Solved papers for JEE Main & Advanced AIEEE Solved Paper-2005

done AIEEE Solved Paper-2005 Total Questions - 225

• question_answer1) A projectile can have the same range R for two angles of projection. If${{t}_{1}}$and${{t}_{2}}$are the times of flights in the two cases, then the product of the two times of flights is proportional to       AIEEE  Solved  Paper-2005

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

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

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

D)
$R$

• question_answer2) An annular ring with inner and outer radii${{R}_{1}}$and${{R}_{2}}$is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring,$\frac{{{F}_{1}}}{{{F}_{2}}}$is     AIEEE  Solved  Paper-2005

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

B)
${{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}$

C)
1

D)
$\frac{{{R}_{1}}}{{{R}_{2}}}$

• question_answer3) A smooth block is released at rest on a$45{}^\circ$incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is     AIEEE  Solved  Paper-2005

A)
${{\mu }_{k}}=1-\frac{1}{{{n}^{2}}}$

B)
${{\mu }_{k}}=\sqrt{1-\frac{1}{{{n}^{2}}}}$

C)
${{\mu }_{s}}=1-\frac{1}{{{n}^{2}}}$

D)
${{\mu }_{s}}=\sqrt{1-\frac{1}{{{n}^{2}}}}$

• question_answer4) The upper half of an inclined plane with inclination$\phi$is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by     AIEEE  Solved  Paper-2005

A)
$2\sin \phi$

B)
$2\cos \phi$

C)
$2\tan \phi$

D)
$\tan \phi$

• question_answer5) A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?     AIEEE  Solved  Paper-2005

A)
3.0 cm

B)
2.0 cm

C)
1.5 cm

D)
1.0 cm

• question_answer6) Out of the following pairs, which one does not have identical dimensions?     AIEEE  Solved  Paper-2005

A)
Angular momentum and Planck's constant

B)
Impulse and momentum

C)
Moment of inertia and moment of a force

D)
Work and torque

• question_answer7) The relation between time t and distance$x$is $t=a{{x}^{2}}+bx,$where a and b are constants. The acceleration is       AIEEE  Solved  Paper-2005

A)
$-2ab{{v}^{2}}$

B)
$2b{{v}^{3}}$

C)
$-2a{{v}^{3}}$

D)
$2a{{v}^{2}}$

• question_answer8) A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance travelled is 15 S, then       AIEEE  Solved  Paper-2005

A)
$S=ft$

B)
$S=\frac{1}{6}f{{t}^{2}}$

C)
$S=\frac{1}{2}f{{t}^{2}}$

D)
$S=\frac{1}{4}f{{t}^{2}}$

• question_answer9) A particle is moving eastwards with a velocity of$5m{{s}^{-1}}$. In 10 s, the velocity changes to$5\text{ }m{{s}^{-1}}$northwards.  The average acceleration in this time is     AIEEE  Solved  Paper-2005

A)
$\frac{1}{\sqrt{2}}m{{s}^{-2}}$towards north-east

B)
$\frac{1}{2}m{{s}^{-2}}$towards north

C)
zero

D)
$\frac{1}{\sqrt{2}}m{{s}^{-2}}$towards north-west

• question_answer10) A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at$2m/{{s}^{2}}$. He peaches the ground with a speed of 3 m/s. At what height, did he bail out?     AIEEE  Solved  Paper-2005

A)
91 m

B)
182 m

C)
293 m

D)
111 m

• question_answer11) A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration a to keep the block stationary. Then, a is equal to AIEEE  Solved  Paper-2005

A)
$g/tan\alpha$

B)
$g\text{ }\cos ec\alpha$

C)
$g$

D)
$g\text{ }tan\alpha$

• question_answer12) A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is     AIEEE  Solved  Paper-2005

A)
40 m/s

B)
20 m/s

C)
10 m/s

D)
$10\sqrt{30}\,m/s$

• question_answer13) A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass$\frac{1}{3}$M and a body C of mass$\frac{2}{3}$M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards     AIEEE  Solved  Paper-2005

A)
depends on height of breaking

B)
does not shift

C)
body C

D)
body B

• question_answer14) The moment of inertia of uniform semi-circular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is     AIEEE  Solved  Paper-2005

A)
$\frac{1}{4}M{{r}^{2}}$

B)
$\frac{2}{5}M{{r}^{2}}$

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

D)
$\frac{1}{2}M{{r}^{2}}$

• question_answer15) A particle of mass 0.3 kg is subjected to a force $F=-\text{ }kx$with$k=15\text{ }N/m.$What will be its initial acceleration, if it is released from a point 20 cm away from the origin?     AIEEE  Solved  Paper-2005

A)
$3\text{ }m/{{s}^{2}}$

B)
$15\text{ }m/{{s}^{2}}$

C)
$5\text{ }m/{{s}^{2}}$

D)
$\text{10 }m/{{s}^{2}}$

• question_answer16) The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is AIEEE  Solved  Paper-2005

A)
$\sqrt{MK}L$

B)
$\frac{k{{L}^{2}}}{2M}$

C)
zero

D)
$\frac{M{{L}^{2}}}{k}$

• question_answer17) A mass m moves with a velocity v and collides   inelastically   with   another identical mass. After collision the 1st mass moves with velocity$\frac{v}{\sqrt{3}}$in a direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision.     AIEEE  Solved  Paper-2005

A)
$v$

B)
$\sqrt{3}v$

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

D)
$\frac{v}{\sqrt{3}}$

• question_answer18) A 20 cm long capillary tube is dipped, in water. The water rises upto 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be     AIEEE  Solved  Paper-2005

A)
8cm

B)
10cm

C)
4cm

D)
20cm

• question_answer19) If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is     AIEEE  Solved  Paper-2005

A)
$2{{S}^{2}}Y$

B)
$\frac{{{S}^{2}}}{2Y}$

C)
$\frac{2Y}{{{S}^{2}}}$

D)
$\frac{S}{2Y}$

• question_answer20) Average density of the earth     AIEEE  Solved  Paper-2005

A)
does not depend on g

B)
is a complex function of g

C)
is directly proportional to g

D)
is inversely proportional to g

• question_answer21) A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time, is given by     AIEEE  Solved  Paper-2005

A)
$\frac{m{{v}^{2}}}{{{T}^{2}}}t$

B)
$\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}$

C)
$\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}$

D)
$\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}$

• question_answer22) Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped, is$[{{\mu }_{k}}=0.5]$     AIEEE  Solved  Paper-2005

A)
800m

B)
1000m

C)
100m

D)
400m

• question_answer23) Which of the following is incorrect regarding  the first law of thermodynamics?     AIEEE  Solved  Paper-2005

A)
It is not applicable to any cyclic process

B)
It is a restatement of the principle of conservation of energy

C)
It introduces the concept of the internal energy

D)
It introduces the concept of the entropy

• question_answer24) AT shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C. AIEEE  Solved  Paper-2005

A)
$\frac{2}{3}l$

B)
$\frac{3}{2}l$

C)
$\frac{4}{3}l$

D)
$l$

• question_answer25) The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?                   AIEEE  Solved  Paper-2005

A)
$d=\frac{h}{2}$

B)
$d=\frac{3h}{2}$

C)
$d=2h$

D)
$d=h$

• question_answer26) A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere. (You may take $G=6.67\times {{10}^{-11}}N{{m}^{2}}/k{{g}^{2}}$)     AIEEE  Solved  Paper-2005

A)
$13.34\times {{10}^{-10}}J$

B)
$3.33\times {{10}^{-10}}J$

C)
$6.67\times {{10}^{-9}}J$

D)
$6.67\times {{10}^{-10}}J$

• question_answer27) A gaseous mixture consists of 16 g of helium and 16 g of oxygen/The ratio$\frac{{{C}_{p}}}{{{C}_{v}}}$ of the mixture is     AIEEE  Solved  Paper-2005

A)
1.59

B)
1.62

C)
1.4

D)
1.54

• question_answer28) The intensity of gamma radiation from a given source is$I$. On passing through 36 mm of lead, it is reduced to $I/8$. The thickness of lead, which will reduce the intensity to $I/2$ will be     AIEEE  Solved  Paper-2005

A)
6mm

B)
9mm

C)
18mm

D)
12mm

• question_answer29) The  electrical  conductivity  of  a semiconductor     increases     when electromagnetic radiation of wavelength shorter than 2480 nm, is incident on it. The bandgap for the semiconductor is     AIEEE  Solved  Paper-2005

A)
1.1 eV

B)
2.5 eV

C)
0.5 eV

D)
0.7 eV

• question_answer30) A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 0.5m away, the number of electrons emitted by photocathode would     AIEEE  Solved  Paper-2005

A)
decrease by a factor of 4

B)
increase by a factor of 4

C)
decrease by a factor of 2

D)
increase by a factor of 2

• question_answer31) Starting with a sample of pure$^{66}Cu,$ 7/8 of it decays into Zn in 15 min. The corresponding half-life is     AIEEE  Solved  Paper-2005

A)
10 min

B)
15 min

C)
5 min

D)
$7\frac{1}{2}$ min

• question_answer32) If radius of the$_{13}^{27}Al$ nucleus is estimated to be $3.6\text{ }fm,$then the radius of $_{52}^{125}Te$nucleus be nearly     AIEEE  Solved  Paper-2005

A)
6fm

B)
8fm

C)
4fm

D)
5fm

• question_answer33) The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is AIEEE  Solved  Paper-2005

A)
1/2

B)
1/4

C)
1/3

D)
2/3

• question_answer34) The figure shows a system of two concentric spheres of radii${{r}_{1}},{{r}_{2}}$and kept at temperatures ${{T}_{1}},{{T}_{2}},$respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to AIEEE  Solved  Paper-2005

A)
$\frac{({{r}_{2}}-{{r}_{1}})}{({{r}_{1}}{{r}_{2}})}$

B)
$\ln \left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)$

C)
$\frac{{{r}_{1}}{{r}_{2}}}{({{r}_{2}}-{{r}_{1}})}$

D)
$({{r}_{2}}-{{r}_{1}})$

• question_answer35) A system goes from A to B via two processes and II as shown in figure. If$\Delta {{U}_{1}}$and$\Delta {{U}_{2}}$are the changes in internal energies in the processes I and II respectively, then AIEEE  Solved  Paper-2005

A)
$\Delta {{U}_{1}}=\Delta {{U}_{2}}$

B)
relation between$\Delta {{U}_{1}}$and$\Delta {{U}_{2}}$cannot be determined

C)
$\Delta {{U}_{2}}>\Delta {{U}_{1}}$

D)
$\Delta {{U}_{2}}<\Delta {{U}_{1}}$

• question_answer36) The function ${{\sin }^{2}}\,(\omega t)$ represents     AIEEE  Solved  Paper-2005

A)
a periodic, but not simple harmonic motion with a period $2\pi /\omega$

B)
a periodic, but not simple harmonic motion with a period $\pi /\omega$

C)
a simple harmonic motion with a period $2\pi /\omega$

D)
a simple harmonic motion with a period $\pi /\omega$

• question_answer37) A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is     AIEEE  Solved  Paper-2005

A)
hyperbola

B)
circle

C)
straight line

D)
parabola

• question_answer38) Two simple harmonic motions are represented by the equations ${{y}_{1}}=0.1\sin \left( 100\pi t+\frac{\pi }{3} \right)$and${{y}_{2}}=0.1\,\cos \pi t.$ The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is     AIEEE  Solved  Paper-2005

A)
$\frac{-\pi }{6}$

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

C)
$\frac{-\pi }{3}$

D)
$\frac{\pi }{6}$

• question_answer39) A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the water surface, the radius of this circle (in cm) is     AIEEE  Solved  Paper-2005

A)
$36\sqrt{7}$

B)
$\frac{36}{\sqrt{7}}$

C)
$36\sqrt{5}$

D)
$4\sqrt{5}$

• question_answer40) Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]     AIEEE  Solved  Paper-2005

A)
5 m

B)
1 m

C)
6 m

D)
3 m

• question_answer41) A thin glass (refractive index 1.5) lens has optical power of - 5 D in air. Its optical power in a liquid medium with refractive index 1.6 will be     AIEEE  Solved  Paper-2005

A)
1 D

B)
-1 D

C)
25 D

D)
- 25 D

• question_answer42) The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy? AIEEE  Solved  Paper-2005

A)
III

B)
IV

C)
I

D)
II

• question_answer43) If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor     AIEEE  Solved  Paper-2005

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

B)
2

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

D)
$\sqrt{2}$

• question_answer44) In a common base amplifier, the phase difference between the input signal voltage and output voltage is     AIEEE  Solved  Paper-2005

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

B)
$\pi$

C)
zero

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

• question_answer45) In a full wave rectifier, circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would be     AIEEE  Solved  Paper-2005

A)
50 Hz

B)
25 Hz

C)
100 Hz

D)
70.7 Hz

• question_answer46) A nuclear transformation is denoted, by$X(n,\text{ }\alpha )\to _{3}^{7}Li$. Which of the following is the nucleus of element X?             AIEEE  Solved  Paper-2005

A)
$_{6}^{12}C$

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

C)
$_{5}^{9}B$

D)
$_{4}^{11}Be$

• question_answer47) A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions per milliampere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 V, the resistance in Ohm's needed to be connected in series with the coil will be     AIEEE  Solved  Paper-2005

A)
${{10}^{3}}$

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

C)
99995

D)
9995

• question_answer48) Two voltameters, one of copper and another of silver, are joined in parallel. When a total charge q flows through the voltameters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are${{z}_{1}}$and${{z}_{2}}$respectively, the charge which flows through the silver voltameter is     AIEEE  Solved  Paper-2005

A)
$\frac{q}{1+\frac{{{z}_{1}}}{{{z}_{2}}}}$

B)
$\frac{q}{1+\frac{{{z}_{2}}}{{{z}_{1}}}}$

C)
$q\frac{{{z}_{1}}}{{{z}_{2}}}$

D)
$q\frac{{{z}_{2}}}{{{z}_{1}}}$

• question_answer49) In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be AIEEE  Solved  Paper-2005

A)
$200\,\Omega$

B)
$100\,\Omega$

C)
$500\,\Omega$

D)
$1000\,\Omega$

• question_answer50) Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are${{R}_{1}}$and${{R}_{2}}({{R}_{2}}>{{R}_{1}})$.   If   the   potential difference across the source having internal resistance${{R}_{2}}$is zero, then     AIEEE  Solved  Paper-2005

A)
$R=\frac{{{R}_{2}}({{R}_{1}}+{{R}_{2}})}{({{R}_{2}}-{{R}_{1}})}$

B)
$R={{R}_{2}}-{{R}_{1}}$

C)
$R=\frac{{{R}_{1}}{{R}_{2}}}{({{R}_{1}}+{{R}_{2}})}$

D)
$R=\frac{{{R}_{1}}{{R}_{2}}}{({{R}_{2}}-{{R}_{1}})}$

• question_answer51) A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by $\Delta T,$ the potential difference V across the capacitance is     AIEEE  Solved  Paper-2005

A)
$\sqrt{\frac{2mC\Delta T}{s}}$

B)
$\frac{mC\Delta T}{s}$

C)
$\frac{ms\Delta T}{C}$

D)
$\sqrt{\frac{2ms\Delta T}{C}}$

• question_answer52) One conducting 17-tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed v, then the emf induced in the circuit in terms of B, l and v, where l is the width of each tube, will be AIEEE  Solved  Paper-2005

A)
$BIl$

B)
$-BIl$

C)
zero

D)
$2\,BIl$

• question_answer53) A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be     AIEEE  Solved  Paper-2005

A)
doubled

B)
four times

C)
one-fourth

D)
halved

• question_answer54) Two thin, long, parallel wires, separated by a distance d carry a current of i ampere in the same direction. They will     AIEEE  Solved  Paper-2005

A)
attract each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi d)}$

B)
repel each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi d)}$

C)
attract each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi {{d}^{2}})}$

D)
repel each other with a force of$\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi {{d}^{2}})}$

• question_answer55) When an unpolarised light of intensity${{I}_{0}}$is incident on a polarising sheet, the intensity of the light which does not get transmitted is -     AIEEE  Solved  Paper-2005

A)
$\frac{1}{2}{{l}_{0}}$

B)
$\frac{1}{4}{{l}_{0}}$

C)
zero

D)
${{l}_{0}}$

• question_answer56) A charged ball B hangs from a silk thread S, which makes an angle $\theta$ with a large charged conducting sheet as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to AIEEE  Solved  Paper-2005

A)
$\cos \theta$

B)
$\cot \theta$

C)
$\sin \theta$

D)
$\tan \theta$

• question_answer57) Two point charges$+8q$and$-2q$are located at$x=0$and$x=L$respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero, is     AIEEE  Solved  Paper-2005

A)
2L

B)
L/4

C)
8L

D)
4L

• question_answer58) Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are $+\text{ }q$and$-\text{ }q$. The potential difference between the centres of the two rings is     AIEEE  Solved  Paper-2005

A)
$\frac{qR}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

B)
$\frac{q}{2\pi {{\varepsilon }_{0}}}\left[ \frac{1}{R}-\frac{1}{\sqrt{{{R}^{2}}+{{d}^{2}}}} \right]$

C)
zero

D)
$\frac{q}{4\pi {{\varepsilon }_{0}}}\left[ \frac{1}{R}-\frac{1}{\sqrt{{{R}^{2}}+{{d}^{2}}}} \right]$

• question_answer59) A parallel plate capacitor is made by stacking  n  equally  spaced  plates connected alternatively. If the capacitance between any two adjacent plates is C, then the resultant capacitance is     AIEEE  Solved  Paper-2005

A)
$(n-1)C$

B)
$(n+1)C$

C)
C

D)
$nC$

• question_answer60) When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats/s are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats/s are heard. If the frequency of for k 1 is 200 Hz, then what was the original frequency of fork 2?     AIEEE  Solved  Paper-2005

A)
200 Hz

B)
202 Hz

C)
196 Hz

D)
204 Hz

• question_answer61) If a simple harmonic motion is represented by $\frac{{{d}^{2}}x}{d{{t}^{2}}}+\alpha x=0,$ its time period is     AIEEE  Solved  Paper-2005

A)
$\frac{2\pi }{\alpha }$

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

C)
$2\pi \alpha$

D)
$2\pi \sqrt{\alpha }$

• question_answer62) The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would     AIEEE  Solved  Paper-2005

A)
first increase and then decrease to the original value

B)
first decrease and then increase to the original value

C)
remain unchanged

D)
increase towards a saturation value

• question_answer63) An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?   AIEEE  Solved  Paper-2005

A)
Zero

B)
0.5%

C)
5%

D)
20%

• question_answer64) If${{I}_{0}}$is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?     AIEEE  Solved  Paper-2005

A)
$2\,{{l}_{0}}$

B)
$4{{l}_{0}}$

C)
${{l}_{0}}$

D)
$\frac{{{l}_{0}}}{2}$

• question_answer65) Two concentric coils each of radius equal to$2\pi$cm are placed at right angles to each other. 3 A and 4 A are the currents flowing in each coil respectively. The magnetic induction in $Wb/{{m}^{2}}$at the centre   of   the   coils , will   be $({{\mu }_{0}}=4\pi \times {{10}^{-7}}Wb/Am)$     AIEEE  Solved  Paper-2005

A)
$12\times {{10}^{-5}}$

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

C)
$5\times {{10}^{-5}}$

D)
$7\times {{10}^{-5}}$

• question_answer66) A coil of inductance 300 mH and resistance$2\Omega$. are connected to a source of voltage 2V. The current reaches half of its steady state value in     AIEEE  Solved  Paper-2005

A)
0.05s

B)
0.1s

C)
0.15s

D)
0.3s

• question_answer67) The self-inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of     AIEEE  Solved  Paper-2005

A)
$4\mu F$

B)
$8\mu F$

C)
$1\mu F$

D)
$2\mu F$

• question_answer68) An energy source will supply a constant current into the load, if its internal resistance is     AIEEE  Solved  Paper-2005

A)
equal to the resistance of the load

B)
very large as compared to the load resistance

C)
zero

D)
non-zero but less than the resistance of the load

• question_answer69) A circuit has a resistance of$12\,\Omega$and an impedance of$15\,\Omega$. The power factor of the circuit will be     AIEEE  Solved  Paper-2005

A)
0.8

B)
0.4

C)
1.25

D)
0.125

• question_answer70) The phase difference between the alternating current and emf is$\pi /2$. Which of the following cannot be the constituent of the circuit?             AIEEE  Solved  Paper-2005

A)
C alone

B)
R, L

C)
L, C

D)
L alone

• question_answer71) A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then     AIEEE  Solved  Paper-2005

A)
its velocity will decrease

B)
its velocity will increase

C)
it will turn towards right of direction of motion

D)
it will turn towards left of direction of motion

• question_answer72) A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is     AIEEE  Solved  Paper-2005

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

B)
$\frac{2\pi {{q}^{2}}B}{m}$

C)
$\frac{2\pi qB}{m}$

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

• question_answer73) In a potentiometer experiment, the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of Q, the balancing length becomes 120 cm. The internal resistance of the cell is     AIEEE  Solved  Paper-2005

A)
$1\,\Omega$

B)
$0.5\,\Omega$

C)
$4\,\Omega$

D)
$2\,\Omega$

• question_answer74) The resistance of hot tungsten filament is about 10 times the cold resistance. What will be the resistance of 100 W and 200 V lamp, when not in use?     AIEEE  Solved  Paper-2005

A)
$40\,\Omega$

B)
$20\,\Omega$

C)
$400\,\Omega$

D)
$200\,\Omega$

• question_answer75) A magnetic needle is kept in a non-uniform magnetic   field.   It experiences     AIEEE  Solved  Paper-2005

A)
a torque but not a force

B)
neither a force nor a torque

C)
a force and a torque

D)
a force but not a torque

• question_answer76) The oxidation state of Cr in${{[Cr{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]}^{+}}$is     AIEEE  Solved  Paper-2005

A)
0

B)
+1

C)
+2

D)
+3

• question_answer77) Which one of the following types of drugs reduces fever?     AIEEE  Solved  Paper-2005

A)
Tranquiliser

B)
Antibiotic

C)
Antipyretic

D)
Analgesic

• question_answer78) Which of the following oxides is amphoteric in character?     AIEEE  Solved  Paper-2005

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

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

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

D)
$CaO$

• question_answer79) Which one of the following species is diamagnetic in nature?     AIEEE  Solved  Paper-2005

A)
$H_{2}^{-}$

B)
$H_{2}^{+}$

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

D)
$He_{2}^{+}$

• question_answer80) If$\alpha$is the degree of dissociation of$N{{a}_{2}}S{{O}_{4}},$ the van't Hoff factor (i) used for calculating the molecular mass is     AIEEE  Solved  Paper-2005

A)
$1-2\alpha$

B)
$1+2\alpha$

C)
$1-\alpha$

D)
$1+\alpha$

• question_answer81) Which of the following is a polyamide?     AIEEE  Solved  Paper-2005

A)
Bakelite

B)
Terylene

C)
Nylon-66

D)
Teflon

• question_answer82) Due to the presence of an unpaired electron, free radicals are     AIEEE  Solved  Paper-2005

A)
cations

B)
anions

C)
chemically inactive

D)
chemically reactive

• question_answer83) For a spontaneous reaction the$\Delta G$ equilibrium constant (K) and$E_{cell}^{o}$will be respectively     AIEEE  Solved  Paper-2005

A)
-ve, > 1, -ve

B)
-ve, <1, -ve

C)
-i-ve, > 1, -ve

D)
-ve, >1, +ve

• question_answer84) Hydrogen bomb is based on the principle of     AIEEE  Solved  Paper-2005

A)

B)
nuclear fusion

C)

D)
nuclear fission

• question_answer85) An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be     AIEEE  Solved  Paper-2005

A)
${{A}_{3}}B$

B)
$A{{B}_{3}}$

C)
${{A}_{2}}B$

D)
$AB$

• question_answer86) The highest electrical conductivity of the following aqueous solutions is of     AIEEE  Solved  Paper-2005

A)
0.1 M difluoroacetic acid

B)
0.1 M fluoroacetic acid

C)
0.1 M chloroacetic acid

D)
0.1 M acetic acid

• question_answer87) Lattice energy of an ionic compound depends upon     AIEEE  Solved  Paper-2005

A)
charge on the ion and size of the ion

B)
packing of ions only

C)
size of the ion only

D)
charge on the ion only

• question_answer88) Consider an endothermic reaction$X\to Y$with the activation energies${{E}_{b}}$and${{E}_{f}}$for the backward and forward reactions respectively. In general     AIEEE  Solved  Paper-2005

A)
there is no definite relation between${{E}_{b}}$and ${{E}_{f}}$

B)
${{E}_{b}}={{E}_{f}}$

C)
${{E}_{b}}>{{E}_{f}}$

D)
${{E}_{b}}<{{E}_{f}}$

• question_answer89) Aluminium oxide may be electrolysed at $1000{}^\circ C$to furnish aluminium metal (Atomic mass$=27u;$ 1 Faraday = 96500. The cathode reaction is $A{{l}^{3+}}+3{{e}^{-}}\to A{{l}^{0}}$ To prepare 5.12 kg of aluminium metal by this method would require     AIEEE  Solved  Paper-2005

A)
$5.49\times {{10}^{1}}C$of electricity

B)
$5.49\times {{10}^{4}}C$of electricity

C)
$1.83\times {{10}^{7}}C$of electricity

D)
$5.49\times {{10}^{7}}C$of electricity

• question_answer90) The volume of a colloidal particle, ${{V}_{C}}$ as compared to the volume of a solute particle in a true solution ${{V}_{S}},$ could be     AIEEE  Solved  Paper-2005

A)
$\frac{{{V}_{C}}}{{{V}_{S}}}\approx {{10}^{3}}$

B)
$\frac{{{V}_{C}}}{{{V}_{S}}}\approx {{10}^{-3}}$

C)
$\frac{{{V}_{C}}}{{{V}_{S}}}\approx {{10}^{23}}$

D)
$\frac{{{V}_{C}}}{{{V}_{S}}}\approx 1$

• question_answer91) Consider the reaction ${{N}_{2}}+3{{H}_{2}}\xrightarrow{\,}2\,N{{H}_{3}}$ carried out at constant temperature and pressure. If$\Delta H$and$\Delta U$are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?     AIEEE  Solved  Paper-2005

A)
$\Delta H>\Delta U$

B)
$\Delta H<\Delta U$

C)
$\Delta H=\Delta U$

D)
$\Delta H=0$

• question_answer92) The solubility product of a salt having general formula$M{{X}_{2}},$in water is$4\times {{10}^{-12}}$. The concentration of${{M}^{2+}}$ions in the aqueous solution of the salt is     AIEEE  Solved  Paper-2005

A)
$4.0\times {{10}^{-1}}M$

B)
$1.6\times {{10}^{-4}}M$

C)
$1.0\times {{10}^{-4}}M$

D)
$2.0\times {{10}^{-6}}M$

• question_answer93) Benzene and toluene form nearly ideal solutions. At$20{}^\circ C,$the vapour pressure of benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of benzene at $20{}^\circ C,$for a solution containing 78 g of benzene and 46 g of toluene in torr is     AIEEE  Solved  Paper-2005

A)
53.5

B)
37.5

C)
25

D)
50

• question_answer94) Which one of the following statements is not true about the effect of an increase in temperature on the distribution, of molecular speeds in a gas?     AIEEE  Solved  Paper-2005

A)
The area under the distribution curve remains the same as under the lower temperature

B)

C)
The fraction of the molecules with the most probable speed increases

D)
The most probable speed increases

• question_answer95) For the reaction, $2N{{O}_{2}}(g)2NO(g)+{{O}_{2}}(g)$ $({{K}_{c}}=1.8\times {{10}^{-6}}at\text{ }184{}^\circ C)$ $(R=0.00831\text{ }kJ/(molK))$ When ${{K}_{p}}$ and${{K}_{c}}$are compared at$184{}^\circ C$it is found that     AIEEE  Solved  Paper-2005

A)
whether ${{K}_{p}}$ is greater than, less than or equal to${{K}_{C}}$depends upon the total gas pressure

B)
${{K}_{p}}={{K}_{c}}$

C)
${{K}_{p}}$ is less than${{K}_{C}}$

D)
${{K}_{p}}$ is greater than${{K}_{C}}$

• question_answer96) The exothermic formation of $Cl{{F}_{3}}$ is represented by the equation $C{{l}_{2}}(g)+3{{F}_{2}}(g)2Cl{{F}_{3}}(g);$ $\Delta {{H}_{r}}=-329kJ$ Which of the following will increase the quantity of$Cl{{F}_{3}}$ in an equilibrium mixture of $C{{l}_{2}},{{F}_{2}}$and$Cl{{F}_{3}}$?     AIEEE  Solved  Paper-2005

A)
Adding${{F}_{2}}$

B)
Increasing the volume of the container

C)
Removing$C{{l}_{2}}$

D)
Increasing the temperature

• question_answer97) Hydrogen ion concentration in mol/L in a solution of$pH=5.4$will be     AIEEE  Solved  Paper-2005

A)
$3.98\times {{10}^{-6}}$

B)
$3.68\times {{10}^{-6}}$

C)
$3.88\times {{10}^{6}}$

D)
$3.98\times {{10}^{8}}$

• question_answer98) A reaction involving two different reactants can never be     AIEEE  Solved  Paper-2005

A)
bimolecular reaction

B)
second order reaction

C)
first order reaction

D)
unimolecular reaction

• question_answer99) Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 mL of 1.5 M first solution +520 mL of 1.2 M second solution. What is the molarity of the final mixture?     AIEEE  Solved  Paper-2005

A)
2.70 M

B)
1.344M

C)
1.50 M

D)
1.20M

• question_answer100) During the process of electrolytic refining of copper, some metals present as impurity settle as 'anode mud'. These are     AIEEE  Solved  Paper-2005

A)
Fe and Ni

B)
Ag and Au

C)
Pb and Zn

D)
Se and Ag

• question_answer101)  Electrolyte $KCl$ $KN{{O}_{3}}$ $HCl$ $NAOAc$ $NaCl$ ${{\Lambda }^{\infty }}$ $(S\,c{{m}^{2}}\,mo{{l}^{-1}})$ 149.9 145.0 426.2 91.0 126.5
Calculate${{\Lambda }^{\infty }}HOAc$using appropriate molar conductances of the electrolytes listed above at infinite dilution in${{H}_{2}}O$at$25{}^\circ C$     AIEEE  Solved  Paper-2005

A)
217.5

B)
390.7

C)
552.7

D)
517.2

• question_answer102) If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will       AIEEE  Solved  Paper-2005

A)
be a function of the molecular mass of the substance

B)
remain unchanged

C)
increase two fold

D)
decrease twice

• question_answer103) In a multi-electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic and electric fields? (A)$n=1,l=0,m=0$           (B)$n=2,l=0,m=0$         (C)$n=2,l=1,\text{ }m=1$           (D)$n=3,l=2,m=1$ (E)$n=3,l=2,m=0$     AIEEE  Solved  Paper-2005

A)
(D) and (E)

B)
(C) and (D)

C)
(B) and (C)

D)
(A) and (B)

• question_answer104) Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point?     AIEEE  Solved  Paper-2005

A)
$RbCl$

B)
$KCl$

C)
$NaCl$

D)
$LiCl$

• question_answer105) A schematic plot of In${{K}_{eq}}$versus inverse of temperature for a reaction is shown below $\log {{K}_{eq}}=\frac{-\Delta {{H}^{o}}}{2.303RT}+\frac{-\Delta {{S}^{o}}}{R}$ The reaction must be     AIEEE  Solved  Paper-2005

A)
highly spontaneous at ordinary temperature

B)
one with negligible enthalpy change

C)
endothermic

D)
exothermic

• question_answer106) Heating mixture of$C{{u}_{2}}O$and$C{{u}_{2}}S$will give     AIEEE  Solved  Paper-2005

A)
$C{{u}_{2}}S{{O}_{3}}$

B)
$CuO+CuS$

C)
$Cu+S{{O}_{3}}$

D)
$Cu+S{{O}_{2}}$

• question_answer107) The molecular shapes of$S{{F}_{4}},C{{F}_{4}}$and$Xe{{F}_{4}}$are     AIEEE  Solved  Paper-2005

A)
different with 1, 0 and 2 lone pairs of electrons on the central atom, respectively

B)
different with 0, 1 and 2 lone pairs of electrons on the central atom, respectively

C)
the same with 1, 1 and 1 lone pair of electrons on the central atoms, respectively

D)
the same with 2, 0 and 1 lone pairs of electrons on the central atom, respectively

• question_answer108) The disperse phase in colloidal iron (III) hydroxide and colloidal gold is positively and negatively charged, respectively. Which of the following statements is not correct?     AIEEE  Solved  Paper-2005

A)
Coagulation in both sols can be brought about by electrophoresis

B)
Mixing the sols has no effect

C)
Sodium sulphate solution causes coagulation in both sols

D)
Magnesium chloride solution coagulates, the gold sol more readily than the iron (III) hydroxide sol

• question_answer109) The number of hydrogen atom (s) attached to phosphorus atom in hypophosphorous acid is     AIEEE  Solved  Paper-2005

A)
three

B)
one

C)
two

D)
zero

• question_answer110) What is the conjugate base of$O{{H}^{-}}$?     AIEEE  Solved  Paper-2005

A)
${{O}^{2-}}$

B)
${{O}^{-}}$

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

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

• question_answer111) Heating an aqueous solution  of aluminium chloride to dryness will give       AIEEE  Solved  Paper-2005

A)
$Al(OH)C{{l}_{2}}$

B)
$A{{l}_{2}}{{O}_{3}}$

C)
$A{{l}_{2}}C{{l}_{6}}$

D)
$AlC{{l}_{3}}$

• question_answer112) The correct order of the thermal stability of hydrogen halides ($H-X$) is     AIEEE  Solved  Paper-2005

A)
$HI>HClHBr$

B)
$HClHBr<HI$

C)
$HF>HCl>HBr>HI$

D)
$HI>HBr>HCl>HF$

• question_answer113) Calomel$(HgC{{l}_{2}})$on reaction with ammonium hydroxide gives     AIEEE  Solved  Paper-2005

A)
$HgO$

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

C)
$N{{H}_{2}}-Hg-Hg-Cl$

D)
$HgN{{H}_{2}}Cl$

• question_answer114) The number and type of bonds between two carbon atoms in calcium carbide are     AIEEE  Solved  Paper-2005

A)
two sigma, two pi

B)
two sigma, one pi

C)
one sigma, two pi

D)
one sigma, one pi

• question_answer115) The oxidation state of chromium in the final product formed by the reaction between $KI$ and acidified potassium dichromate solution is     AIEEE  Solved  Paper-2005

A)
+3

B)
+2

C)
+6

D)
+4

• question_answer116) In silicon dioxide     AIEEE  Solved  Paper-2005

A)
there are double bonds between silicon and oxygen citoms

B)
silicon atom is bonded to two oxygen atoms

C)
each silicon atom is surrounded by two oxygen atoms and each oxygen atom is bounded to two silicon atoms

D)
each silicon atom is surrounded by four oxygen atoms and each oxygen atom is bonded to two silicon atoms

• question_answer117) The lanthanide contraction is responsible for the fact that     AIEEE  Solved  Paper-2005

A)
$Zr$and$Zn$have the same oxidation state

B)
$Zr$and$Hf$have about the same radius

C)
$Zr$and$Nb$have similar oxidation state

D)
$Zr$and Y have about the same radius

• question_answer118) The IUPAC name of the coordination compound${{K}_{3}}[Fe{{(CN)}_{6}}]$is     AIEEE  Solved  Paper-2005

A)
tripotassium hexacyanoiron (II)

B)
potassium hexacyanoiron (II)

C)
potassium hexacyanoferrate (III)

D)
potassium hexacyanoferrate (II)

• question_answer119) In which of the following arrangements the order is not according to the property indicated against it?     AIEEE  Solved  Paper-2005

A)
$Li<Na<K<Rb$: Increasing metallic radius

B)
$I<Br<F<Cl$: Increasing electron gain enthalpy (with negative sign)

C)
$B<C<N<O$: Increasing first ionization enthalpy

D)
$A{{l}^{3+}}<M{{g}^{2+}}<N{{a}^{+}}<{{F}^{-}}$: Increasing ionic size

• question_answer120) Of the following sets which one does not contain isoelectronic species?     AIEEE  Solved  Paper-2005

A)
$BO_{3}^{3-},CO_{3}^{2-},NO_{3}^{-}$

B)
$SO_{3}^{2-},CO_{3}^{2-},NO_{3}^{-}$

C)
$C{{N}^{-}},{{N}_{2}},C_{2}^{2-}$

D)
$PO_{4}^{3-},SO_{4}^{2-},CIO_{4}^{-}$

• question_answer121) 2 -methylbutane on reacting with bromine in the presence of sunlight gives mainly     AIEEE  Solved  Paper-2005

A)
1-bromo-3-methylbutane

B)
2-bromo-3-methylbutane

C)
2-bromo-2-methylbutane

D)
1-bromo-2-methylbutane

• question_answer122) Which of the following compounds shows optical isomerism?     AIEEE  Solved  Paper-2005

A)
${{[Co{{(CN)}_{6}}]}^{3-}}$

B)
${{[Cr{{({{C}_{2}}{{O}_{4}})}_{3}}]}^{3-}}$

C)
${{[ZnC{{l}_{4}}]}^{2-}}$

D)
${{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}$

• question_answer123) Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour? (Atomic number$Cr=24,Mn=25,\text{ }Fe=26,$ $Co=27$)     AIEEE  Solved  Paper-2005

A)
${{[Co{{(CN)}_{6}}]}^{3-}}$

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

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

D)
${{[Cr{{(CN)}_{6}}]}^{3-}}$

• question_answer124) The   best   reagent   to   convert pent-S-en-2-ol into pent-3-en-2-one is     AIEEE  Solved  Paper-2005

A)
pyridinium chioro-chromate

B)
chromic anhydride in glacial acetic acid

C)
acidic dichromate

D)
acidic permanganate

• question_answer125) A photon of hard gamma radiation knocks a proton out of$_{12}^{24}Mg$nucleus to form     AIEEE  Solved  Paper-2005

A)
the isobar of$_{11}^{23}Na$

B)
the nuclide$_{11}^{23}Na$

C)
the isobar of parent nucleus

D)
the isotope of parent nucleus

• question_answer126) Reaction of one molecule of$HBr$with one molecule of 1, 3-butadiene at$40{}^\circ C$gives predominantly     AIEEE  Solved  Paper-2005

A)
1-bromo-2-butene under kinetically controlled conditions

B)
3-bromobutene  under   thermodynamically controlled conditions

C)
1-bromo-2-butene under thermodynamically controlled conditions

D)
3-bromobutene under kinetically controlled conditions

• question_answer127) The decreasing order of nucleophilicity among the nucleophiles (A)$C{{H}_{3}}\underset{\begin{smallmatrix} |\,| \\ O \end{smallmatrix}}{\mathop{C}}\,-{{O}^{-}}$                    (B) $C{{H}_{3}}{{O}^{-}}$ (C) $C{{N}^{-}}$ (D) AIEEE  Solved  Paper-2005

A)
(C), (B), (A), (D)

B)
(B), (C), (A), (D)

C)
(D), (C), (B), (A)

D)
(A), (B), (C), (D)

• question_answer128) Tertiary alkyi halides are practically inert to substitution by${{S}_{N}}2$mechanism because of     AIEEE  Solved  Paper-2005

A)
steric hindrance

B)
inductive effect

C)
instability

D)
insolubility

• question_answer129) In both DNA and RNA, heterocyclic base and phosphate ester linkages are at     AIEEE  Solved  Paper-2005

A)
$C_{5}^{'}$and$C_{1}^{'}$respectively of the sugar molecule

B)
$C_{1}^{'}$and$C_{5}^{'}$respectively of the sugar molecule

C)
$C_{2}^{'}$and$C_{5}^{'}$respectively of the sugar molecule

D)
$C_{5}^{'}$and$C_{2}^{'}$respectively of the sugar molecule

• question_answer130) Among the following acids which has the lowest$p{{K}_{a}}$value?     AIEEE  Solved  Paper-2005

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

B)
${{(C{{H}_{3}})}_{2}}CHCOOH$

C)
$HCOOH$

D)
$C{{H}_{3}}COOH$

• question_answer131) Of the five isomeric hexanes, the isomer which can give two monochlorinated compounds is     AIEEE  Solved  Paper-2005

A)
2-methylpentane

B)
2, 2-dimethylbutane

C)
2, 3-dimethylbutane

D)
$n-$hexane

• question_answer132) Alkyi halides react with dialkyi copper reagents to give     AIEEE  Solved  Paper-2005

A)
alkenyl halides

B)
alkanes

C)
alkyi copper halides

D)
alkenes

• question_answer133) Which one of the following methods is neither meant for the synthesis nor for separation of amines?     AIEEE  Solved  Paper-2005

A)
Curtius reaction

B)
Wurtz reaction

C)
Hofmann method

D)
Hinsberg method

• question_answer134) Which types of isomerism is shown by 2, 3-dichlorobutane?     AIEEE  Solved  Paper-2005

A)
Structural

B)
Geometric

C)
Optical

D)
Diastereo

• question_answer135) Amongst the following the most basic compound is     AIEEE  Solved  Paper-2005

A)
p-nitroaniline

B)
acetanilide

C)
aniline

D)
benzylamine

• question_answer136) Acid catalysed hydration of alkenes except ethene leads to the formation of     AIEEE  Solved  Paper-2005

A)
pmixture of secondary and tertiary alcohols

B)
mixture of primary and secondary alcohols

C)
secondary or tertiary alcohol

D)
primary alcohol

• question_answer137) Which of the following is fully fluorinated polymer?     AIEEE  Solved  Paper-2005

A)
PVC

B)
Thiokol

C)
Teflon

D)
Neoprene

• question_answer138) Elimination of bromine from 2-bromobutane results in the formation of     AIEEE  Solved  Paper-2005

A)
predominantly 2-butyne

B)
predominantly 1 ?butene

C)
ppredominantly 2-butene

D)
equimolar mixture of 1 and 2-butene

• question_answer139) Equimolar solutions in the same solvent have     AIEEE  Solved  Paper-2005

A)
different boiling and different freezing points

B)
same boiling and same freezing points

C)
same freezing point but different boiling point

D)
same boiling point but different freezing point

• question_answer140) The reaction, $R-\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,-X+N{{u}^{\text{O-}}}$                                 $\xrightarrow{{}}R-\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,-Nu+{{X}^{\text{O-}}}$ is fastest when X is     AIEEE  Solved  Paper-2005

A)
$OCOR$

B)
$O{{C}_{2}}{{H}_{5}}$

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

D)
$Cl$

• question_answer141) The structure of diborane$({{B}_{2}}{{H}_{6}})$contains     AIEEE  Solved  Paper-2005

A)
four$2C-2{{e}^{-}}$bonds and four$3C-2{{e}^{-}}$bonds

B)
two$2C-2{{e}^{-}}$bonds and two$3C-3{{e}^{-}}$bonds

C)
two$2C-2{{e}^{-}}$bonds and four$3C-2{{e}^{-}}$bonds

D)
four$2C-2{{e}^{-}}$bonds and two$3C-2{{e}^{-}}$bonds

• question_answer142) Which of the following statements in relation to the hydrogen atom is correct?     AIEEE  Solved  Paper-2005

A)
3s, 3pand 3d orbitals all have the same energy

B)
3s and 3p orbitals are of lower energy than 3d orbital

C)
3porbital is lower in energy than 3d orbital

D)
3s orbital is lower in energy than 3porbital

• question_answer143) Which of the following factors may be regarded as the main cause of lanthanide contraction?     AIEEE  Solved  Paper-2005

A)
Greater shielding of 5d electron by 4f electrons

B)
Poorer shielding of 5d electron by 4f electrons

C)
Effective shielding of one of 4f electrons by another in the sub-shell

D)
Poor shielding of one of 4f electron by another in the sub-shell

• question_answer144) The value of the 'spin only' magnetic moment for one of the following configurations is 2.84 BM. The correct one is     AIEEE  Solved  Paper-2005

A)
${{d}^{5}}$(in strong ligand field)

B)
${{d}^{3}}$(in weak as well as in strong fields)

C)
${{d}^{4}}$(in weak ligand field)

D)
${{d}^{4}}$(in strong ligand field)

• question_answer145) Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount of an acid forms a compound. Water during the reaction is continuously removed. The compound formed is generally known as     AIEEE  Solved  Paper-2005

A)
an amine

B)
an imine

C)
anenamine

D)
a Schiff's base

• question_answer146) p-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound B. The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is     AIEEE  Solved  Paper-2005

A) B) C) D) • question_answer147) If the bond dissociation energies of$XY,{{X}_{2}}$and ${{Y}_{2}}$(all diatomic molecules) are in the ratio of 1: 1: 0.5 and$\Delta {{H}_{f}}$for the formation of$XY$is$-200\text{ }kJ\text{ }mo{{l}^{-1}}$. The bond dissociation energy of ${{X}_{2}}$ will be     AIEEE  Solved  Paper-2005

A)
$400\text{ }kJ\text{ }mo{{l}^{-1}}$

B)
$300\text{ }kJ\text{ }mo{{l}^{-1}}$

C)
$200\text{ }kJ\text{ }mo{{l}^{-1}}$

D)
None of these

• question_answer148) An amount of solid$N{{H}_{4}}HS$is placed in a flask already containing ammonia   gas   at   a   certain temperature and 0.50 atm pressure. Ammonium   hydrogen   sulphide decomposes to yield$N{{H}_{3}}$and${{H}_{2}}S$gases in the flask. When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to 0.84 atm? The equilibrium constant for $N{{H}_{4}}HS$ decomposition at this temperature is     AIEEE  Solved  Paper-2005

A)
0.11

B)
0.17

C)
0.18

D)
0.30

• question_answer149) An organic compound having molecular mass 60 is found to contain C = 20%, H = 6.67% and N = 46.67% while rest is oxygen. On heating it gives$N{{H}_{3}}$along with a solid residue. The solid residue give violet colour with alkaline copper sulphate solution. The compound is     AIEEE  Solved  Paper-2005

A)
$C{{H}_{3}}C{{H}_{2}}CON{{H}_{2}}$

B)
${{(N{{H}_{2}})}_{2}}CO$

C)
$C{{H}_{3}}CON{{H}_{2}}$

D)
$C{{H}_{3}}NCO$

• question_answer150) ${{t}_{1/4}}$can be taken as the time taken for the concentration of a reactant to drop to 3/4 of its Initial value. If the rate constant for a first order reaction is k, the ${{t}_{1/4}}$ can be written as     AIEEE  Solved  Paper-2005

A)
0.75/k

B)
0.69/k

C)
0.291k

D)
0.10/k

• question_answer151) If C is the mid-point of AB and P is any point outside AB, then     AIEEE  Solved  Paper-2005

A)
$PA+PB+PC=0$

B)
$PA+PB+2PC=0$

C)
$PA+PB=PC$

D)
PA + PB = 2PC

• question_answer152) Let P be the point (1, 0) and Q be a point on the locus${{y}^{2}}=8x.$The locus of mid-point of PQ is     AIEEE  Solved  Paper-2005

A)
${{x}^{2}}-4y+2=0$

B)
${{x}^{2}}+4y+2=0$

C)
${{y}^{2}}+4x+2=0$

D)
${{y}^{2}}-4x+2=0$

• question_answer153) If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately     AIEEE  Solved  Paper-2005

A)
24.0

B)
25.5

C)
20.5

D)
22.0

• question_answer154) Let$R=\{(3,3),(6,6),(9,9),(12,12),$$(6,12),$$(3,9),(3,12),(3,6)\}$be a relation on the set A$=\{3,6,9,12\}$. The relation is     AIEEE  Solved  Paper-2005

A)
reflexive and symmetric only

B)
an equivalence relation

C)
reflexive only

D)
reflexive and transitive only

• question_answer155) If ${{A}^{2}}-A+I=O,$ then the inverse of A is       AIEEE  Solved  Paper-2005

A)
$l-A$

B)
$A-l$

C)
A

D)
$A+l$

• question_answer156) If the cube roots of unity are$1,\omega ,{{\omega }^{2}}$then the roots of the equation ${{(x-1)}^{3}}+8=0,$ are     AIEEE  Solved  Paper-2005

A)
$-1,1+2\omega ,1+2{{\omega }^{2}}$

B)
$-1,1-2\omega ,1-2{{\omega }^{2}}$

C)
$-1,-1,-1$

D)
$-1,-1+2\omega ,-1-2{{\omega }^{2}}$

• question_answer157) $\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{{{n}^{2}}}{{\sec }^{2}}\frac{1}{{{n}^{2}}}+\frac{2}{{{n}^{2}}}{{\sec }^{2}}\frac{4}{{{n}^{2}}} \right.$ $\left. +....+\frac{n}{{{n}^{2}}}{{\sec }^{2}}1 \right]$ equals     AIEEE  Solved  Paper-2005

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

B)
$tan\text{ }1$

C)
$\frac{1}{2}cosec\text{ }1$

D)
$\frac{1}{2}sec\text{ }1$

• question_answer158) Area of the greatest rectangle that can be inscribed in the ellipse$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$is     AIEEE  Solved  Paper-2005

A)
$\frac{a}{b}$

B)
$\sqrt{ab}$

C)
$ab$

D)
$2ab$

• question_answer159) The differential equation representing the family of curves${{y}^{2}}=2c(x+\sqrt{c}),$where$c>0,$is a parameter, is of order and degree as follows       AIEEE  Solved  Paper-2005

A)
order 2, degree 2

B)
order 1, degree 3

C)
order 1, degree 1

D)
order 1, degree 2

• question_answer160) ABC is a triangle. Forces P,Q,R acting along $I,A,IB$and$IC$respectively are in equilibrium, where I is the incentre of$\Delta ABC.$Then, P : Q : R is     AIEEE  Solved  Paper-2005

A)
$\cos A:\cos B:\cos \,C$

B)
$\cos \frac{A}{2}:\cos \frac{B}{2}:\cos \,\frac{C}{2}$

C)
$\sin \frac{A}{2}:\sin \frac{B}{2}:\sin \,\frac{C}{2}$

D)
$\sin A:\sin B:\sin C$

• question_answer161) If the coefficients of rth,$(r+1)th$ and$(r+2)th$terms in the binomial expansion of${{(1+y)}^{m}}$are in AP, then m and r satisfy the equation     AIEEE  Solved  Paper-2005

A)
${{m}^{2}}-m(4r-1)+4{{r}^{2}}+2=0$

B)
${{m}^{2}}-m(4r+1)+4{{r}^{2}}-2=0$

C)
${{m}^{2}}-m(4r+1)+4{{r}^{2}}+2=0$

D)
${{m}^{2}}-m(4r-1)+4{{r}^{2}}-2=0$

• question_answer162) In a$\Delta PQR,\angle R=\frac{\pi }{2}$If$\tan \left( \frac{P}{2} \right)$and$\tan \left( \frac{Q}{2} \right)$are the roots of$a{{x}^{2}}+bx+c=0,a\ne 0,$then     AIEEE  Solved  Paper-2005

A)
$d=a+c$

B)
$b=c$

C)
$c=a+b$

D)
$a=o+c,$

• question_answer163) If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number     AIEEE  Solved  Paper-2005

A)
602

B)
603

C)
600

D)
601

• question_answer164) The value of $^{50}{{C}_{4}}+\sum\limits_{r=1}^{6}{^{56-r}{{C}_{3}}}$is     AIEEE  Solved  Paper-2005

A)
$^{56}{{C}_{4}}$

B)
$^{56}{{C}_{3}}$

C)
$^{55}{{C}_{3}}$

D)
$^{55}{{C}_{4}}$

• question_answer165) If $A=\left[ \begin{matrix} 1 & 0 \\ 1 & 1 \\ \end{matrix} \right]$and$I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right],$then which one of the following holds for all$n\ge 1,$the principle of mathematical induction?     AIEEE  Solved  Paper-2005

A)
${{A}^{n}}={{2}^{n-1}}A+(n-1)l$

B)
${{A}^{n}}=nA+(n-1)l$

C)
${{A}^{n}}={{2}^{n-1}}A+(n-1)l$

D)
${{A}^{n}}=nA+(n-1)l$

• question_answer166) If the coefficient of${{x}^{7}}$in${{\left[ a{{x}^{2}}+\left( \frac{1}{bx} \right) \right]}^{11}}$equals  the  coefficient  of${{x}^{-7}}$in${{\left[ ax-\left( \frac{1}{b{{x}^{2}}} \right) \right]}^{11}},$then a and b satisfy the relation     AIEEE  Solved  Paper-2005

A)
$ab=1$

B)
$\frac{a}{b}=1$

C)
$a+b=1$

D)
$a-d=1$

• question_answer167) Let$f:(-1,1)\to B$ be a function defined by$f(x)={{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}},$ then f is both one-one and onto when B is the interval     AIEEE  Solved  Paper-2005

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

B)
$\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]$

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

D)
$\left( 0,\frac{\pi }{2} \right)$

• question_answer168) If${{z}_{1}}$and${{z}_{2}}$are two non-zero complex numbers such that$|{{z}_{1}}+{{z}_{2}}|=|{{z}_{1}}|+|{{z}_{2}}|$then $\arg ({{z}_{1}})-\arg ({{z}_{2}})$is equal to

A)
$-\frac{\pi }{2}$

B)
0

C)
$-\pi$

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

• question_answer169) If$W=\frac{z}{z-\frac{1}{3}i}$and$|w|=1,$then z lies on     AIEEE  Solved  Paper-2005

A)
a parabola

B)
a straight line

C)
a circle

D)
an ellipse

• question_answer170) If${{a}^{2}}+{{b}^{2}}+{{c}^{2}}=-2$and $f(x)=\left| \begin{matrix} 1+{{a}^{2}}x & (1+{{b}^{2}})x & (1+{{c}^{2}})x \\ {{(1+a)}^{2}}x & 1+{{b}^{2}}x & (1+{{c}^{2}})x \\ (1+{{a}^{2}})x & (1+{{b}^{2}})x & 1+{{c}^{2}}x \\ \end{matrix} \right|,$ then$f(x)$is a polynomial of degree     AIEEE  Solved  Paper-2005

A)
2

B)
3

C)
0

D)
1

• question_answer171) The system of equations $\alpha x+y+z=\alpha -1,x+\alpha \,y+z=\alpha -l$ $x+y+\alpha z=\alpha -1$has no solution, if $\alpha$ is     AIEEE  Solved  Paper-2005

A)
1

B)
not-2

C)
either - 2 or 1

D)
- 2

• question_answer172) The value of a for which the sum of the squares of the roots of the equation${{x}^{2}}-(a-2)x-a-1=0$assume the least value is     AIEEE  Solved  Paper-2005

A)
2

B)
3

C)
0

D)
1

• question_answer173) If the roots of the equation${{x}^{2}}-bx+c=0$are two consecutive integers, then${{b}^{2}}-4c$equals     AIEEE  Solved  Paper-2005

A)
1

B)
2

C)
3

D)
-2

• question_answer174) Suppose$f(x)$is differentiable at$x=1$and$\underset{h\to 0}{\mathop{\lim }}\,\frac{1}{h}f(1+h)=5,$then$f'(1)$equals     AIEEE  Solved  Paper-2005

A)
6

B)
5

C)
4

D)
3

• question_answer175) Let f be differentiable for all$x$. If$f(1)=-2$and $f'(x)\ge 2$for$x\in [1,6],$then     AIEEE  Solved  Paper-2005

A)
$f(6)=5$

B)
$f(6)<5$

C)
$f(6)<8$

D)
$f(6)\ge 8$

• question_answer176) If$f$is a real-valued differentiable function satisfying$|f(x)-f(y)|\le {{(x-y)}^{2}},x,y\in R$and $f(0)=0,$then$f(1)$equals     AIEEE  Solved  Paper-2005

A)
1

B)
2

C)
0

D)
-1

• question_answer177) If$x$is so small that${{x}^{3}}$and higher powers of$x$   may  be   neglected, then $\frac{{{(1+x)}^{3/2}}-{{\left( 1+\frac{1}{2}x \right)}^{3}}}{{{(1-x)}^{1/2}}}$may be approximated as     AIEEE  Solved  Paper-2005

A)
$\frac{x}{2}-\frac{3}{8}{{x}^{2}}$

B)
$-\frac{3}{8}{{x}^{2}}$

C)
$3x+\frac{3}{8}{{x}^{2}}$

D)
$1-\frac{3}{8}{{x}^{2}}$

• question_answer178) If$x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}},y=\sum\limits_{n=0}^{\infty }{{{b}^{n}}},z=\sum\limits_{n=0}^{\infty }{{{c}^{n}}},$where a, b, c are in AP and$|a|<1,|b|<1,|c|<1,$then$x,\text{ }y,\text{ }z$are in     AIEEE  Solved  Paper-2005

A)
HP

B)
AGP

C)
AP

D)
GP

• question_answer179) In a$\Delta ABC,$let $\angle C=\pi /2,$ if r is the inradius and R is the circumradius of the$\Delta ABC,$then $2(r+R)$equals     AIEEE  Solved  Paper-2005

A)
$c+a$

B)
$a+b+c$

C)
$a+b$

D)
$b+c$

• question_answer180) If${{\cos }^{-1}}x-{{\cos }^{-1}}\frac{y}{2}=\alpha ,$then$4{{x}^{2}}-4xy\,\cos \alpha +{{y}^{2}}$ is equal to     AIEEE  Solved  Paper-2005

A)
$-4\text{ }{{\sin }^{2}}\alpha$

B)
$4\text{ }{{\sin }^{2}}\alpha$

C)
4

D)
$2\text{ }{{\sin }^{2}}\alpha$

• question_answer181) If in a$\Delta ABC,$the altitudes from the vertices A,B,C on opposite sides are in HP, then sin A, sin B, sin C are in     AIEEE  Solved  Paper-2005

A)
HP

B)
Arithmetico-Geometric Progression

C)
AP

D)
GP

• question_answer182) The normal to the curve $x=a(\cos \theta +\theta \sin \theta ),y=a(\sin \theta -\theta \cos \theta )$at any point$'\theta '$is such that     AIEEE  Solved  Paper-2005

A)
it is at a constant distance from the origin

B)
it passes through$(a\text{ }\pi /2,-a)$

C)
it makes angle$\pi /2+\theta$with the X-axis

D)
it passes through the origin

• question_answer183) A function is matched below against an interval, where it is supposed to be increasing. Which of the following pairs is incorrectly matched? Interval                Function     AIEEE  Solved  Paper-2005

A)
$(-\infty ,\,\,-4]$           ${{x}^{3}}+6{{x}^{2}}+6$

B)
$\left( -\infty ,\frac{1}{3} \right]$           $3{{x}^{2}}-2x+1$

C)
$[2,\,\infty )$                  $2{{x}^{3}}-3{{x}^{2}}-12{{x}^{4}}-6$

D)
$(-\infty ,\infty )$                          ${{x}^{3}}-3{{x}^{2}}+3x+3$

• question_answer184) Let $\alpha$ and $\beta$ be the distinct roots of$a{{x}^{2}}+bx+c=0,$then $\underset{x\to \alpha }{\mathop{\lim }}\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}}$is equal to     AIEEE  Solved  Paper-2005

A)
$\frac{1}{2}{{(\alpha -\beta )}^{2}}$

B)
$-\frac{{{a}^{2}}}{2}{{(\alpha -\beta )}^{2}}$

C)
0

D)
$\frac{{{a}^{2}}}{2}{{(\alpha -\beta )}^{2}}$

• question_answer185) If$x\frac{dy}{dx}=y(\log \text{ }y-\log \text{ }x+1),$then the solution of the equation is     AIEEE  Solved  Paper-2005

A)
$\log \left( \frac{x}{y} \right)=Cy$

B)
$\log \left( \frac{y}{x} \right)=Cx$

C)
$x\log \left( \frac{y}{x} \right)=Cy$

D)
$y\log \left( \frac{x}{y} \right)=Cx$

• question_answer186) The line parallel to the X-axis and passing through the intersection of the lines $ax+2\,by+3b=0$and$bx-2ay-3a=0,$where $(a,b)\ne (0,0)$is     AIEEE  Solved  Paper-2005

A)
above the X-axis at a distance of (2/3) from it

B)
above the X-axis at a distance of (3/2) from it

C)
below the X-axis at a distance of (2/3) from it

D)
below the X-axis at a distance of (3/2) from it

• question_answer187) A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of$50\text{ }c{{m}^{3}}/\min$. When the thickness of ice is 15 cm, then the rate at which the thickness of ice decreases, is     AIEEE  Solved  Paper-2005

A)
$\frac{5}{6\pi }cm/\min$

B)
$\frac{1}{54\pi }cm/\min$

C)
$\frac{1}{18\pi }cm/\min$

D)
$\frac{1}{36\pi }cm/\min$

• question_answer188) ${{\int{\left\{ \frac{(\log x-1)}{1+{{(\log \,x)}^{2}}} \right\}}}^{2}}dx$is equal to     AIEEE  Solved  Paper-2005

A)
$\frac{x}{{{(\log \,x)}^{2}}+1}+C$

B)
$\frac{x{{e}^{x}}}{1+\,{{x}^{2}}}+C$

C)
$\frac{x}{\,{{x}^{2}}+1}+C$

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

• question_answer189) Let$f:\text{ }R\to R$be a differentiable function having$f(2)=6,f'(2)=\left( \frac{1}{48} \right)$ Then,$\underset{x\to 2}{\mathop{\lim }}\,\int_{6}^{f(x)}{\frac{4{{t}^{3}}}{x-2}}dt$ equals       AIEEE  Solved  Paper-2005

A)
18

B)
12

C)
36

D)
24

• question_answer190) Let$f(x)$be a non-negative continuous function such that the area bounded by the curve$y=f(x),$X-axis and the ordinates$x=\pi /4$ and $x=\beta >\pi /4$ is$\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \right)$.Then$f\left( \frac{\pi }{2} \right)$,is     AIEEE  Solved  Paper-2005

A)
$\left( 1-\frac{\pi }{4}+\sqrt{2} \right)$

B)
$\left( 1-\frac{\pi }{4}-\sqrt{2} \right)$

C)
$\left( \frac{\pi }{4}-\sqrt{2}+1 \right)$

D)
$\left( \frac{\pi }{4}+\sqrt{2}-1 \right)$

• question_answer191) If${{I}_{1}}=\int_{0}^{1}{{{2}^{{{x}^{2}}}}}dx$${{I}_{2}}=\int_{0}^{1}{{{2}^{{{x}^{3}}}}}dx,$ ${{I}_{3}}=\int_{1}^{2}{{{2}^{{{x}^{2}}}}}dx$and${{I}_{4}}=\int_{1}^{2}{{{2}^{{{x}^{3}}}}}dx,$then     AIEEE  Solved  Paper-2005

A)
${{l}_{3}}>{{l}_{4}}$

B)
${{l}_{3}}={{l}_{4}}$

C)
${{l}_{1}}>{{l}_{2}}$

D)
${{l}_{2}}>{{l}_{1}}$

• question_answer192) The area enclosed between the curve$y={{\log }_{e}}(x+e)$and the coordinate axes is     AIEEE  Solved  Paper-2005

A)
4

B)
3

C)
2

D)
1

• question_answer193) The parabolas${{y}^{2}}=4x$and${{x}^{2}}=4y$divide the square region bounded by the lines $x=4,\text{ }y=4$and the coordinate axes. If ${{S}_{1}},{{S}_{2}},{{S}_{3}}$are respectively the areas of these parts numbered from top to bottom, then${{S}_{1}}:{{S}_{2}}:{{S}_{3}}$     AIEEE  Solved  Paper-2005

A)
1 : 1 : 1

B)
2 : 1 : 2

C)
1 : 2 : 3

D)
1 : 2 : 1

• question_answer194) If the plane$2ax-3ay+4az+6=0$passes through the mid-point of the line joining the    centres    of    the    spheres${{x}^{2}}+{{y}^{2}}+{{z}^{2}}+6x-8y-2z=13$ and${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-10x+4y-2z=8,$then a equals     AIEEE  Solved  Paper-2005

A)
2

B)
$-2$

C)
1

D)
$-1$

• question_answer195) The distance between the line$r=2\hat{i}-2\hat{j}+3\hat{k}+\lambda (\hat{i}-\hat{j}+4\hat{k})$and the plane$r.(\hat{i}+5\hat{j}+\hat{k})=5$is     AIEEE  Solved  Paper-2005

A)
$\frac{10}{3}$

B)
$\frac{3}{10}$

C)
$\frac{10}{3\sqrt{3}}$

D)
$\frac{10}{9}$

• question_answer196) For  any  vector a,   the  value of${{(a\times \hat{i})}^{2}}+{{(a\times \hat{j})}^{2}}+{{(a\times \hat{k})}^{2}}$is equal to     AIEEE  Solved  Paper-2005

A)
$4{{a}^{2}}$

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

C)
${{a}^{2}}$

D)
$3{{a}^{2}}$

• question_answer197) If non-zero numbers a, b, c are in HP, then the straight line $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$always passes through a fixed point. That point is     AIEEE  Solved  Paper-2005

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

B)
$(1,-2)$

C)
$(-1,-2)$

D)
$(-1,2)$

• question_answer198) It a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is     AIEEE  Solved  Paper-2005

A)
$\left( \frac{1}{3},\frac{7}{3} \right)$

B)
$\left( 1,\frac{7}{3} \right)$

C)
$\left( -\frac{1}{3},\frac{7}{3} \right)$

D)
$\left( -1,\frac{7}{3} \right)$

• question_answer199) If the circles${{x}^{2}}+{{y}^{2}}+2ax+cy+a=0$and ${{x}^{2}}+{{y}^{2}}-3\text{ }ax+dy-1=0$intersect in two distinct points P and 0, then the line $5x+by-a=0$passes through P and Q for     AIEEE  Solved  Paper-2005

A)
exactly two values of a

B)
infinitely many values of a

C)
no value of a

D)
exactly one value of a

• question_answer200) A circle touches the X-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is       AIEEE  Solved  Paper-2005

A)
a parabola

B)
a hyperbola

C)
a circle

D)
an ellipse

• question_answer201) If a circle passes through the point (a, b) and  cuts  the  circle${{x}^{2}}+{{y}^{2}}={{p}^{2}}$orthogonally, then the equation of the locus of its centre is     AIEEE  Solved  Paper-2005

A)
$2ax+2by-({{a}^{2}}+{{b}^{2}}+{{p}^{2}})=0$

B)
${{x}^{2}}+{{y}^{2}}-2ax-3by+({{a}^{2}}-{{b}^{2}}-{{p}^{2}})=0$

C)
$2ax+2by-({{a}^{2}}-{{b}^{2}}+{{p}^{2}})=0$

D)
${{x}^{2}}+{{y}^{2}}-3ax-4by+({{a}^{2}}+{{b}^{2}}-{{p}^{2}})=0$

• question_answer202) An ellipse has OB as semi-minor axis, F and F' its foci and the angle FBF' is a right angle. Then, the eccentricity of the ellipse is     AIEEE  Solved  Paper-2005

A)
$1/\sqrt{3}$

B)
$1/4$

C)
$1/2$

D)
$1/\sqrt{2}$

• question_answer203) The locus of a point $P(\alpha ,\beta )$ moving under the condition that the line$y=\alpha x+\beta$is a tangent to the hyperbola$\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$is     AIEEE  Solved  Paper-2005

A)
a hyperbola

B)
a parabola

C)
a circle

D)
an ellipse

• question_answer204) If the angle$\theta$between the line$\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$and  the  plane $2x-y+\sqrt{\lambda }z+4=0$is such that $\sin \theta =\frac{1}{3}$The value of$\lambda$is     AIEEE  Solved  Paper-2005

A)
$-\frac{4}{3}$

B)
$\frac{3}{4}$

C)
$-\frac{3}{5}$

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

• question_answer205) The angle between the lines$2x=3y=-z$and $6x=-y=-4z$is     AIEEE  Solved  Paper-2005

A)
$30{}^\circ$

B)
$45{}^\circ$

C)
$90{}^\circ$

D)
$0{}^\circ$

• question_answer206) Let A and B be two events such that $P\overline{(A\cup B)}=\frac{1}{6},P(A\cap B)=\frac{1}{4}$and$P(\overline{A})=\frac{1}{4},$where $\overline{A}$ stands for complement of event A. Then, events A and B are     AIEEE  Solved  Paper-2005

A)
mutually exclusive and independent

B)
independent but not equally likely

C)
equally likely but not independent

D)
equally likely and mutuaiiy exclusive

• question_answer207) Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house, is     AIEEE  Solved  Paper-2005

A)
7/9

B)
8/9

C)
1/9

D)
2/9

• question_answer208) A random variable X has Poisson distribution with mean 2. Then,$P(X>1.5)$equals     AIEEE  Solved  Paper-2005

A)
$\frac{3}{{{e}^{2}}}$

B)
$1-\frac{3}{{{e}^{2}}}$

C)
0

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

• question_answer209) Two points A and B move from rest along a straight line with constant acceleration f and f?, respectively. If A takes m second more than B and describes n unit more than B in acquiring the same speed, then     AIEEE  Solved  Paper-2005

A)
$(f'-f)n=\frac{1}{2}ff'{{m}^{2}}$

B)
$\frac{1}{2}(f+f')m=ff'{{n}^{2}}$

C)
$(f+f'){{m}^{2}}=ff'n$

D)
$(f+f'){{m}^{2}}=ff'n$

• question_answer210) A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of$2\text{ }cm/{{s}^{2}}$and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then, the lizard will catch the insect after     AIEEE  Solved  Paper-2005

A)
24 s

B)
21 s

C)
1 s

D)
20 s

• question_answer211) The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one-third of the other force. The ratio of larger force to smaller one is     AIEEE  Solved  Paper-2005

A)
$3:2\sqrt{2}$

B)
$3:2$

C)
$3:\sqrt{2}$

D)
$2:1$

• question_answer212) Let$a=\hat{i}-\hat{k},b=x\hat{i}+\hat{j}+(1-x)\hat{k}$and $c=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$. Then,$[a\,\,b\,\,c]$depends on     AIEEE  Solved  Paper-2005

A)
neither$x$nor y

B)
both$x$and y

C)
only $x$

D)
only y

• question_answer213) Let a, b and c be distinct non-negative numbers. If the vectors$a\hat{i}+a\hat{j}+c\hat{k},\hat{i}+\hat{k}$and $c\hat{i}+c\hat{j}+b\hat{k}$ lie in a plane, then c is     AIEEE  Solved  Paper-2005

A)
the harmonic mean of a and b

B)
equal to zero

C)
the arithmetic mean of a and b

D)
the geometric mean of a and b

• question_answer214) If a, b, b are non-coplanar vectors and $\lambda$, is a real number, then$[\lambda (a+b){{\lambda }^{2}}\,b\,\,\lambda c]=[ab+cd]$for     AIEEE  Solved  Paper-2005

A)
exactly two values of $\lambda$

B)
exactly three values of $\lambda$

C)
no value of$\lambda$

D)
exactly one value of$\lambda$

• question_answer215) A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance     AIEEE  Solved  Paper-2005

A)
$\frac{H}{A-B}$

B)
$\frac{H}{2(A+B)}$

C)
$\frac{H}{A+B}$

D)
$\frac{2H}{A-B}$

• question_answer216) The sum of the series$1+\frac{1}{4.2!}+\frac{1}{16.4!}+\frac{1}{64.6!}+.....\infty$is     AIEEE  Solved  Paper-2005

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

B)
$\frac{e-1}{2\sqrt{e}}$

C)
$\frac{e+1}{\sqrt{e}}$

D)
$\frac{e-1}{\sqrt{e}}$

• question_answer217) Let${{x}_{1}},{{x}_{2}},.....,{{x}_{n}}$be n observations such that $\Sigma x_{i}^{2}=400$and$\Sigma {{x}_{i}}=80$. Then, a possible value of n among the following is     AIEEE  Solved  Paper-2005

A)
12

B)
9

C)
18

D)
15

• question_answer218) A particle is projected from a point O with velocity u at an angle of$60{}^\circ$with the horizontal. When it is moving in a direction at right angle to its direction at O, then its velocity is given by     AIEEE  Solved  Paper-2005

A)
$\frac{u}{\sqrt{3}}$

B)
$\frac{2u}{3}$

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

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

• question_answer219) If both the roots of the quadratic equation${{x}^{2}}-2kx+{{k}^{2}}+k-5=0$are less than 5, then k lies in the interval     AIEEE  Solved  Paper-2005

A)
[4, 5]

B)
$(-\infty ,4)$

C)
$(6,\infty )$

D)
(5, 6]

• question_answer220) If${{a}_{1}},{{a}_{2}},{{a}_{3}},....,{{a}_{n}},....$are in GP, then the determinant $\Delta =\left| \begin{matrix} \log {{a}_{n}} & \log {{a}_{n+1}} & \log {{a}_{n+2}} \\ \log {{a}_{n+3}} & \log {{a}_{n+4}} & \log {{a}_{n+5}} \\ \log {{a}_{n+6}} & \log {{a}_{n+7}} & {{\log }_{n+8}} \\ \end{matrix} \right|$is equal to     AIEEE  Solved  Paper-2005

A)
2

B)
4

C)
0

D)
1

• question_answer221) A real valued function$f(x)$satisfies the functional equation $f(x-y)=f(x)\text{ }f(y)-f(a-x)\text{ }f(a+y)$ where, a is a given constant and$f(0)=1$$f(2\text{ }a-x)$is equal to     AIEEE  Solved  Paper-2005

A)
$f(-\text{ }x)$

B)
$f(a)+f(a-x)$

C)
$f(x)$

D)
$-f(x)$

• question_answer222) If the equation ${{a}_{n}}{{X}^{n}}+{{a}_{n-1}}{{X}^{n-1}}+....+{{a}_{1}}x=0,$ ${{a}_{1}}\ne 0,n\ge 2,$has a positive root $x=\alpha ,$ then the equation $n{{a}_{n}}{{x}^{n-1}}+(n-1){{a}_{n-1}}{{X}^{n-2}}+....+{{a}_{1}}=0$ has a positive root, which is     AIEEE  Solved  Paper-2005

A)
equal to$\alpha$

B)
greater than or equal to$\alpha$

C)
smaller than$\alpha$

D)
greater than $\alpha$

• question_answer223) The value of $\int_{-\pi }^{\pi }{\frac{{{\cos }^{2}}x}{1+{{a}^{x}}}}dx,a>0,$is     AIEEE  Solved  Paper-2005

A)
$2\pi$

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

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

D)
$a\pi$

• question_answer224) The plane$x+2y-z=4$cuts the sphere${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-x+z-2=0$in a circle of radius     AIEEE  Solved  Paper-2005

A)
$\sqrt{2}$

B)
2

C)
1

D)
3

• question_answer225) If the pair of linesa${{x}^{2}}+2(a+b)xy+b{{y}^{2}}=0$ lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sector is thrice the area of another sector, then     AIEEE  Solved  Paper-2005

A)
$3{{a}^{2}}+2ab+3{{b}^{2}}=0$

B)
$3{{a}^{2}}+10ab+3{{b}^{2}}=0$

C)
$3{{a}^{2}}-2ab+3{{b}^{2}}=0$

D)
$3{{a}^{2}}-10ab+3{{b}^{2}}=0$

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