# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2002

### done AIEEE Solved Paper-2002 Total Questions - 225

• question_answer1) The inductance between A and D is              AIEEE  Solved  Paper-2002

A)
3.66 H

B)
9 H

C)
0.66 H

D)
1 H

• question_answer2) A ball whose kinetic energy is E, is projected at an angle of ${{45}^{o}}$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be   AIEEE  Solved  Paper-2002

A)
E

B)
$E/\sqrt{2}$.

C)
$E/2$

D)
zero

• question_answer3) From a building, two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically). If ${{v}_{A}}$ and ${{v}_{B}}$ are their respective velocities on reaching the ground, then   AIEEE  Solved  Paper-2002

A)
${{v}_{B}}>{{v}_{A}}$

B)
${{v}_{A}}={{v}_{B}}$

C)
${{v}_{A}}>{{v}_{B}}$

D)
their velocities depend on their masses

• question_answer4) If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest? AIEEE  Solved  Paper-2002

A)
1 cm

B)
2 cm

C)
3 cm

D)
4 cm

• question_answer5) If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will   AIEEE  Solved  Paper-2002

A)
continue to move in its orbit with same velocity

B)
move tangentially to the original orbit with the same velocity

C)
become stationary in its orbit

D)
move towards the earth

• question_answer6) If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a   AIEEE  Solved  Paper-2002

A)
low resistance in parallel

B)
high resistance in parallel

C)
high resistance in series

D)
low resistance in series

• question_answer7) If in a circular coil A of radius R, current j is flowing and in another coil B of radius 2 R, a current 2 i is flowing, then the ratio of the magnetic fields, ${{B}_{A}}$ and ${{B}_{B}}$ produced by them will be   AIEEE  Solved  Paper-2002

A)
1

B)
2

C)
$1/2$

D)
4

• question_answer8) If two mirrors are kept at 60° to each other, then the number of images formed by them is   AIEEE  Solved  Paper-2002

A)
5

B)
6

C)
7

D)
8

• question_answer9) A wire when connected to 220 V mains supply has power dissipation ${{P}_{1}}$. Now, the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is ${{P}_{2}}$. Then, ${{P}_{2}}:{{P}_{1}}$ is   AIEEE  Solved  Paper-2002

A)
1

B)
4

C)
2

D)
3

• question_answer10) If $13.6$ eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from $n=2$, is   AIEEE  Solved  Paper-2002

A)
$10.2$ eV

B)
0 eV

C)
$3.4$ eV

D)
$6.8$ eV

• question_answer11) Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tubes A and B is   AIEEE  Solved  Paper-2002

A)
$1:2$

B)
$1:4$

C)
$2:1$

D)
$4:1$

• question_answer12) A tuning fork arrangement (pair) produces 4 beats/s with one fork of frequency 288 cps. A little wax is placed on the unknown fork and it then produces 2 beats/s. The frequency of the unknown fork is   AIEEE  Solved  Paper-2002

A)
286 cps

B)
292 cps

C)
294 cps

D)
288 cps

• question_answer13) A wave $y=a\sin \,(\omega t-kx)$ on a string meets with another wave producing a node at $x=0$. Then, the equation of the unknown wave is   AIEEE  Solved  Paper-2002

A)
$y=a\sin \,(\omega \,t+kx)$

B)
$y=-a\sin \,(\omega \,t+kx)$

C)
$y=a\sin \,(\omega \,t-kx)$

D)
$y=-a\sin \,(\omega \,t-kx)$

• question_answer14) On moving a charge of 20 C by 2 cm, 2 J of work is done, then the potential difference between the points is   AIEEE  Solved  Paper-2002

A)
$0.1$ V

B)
8 V

C)
2 V

D)
$0.2$ V

• question_answer15) If an electron and a proton having same momenta enter perpendicularly to a magnetic field, then   AIEEE  Solved  Paper-2002

A)
curved path of electron and proton will be same (ignoring the sense of revolution)

B)
they will move undeflected

C)
curved path of electron is more curved than that of proton

D)
path of proton is more curved

• question_answer16) Energy required to move a body of mass m from an orbit of radius 2 R to 3 R is   AIEEE  Solved  Paper-2002

A)
$GMm/12{{R}^{2}}$

B)
$GMm/3{{R}^{2}}$

C)
$GMm/8R$

D)
$GMm/6R$

• question_answer17) If a spring has time period T, and is cut into n equal parts, then the time period of each part will be   AIEEE  Solved  Paper-2002

A)
$T\sqrt{n}$

B)
$\frac{T}{\sqrt{n}}$

C)
$nT$

D)
T

• question_answer18) A charged particle g is placed at the centre O of cube of length L (ABCDEFGH). Another same charge q is placed at a distance L from O. Then, the electric flux through ABCD is     AIEEE  Solved  Paper-2002

A)
$q/4\pi {{\varepsilon }_{0}}L$

B)
zero

C)
$q/2\pi {{\varepsilon }_{0}}L$

D)
$q/3\pi {{\varepsilon }_{0}}L$

• question_answer19) If in the circuit, power dissipation is 150 W, then R is   AIEEE  Solved  Paper-2002

A)
$2\,\,\Omega$

B)
$6\,\,\Omega$

C)
$5\,\,\Omega$

D)
$4\,\,\Omega$

• question_answer20) Wavelength of light used in an optical instrument   are   ${{\lambda }_{1}}=4000\,\overset{0}{\mathop{A}}\,$   and ${{\lambda }_{2}}=5000\,\overset{0}{\mathop{A}}\,$, then ratio of their respective resolving powers (corresponding to ${{\lambda }_{1}}$ and ${{\lambda }_{2}}$) is   AIEEE  Solved  Paper-2002

A)
$16:25$

B)
$9:1$

C)
$4:5$

D)
$5:4$

• question_answer21) Two identical particles move towards each other with velocity 2v and v respectively. The velocity of centre of mass is   AIEEE  Solved  Paper-2002

A)

B)
$v/3$

C)
$v/2$

D)
zero

• question_answer22) If a current is passed through a spring, then the spring will   AIEEE  Solved  Paper-2002

A)
expand

B)
compress

C)
remain same

D)
None of these

• question_answer23) Heat given to a body which raises its temperature by ${{1}^{o}}C$ is   AIEEE  Solved  Paper-2002

A)
water equivalent

B)
thermal capacity

C)
specific heat

D)

• question_answer24) At absolute zero, Si acts as   AIEEE  Solved  Paper-2002

A)
non-metal

B)
metal

C)
insulator

D)
None of these

• question_answer25) Electromagnetic waves are transverse in nature is evident by   AIEEE  Solved  Paper-2002

A)
polarisation

B)
interference

C)
reflection

D)
diffraction

• question_answer26) Which of the following is used in optical fibres?   AIEEE  Solved  Paper-2002

A)
Total internal reflection

B)
Scattering

C)
Diffraction

D)
Refraction

• question_answer27) The escape velocity of a body depends upon mass as   AIEEE  Solved  Paper-2002

A)
${{m}^{o}}$

B)
${{m}^{1}}$

C)
${{m}^{2}}$

D)
${{m}^{3}}$

• question_answer28) Which of the following are not electromagnetic waves?   AIEEE  Solved  Paper-2002

A)
Cosmic-rays

B)
$\gamma$-rays

C)
$\beta$-rays

D)
X-rays

• question_answer29) Identify the pair whose dimensions are equal.   AIEEE  Solved  Paper-2002

A)
Torque and work

B)
Stress and energy

C)
Force and stress

D)
Force and work

• question_answer30) If ${{\theta }_{i}}$ is the inversion temperature, ${{\theta }_{n}}$ is the neutral temperature, ${{\theta }_{c}}$ is the temperature of the cold junction, then   AIEEE  Solved  Paper-2002

A)
${{\theta }_{i}}+{{\theta }_{c}}={{\theta }_{n}}$

B)
${{\theta }_{i}}-{{\theta }_{c}}=2{{\theta }_{n}}$

C)
$\frac{{{\theta }_{i}}+{{\theta }_{c}}}{2}={{\theta }_{n}}$

D)
${{\theta }_{c}}-{{\theta }_{i}}=2{{\theta }_{n}}$

A)
spectrometer

B)
pyrometer

C)
nanometer

D)
photometer

• question_answer32) If ${{N}_{0}}$ is the original mass of the substance of half-life period ${{t}_{1/2}}\,=5\,\,yr,$ then the amount of substance left after $15\,yr$ is   AIEEE  Solved  Paper-2002

A)
$\frac{{{N}_{0}}}{8}$

B)
$\frac{{{N}_{0}}}{16}$

C)
$\frac{{{N}_{0}}}{2}$

D)
$\frac{{{N}_{0}}}{4}$

• question_answer33) By increasing the temperature, the specific resistance of a conductor and a semiconductor,   AIEEE  Solved  Paper-2002

A)
increases for both

B)
decreases for both

C)
increases and decreases, respectively

D)
decreases and increases, respectively

• question_answer34) If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to AIEEE  Solved  Paper-2002

A)
CV

B)
$\frac{1}{2}nC{{V}^{2}}$

C)
$C{{V}^{2}}$

D)
$\frac{1}{2n}C{{V}^{2}}$

• question_answer35) Which of the following is more close to a black body?   AIEEE  Solved  Paper-2002

A)
Black board paint

B)
Green leaves

C)
Black holes

D)
Red roses

• question_answer36) Which statement is incorrect?   AIEEE  Solved  Paper-2002

A)
All reversible cycles have same efficiency

B)
Reversible cycle has more efficiency than an irreversible one

C)
Carnot cycle is a reversible one

D)
Carnot cycle has the maximum efficiency in all cycles

• question_answer37) Length of a string tied to two rigid supports is 40 cm. Maximum length (wavelength in cm) of a stationary wave produced on it, is   AIEEE  Solved  Paper-2002

A)
20

B)
80

C)
40

D)
120

• question_answer38) The power factor of an AC circuit having resistance R and inductance L (connected in series) and an angular velocity co is   AIEEE  Solved  Paper-2002

A)
$\frac{R}{\omega L}$

B)
$\frac{R}{{{({{R}^{2}}+{{\omega }^{2}}{{L}^{2}})}^{1/2}}}$

C)
$\frac{\omega L}{R}$

D)
$\frac{R}{{{({{R}^{2}}-{{\omega }^{2}}{{L}^{2}})}^{1/2}}}$

• question_answer39) An astronomical telescope has a large aperture to   AIEEE  Solved  Paper-2002

A)
reduce spherical aberration

B)
have high resolution

C)
increase span of observation

D)
have low dispersion

• question_answer40) The kinetic energy needed to project a body of mass m from the earth's surface (radius R) to infinity is AIEEE  Solved  Paper-2002

A)
$\frac{mgR}{2}$

B)
$2mgR$

C)
$mgR$

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

• question_answer41) Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will AIEEE  Solved  Paper-2002

A)
increase

B)
decrease

C)
remain same

D)
decrease for some while increase for others

• question_answer42) When temperature increases, the frequency of a tuning fork   AIEEE  Solved  Paper-2002

A)
increases

B)
decreases

C)
remains same

D)
increases or decreases depending on the material

• question_answer43) If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should   AIEEE  Solved  Paper-2002

A)
increase

B)
remain unchanged

C)
decrease

D)
first increase then decrease

• question_answer44) The energy band gap is maximum in AIEEE  Solved  Paper-2002

A)
metals

B)
superconductors

C)
insulators

D)
semiconductors

• question_answer45) The part of a transistor which is most heavily doped to produce large number of majority carriers is   AIEEE  Solved  Paper-2002

A)
emitter

B)
base

C)
collector

D)
can be any of the above three

• question_answer46) In a simple harmonic oscillator, at the mean position   AIEEE  Solved  Paper-2002

A)
kinetic energy is minimum, potential energy is maximum

B)
both kinetic and potential energies are maximum

C)
kinetic energy is maximum, potential energy is minimum

D)
both kinetic and potential energies are minimum

• question_answer47) Initial angular velocity of a circular disc of mass M is ${{\omega }_{\,1}}$. Then, two small spheres of mass m are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?   AIEEE  Solved  Paper-2002

A)
$\left( \frac{M+m}{M} \right){{\omega }_{1}}$

B)
$\left( \frac{M+m}{m} \right){{\omega }_{1}}$

C)
$\left( \frac{M}{M+4m} \right){{\omega }_{1}}$

D)
$\left( \frac{M}{M+2m} \right){{\omega }_{1}}$

• question_answer48) The minimum velocity (in $m{{s}^{-1}}$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction $0.6$ to avoid skidding is   AIEEE  Solved  Paper-2002

A)
60

B)
30

C)
15

D)
25

• question_answer49) A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in $m{{s}^{-1}}$) through a small hole on the side wall of the cylinder near its bottom, is   AIEEE  Solved  Paper-2002

A)
10

B)
20

C)
$25.5$

D)
5

• question_answer50) A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is   AIEEE  Solved  Paper-2002

A)
16 J

B)
8 J

C)
32 J

D)
24 J

• question_answer51) A child swinging on a swing in sitting position, stands up, then the time period of the swing will   AIEEE  Solved  Paper-2002

A)
increase

B)
decrease

C)
remain same

D)
increase if the child is long and decrease if the child is short

• question_answer52) A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively   AIEEE  Solved  Paper-2002

A)
g, g

B)
g-a, g-a

C)
g-a, g

D)
a, g

• question_answer53) The mass of a product liberated on anode in an electrochemical cell depends on   AIEEE  Solved  Paper-2002

A)
${{(lt)}^{1/2}}$

B)
$lt$

C)
$l/t$

D)
${{l}^{2}}t$ (where t is the time period for which the current is passed)

• question_answer54) At what temperature is the $rms$ velocity of a hydrogen molecule equal to that of an oxygen molecule at ${{47}^{o}}C$?   AIEEE  Solved  Paper-2002

A)
80 K

B)
-73 K

C)
3 K

D)
20 K

• question_answer55) The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its   AIEEE  Solved  Paper-2002

A)
speed

B)
mass

C)
charge

D)
magnetic induction

• question_answer56) A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then, maximum acceleration down the plane is for (no rolling)   AIEEE  Solved  Paper-2002

A)
solid sphere

B)
hollow sphere

C)
ring

D)
All same

• question_answer57) In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is 4 A, then that in the secondary is AIEEE  Solved  Paper-2002

A)
4 A

B)
2 A

C)
6 A

D)
10 A

• question_answer58) Even Carnot engine cannot give 100% efficiency because we cannot   AIEEE  Solved  Paper-2002

A)

B)
find ideal sources

C)
reach absolute zero temperature

D)
eliminate friction

• question_answer59) Moment of inertia of a circular wire of mass M and radius R about its diameter is   AIEEE  Solved  Paper-2002

A)
$M{{R}^{2}}/2$

B)
$M{{R}^{2}}$

C)
$2M{{R}^{2}}$

D)
$M{{R}^{2}}/4$

• question_answer60) When forces ${{F}_{1}},{{F}_{2}},{{F}_{3}}$ are acting on a particle of mass m such that ${{F}_{1}}$ and ${{F}_{2}}$ are mutually perpendicular, then the particle remains stationary. If the force ${{F}_{1}}$ is now removed, then the acceleration of the particle is   AIEEE  Solved  Paper-2002

A)
${{F}_{1}}/m$

B)
${{F}_{2}}{{F}_{3}}/m{{F}_{1}}$

C)
$({{F}_{2}}-{{F}_{3}})/m$

D)
${{F}_{2}}/m$

• question_answer61) Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then, the magnitudes of the forces are   AIEEE  Solved  Paper-2002

A)
12 N, 6 N

B)
13 N, 5 N

C)
10 N, 8 N

D)
16 N, 2 N

• question_answer62) Speeds of two identical cars are u and 4 u at a specific instant. The ratio of the respective distances at which the two cars are stopped from that instant is   AIEEE  Solved  Paper-2002

A)
$1:1$

B)
$1:4$

C)
$1:8$

D)
$1:16$

• question_answer63) 1 mole of a gas with $\gamma =7/5$ is mixed with 1 mole of a gas with $\gamma =5/3$ , then the value of y for the resulting mixture is   AIEEE  Solved  Paper-2002

A)
$7/5$

B)
$2/5$

C)
$24/16$

D)
$12/7$

• question_answer64) If a charge q is placed at the centre of the line joining two equal charges Q such that the system is in equilibrium, then the value of q is   AIEEE  Solved  Paper-2002

A)
$Q/2$

B)
$-Q/2$

C)
$Q/4$

D)
$-Q/4$

• question_answer65) Capacitance (in F) of a spherical conductor having radius 1 m, is   AIEEE  Solved  Paper-2002

A)
$1.1\times {{10}^{-10}}$

B)
${{10}^{-6}}$

C)
$9\times {{10}^{-9}}$

D)
${{10}^{-3}}$

• question_answer66) A light string passing over a smooth light pulley connects two blocks of masses ${{m}_{1}}$ and ${{m}_{2}}$ (vertically). If the acceleration of the system is g/8, then the ratio of the masses is   AIEEE  Solved  Paper-2002

A)
$8:1$

B)
$9:7$

C)
$4:3$

D)
$5:3$

• question_answer67) Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the first sphere to that by the second is   AIEEE  Solved  Paper-2002

A)
$1:1$

B)
$16:1$

C)
$4:1$

D)
$1:9$

• question_answer68) Three identical blocks of masses $m=2$ kg are drawn by a force $F=10.2$ N with an acceleration of $0.6\,\,m{{s}^{-2}}$ on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C?                AIEEE  Solved  Paper-2002

A)
$9.2$

B)
$7.8$

C)
4

D)
$9.8$

• question_answer69) One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of maximum safe acceleration (in $m{{s}^{-2}}$) can a man of 60 kg climb on the rope?                             AIEEE  Solved  Paper-2002

A)
16

B)
6

C)
4

D)
8

• question_answer70) A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about O?                AIEEE  Solved  Paper-2002

A)
$mvL$

B)
$mvl$

C)
$mvr$

D)
0

• question_answer71) Wires 1 and 2 carrying currents, ${{i}_{1}}$ and ${{i}_{2}}$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element dl of wire 2 at a distance r from wire 1 (as shown in figure) due to the magnetic field of wire 1?                             AIEEE  Solved  Paper-2002

A)
$\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}{{i}_{2}}\,dl\tan \theta$

B)
$\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}{{i}_{2}}\,dl\sin \theta$

C)
$\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}{{i}_{2}}\,dl\cos \theta$

D)
$\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}{{i}_{2}}\,dl\sin \theta$

• question_answer72) At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit (i) electrons                           (ii) protons (iii) $H{{e}^{+}}$                                (iv) neutrons The emission at the instant can be   AIEEE  Solved  Paper-2002

A)
(i), (ii), (iii)

B)
(i), (ii), (iii), (iv)

C)
(iv)

D)
(ii), (iii)

• question_answer73) Sodium and copper have work functions $2.3$ eV and $4.5$ eV respectively. Then, the ratio of the wavelengths is nearest to   AIEEE  Solved  Paper-2002

A)
$1:2$

B)
$4:1$

C)
$2:1$

D)
$1:4$

• question_answer74) Formation of covalent bonds in compounds exhibits   AIEEE  Solved  Paper-2002

A)
wave nature of electron

B)
particle nature of electron

C)
both wave and particle nature of electron

D)
None of the above

• question_answer75) A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into the plane at the loop exist everywhere with half the loop outside the field, as shown in figure. The induced emf is                AIEEE  Solved  Paper-2002

A)
zero

B)
$RvB$

C)
$\frac{vBL}{R}$

D)
$vBL$

• question_answer76) Which of the following is a redox reaction?   AIEEE  Solved  Paper-2002

A)
$NaCl+KN{{O}_{3}}\xrightarrow{{}}NaN{{O}_{3}}+KCl$

B)
$Ca{{C}_{2}}{{O}_{4}}+2HCl\xrightarrow{{}}CaC{{l}_{2}}+{{H}_{2}}{{C}_{2}}{{O}_{4}}$

C)
$Ca{{(OH)}_{2}}+2N{{H}_{4}}Cl\xrightarrow{{}}CaC{{l}_{2}}+2N{{H}_{3}}$$+2{{H}_{2}}O$

D)
$2K[Ag{{(CN)}_{2}}]+Zn\xrightarrow{{}}2Ag+{{K}_{2}}[Zn{{(CN)}_{4}}]$

• question_answer77) For an ideal gas, number of mol per litre in terms of its pressure p, temperature T and gas constant R is   AIEEE  Solved  Paper-2002

A)
$\frac{pT}{R}$

B)
pRT

C)
$\frac{p}{RT}$

D)
$\frac{RT}{p}$

• question_answer78) Number of P - O bonds in ${{P}_{4}}{{O}_{10}}$ is   AIEEE  Solved  Paper-2002

A)
17

B)
16

C)
15

D)
6

• question_answer79) $K{{O}_{2}}$ is used in space and submarines because it   AIEEE  Solved  Paper-2002

A)
absorbs $C{{O}_{2}}$ and increases ${{O}_{2}}$ concentration

B)
absorbs moisture

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

D)
produces ozone

• question_answer80) Which of the following ions has the maximum magnetic moment?   AIEEE  Solved  Paper-2002

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

B)
$F{{e}^{2+}}$

C)
$T{{i}^{2+}}$

D)
$C{{r}^{2+}}$

• question_answer81) Acetylene does not react with AIEEE  Solved  Paper-2002

A)
Na

B)
ammoniacal $AgN{{O}_{3}}$

C)
$HCl$

D)
$NaOH$

• question_answer82) Compound A given below is              AIEEE  Solved  Paper-2002

A)
antiseptic

B)
antibiotic

C)
analgesic

D)
pesticide

• question_answer83) For the following cell with hydrogen electrodes at two different pressures pi and?2 $\underset{{{p}_{1}}}{\mathop{\operatorname{P}t({{H}_{2}})}}\,\,\,\underset{1M}{\mathop{\left| {{H}^{+}}(aq) \right|}}\,\,\,\underset{{{p}_{2}}}{\mathop{\operatorname{P}t({{H}_{2}})}}\,$  emf is given by   AIEEE  Solved  Paper-2002

A)
$\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}$

B)
$\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}$

C)
$\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}$

D)
$\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}$

• question_answer84) Acetylene reacts with hypochlorous acid to form   AIEEE  Solved  Paper-2002

A)
$C{{l}_{2}}CHCHO$

B)
$ClC{{H}_{2}}COOH$

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

D)
$ClC{{H}_{2}}CHO$

• question_answer85) On heating benzyl amine with chloroform and ethanolic KOH, product obtained is   AIEEE  Solved  Paper-2002

A)
benzyl alcohol

B)
benzaldehyde

C)
benzonitrile

D)
benzyl isocyanide

• question_answer86) Which of the following reaction is possible at anode?   AIEEE  Solved  Paper-2002

A)
${{F}_{2}}+2{{e}^{-}}\xrightarrow{{}}2{{F}^{-}}$

B)
$2{{H}^{+}}+\frac{1}{2}{{O}_{2}}+2{{e}^{-}}\xrightarrow{{}}{{H}_{2}}O$

C)
$2C{{r}^{3+}}+7{{H}_{2}}O\xrightarrow{{}}C{{r}_{2}}O_{7}^{2-}+14{{H}^{+}}+6{{e}^{-}}$

D)
$F{{e}^{2+}}\xrightarrow{{}}F{{e}^{3+}}+{{e}^{-}}$

• question_answer87) Which of the following concentration factor is affected by change in temperature?   AIEEE  Solved  Paper-2002

A)
Molarity

B)
Molality

C)
Mole fraction

D)
Weight fraction

• question_answer88) Cyanide process is used for the extraction of   AIEEE  Solved  Paper-2002

A)
barium

B)
silver

C)
boron

D)
zinc

• question_answer89) Following reaction, ${{(C{{H}_{3}})}_{3}}CBr+{{H}_{2}}O\xrightarrow{{}}{{(C{{H}_{3}})}_{3}}COH+HBr$              is an example of     AIEEE  Solved  Paper-2002

A)
elimination reaction

B)

C)
nucleophilic substitution

D)
electrophilic substitution

• question_answer90) A metal M forms water soluble $MS{{O}_{4}}$ and inert MO. MO in aqueous solution forms insoluble $M{{(OH)}_{2}}$ soluble in $NaOH$. Metal M is   AIEEE  Solved  Paper-2002

A)
$Be$

B)
$Mg$

C)
$Ca$

D)
$Si$

• question_answer91) Half-life of a substance A following first order kinetics is 5 days. Starting with 100g of A, amount left after 15 days is   AIEEE  Solved  Paper-2002

A)
25 g

B)
50 g

C)
$12.5$g

D)
$6.25$g

• question_answer92) The most stable ion is   AIEEE  Solved  Paper-2002

A)
${{[Fe{{(OH)}_{5}}]}^{3-}}$

B)
${{[FeC{{l}_{6}}]}^{3-}}$

C)
${{[Fe{{(CN)}_{6}}]}^{3-}}$

D)
${{[Fe{{({{H}_{2}}O)}_{6}}]}^{3+}}$

• question_answer93) A substance forms Zwitter ion. It can have functional groups   AIEEE  Solved  Paper-2002

A)
$-N{{H}_{2}},-COOH$

B)
$-N{{H}_{2}},-S{{O}_{3}}H$

C)
Both (a) and (b)

D)
None of these

• question_answer94) If $F{{e}^{3+}}$ and $C{{r}^{3+}}$ both are present in group III of qualitative analysis, then distinction can be made by   AIEEE  Solved  Paper-2002

A)
addition of $N{{H}_{4}}OH$ in the presence of $N{{H}_{4}}Cl$ when only $Fe{{(OH)}_{3}}$ is precipitated

B)
addition of $N{{H}_{4}}OH$) in the presence of $N{{H}_{4}}Cl$I when $Cr{{(OH)}_{3}}$ and $Fe{{(OH)}_{3}}$ both are precipitated and on adding $B{{r}_{2}}$ water and NaOH, $Cr{{(OH)}_{3}}$ dissolves

C)
precipitate of $Cr{{(OH)}_{3}}$ and $Fe{{(OH)}_{3}}$ as obtained in (b) are treated with cone. HCI when only $Fe{{(OH)}_{3}}$ dissolves

D)
Both (b) and (c)

• question_answer95) In an organic compound of molar mass $108\,g\,mo{{l}^{-1}}$ C, H and N atoms are present in $9:1:3.5$ by weight. Molecular formula can be   AIEEE  Solved  Paper-2002

A)
${{C}_{6}}{{H}_{8}}{{N}_{2}}$

B)
${{C}_{7}}{{H}_{10}}N$

C)
${{C}_{5}}{{H}_{6}}{{N}_{3}}$

D)
${{C}_{4}}{{H}_{18}}{{N}_{3}}$

• question_answer96) Solubility of $Ca{{(OH)}_{2}}$ is s $mol{{L}^{-1}}$. The solubility product $({{K}_{sp}})$ under the same condition is   AIEEE  Solved  Paper-2002

A)
$4{{s}^{3}}$

B)
$3{{s}^{4}}$

C)
$4{{s}^{2}}$

D)
${{s}^{3}}$

• question_answer97) Heat required to raise the temperature of mole of a substance by ${{1}^{o}}C$ is called   AIEEE  Solved  Paper-2002

A)
specific heat

B)
molar heat capacity

C)
water equivalent

D)
specific gravity

• question_answer98) $\beta$-particle is emitted in a radioactive reaction when   AIEEE  Solved  Paper-2002

A)
a proton changes to neutron

B)
a neutron changes to proton

C)
a neutron changes to electron

D)
an electron changes to neutron

• question_answer99) In a mixture of A and B, components show negative deviation when   AIEEE  Solved  Paper-2002

A)
A-B interaction is stronger than A-A and B-B interaction

B)
A-B interaction is weaker than A-A and B-B interaction

C)
$\Delta {{V}_{\operatorname{mi}x}}>0$,  $\Delta {{S}_{\operatorname{mi}x}}>0$

D)
$\Delta {{V}_{\operatorname{mi}x}}=0$, $\Delta {{S}_{\operatorname{mi}x}}>0$

• question_answer100) Refining of impure copper with zinc impurity is to be done by electrolysis using electrodes as   AIEEE  Solved  Paper-2002

A)
Cathode - pure copper                  Anode- pure zinc

B)
Cathode - pure zinc                         Anode- pure copper

C)
Cathode - pure copper                  Anode- impure copper

D)
Cathode - pure zinc                         Anode- impure zinc

• question_answer101) Aluminium is extracted by the electrolysis of   AIEEE  Solved  Paper-2002

A)
alumina

B)
bauxite

C)
molten cryolite

D)
alumina mixed with molten cryolite

• question_answer102) For an aqueous solution, freezing point is${{0.186}^{o}}C$. Elevation of the boiling point of the same solution is (${{K}_{f}}={{1.86}^{o}}mo{{l}^{-1}}kg$ and ${{K}_{b}}={{0512}^{o}}mo{{l}^{-1}}kg$)   AIEEE  Solved  Paper-2002

A)
${{0.186}^{o}}$

B)
${{0.0.512}^{o}}$

C)
${{186}^{o}}$

D)
${{5.12}^{o}}$

• question_answer103) Underlined carbon is $s{{p}^{3}}$ hybridised in   AIEEE  Solved  Paper-2002

A)
$C{{H}_{3}}\underline{C}H=C{{H}_{2}}$

B)
$C{{H}_{3}}\underline{C}{{H}_{2}}N{{H}_{2}}$

C)
$C{{H}_{3}}\underline{C}ON{{H}_{2}}$

D)
$C{{H}_{3}}C{{H}_{2}}\underline{C}N$

• question_answer104) Bond angle of ${{109}^{o}}28$'is found in   AIEEE  Solved  Paper-2002

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

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

C)
$\overset{\oplus }{\mathop{C}}\,{{H}_{5}}$

D)
$\overset{\oplus }{\mathop{N}}\,{{H}_{4}}$

• question_answer105) For a reaction $A+2B\xrightarrow{{}}C$, rate is given by $+\frac{d[C]}{dt}=k[A][B]$, hence the order of the reaction is   AIEEE  Solved  Paper-2002

A)
3

B)
2

C)
1

D)
0

• question_answer106) $C{{H}_{3}}MgI$is an organometallic compound due to   AIEEE  Solved  Paper-2002

A)
Mg-l bond

B)
C-l bond

C)
C-Mg bond

D)
C-H bond

• question_answer107) One of the following species acts as both Bronsted acid and base   AIEEE  Solved  Paper-2002

A)
${{H}_{2}}PO_{2}^{-}$

B)
$HPO_{3}^{2-}$

C)
$HPO_{4}^{2-}$

D)
All of these

• question_answer108) Hybridisation of the underline atom changes in   AIEEE  Solved  Paper-2002

A)
$\underline{A}\,l{{H}_{3}}$ changes to $\underline{A}\,lH_{4}^{-}$

B)
${{H}_{2}}\underline{O}$ changes to ${{H}_{3}}{{O}^{+}}$

C)
$\underline{N}{{H}_{3}}$ changes to $NH_{4}^{+}$

D)
in all the above cases

• question_answer109) Racemic mixture is formed by mixing two   AIEEE  Solved  Paper-2002

A)
isomeric compounds

B)
chiral compounds

C)
meso compounds

D)
enantiomers with chiral carbon

• question_answer110) The number of lone pairs on $Xe$ in $Xe{{F}_{2}},Xe{{F}_{4}}$ and $Xe{{F}_{6}}$respectively are   AIEEE  Solved  Paper-2002

A)
3, 2, 1

B)
2, 4, 6

C)
1, 2, 3

D)
6, 4, 2

• question_answer111) An aqueous solution of $1\,M\,NaCl$ and $1\,M\,HCl$ is   AIEEE  Solved  Paper-2002

A)
not a buffer but $pH<7$

B)
not a buffer but $pH>7$

C)
a buffer with $pH<7$

D)
a buffer with $pH>7$

• question_answer112) Consider the following two reactions, $A\xrightarrow{{}}$ Product $-\frac{d[A]}{dt}={{k}_{1}}{{[A]}^{o}}$ $B\xrightarrow{{}}$ Product $-\frac{d[B]}{dt}={{k}_{2}}[B]$ ${{k}_{1}}$ and ${{k}_{2}}$ are expressed in terms of molarity(mol ${{L}^{-1}}$) and time $({{s}^{-1}})$ as   AIEEE  Solved  Paper-2002

A)
${{s}^{-1}},M\,{{s}^{-1}}\,{{L}^{-1}}$

B)
$M\,{{s}^{-1}},\,\,M\,{{s}^{-1}}$

C)
${{s}^{-1}},{{M}^{-1}}\,{{s}^{-1}}$

D)
$M\,{{s}^{-1}},\,{{s}^{-1}}$

A)
ribose sugar and thymine

B)
ribose sugar and uracil

C)
deoxyribose sugar and uracil

D)
deoxyribose sugar and thymine

• question_answer114) For a cell given below $Ag\,\left| A{{g}^{+}} \right|\left| C{{u}^{2+}} \right|\,\,Cu$                                                                                                    -                    + $A{{g}^{+}}+{{e}^{-}}\xrightarrow{{}}Ag,\,{{E}^{o}}=x$ $C{{u}^{2+}}2\,{{e}^{-}}\xrightarrow{{}}Cu,\,{{E}^{o}}=y$ ${{E}^{o}}_{cell}$ is   AIEEE  Solved  Paper-2002

A)
$x+2y$

B)
$2x+y$

C)
$y-x$

D)
$y-2x$

• question_answer115) Based on kinetic theory of gases, following laws can be proved   AIEEE  Solved  Paper-2002

A)
Boyle's law

B)
Charle's law

C)

D)
All of the above

• question_answer116) $MnO_{4}^{-}$ is a good oxidising agent in different medium changing to                    $MnO_{4}^{-}$              $\xrightarrow{{}}M{{n}^{2+}}$                                    $\xrightarrow{{}}MnO_{4}^{2+}$                                    $\xrightarrow{{}}Mn{{O}_{2}}$                                    $\xrightarrow{{}}M{{n}_{2}}{{O}_{3}}$ Changes    in    oxidation    number respectively are   AIEEE  Solved  Paper-2002

A)
1, 3, 4, 5

B)
5, 4, 3, 2

C)
5, 1, 3, 4

D)
2, 6, 4, 3

• question_answer117) For the reaction, ${{H}_{2}}+{{I}_{2}}\xrightarrow{{}}2Hl$, the differential rate law is   AIEEE  Solved  Paper-2002

A)
$-\frac{d\,[{{H}_{2}}]}{dt}=-\frac{d\,[{{l}_{2}}]}{dt}=2\frac{d\,[Hl]}{dt}$

B)
$-2\frac{d\,[{{H}_{2}}]}{dt}=-2\frac{d\,[{{l}_{2}}]}{dt}=\frac{d\,[Hl]}{dt}$

C)
$-\frac{d\,[{{H}_{2}}]}{dt}=-\frac{d\,[{{l}_{2}}]}{dt}=\frac{d\,[Hl]}{dt}$

D)
$-\frac{d\,[{{H}_{2}}]}{2dt}=-\frac{d\,[{{l}_{2}}]}{2dt}=\frac{d\,[Hl]}{dt}$

• question_answer118) Number of atoms in 560 g of Fe (atomic mass 56 g $mo{{l}^{-1}}$) is   AIEEE  Solved  Paper-2002

A)
twice that of 70 g N

B)
half that of 20 g H

C)
Both (a) and (b)

D)
None of these

• question_answer119) Geometrical isomerism is not shown by   AIEEE  Solved  Paper-2002

A)
1, 1 -dichloro-1 ?pentene

B)
1, 2-dichloro-l-pentene

C)
1, 3-dichloro-2-pentene

D)
1, 4-dichloro-2-pentene

• question_answer120) Number of atoms in the unit cell of Na (bcc type crystal) and Mg (fee type crystal) are respectively   AIEEE  Solved  Paper-2002

A)
4, 4

B)
4, 2

C)
2, 4

D)
1, 1

• question_answer121) Which of the following compounds has incorrect IUPAC nomenclature?   AIEEE  Solved  Paper-2002

A)
$C{{H}_{3}}\underset{\,\text{Ethylbutanoate}}{\mathop{C{{H}_{2}}\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,{{H}_{2}}CO{{C}_{2}}}}\,{{H}_{5}}$

B)
$C{{H}_{3}}CH\underset{\begin{smallmatrix} | \\ \underset{\text{3}-\text{ methyl butanal}}{\mathop{C{{H}_{3}}}}\, \end{smallmatrix}}{\mathop{C}}\,{{H}_{2}}CHO$

C)
$C{{H}_{3}}CH\underset{\begin{smallmatrix} | \\ \underset{\text{2}-\text{methyl }-\text{3}-\text{ pentanone}}{\mathop{C{{H}_{3}}}}\, \end{smallmatrix}}{\mathop{\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,C}}\,{{H}_{2}}C{{H}_{3}}$

D)
$\underset{\text{2}-\text{ methyl }-\text{3}-\text{ butanol}}{\mathop{C{{H}_{3}}\underset{\begin{smallmatrix} | \\ {{H}_{3}}C \end{smallmatrix}}{\mathop{C}}\,H\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{3}}}}\,$

• question_answer122) End product of the following reaction is $C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[\text{Red P}]{C\,{{l}_{2}}}\xrightarrow{\text{Alcoholic KOH}}$   AIEEE  Solved  Paper-2002

A)
$C{{H}_{3}}\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,HCOOH$

B)
$C{{H}_{2}}\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,{{H}_{2}}COOH$

C)
$C{{H}_{2}}=CHCOOH$

D)
$\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{C}}\,{{H}_{2}}\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,HCOOH$

• question_answer123) For the following reaction in gaseous phase $CO+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}$ ${{K}_{c}}/{{K}_{p}}$ is   AIEEE  Solved  Paper-2002

A)
${{(RT)}^{1/2}}$

B)
${{(RT)}^{-1/2}}$

C)
(RT)

D)
${{(RT)}^{-1}}$

• question_answer124) Energy of H-atom in the ground state is -13.6 eV, hence energy in the second excited state is   AIEEE  Solved  Paper-2002

A)
$-6.8$ eV

B)
$-3.4$ eV

C)
$-1.51$ eV

D)
$-4.53$ Ev

• question_answer125) A square planar complex is formed by hybridisation of the following atomic orbitals   AIEEE  Solved  Paper-2002

A)
$s,{{p}_{x}},{{p}_{y}},{{p}_{Z}}$

B)
$s,{{p}_{x}},{{p}_{y}},{{p}_{Z}},d$

C)
$d,s,{{p}_{x}},{{p}_{y}}$

D)
$s,{{p}_{x}},{{p}_{y}},{{p}_{Z}},d,d$

• question_answer126) Type   of   isomerism   shown   by $[Cr{{(N{{H}_{3}})}_{5}}N{{O}_{2}}]C{{l}_{2}}$ is   AIEEE  Solved  Paper-2002

A)
optical

B)
ionization

C)
geometrical

D)

• question_answer127) One of the following equilibria is not affected by change in volume of the flask   AIEEE  Solved  Paper-2002

A)
$PC{{l}_{5}}(g)\underset{{}}{\leftrightarrows}PC{{l}_{3}}(g)+C{{l}_{2}}(g)$

B)
${{N}_{2}}(g)+3{{H}_{2}}(g)\underset{\,}{\leftrightarrows}2N{{H}_{3}}(g)$

C)
${{N}_{2}}(g)+{{O}_{2}}(g)\overset{\,}{leftrightarrows}2NO(g)$

D)
$S{{O}_{2}}C{{l}_{2}}(g)\underset{\,}{\leftrightarrows}S{{O}_{2}}(g)+C{{l}_{2}}(g)$

• question_answer128) Uncertainty in position of a particle of 25 g in space is ${{10}^{-5}}$ m. Hence, uncertainty in velocity $(m{{s}^{-1}})$ is (Planck's constant $h=6.6\times {{10}^{-34}}Js$)   AIEEE  Solved  Paper-2002

A)
$2.1\times {{10}^{-28}}$

B)
$2.1\times {{10}^{-34}}$

C)
$0.5\times {{10}^{-34}}$

D)
$5.0\times {{10}^{-24}}$

• question_answer129) Consider the following reactions at ${{1100}^{o}}C$ (I) $2C+{{O}_{2}}\xrightarrow{{}}2CO$, $\Delta {{G}^{o}}=-460\,kJ\,mo{{l}^{-1}}$ (II) $2Zn+{{O}_{2}}\xrightarrow{{}}2ZnO$, $\Delta {{G}^{o}}+=-360\,kJ\,mo{{l}^{-1}}$ Based on these, select the correct alternate.   AIEEE  Solved  Paper-2002

A)
Zinc can be oxidised by CO

B)
Zinc oxide can be reduced by carbon

C)
Both (a) and (b)

D)
None of the above

• question_answer130) A reaction is non-spontaneous at the freezing point of water but is spontaneous at the boiling point of water then   AIEEE  Solved  Paper-2002

A)
$\Delta H\,\,\,\,\,+ve$                $\Delta S\,\,\,\,+ve$

B)
$\Delta H\,\,\,\,\,-ve$                 $\Delta S\,\,\,\,-ve$

C)
$\Delta H\,\,\,\,\,-ve$                 $\Delta S\,\,\,\,+ve$

D)
$\Delta H\,\,\,\,\,+ve$                $\Delta S\,\,\,\,-ve$

• question_answer131) Monomers are converted to polymer by   AIEEE  Solved  Paper-2002

A)
hydrolysis of monomers

B)
condensation reaction between monomers

C)
protonation of monomers

D)
None of the above

• question_answer132) Increasing order of bond strength of ${{O}_{2}},O_{2}^{-}\,O_{2}^{2-}$ and $O_{2}^{+}$ is   AIEEE  Solved  Paper-2002

A)
$O_{2}^{+}<{{O}_{2}}<O_{2}^{-}<O_{2}^{2-}$

B)
${{O}_{2}}<O_{2}^{+}<O_{2}^{-}<O_{2}^{2-}$

C)
$O_{2}^{-}<O_{2}^{2-}<O_{2}^{+}<{{O}_{2}}$

D)
$O_{2}^{2-}<O_{2}^{-}<{{O}_{2}}<O_{2}^{+}$

• question_answer133) Most common oxidation states of Ce (cerium) are   AIEEE  Solved  Paper-2002

A)
$+3,\,\,+4$

B)
$+2,\,\,+3$

C)
$+2,\,\,+4$

D)
$+3,\,\,+5$

• question_answer134) $C{{e}^{3+}},\,\,L{{a}^{3+}},\,P{{m}^{3+}}$ and $Y{{b}^{3+}}$ have ionic radii in the increasing order as   AIEEE  Solved  Paper-2002

A)
$L{{a}^{3+}}<C{{e}^{3+}}<P{{m}^{3+}}<Y{{b}^{3+}}$

B)
$Y{{b}^{3+}}<P{{m}^{3+}}<C{{e}^{3+}}<L{{a}^{3+}}$

C)
$L{{a}^{3+}}\,=C{{e}^{3+}}\,<P{{m}^{3+}}\,<Y{{b}^{3+}}$

D)
$Y{{b}^{3+}}<P{{m}^{3+}}<L{{a}^{3+}}<C{{e}^{3+}}$

• question_answer135) pH of $0.005$ M calcium acetate ($P{{K}_{a}}$ of $C{{H}_{3}}COOH=4.74$) is   AIEEE  Solved  Paper-2002

A)
$7.04$

B)
$9.37$

C)
$9.26$

D)
$8.37$

• question_answer136) ${{H}_{2}}$ gas is absorbed on the metal surface like tungsten. This follows ...... order reaction.     AIEEE  Solved  Paper-2002

A)
third

B)
second

C)
zero

D)
first

• question_answer137) Rate constant k of the first order reaction when initial concentration ${{C}_{0}}$ and concentration ${{C}_{t}}$ at time $t$ is given by equation $kt=\log \,{{C}_{0}}-\log {{C}_{t}}$ Graph is a straight line if we plot   AIEEE  Solved  Paper-2002

A)
$t\,\,vs\,\,\log \,\,{{C}_{0}}$

B)
$t\,\,vs\,\,\log \,{{C}_{t}}$

C)
${{t}^{-1}}\,\,vs\,\,\log \,{{C}_{t}}$

D)
$\log \,\,{{C}_{t}}\,vs\,\,\log \,\,{{C}_{t}}$

• question_answer138) Alum is widely used to purify water since   AIEEE  Solved  Paper-2002

A)
it forms complex with clay particles

B)
it coagulates the mud particles

C)
it exchanges $C{{a}^{2+}}$ and $M{{g}^{2+}}$ ions present in hard water

D)
its sulphate ion is water purifier

• question_answer139) On vigorous oxidation by permangnate solution ${{(C{{H}_{3}})}_{2}}C=CHC{{H}_{2}}CHO$ gives   AIEEE  Solved  Paper-2002

A)
${{(C{{H}_{3}})}_{2}}CO$ and $OHCC{{H}_{2}}CHO$

B)
${{(C{{H}_{3}})}_{2}}\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{2}}CHO$

C)
${{(C{{H}_{3}})}_{2}}CO$ and $OHCC{{H}_{2}}COOH$

D)
${{(C{{H}_{3}})}_{2}}CO$ and $C{{H}_{2}}{{(COOH)}_{2}}$

• question_answer140) In the following benzyl/allyl system $R-CH=C{{H}_{2}}$      or      [R is alkyl group)             decreasing order of inductive effect is   AIEEE  Solved  Paper-2002

A)
${{(C{{H}_{3}})}_{3}}C->{{(C{{H}_{3}})}_{2}}CH->C{{H}_{3}}C{{H}_{2}}-$

B)
$C{{H}_{3}}C{{H}_{2}}->{{(C{{H}_{3}})}_{2}}CH->{{(C{{H}_{3}})}_{3}}C-$

C)
$(C{{H}_{3}}){{ }_{2}}CH->C{{H}_{3}}C{{H}_{2}}->{{(C{{H}_{3}})}_{3}}C-$

D)
$(C{{H}_{3}}){{ }_{2}}C->C{{H}_{3}}C{{H}_{2}}->{{(C{{H}_{3}})}_{3}}CH-$

• question_answer141) $PC{{l}_{3}}$ and $PC{{l}_{5}}$, both exist; $NC{{l}_{3}}$ exists but $NC{{l}_{5}}$ does not exist. It is due to   AIEEE  Solved  Paper-2002

A)
lower electronegativity of P than N

B)
lower tendency of N to form covalent bond

C)
availability of vacant d-obital in P but not in N

D)
statement is itself incorrect

• question_answer142) Following types of compounds (as I, II) (I) $C{{H}_{3}}CH=CHC{{H}_{3}}$ (II) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{2}}C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-OH$ are studied in terms of isomerism in   AIEEE  Solved  Paper-2002

A)
chain isomerism

B)
position isomerism

C)
conformers

D)
stereoisomerism

• question_answer143) Conductivity (Seimen's S) is directly proportional to area of the vessel and the concentration of the solution in it and is inversely proportional to the length of the vessel, then constant of  proportionality is expressed in   AIEEE  Solved  Paper-2002

A)
S m $mo{{l}^{-1}}$

B)
${{S}^{2}}\,{{m}^{2}}\,mo{{l}^{-2}}$

C)
S ${{m}^{2}}\,mo{{l}^{-1}}$

D)
${{S}^{2}}\,{{m}^{2}}\,mol$

• question_answer144) A heat engine absorbs heat ${{q}_{1}}$ from a source at temperature ${{T}_{1}}$ and heat ${{q}_{2}}$ from a source at temperature ${{T}_{2}}$. Work done is found to be $J({{q}_{1}}+{{q}_{2}})$ This is in accordance with

A)
first law of thermodynamics

B)
second law of thermodynamics

C)
Joules equivalent law

D)
None of the above

• question_answer145) Select the correct statement.   AIEEE  Solved  Paper-2002

A)
When a covalent bond is formed, transfer of electrons takes place

B)
Pure ${{H}_{2}}O$ does not contain any ion

C)
A bond is formed when attractive forces overcome repulsive forces

D)
HF is less polar than $HBr$

• question_answer146) The metallic sodium dissolves in liquid ammonia to form a deep blue coloured solution. The deep blue colour is due to formation of   AIEEE  Solved  Paper-2002

A)
solvated electron, ${{e}^{-}}(N{{H}_{3}})_{x}^{-}$

B)
solvated atomic sodium, $Na{{(N{{H}_{3}})}_{y}}$

C)
$(N{{a}^{+}}+N{{a}^{-}})$

D)
$NaN{{H}_{2}}+{{H}_{2}}$

• question_answer147) Maximum dehydration takes place that of   AIEEE  Solved  Paper-2002

A)

B)

C)

D)

• question_answer148) ${{S}_{N}}1$ reaction is feasible in   AIEEE  Solved  Paper-2002

A)
$->-\,Cl+KOH\xrightarrow{{}}$

B)
$+KOH\xrightarrow{{}}$

C)

D)

• question_answer149) Oxidation number of $Cl$ in $CaOC{{l}_{2}}$ (bleaching powder) is   AIEEE  Solved  Paper-2002

A)
zero, since it contains $C{{l}_{2}}$

B)
-1, since it contains $C{{l}^{-}}$

C)
+1, since it contains $Cl{{O}^{-}}$

D)
+1 and -1 since it contains $Cl{{O}^{-}}$ and $C{{l}^{-}}$

• question_answer150) Picric acid is   AIEEE  Solved  Paper-2002

A)

B)

C)

D)

• question_answer151) If $\alpha \ne \beta ,\,{{\alpha }^{2}}=5\alpha -3$ and ${{\beta }^{2}}=5\beta -3$, then the equation having $\alpha /\beta$ and $\beta /\alpha$ as its roots, is   AIEEE  Solved  Paper-2002

A)
$3{{x}^{2}}+19x+3=0$

B)
$3{{x}^{2}}-19x+3=0$

C)
$3{{x}^{2}}-19x-3=0$

D)
${{x}^{2}}-16x+1=0$

• question_answer152) If $y={{(x+\sqrt{1+{{x}^{2}}})}^{n}}$ , then $(1+{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}$ is   AIEEE  Solved  Paper-2002

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

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

C)
$-y$

D)
$2{{x}^{2}}y$

• question_answer153) If 1, ${{\log }_{3}}\sqrt{({{3}^{1-x}}+2)},\,{{\log }_{3}}\,({{4.3}^{x}}-1)$ are in AP, then x equals   AIEEE  Solved  Paper-2002

A)
${{\log }_{3}}4$

B)
$1-{{\log }_{3}}4$

C)
$1-{{\log }_{4}}3$

D)
${{\log }_{4}}3$

• question_answer154) A problem in Mathematics is given to three students A, B, C and their respective probability of solving the problem is $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$. Probability that the problem is solved, is   AIEEE  Solved  Paper-2002

A)
3/4

B)
1/2

C)
2/3

D)
1/3

• question_answer155) The period of ${{\sin }^{2}}\theta$ is   AIEEE  Solved  Paper-2002

A)
${{\pi }^{2}}$

B)
$\pi$

C)
$2\pi$

D)
$\pi /2$

• question_answer156) $l,\,m,\,n$ are the pth, qth and rth terms of a GP and all positive, then $\left| \begin{matrix} \log \,\,l & p & 1 \\ \log \,\,m & q & 1 \\ \log \,\,n & r & 1 \\ \end{matrix} \right|$ equals   AIEEE  Solved  Paper-2002

A)
3

B)
2

C)
1

D)
zero

• question_answer157) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}$ is   AIEEE  Solved  Paper-2002

A)
$\lambda$

B)
$-1$

C)
zero

D)
does not exist

• question_answer158) A triangle with vertices (4, 0), (-1, -1), (3, 5) is

A)
isosceles and right angled

B)
isosceles but not right angled

C)
right angled but not isosceles

D)
neither right angled nor isosceles

• question_answer159) In a class of 100 students, there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?   AIEEE  Solved  Paper-2002

A)
73

B)
65

C)
68

D)
74

• question_answer160) If ${{\cot }^{-1}}(\sqrt{\cos \alpha })-{{\tan }^{-1}}(\sqrt{\cos \alpha })=x$, then $\sin x$ is equal to   AIEEE  Solved  Paper-2002

A)
${{\tan }^{2}}\left( \frac{\alpha }{2} \right)$

B)
${{\cot }^{2}}\left( \frac{\alpha }{2} \right)$

C)
$\tan \alpha$

D)
$\cot \left( \frac{\alpha }{2} \right)$

• question_answer161) The order and degree of the differential equation ${{\left( 1+3\frac{dy}{dx} \right)}^{2/3}}$ are   AIEEE  Solved  Paper-2002

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

B)
(3, 1)

C)
(3, 3)

D)
(1, 2)

• question_answer162) A plane which passes through the point (3, 2, 0) and the line $\frac{x-4}{1}=\frac{y-7}{5}\frac{z-4}{4}$ is   AIEEE  Solved  Paper-2002

A)
$x-y+z=1$

B)
$x+y+z=5$

C)
$x+2y-z=1$

D)
$2x-y+z=5$

• question_answer163) The solution of the equation $\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}$ is   AIEEE  Solved  Paper-2002

A)
$\frac{{{e}^{-2x}}}{4}$

B)
$\frac{{{e}^{-2x}}}{4}\,+cx+d$

C)
$\frac{1}{4}{{e}^{-2x}}+c\,{{x}^{2}}+d$

D)
$\frac{1}{4}{{e}^{-2x}}+c\,+d$

• question_answer164) $\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+2} \right)}^{x}}$ is equal to   AIEEE  Solved  Paper-2002

A)
${{e}^{4}}$

B)
${{e}^{2}}$

C)
${{e}^{3}}$

D)
e

• question_answer165) The domain of ${{\sin }^{-1}}[{{\log }_{3}}(x/3)]$ is   AIEEE  Solved  Paper-2002

A)
[1, 9]

B)
[-1, 9]

C)
[-9, 1]

D)
[-9,-1]

• question_answer166) The value of ${{2}^{1/4}}.\,{{4}^{1/8}}.\,\,{{8}^{1/16}}.....\,\,\infty$ is   AIEEE  Solved  Paper-2002

A)
1

B)
2

C)
3/2

D)
4

• question_answer167) Fifth term of a GP is 2, then the product of its 9 terms is   AIEEE  Solved  Paper-2002

A)
256

B)
512

C)
1024

D)
None of these

• question_answer168) $\int{{{_{0}}^{10\pi }}}\left| \sin x \right|dx$ is   AIEEE  Solved  Paper-2002

A)
20

B)
8

C)
10

D)
18

• question_answer169) ${{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\,x\,dx,}$ , then    $\underset{x\to \infty }{\mathop{\lim }}\,n\,[{{I}_{n}}+{{I}_{n+2}}]$ equals   AIEEE  Solved  Paper-2002

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

B)
1

C)
$\infty$

D)
zero

• question_answer170) $\int_{0}^{2}{[{{x}^{2}}]}\,dx$ is   AIEEE  Solved  Paper-2002

A)
$2-\sqrt{2}$

B)
$2+\sqrt{2}$

C)
$\sqrt{2}-1$

D)
$-\sqrt{2}-\sqrt{3}+5$

• question_answer171) $\int{_{-\pi }^{\pi }}\frac{2\pi (1+\sin x)}{1+{{\cos }^{2}}x}dx$ is   AIEEE  Solved  Paper-2002

A)
$\frac{{{\pi }^{2}}}{4}$

B)
${{\pi }^{2}}$

C)
zero

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

• question_answer172) The    period    of   the    function $f(x)={{\sin }^{4}}x+{{\cos }^{4}}x$ is   AIEEE  Solved  Paper-2002

A)
$\pi$

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

C)
$2\pi$

D)
None of these

• question_answer173) The domain of definition of the function$f(x)=\sqrt{{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)}$ is   AIEEE  Solved  Paper-2002

A)
[1, 4]

B)
[1, 0]

C)
[0, 5]

D)
[5, 0]

• question_answer174) If $\sin y=x\sin (a+y)$, then-,-is   AIEEE  Solved  Paper-2002

A)
$\frac{\sin a}{{{\sin }^{2}}(a+y)}$

B)
$\frac{{{\sin }^{2}}\,(a+y)}{\sin \,\,a}$

C)
$\sin \,a\,{{\sin }^{2}}(a+y)$

D)
$\frac{{{\sin }^{2}}(a-y)}{\sin a}$

• question_answer175) If ${{x}^{y}}={{e}^{x-y}}$, then $\frac{dy}{dx}$ is   AIEEE  Solved  Paper-2002

A)
$\frac{1+x}{1+\log x}$

B)
$\frac{1-\log x}{{{(1+\log x)}^{2}}}$

C)
not defined

D)
$\frac{\log x}{{{(1+\log x)}^{2}}}$

• question_answer176) The two curves ${{x}^{3}}-3x{{y}^{2}}+2=0$ and $3\,{{x}^{2}}y-{{y}^{3}}-2=0$   AIEEE  Solved  Paper-2002

A)
cut at right angle

B)
touch each other

C)
cut at an angle $\frac{\pi }{3}$

D)
cut at an angle $\frac{\pi }{4}$

• question_answer177) The function $f(x)={{\cot }^{-1}}x+x$ increases in the interval   AIEEE  Solved  Paper-2002

A)
$(1,\infty )$

B)
$(-1,\infty )$

C)
$(-\infty ,\infty )$

D)
$(0,\infty )$

• question_answer178) The greatest value of $f(x)={{(x+1)}^{1/3}}-{{(x-1)}^{1/3}}$ on [0, 1] is   AIEEE  Solved  Paper-2002

A)
1

B)
2

C)
3

D)
1/3

• question_answer179) Evaluate $\int{{{_{0}}^{\pi /2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx}$   AIEEE  Solved  Paper-2002

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

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

C)
0

D)
1

• question_answer180) $\int{\frac{dx}{x({{x}^{n}}+1)}}$ is equal to   AIEEE  Solved  Paper-2002

A)
$\frac{1}{n}\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+C$

B)
$\frac{1}{n}\log \left( \frac{{{x}^{n}}+1}{{{x}^{n}}} \right)+C$

C)
$\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+C$

D)
None of these

• question_answer181) The area bounded by the curve $y=2x-{{x}^{2}}$ and the straight line $y=-x$ is given by   AIEEE  Solved  Paper-2002

A)
$\frac{9}{2}$ sq units

B)
$\frac{43}{6}$ sq units

C)
$\frac{35}{6}$ sq units

D)
None of these

• question_answer182) The differential equation of all non-vertical lines in a plane is   AIEEE  Solved  Paper-2002

A)
$\frac{{{d}^{2}}y}{d{{x}^{2}}}=0$

B)
$\frac{{{d}^{2}}x}{d{{y}^{2}}}=0$

C)
$\frac{dy}{dx}=0$

D)
$\frac{dx}{dy}=0$

• question_answer183) Given two vectors are $\hat{i}-\hat{j}$ and $\hat{i}+2\hat{j}$, the unit vector coplanar with the two vectors and perpendicular to first is   AIEEE  Solved  Paper-2002

A)
$\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$

B)
$\frac{1}{\sqrt{5}}(2\hat{i}-\hat{j})$

C)
$\pm \frac{1}{\sqrt{2}}(\hat{i}-\hat{k})$

D)
None of these

• question_answer184) The vector $\hat{i}+x\hat{j}+3\hat{k}$ is rotated through an angle $\theta$ and doubled in magnitude, then it becomes $4\hat{i}+(4x-2)\hat{j}+2\hat{k}$. The values of $x$ are   AIEEE  Solved  Paper-2002

A)
$\left\{ -\frac{2}{3},2 \right\}$

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

C)
$\left\{ \frac{2}{3},0 \right\}$

D)
$\left\{ 2,7 \right\}$

• question_answer185) A parallelepiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is   AIEEE  Solved  Paper-2002

A)
7 units

B)
$\sqrt{38}$ units

C)
$\sqrt{155}$ units

D)
None of these

• question_answer186) The equation of the plane containing the line $\frac{x-{{x}_{1}}}{l}=\frac{y-{{y}_{1}}}{m}=\frac{z-{{z}_{1}}}{n}$ is $a(x-{{x}_{1}})+b(y-{{y}_{1}})+c(z-{{z}_{1}})=0$              where   AIEEE  Solved  Paper-2002

A)
$a{{x}_{1}}+b{{y}_{1}}+c{{z}_{1}}=0$

B)
$al+bm+cn=0$

C)
$\frac{a}{l}=\frac{b}{m}=\frac{c}{n}$

D)
$l\,{{x}_{1}}+m{{y}_{1}}+n{{z}_{1}}=0$

• question_answer187) A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial, is   AIEEE  Solved  Paper-2002

A)
$\frac{1}{25}$

B)
$\frac{24}{25}$

C)
$\frac{2}{25}$

D)
None of these

• question_answer188) If A and B are two mutually exclusive events, then   AIEEE  Solved  Paper-2002

A)
$P(A)<P(\overline{B})$

B)
$P(A)>P(\overline{B})$

C)
$P(A)<P(B)$

D)
None of these

• question_answer189) The equation of the directrix of the parabola ${{y}^{2}}+4y+4x+2=0$ is   AIEEE  Solved  Paper-2002

A)
$x=-1$

B)
$x=1$

C)
$x=-3/2$

D)
$x=3/2$

• question_answer190) Let ${{T}_{n}}$ denotes the number of triangles which can be formed using the vertices of a regular polygon of n sides. If ${{T}_{n\,+1}}-{{T}_{n}}=21$, then n equals   AIEEE  Solved  Paper-2002

A)
5

B)
7

C)
6

D)
4

• question_answer191) In a $\Delta ABC,\,\,2ca\,\sin \,\left( \frac{A-B+C}{2} \right)$ is equal to   AIEEE  Solved  Paper-2002

A)
${{a}^{2}}+{{b}^{2}}-{{c}^{2}}$

B)
${{c}^{2}}+{{a}^{2}}-{{b}^{2}}$

C)
${{b}^{2}}-{{c}^{2}}-{{a}^{2}}$

D)
${{c}^{2}}-{{a}^{2}}-{{b}^{2}}$

• question_answer192) For $x\in R\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x-3}{x+2} \right)}^{x}}$ is equal to   AIEEE  Solved  Paper-2002

A)
e

B)
${{e}^{-1}}$

C)
${{e}^{-5}}$

D)
${{e}^{5}}$

• question_answer193) The incentre of the triangle with vertices              $(1,\sqrt{3})$, (0, 0) and (2,0) is   AIEEE  Solved  Paper-2002

A)
$\left( 1,\frac{\sqrt{3}}{2} \right)$

B)
$\left( \frac{2}{3},\frac{1}{\sqrt{3}} \right)$

C)
$\left( \frac{2}{3},\frac{\sqrt{3}}{2} \right)$

D)
$\left( 1,\frac{1}{\sqrt{3}} \right)$

• question_answer194) If the vectors a, b and c from the sides BC, CA and AB respectively of a $\Delta ABC$, then   AIEEE  Solved  Paper-2002

A)
$a.\,b=b.\,c=c.\,b=0$

B)
$a\times b=b\times c=c\times a$

C)
$a.\,b=b.\,c=c.\,a=0$

D)
$a\times a+a\times c+c\times a=0$

• question_answer195) If $\omega$ is an imaginary cube root of unity, then ${{(1+\omega -{{\omega }^{2}})}^{7}}$ equals   AIEEE  Solved  Paper-2002

A)
$128\,\omega$

B)
$-128\,\omega$

C)
$128\,{{\omega }^{2}}$

D)
$-128\,{{\omega }^{2}}$

• question_answer196) If $\left| \begin{matrix} 6\,i & -3\,i & 1 \\ 4 & 3\,i & -1 \\ 20 & 3 & i \\ \end{matrix} \right|=x+iy$, then   AIEEE  Solved  Paper-2002

A)
$x=3,\,y=1$

B)
$x=1,\,y=3$

C)
$x=0,\,y=3$

D)
$x=0,\,y=0$

• question_answer197) ${{\sin }^{2}}\theta =\frac{4xy}{{{(x+y)}^{2}}}$ is true if and only if   AIEEE  Solved  Paper-2002

A)
$x-y\ne 0$

B)
$x=-y$

C)
$x=y$

D)
$x\ne 0,y\ne 0$

• question_answer198) The radius of the circle passing through the foci of the ellipse $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}$ and having its centre at (0, 3), is

A)
4 units

B)
3 units

C)
$\sqrt{12}$ units

D)
$\frac{7}{2}$ units

• question_answer199) The probability of India winning a test match against West-Indies is $1/2$ assuming independence from match to match. The probability that in a match series India's second win occurs at the third test is

A)
$1/8$

B)
$1/4$

C)
$1/2$

D)
$2/3$

• question_answer200) If $(\omega \ne 1)$ is a cubic root of unity, then $\left| \begin{matrix} 1 & 1+i+{{\omega }^{2}} & {{\omega }^{2}} \\ 1-i & -1 & {{\omega }^{2}}-1 \\ -i & -1+\omega -i & -1 \\ \end{matrix} \right|$ equals   AIEEE  Solved  Paper-2002

A)
0

B)
1

C)
$i$

D)
$\omega$

• question_answer201) A biased coin with probability $p,0<p<1$, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even, is $2/5$, then p equals   AIEEE  Solved  Paper-2002

A)
$1/3$

B)
$2/3$

C)
$2/5$

D)
$3/5$

• question_answer202) A fair die is tossed eight times. The probability that a third six is observed on the eighth throw, is   AIEEE  Solved  Paper-2002

A)
$\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{7}}}$

B)
$\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{8}}}$

C)
$\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{6}}}$

D)
None of these

• question_answer203) Let $f(2)=4$ and $f'\,(2)=4$. Then,$\underset{x\to 2}{\mathop{\lim }}\,\frac{xf(2)-2f(x)}{x-2}$ is given by   AIEEE  Solved  Paper-2002

A)
2

B)
$-2$

C)
$-4$

D)
3

• question_answer204) Three   straight   lines   $2x+11y-5=0$, $24x+7y-20=0$ and $4x-3y-2=0$   AIEEE  Solved  Paper-2002

A)
form a triangle

B)
are only concurrent

C)
are concurrent with one line bisecting the angle between the other two

D)
None of the above

• question_answer205) A straight line through the point (2, 2) intersects   the   lines   $\sqrt{3}x+y=0$   and $\sqrt{3}x-y=0$ at the points A and B. The equation to the line AB so that the $\Delta OAB$ is equilateral, is   AIEEE  Solved  Paper-2002

A)
$x-2=0$

B)
$y-2=0$

C)
$x+y-4=0$

D)
None of these

• question_answer206) The greatest distance of the point P(10,7) from the circle ${{x}^{2}}+{{y}^{2}}-4x-2y-20=0$ is   AIEEE  Solved  Paper-2002

A)
10 units

B)
15 units

C)
5 units

D)
None of these

• question_answer207) The equation of the tangent to the circle ${{x}^{2}}+{{y}^{2}}+4x-4y+4=0$ which make equal intercepts on the positive coordinate axes, is   AIEEE  Solved  Paper-2002

A)
$x+y=2$

B)
$x+y=2\sqrt{2}$

C)
$x+y=4$

D)
$x+y=8$

• question_answer208) The equation of the ellipse whose foci are $(\pm \,2,0)$ and eccentricity is $1/2$, is AIEEE  Solved  Paper-2002

A)
$\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{16}=1$

B)
$\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1$

C)
$\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{8}=1$

D)
None of these

• question_answer209) The equation of the chord joining two points $({{x}_{1}},{{y}_{1}})$ and $({{x}_{2}},{{y}_{2}})$ on the rectangular hyperbola $xy={{c}^{2}}$is   AIEEE  Solved  Paper-2002

A)
$\frac{x}{{{x}_{1}}+{{x}_{2}}}+\frac{y}{{{y}_{1}}+{{y}_{2}}}=1$

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

C)
$\frac{x}{{{y}_{1}}+{{y}_{2}}}+\frac{y}{{{x}_{1}}+{{x}_{2}}}=1$

D)
$\frac{x}{{{y}_{1}}-{{y}_{2}}}+\frac{y}{{{x}_{1}}-{{x}_{2}}}=1$

• question_answer210) If the vectors $c,a=x\,\hat{i}+y\hat{j}+z\hat{k}$ and $b=\hat{j}$ are such that a, c and b form a right handed system, then c is   AIEEE  Solved  Paper-2002

A)
$z\hat{i}-x\hat{k}$

B)
0

C)
$y\,\hat{i}$

D)
$-z\,\hat{i}+x\,\hat{k}$

• question_answer211) The centre of the circle given by $r.\,(\hat{i}+2\hat{j}+2\hat{k})=15$ and $\left| r-(\hat{j}+2\hat{k} \right|=4$is

A)
(0, 1, 2)

B)
(1, 3, 4)

C)
(-1, 3, 4)

D)
None of these

• question_answer212) The value of $\frac{1-{{\tan }^{2}}{{15}^{o}}}{1+{{\tan }^{2}}{{15}^{o}}}$ is   AIEEE  Solved  Paper-2002

A)
1

B)
$\sqrt{3}$

C)
$\frac{\sqrt{3}}{2}$

D)
2

• question_answer213) If $\tan \theta =-\frac{4}{3}$ then sine is   AIEEE  Solved  Paper-2002

A)
$-\frac{4}{5}$ but not $\frac{4}{5}$

B)
$-\frac{4}{5}$ or $\frac{4}{5}$

C)
$\frac{4}{5}$ but not $-\frac{4}{5}$

D)
None of these

• question_answer214) If $\sin (\alpha +\beta )=1,\,\,\sin (\alpha -\beta )=\frac{1}{2}$ then $\tan \,(a+2\beta )\tan \,(2\alpha +\beta )$ is equal to   AIEEE  Solved  Paper-2002

A)
1

B)
- 1

C)
zero

D)
None of these

• question_answer215) If $y={{\sin }^{2}}\theta +\cos e{{c}^{2}}\theta ,\,\,\theta \ne 0$, then   AIEEE  Solved  Paper-2002

A)
$y=0$

B)
$y\le 2$

C)
$y\ge -2$

D)
$y\ge 2$

• question_answer216) In a $\Delta ABC$, $a=4,\,b=3,\,\,\angle A={{60}^{o}}$, then c is the root of the equation   AIEEE  Solved  Paper-2002

A)
${{c}^{2}}-3c-7=0$

B)
${{c}^{2}}+3c+7=0$

C)
${{c}^{2}}-3c+7=0$

D)
${{c}^{2}}+3c-7=0$

• question_answer217) In a $\Delta ABC,\,\tan \frac{A}{2}=\frac{5}{6},\tan \frac{C}{2}=\frac{2}{5}$, then   AIEEE  Solved  Paper-2002

A)
a, c, b are in AP

B)
a, b, c are in AP

C)
b, a, c are in AP

D)
a, b, care in GP

• question_answer218) The equation   $a\sin x+b\cos x=c$, where $\left| c \right|>\sqrt{{{a}^{2}}+{{b}^{2}}}$ has   AIEEE  Solved  Paper-2002

A)
a unique solution

B)
infinite number of solutions

C)
no solution

D)
None of the above

• question_answer219) If $\alpha$ is a root of $25{{\cos }^{2}}\theta +5\cos \theta -12=0\frac{\pi }{2}<a<\pi$, then $\sin 2\alpha$ is equal to   AIEEE  Solved  Paper-2002

A)
$\frac{24}{25}$

B)
$-\frac{24}{25}$

C)
$\frac{13}{18}$

D)
$-\frac{13}{18}$

• question_answer220) ${{\tan }^{-1}}\left( \frac{1}{4} \right)+{{\tan }^{-1}}\left( \frac{2}{9} \right)$ is equal to   AIEEE  Solved  Paper-2002

A)
$\frac{1}{2}{{\cos }^{-1}}\left( \frac{3}{5} \right)$

B)
$\frac{1}{2}{{\sin }^{-1}}\left( \frac{3}{5} \right)$

C)
$\frac{1}{2}{{\tan }^{-1}}\left( \frac{3}{5} \right)$

D)
${{\tan }^{-1}}\left( \frac{1}{2} \right)$

• question_answer221) $\sum\limits_{n=0}^{\infty }{\frac{{{({{\log }_{e}}x)}^{n}}}{n!}}$ is equal to   AIEEE  Solved  Paper-2002

A)
${{\log }_{e}}x$

B)
$x$

C)
${{\log }_{x}}e$

D)
None of these

• question_answer222) ${{x}^{(x-1)-\frac{1}{2}{{(x-1)}^{2}}+\frac{{{(x-1)}^{3}}}{3}-\frac{{{(x-1)}^{4}}}{4}+....}}$ is equal to   AIEEE  Solved  Paper-2002

A)
$\log \,(x-1)$

B)
$\log \,\,x$

C)
$x$

D)
None of these

• question_answer223) The     coefficient    of    ${{x}^{5}}$  in ${{(1+2x+3{{x}^{2}}+....)}^{-3/2}}$ is   AIEEE  Solved  Paper-2002

A)
21

B)
25

C)
26

D)
None of these

• question_answer224) If $\left| x \right|<1$, then the coefficient of ${{x}^{n}}$ in expansion of ${{(1+x+{{x}^{2}}+{{x}^{3}}+....)}^{2}}$ is   AIEEE  Solved  Paper-2002

A)
n

B)
$n-1$

C)
$n+2$

D)
$n+1$

• question_answer225) The number of real roots of ${{3}^{2{{x}^{2}}-7x+7}}=9$ is   AIEEE  Solved  Paper-2002

A)
zero

B)
2

C)
1

D)
4