1/3

D)
-1/3

• question_answer159) If $A=\left| \begin{matrix} a & b \\ b & a \\ \end{matrix} \right|$ and ${{A}^{2}}=\left| \begin{matrix} \alpha & \beta \\ \beta & \alpha \\ \end{matrix} \right|$,  then     AIEEE  Solved  Paper-2003

A)
$\alpha ={{a}^{2}}+{{b}^{2}},\,\beta =ab$

B)
$\alpha ={{a}^{2}}+{{b}^{2}},\,\beta =2ab$

C)
$\alpha ={{a}^{2}}+{{b}^{2}},\,\beta ={{a}^{2}}-{{b}^{2}}$

D)
$\alpha =2ab,\,\,\beta ={{a}^{2}}+{{b}^{2}}$

• question_answer160) A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is     AIEEE  Solved  Paper-2003

A)
140

B)
196

C)
280

D)
346

• question_answer161) The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by     AIEEE  Solved  Paper-2003

A)
$6!\,\,\times 5!$

B)
30

C)
$5!\,\,\times 4!$

D)
$7!\,\,\times 5!$

• question_answer162) If $1,\,\omega ,\,{{\omega }^{2}}$are the cube roots of unity, then                 $\Delta =\left| \begin{matrix} 1 & {{\omega }^{n}} & {{\omega }^{2n}} \\ {{\omega }^{n}} & {{\omega }^{2n}} & 1 \\ {{\omega }^{2n}} & 1 & {{\omega }^{n}} \\ \end{matrix} \right|$ is equal to     AIEEE  Solved  Paper-2003

A)
0

B)
1

C)
$\omega$

D)
${{\omega }^{2}}$

• question_answer163) If $^{n}{{C}_{r}}$ denotes the number of combinations of n things taken r at a time, then the expression $^{n}{{C}_{r+1}}{{+}^{n}}{{C}_{r-1}}+2{{\times }^{n}}{{C}_{r}}$ equals     AIEEE  Solved  Paper-2003

A)
$^{n+2}{{C}_{r}}$

B)
$^{n+2}{{C}_{r+1}}$

C)
$^{n+1}{{C}_{r}}$

D)
$^{n+1}{{C}_{r+1}}$

• question_answer164) The number of integral terms in the expansion of ${{(\sqrt{3}+\sqrt[8]{5})}^{256}}$ is     AIEEE  Solved  Paper-2003

A)
32

B)
33

C)
34

D)
35

• question_answer165) If $x$ is positive, the first negative term in the expansion of ${{(1+x)}^{27/5}}$ is     AIEEE  Solved  Paper-2003

A)
7th term

B)
5th term

C)
8th term

D)
6th term

• question_answer166) The     sum     of     the     series $\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-$... upto $\infty$ is equal to     AIEEE  Solved  Paper-2003

A)
$2\,\,{{\log }_{e}}2$

B)
${{\log }_{e}}\,\,2-1$

C)
${{\log }_{e}}\,\,2$

D)
${{\log }_{e}}\,\,\left( \frac{4}{e} \right)$

• question_answer167) Let $f(x)$ be a polynomial function of second degree. If $f(1)=f(-1)$ and a, b, c are in AP, then $f'\,(a),\,\,f'(b)$ and $f'(c)$ are in     AIEEE  Solved  Paper-2003

A)
AP

B)
GP

C)
HP

D)
arithmetico-geometric progression

• question_answer168) If ${{x}_{1}},{{x}_{2}},{{x}_{3}}$ and ${{y}_{1}},{{y}_{2}},{{y}_{3}}$ are both in GP with the same common ratio, then the points $({{x}_{1}},{{y}_{1}}),\,({{x}_{2}},{{y}_{2}})$ and $({{x}_{3}},{{y}_{3}})$      AIEEE  Solved  Paper-2003

A)
lie on a straight

B)
line lie on an ellipse

C)
lie on a circle

D)
are vertices of a triangle

• question_answer169) The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is     AIEEE  Solved  Paper-2003

A)
$a\cot \,\left( \frac{\pi }{v} \right)$

B)
$\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)$

C)
$a\cot \,\left( \frac{\pi }{2n} \right)$

D)
$\frac{a}{4}\cot \left( \frac{\pi }{2n} \right)$

• question_answer170) If a $\Delta ABC$,                 $a{{\cos }^{2}}\left( \frac{C}{2} \right)+c{{\cos }^{2}}\left( \frac{A}{2} \right)=\frac{3b}{2}$ then the sides a, b and c     AIEEE  Solved  Paper-2003

A)
are in AP

B)
are in GP

C)
are in HP

D)
satisfy a + b = c

• question_answer171) In $\Delta ABC$, medians AD and BE are drawn. If AD = 4, $\angle DAB=\frac{\pi }{6}$ and $\angle ABE=\frac{\pi }{3}$, then the area of the $\Delta ABC$ is     AIEEE  Solved  Paper-2003

A)
8/3

B)
16/3

C)
32/3

D)
64/3

• question_answer172) The trigonometric equation ${{\sin }^{-1}}x=2{{\sin }^{-1}}a$, has a solution for     AIEEE  Solved  Paper-2003

A)
$-\frac{1}{\sqrt{2}}<a<\frac{1}{\sqrt{2}}$

B)
all real values of a

C)
$\left| a \right|<\frac{1}{2}$

D)
$\left| a \right|\ge \frac{1}{\sqrt{2}}$

• question_answer173) The upper 3/4th portion of a vertical pole subtends an angle ${{\tan }^{-1}}3/5$ at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is     AIEEE  Solved  Paper-2003

A)
20m

B)
40m

C)
60m

D)
80 m

• question_answer174) The real number $x$ when added to its inverse gives the minimum sum at $x$ equals to     AIEEE  Solved  Paper-2003

A)
2

B)
1

C)
-1

D)
-2

• question_answer175) If $f:R\to R$ satisfies$f(x+y)=f(x)+f(y)$, for all $x,y\in R$ and $f(1)=7$, then $\sum\limits_{r=1}^{n}{f(r)}$ is     AIEEE  Solved  Paper-2003

A)
$\frac{7n}{2}$

B)
$\frac{7(n+1)}{2}$

C)
$7n\,(n+1)$

D)
$\frac{7n\,(n+1)}{2}$

• question_answer176) If $f(x)={{x}^{n}}$, then the value of $f(1)-\frac{f'(1)}{1!}+\frac{f''(1)}{2!}-\frac{f'''(1)}{3!}+...+\frac{{{(-1)}^{n}}{{f}^{n}}(1)}{n!}$     AIEEE  Solved  Paper-2003

A)
${{2}^{n}}$

B)
${{2}^{n-1}}$

C)
0

D)
1

• question_answer177) Domain of definition of the function $f(x)=\frac{3}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x)$, is     AIEEE  Solved  Paper-2003

A)
(1, 2)

B)
$(-1,0)\cup (1,2)$

C)
$(1,2)\cup (2,\infty )$

D)
$(-1,0)\cup (1,2,)\cup (2,\infty )$

• question_answer178) $\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\left[ 1-\tan \left( \frac{x}{2} \right) \right][1-\sin x]}{\left[ 1+\tan \left( \frac{x}{2} \right) \right]{{[x-2x]}^{3}}}$  is     AIEEE  Solved  Paper-2003

A)
$\frac{1}{8}$

B)
0

C)
$\frac{1}{32}$

D)
$\infty$

• question_answer179) If $\underset{x\to 0}{\mathop{\lim }}\,\frac{\log \,(3+x)-\log \,(3-x)}{x}=k$ then value of k is     AIEEE  Solved  Paper-2003

A)
0

B)
-1/3

C)
2/3

D)
-2/3

• question_answer180) Let f(a) = g(a) = k and their nth derivatives ${{f}^{n}}(a),\,{{g}^{n}}(a)$ exist and are not equal for some n. Further, if $\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)\,g(x)-i(a)-g(a)f(x)+g(a)}{g(x)-f(x)}=4$, then the value of k is equal to     AIEEE  Solved  Paper-2003

A)
4

B)
2

C)
1

D)
0

• question_answer181) The function $f(x)=\log \,(x+\sqrt{\,{{x}^{2}}+1})$, is     AIEEE  Solved  Paper-2003

A)
an even function

B)
an odd function

C)
a periodic function

D)
neither an even nor an odd function

• question_answer182) If $f(x)=\left\{ \begin{matrix} x{{e}^{-\left[ \frac{1}{\left| x \right|}+\frac{1}{x} \right]}} & ,x\ne 0 \\ 0 & ,x=0 \\ \end{matrix} \right.$ , then f(x) is     AIEEE  Solved  Paper-2003

A)
continuous as well as differentiable for all x

B)
continuous for all x but not differentiable at $x=0$

C)
neither differentiable nor continuous at $x=0$

D)
discontinuous everywhere

• question_answer183) If the function $f(x)=2{{x}^{3}}-9a{{x}^{2}}+12{{a}^{2}}x+1$, where a > 0, attains its maximum and minimum at p and q respectively such that ${{p}^{2}}=q$, then a equals     AIEEE  Solved  Paper-2003

A)
3

B)
1

C)
2

D)
1/2

• question_answer184) If $f(y)={{e}^{y}},g(y)=y;y>0$ and$F(t)=\int_{0}^{t}{f(t-y)\,g(y)\,dy}$, then      AIEEE  Solved  Paper-2003

A)
$F(t)=1-{{e}^{-t}}(1+t)$

B)
$F(t)\,={{e}^{t}}\,-(1+t)$

C)
$F(t)=t{{e}^{-t}}$

D)
$F(t)=t{{e}^{-t}}$

• question_answer185) If $f(a+b-x)=f(x)$, then $\int_{a}^{b}{x\,f(x)\,dx}$ is equal to     AIEEE  Solved  Paper-2003

A)
$\frac{a+b}{2}\int_{a}^{b}{f(b-x)\,dx}$

B)
$\frac{a+b}{2}\int_{a}^{b}{f(x)\,dx}$

C)
$\frac{b-a}{2}\int_{a}^{b}{f(x)\,dx}$

D)
$\frac{a+b}{2}\int_{a}^{b}{f(a+b+x)\,dx}$

• question_answer186) The value of $\underset{x\to 0}{\mathop{\lim }}\,\frac{\int_{0}^{{{x}^{2}}}{{{\sec }^{2}}t\,dt}}{x\sin x}$ is     AIEEE  Solved  Paper-2003

A)
3

B)
2

C)
1

D)
-1

• question_answer187) The    value    of    the    integral $I=\int_{0}^{1}{x{{(1-x)}^{n}}dx}$ is     AIEEE  Solved  Paper-2003

A)
$\frac{1}{n+1}$

B)
$\frac{1}{n+2}$

C)
$\frac{1}{n+1}-\frac{1}{n+2}$

D)
$\frac{1}{n+1}+\frac{1}{n+2}$

• question_answer188) $\underset{x\to \infty }{\mathop{\lim }}\,\frac{1+{{2}^{4}}+{{3}^{4}}+....+{{n}^{4}}}{{{n}^{5}}}$                                                                             $-\underset{x\to \infty }{\mathop{\lim }}\,\frac{1+{{2}^{3}}+{{3}^{3}}+....+{{n}^{3}}}{{{n}^{5}}}$ is

A)
1/30

B)
0

C)
1/4

D)
1/5

• question_answer189) Let $\frac{d}{dx}F(x)=\left( \frac{{{e}^{\sin x}}}{x} \right),x>0$. If $\int_{1}^{4}{\,\,\,\frac{3}{x}{{e}^{\sin {{x}^{3}}}}dx=F(k)-F(1)}$. then one of the possible value of k, is     AIEEE  Solved  Paper-2003

A)
15

B)
16

C)
63

D)
64

• question_answer190) The area of the region bounded by the curves $y=\left| x-1 \right|$ and $y=3-\left| x \right|$ is     AIEEE  Solved  Paper-2003

A)
2 sq units

B)
3 sq units

C)
4 sq units

D)
6 sq units

• question_answer191) Let $f(x)$ be a function satisfying $f'(x)=f(x)$ with $f(0)=1$ and $g(x)$ be a function that satisfies $f(x)+g(x)={{x}^{2}}$. Then, the value of the integral $\int_{0}^{1}{f(x)\,g(x)\,dx}$, is     AIEEE  Solved  Paper-2003

A)
$e-\frac{{{e}^{2}}}{2}-\frac{5}{2}$

B)
$e+\frac{{{e}^{2}}}{2}-\frac{3}{2}$

C)
$-\frac{{{e}^{2}}}{2}-\frac{3}{2}$

D)
$e+\frac{{{e}^{2}}}{2}+\frac{5}{2}$

• question_answer192) The degree and order of the differential equation of the family of all parabolas whose axis is X-axis, are respectively     AIEEE  Solved  Paper-2003

A)
2, 1

B)
1, 2

C)
3, 2

D)
2, 3

• question_answer193) The solution of the differential equation $(1+{{y}^{2}})+(x-{{e}^{{{\tan }^{-1}}}}y)\frac{dy}{dx}=0$, is     AIEEE  Solved  Paper-2003

A)
$(x-2)=k{{e}^{-{{\tan }^{-1}}y}}$

B)
$2\,x\,{{e}^{-{{\tan }^{-1}}y}}={{e}^{2\,{{\tan }^{-1}}y}}+k$

C)
$x{{e}^{{{\tan }^{-1}}}}={{\tan }^{-1}}\,y+k$

D)
$x{{e}^{2\,\,{{\tan }^{-1}}y}}={{e}^{{{\tan }^{-1}}y}}+k$

• question_answer194) If the equation of the locus of a point equidistant from the points $({{a}_{1}}-{{b}_{1}})$ and $({{a}_{2}}-{{b}_{2}})$ is $({{a}_{1}}-{{a}_{2}})x+({{b}_{1}}-{{b}_{2}})\,y+c=0$, then the value of 'c' is     AIEEE  Solved  Paper-2003

A)
$\frac{1}{2}(a_{2}^{2}+b_{2}^{2}-a_{1}^{2}-b_{1}^{2})$

B)
$a_{1}^{2}-a_{2}^{2}+b_{1}^{2}-b_{2}^{2}$

C)
$\frac{1}{2}\,\,(a_{1}^{2}+a_{2}^{2}+b_{1}^{2}+b_{2}^{2})$

D)
$\sqrt{a_{1}^{2}+b_{1}^{2}-a_{2}^{2}-b_{2}^{2}}$

• question_answer195) Locus of centroid of the triangle whose vertices are (b sin t, - b cost) and (1, 0), where t is a parameter, is     AIEEE  Solved  Paper-2003

A)
${{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}$

B)
${{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}$

C)
${{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}$

D)
${{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}$

• question_answer196) If   the   pair   of   straight   lines ${{x}^{2}}-2pxy-{{y}^{2}}=0$and ${{x}^{2}}-2qxy-{{y}^{2}}=0$ be such that each pair bisects the angle between the other pair, then     AIEEE  Solved  Paper-2003

A)
$p=q$

B)
$p=-q$

C)
$pq=1$

D)
$pq=-1$

• question_answer197) A square of side a lies above the X-axis and has one vertex at the origin. The side passing through the origin makes an angle $\left( 0<\alpha <\frac{\pi }{4} \right)$ with the positive direction of X-axis. The equation of its diagonal not passing through the origin is     AIEEE  Solved  Paper-2003

A)
$y(\cos \alpha -\sin \alpha )-x(\sin \alpha -\cos \alpha )=a$

B)
$y(\cos \alpha +\sin \alpha )+x(\sin \alpha -\cos \alpha )=a$

C)
$y(\cos \alpha +\sin \alpha )+x(\sin \alpha +\cos \alpha )=a$

D)
$y(\cos \alpha +\sin \alpha )+x(\cos \alpha -\sin \alpha )=a$

• question_answer198) If the two circles ${{(x-1)}^{2}}+{{(y-3)}^{2}}={{r}^{2}}$ and ${{x}^{2}}+{{y}^{2}}-8x+2y+8=0$ intersect in two distinct points, then     AIEEE  Solved  Paper-2003

A)
$2<r<8$

B)
$r<2$

C)
$r=2$

D)
$r>2$

• question_answer199) The lines $2x-3y=5$ and $3x-4y=7$ are diameters of a circle having area as 154 sq units. Then, the equation of the circle is     AIEEE  Solved  Paper-2003

A)
${{x}^{2}}+{{y}^{2}}+2x-2y=62$

B)
${{x}^{2}}+{{y}^{2}}+2x-2y=47$

C)
${{x}^{2}}+{{y}^{2}}-2x+2y=47$

D)
${{x}^{2}}+{{y}^{2}}-2x+2y=62$

• question_answer200) The normal at the point $(bt_{1}^{2},b{{t}_{1}})$ on a parabola meets the parabola again in the point$(bt_{2}^{2},2b{{t}_{2}})$, then     AIEEE  Solved  Paper-2003

A)
${{t}_{2}}=-{{t}_{1}}-\frac{2}{{{t}_{1}}}$

B)
${{t}_{2}}=-{{t}_{1}}+\frac{2}{{{t}_{1}}}$

C)
${{t}_{2}}={{t}_{1}}-\frac{2}{{{t}_{1}}}$

D)
${{t}_{2}}={{t}_{1}}+\frac{2}{{{t}_{1}}}$

• question_answer201) The foci of the ellipse $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$ and the hyperbola $\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25}$ coincide. Then, the value of ${{b}^{2}}$ is     AIEEE  Solved  Paper-2003

A)
1

B)
5

C)
7

D)
9

• question_answer202) A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 3), B(2, 1, 3) and C(-1, 1, 2). Then, the angle between the faces OAB and ABC will be     AIEEE  Solved  Paper-2003

A)
${{\cos }^{-1}}\left( \frac{19}{35} \right)$

B)
${{\cos }^{-1}}\left( \frac{17}{31} \right)$

C)
${{30}^{o}}$

D)
${{90}^{o}}$

• question_answer203) The radius of the circle in which the sphere ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2x-2y-4z-19=0$ is cut by the plane $x+2y+2z+7=0$, is     AIEEE  Solved  Paper-2003

A)
1

B)
2

C)
3

D)
4

• question_answer204) The lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and $\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar, if     AIEEE  Solved  Paper-2003

A)
k = 0 or - 1

B)
k = 1 or ? 1

C)
k = 0 or -3

D)
k = 3 or -3

• question_answer205) The two lines $x=ay\,+b,\,\,z=cy+d$ and$x=a'\,y+b',\,z=c'\,y+d'$ will be perpendicular, if and only if     AIEEE  Solved  Paper-2003

A)
$aa'+bb'+cc'+1=0$

B)
$aa'+bb'+cc'=0$

C)
$(a+a')\,(b+b')+(c+c')=0$

D)
$aa'+cc'+1=0$

• question_answer206) The shortest distance from the plane $12x+4y+3z=327$ to the sphere ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}+4x-2y-6z=155$ is     AIEEE  Solved  Paper-2003

A)
26

B)
$11\frac{4}{13}$

C)
13

D)
39

• question_answer207) Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b?, c from the origin, then     AIEEE  Solved  Paper-2003

A)
$\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}+\frac{1}{a{{'}^{2}}}+\frac{1}{{{b}^{'2}}}+\frac{1}{c{{'}^{2}}}=0$

B)
$\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}-\frac{1}{{{c}^{2}}}+\frac{1}{a{{'}^{2}}}+\frac{1}{{{b}^{'2}}}-\frac{1}{c{{'}^{2}}}=0$

C)
$\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}-\frac{1}{{{c}^{2}}}+\frac{1}{a{{'}^{2}}}-\frac{1}{{{b}^{'2}}}-\frac{1}{c{{'}^{2}}}=0$

D)
$\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}-\frac{1}{a{{'}^{2}}}-\frac{1}{{{b}^{'2}}}-\frac{1}{c{{'}^{2}}}=0$

• question_answer208) a, b, c   are three vectors, such that $a+b+c=0,\,\,\left| a \right|=1,\,\,\left| b \right|=2,\,\,\left| c \right|=3$, then $a\,.\,b+b\,.\,\,c+c\,.\,\,a$ is equal to     AIEEE  Solved  Paper-2003

A)
0

B)
-7

C)
7

D)
1

• question_answer209) If u, v and w are three non-coplanar vectors, then (u + v - w) . [(u - v) $\times$ (v - w)] equals     AIEEE  Solved  Paper-2003

A)
0

B)
$u\,.\,v\times w$

C)
$u\,.\,w\times v$

D)
$3u\,.\,v\times w$

• question_answer210) Consider points A, B, C and D with position vectors  $7\hat{i}-4\hat{j}+7\hat{k}$, $\hat{i}-6\hat{j}+10\hat{k}$, $-\hat{i}-3\hat{j}+4\,\hat{k}$and $5\,\hat{i}-\hat{j}+5\,\hat{k}$, respectively. Then, ABCD is a     AIEEE  Solved  Paper-2003

A)
square

B)
rhombus

C)
rectangle

D)
parallelogram but not a rhombus None of the given option is correct.

• question_answer211) The vectors $AB=3\hat{i}+4\hat{k}$ and $AC=5\,\hat{i}-2\,\hat{j}+4\,\hat{k}$ are the sides of a $\Delta ABC$. The length of the median through A is     AIEEE  Solved  Paper-2003

A)
$\sqrt{18}$

B)
$\sqrt{72}$

C)
$\sqrt{33}$

D)
$\sqrt{288}$

• question_answer212) A particle acted on by constant forces $4\,\hat{i}+\hat{j}-3\,\hat{k}$ and $3\,\hat{i}+\hat{j}-\,\hat{k}$ is displaced from the point $\hat{i}+2\hat{j}+3\,\hat{k}$ to the point $5\,\hat{i}+4\,\hat{j}+\,\hat{k}$. The total work done by the forces is     AIEEE  Solved  Paper-2003

A)
20 units

B)
30 units

C)
40 units

D)
50 units

• question_answer213) Let $u=\hat{i}+\hat{j},\,v=\hat{i}-\hat{j}$ and $w=\hat{i}+2\,\hat{j}+3\,\,\hat{k}$. If $\hat{n}$ is a unit vector such that $u\,.\,\,\hat{n}=0$ and $v\,.\,\,\hat{n}=0$, then $\left| w\,.\,\,\hat{n} \right|$ is equal to     AIEEE  Solved  Paper-2003

A)
0

B)
1

C)
2

D)
3

• question_answer214) The median of a set of 9 distinct observations is 205. If each of the largest 4 observations of the set is increased by 2, then the median of the new set     AIEEE  Solved  Paper-2003

A)
is increased by 2

B)
is decreased by 2

C)
is two times the original median

D)
remains the same as that of the original set

• question_answer215) In an experiment with 15 observations on x, the following results were available $\sum {{x}^{2}}=2830,\,\,\sum x=170$. One observation that was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance is     AIEEE  Solved  Paper-2003

A)
78.00

B)
188.66

C)
177.33

D)
8.33

• question_answer216) Five horses are in a race. Mr A selects two of the horses at random and bets on them. The probability that Mr A selected the winning horse, is     AIEEE  Solved  Paper-2003

A)
$\frac{4}{5}$

B)
$\frac{3}{5}$

C)
$\frac{1}{5}$

D)
$\frac{2}{5}$

• question_answer217) Events A, B, C are mutually exclusive 3x +1 events   such that $P(A)=\frac{3x+1}{3},\,P(B)=\frac{1-x}{4}$ and $P(C)=\frac{1-2x}{2}$. The set of possible values of x are in the interval     AIEEE  Solved  Paper-2003

A)
$\left[ \frac{1}{3},\frac{1}{2} \right]$

B)
$\left[ \frac{1}{3},\frac{2}{3} \right]$

C)
$\left[ \frac{1}{3},\frac{13}{3} \right]$

D)
$\left[ 0,1 \right]$

• question_answer218) The mean and variance of a random variable  X  having a binomial distribution are 4 and 2 respectively, then $P(X=1)$ is     AIEEE  Solved  Paper-2003

A)
$\frac{1}{32}$

B)
$\frac{1}{16}$

C)
$\frac{1}{8}$

D)
$\frac{1}{4}$

• question_answer219) The resultant of forces P and Q is R. If Q is doubled, then R is doubled. If the direction of Q is reversed, then R is again doubled, then? ${{P}^{2}}:{{Q}^{2}}:{{R}^{2}}$ is     AIEEE  Solved  Paper-2003

A)
3 : 1 : 1

B)
2 : 3 : 2

C)
1 : 2 : 3

D)
2 : 3 : 1

• question_answer220) Let ${{R}_{1}}$ and ${{R}_{2}}$ respectively be the maximum ranges up and down an inclined plane and R be the maximum range on the horizontal plane. Then. ${{R}_{1}},R,{{R}_{2}}$ are in     AIEEE  Solved  Paper-2003

A)
AGP

B)
AP

C)
GP

D)
HP

• question_answer221) A couple is of moment G and the force forming the couple is P. If P is turned through a right angle, the moment of the couple thus formed is H. If instead, the forces P is turned through an angle a, then the moment of couple becomes     AIEEE  Solved  Paper-2003

A)
$G\sin \alpha -H\cos \alpha$

B)
$H\cos \alpha +G\sin \alpha$

C)
$G\cos \alpha +H\sin \alpha$

D)
$H\sin \alpha -G\cos \alpha$

• question_answer222) Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uniform acceleration f. Let $\alpha$ be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time     AIEEE  Solved  Paper-2003

A)
$\frac{u\sin \alpha }{f}$

B)
$\frac{f\cos \alpha }{u}$

C)
$u\sin \alpha$

D)
$\frac{u\cos \alpha }{f}$

• question_answer223) Two stones are projected from the top of a cliff h metres high, with the same speed u, so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle $\theta$ to the horizontal, then tan $\theta$ equals       AIEEE  Solved  Paper-2003

A)
$\sqrt{\frac{2u}{gh}}$

B)
$2g\,\sqrt{\frac{u}{h}}$

C)
$2h\,\sqrt{\frac{u}{g}}$

D)
$u\,\sqrt{\frac{2}{gh}}$

• question_answer224) A body travels a distance s in t seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration f and in the second part with constant retardation r. The value of t is given by     AIEEE  Solved  Paper-2003

A)
$2s\left( \frac{1}{f}+\frac{1}{r} \right)$

B)
$\frac{2s}{\frac{1}{f}+\frac{1}{r}}$

C)
$\sqrt{2s\,(f+r)}$

D)
$\sqrt{2s\,\left( \frac{1}{f}+\frac{1}{r} \right)}$