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

AIEEE Solved Paper-2005 Total Questions - 225

1) 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)

       \[R\]

View Answer
2) 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)

       \[\frac{{{R}_{1}}}{{{R}_{2}}}\]

View Answer
3) 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)

       \[{{\mu }_{s}}=\sqrt{1-\frac{1}{{{n}^{2}}}}\]

View Answer
4) 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)

       \[\tan \phi \]

View Answer
5) 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

View Answer
6) 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

View Answer
7) 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)

       \[2a{{v}^{2}}\]

View Answer
8) 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)

       \[S=\frac{1}{4}f{{t}^{2}}\]

View Answer
9) 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

View Answer
10) 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

View Answer
11) 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)

       \[g\text{ }tan\alpha \]

View Answer
12) 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)

       \[10\sqrt{30}\,m/s\]

View Answer
13) 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

View Answer
14) 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)

                       \[\frac{1}{2}M{{r}^{2}}\]

View Answer
15) 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)

       \[\text{10 }m/{{s}^{2}}\]

View Answer
16) 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)

       \[\frac{M{{L}^{2}}}{k}\]

View Answer
17) 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)

       \[\frac{v}{\sqrt{3}}\]

View Answer
18) 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

View Answer
19) 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)

       \[\frac{S}{2Y}\]

View Answer
20) 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

View Answer
21) 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)

       \[\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}\]

View Answer
22) 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

View Answer
23) 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

View Answer
24) 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)

       \[l\]

View Answer
25) 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)

       \[d=h\]

View Answer
26) 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)

       \[6.67\times {{10}^{-10}}J\]

View Answer
27) 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

View Answer
28) 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

View Answer
29) 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

View Answer
30) 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

View Answer
31) 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

View Answer
32) 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

View Answer
33) 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

View Answer
34) 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)

       \[({{r}_{2}}-{{r}_{1}})\]

View Answer
35) 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)

\[\Delta {{U}_{2}}<\Delta {{U}_{1}}\]

View Answer
36) 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 \[\pi /\omega \]

View Answer
37) 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

View Answer
38) 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)

       \[\frac{\pi }{6}\]

View Answer
39) 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)

       \[4\sqrt{5}\]

View Answer
40) 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

View Answer
41) 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

View Answer
42) 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

View Answer
43) 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)

       \[\sqrt{2}\]

View Answer
44) 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)

       \[\frac{\pi }{2}\]

View Answer
45) 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

View Answer
46) 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)

       \[_{4}^{11}Be\]

View Answer
47) 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

View Answer
48) 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)

       \[q\frac{{{z}_{2}}}{{{z}_{1}}}\]

View Answer
49) 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)

       \[1000\,\Omega \]

View Answer
50) 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)

\[R=\frac{{{R}_{1}}{{R}_{2}}}{({{R}_{2}}-{{R}_{1}})}\]

View Answer
51) 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)

       \[\sqrt{\frac{2ms\Delta T}{C}}\]

View Answer
52) 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)

       \[2\,BIl\]

View Answer
53) 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

View Answer
54) 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\[\frac{{{\mu }_{0}}{{i}^{2}}}{(2\pi {{d}^{2}})}\]

View Answer
55) 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)

       \[{{l}_{0}}\]

View Answer
56) 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)

       \[\tan \theta \]

View Answer
57) 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

View Answer
58) 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)

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

View Answer
59) 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)

       \[nC\]

View Answer
60) 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

View Answer
61) 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)

       \[2\pi \sqrt{\alpha }\]

View Answer
62) 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

View Answer
63) 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%

View Answer
64) 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)

       \[\frac{{{l}_{0}}}{2}\]

View Answer
65) 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)

       \[7\times {{10}^{-5}}\]

View Answer
66) 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

View Answer
67) 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)

       \[2\mu F\]

View Answer
68) 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

View Answer
69) 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

View Answer
70) 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

View Answer
71) 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

View Answer
72) 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)

       \[\frac{2\pi m}{qB}\]

View Answer
73) 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)

       \[2\,\Omega \]

View Answer
74) 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)

       \[200\,\Omega \]

View Answer
75) 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

View Answer
76) 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

View Answer
77) Which one of the following types of drugs reduces fever? AIEEE Solved Paper-2005

A)

Tranquiliser

B)

       Antibiotic

C)

       Antipyretic

D)

       Analgesic

View Answer
78) 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)

       \[CaO\]

View Answer
79) Which one of the following species is diamagnetic in nature? AIEEE Solved Paper-2005

A)

\[H_{2}^{-}\]

B)

       \[H_{2}^{+}\]

C)

       \[{{H}_{2}}\]

D)

       \[He_{2}^{+}\]

View Answer
80) 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)

       \[1+\alpha \]

View Answer
81) Which of the following is a polyamide? AIEEE Solved Paper-2005

A)

Bakelite

B)

Terylene

C)

       Nylon-66

D)

       Teflon

View Answer
82) 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

View Answer
83) 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

View Answer
84) Hydrogen bomb is based on the principle of AIEEE Solved Paper-2005

A)

artificial radioactivity

B)

nuclear fusion

C)

natural radioactivity

D)

nuclear fission

View Answer
85) 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)

       \[AB\]

View Answer
86) 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

View Answer
87) 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

View Answer
88) 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)

\[{{E}_{b}}<{{E}_{f}}\]

View Answer
89) 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

View Answer
90) 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)

       \[\frac{{{V}_{C}}}{{{V}_{S}}}\approx 1\]

View Answer
91) 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)

       \[\Delta H=0\]

View Answer
92) 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)

       \[2.0\times {{10}^{-6}}M\]

View Answer
93) 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

View Answer
94) 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)

The distribution becomes broader

C)

The fraction of the molecules with the most probable speed increases

D)

The most probable speed increases

View Answer
95) 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\[{{K}_{C}}\]

View Answer
96) 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

View Answer
97) 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)

       \[3.98\times {{10}^{8}}\]

View Answer
98) 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

View Answer
99) 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

View Answer
100) 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

View Answer
101)

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

View Answer
102) 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

View Answer
103) 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)

View Answer
104) 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)

       \[LiCl\]

View Answer
105) 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

View Answer
106) 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)

       \[Cu+S{{O}_{2}}\]

View Answer
107) 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

View Answer
108) 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

View Answer
109) 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

View Answer
110) What is the conjugate base of\[O{{H}^{-}}\]? AIEEE Solved Paper-2005

A)

\[{{O}^{2-}}\]

B)

       \[{{O}^{-}}\]

C)

       \[{{H}_{2}}O\]

D)

       \[{{O}_{2}}\]

View Answer
111) 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)

       \[AlC{{l}_{3}}\]

View Answer
112) 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)

\[HI>HBr>HCl>HF\]

View Answer
113) 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)

\[HgN{{H}_{2}}Cl\]

View Answer
114) 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

View Answer
115) 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

View Answer
116) 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

View Answer
117) 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

View Answer
118) 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)

View Answer
119) 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

View Answer
120) 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)

\[PO_{4}^{3-},SO_{4}^{2-},CIO_{4}^{-}\]

View Answer
121) 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

View Answer
122) 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)

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

View Answer
123) 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)

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

View Answer
124) 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

View Answer
125) 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

View Answer
126) 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

View Answer
127) 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)

View Answer
128) 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

View Answer
129) 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

View Answer
130) 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)

\[C{{H}_{3}}COOH\]

View Answer
131) 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

View Answer
132) Alkyi halides react with dialkyi copper reagents to give AIEEE Solved Paper-2005

A)

alkenyl halides

B)

alkanes

C)

alkyi copper halides

D)

alkenes

View Answer
133) 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

View Answer
134) Which types of isomerism is shown by 2, 3-dichlorobutane? AIEEE Solved Paper-2005

A)

Structural

B)

      Geometric

C)

       Optical

D)

       Diastereo

View Answer
135) Amongst the following the most basic compound is AIEEE Solved Paper-2005

A)

p-nitroaniline

B)

acetanilide

C)

aniline

D)

benzylamine

View Answer
136) 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

View Answer
137) Which of the following is fully fluorinated polymer? AIEEE Solved Paper-2005

A)

                                        PVC

B)

Thiokol

C)

Teflon

D)

       Neoprene

View Answer
138) 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

View Answer
139) 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

View Answer
140) 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)

       \[Cl\]

View Answer
141) 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

View Answer
142) 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

View Answer
143) 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

View Answer
144) 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)

View Answer
145) 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

View Answer
146) 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)

View Answer
147) 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

View Answer
148) 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

View Answer
149) 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)

       \[C{{H}_{3}}NCO\]

View Answer
150) \[{{t}_{1/4}}\]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

View Answer
151) 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

View Answer
152) 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)

       \[{{y}^{2}}-4x+2=0\]

View Answer
153) 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

View Answer
154) 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

View Answer
155) 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)

       \[A+l\]

View Answer
156) 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)

\[-1,-1+2\omega ,-1-2{{\omega }^{2}}\]

View Answer
157) \[\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{{{n}^{2}}}{{\sec }^{2}}\frac{1}{{{n}^{2}}}+\frac{2}{{{n}^{2}}}{{\sec }^{2}}\frac{4}{{{n}^{2}}} \right.\] \[\left. +....+\frac{n}{{{n}^{2}}}{{\sec }^{2}}1 \right]\] 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)

       \[\frac{1}{2}sec\text{ }1\]

View Answer
158) 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)

       \[2ab\]

View Answer
159) 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

View Answer
160) 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)

\[\sin A:\sin B:\sin C\]

View Answer
161) 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)

\[{{m}^{2}}-m(4r-1)+4{{r}^{2}}-2=0\]

View Answer
162) 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)

\[a=o+c,\]

View Answer
163) 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

View Answer
164) 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)

       \[^{55}{{C}_{4}}\]

View Answer
165) 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)

\[{{A}^{n}}=nA+(n-1)l\]

View Answer
166) 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)

       \[a-d=1\]

View Answer
167) 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)

       \[\left( 0,\frac{\pi }{2} \right)\]

View Answer
168) 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)

       \[\frac{\pi }{2}\]

View Answer
169) 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

View Answer
170) 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

View Answer
171) 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

View Answer
172) 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

View Answer
173) 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

View Answer
174) 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

View Answer
175) 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)

       \[f(6)\ge 8\]

View Answer
176) 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

View Answer
177) 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)

       \[1-\frac{3}{8}{{x}^{2}}\]

View Answer
178) 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

View Answer
179) 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)

       \[b+c\]

View Answer
180) 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)

       \[2\text{ }{{\sin }^{2}}\alpha \]

View Answer
181) 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

View Answer
182) 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

View Answer
183) 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)

\[(-\infty ,\infty )\]                          \[{{x}^{3}}-3{{x}^{2}}+3x+3\]

View Answer
184) 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)

       \[\frac{{{a}^{2}}}{2}{{(\alpha -\beta )}^{2}}\]

View Answer
185) 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)

\[y\log \left( \frac{x}{y} \right)=Cx\]

View Answer
186) 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

View Answer
187) 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)

\[\frac{1}{36\pi }cm/\min \]

View Answer
188) \[{{\int{\left\{ \frac{(\log x-1)}{1+{{(\log \,x)}^{2}}} \right\}}}^{2}}dx\]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)

\[\frac{\log \,\,x}{\,{{(\log x)}^{2}}+1}+C\]

View Answer
189) 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

View Answer
190) 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)

       \[\left( \frac{\pi }{4}+\sqrt{2}-1 \right)\]

View Answer
191) 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)

       \[{{l}_{2}}>{{l}_{1}}\]

View Answer
192) 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

View Answer
193) 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

View Answer
194) 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)

       \[-1\]

View Answer
195) 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)

\[\frac{10}{9}\]

View Answer
196) 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)

       \[3{{a}^{2}}\]

View Answer
197) 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)

       \[(-1,2)\]

View Answer
198) 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)

       \[\left( -1,\frac{7}{3} \right)\]

View Answer
199) 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

View Answer
200) 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

View Answer
201) 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)

\[{{x}^{2}}+{{y}^{2}}-3ax-4by+({{a}^{2}}+{{b}^{2}}-{{p}^{2}})=0\]

View Answer
202) 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)

       \[1/\sqrt{2}\]

View Answer
203) 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

View Answer
204) 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)

       \[\frac{5}{3}\]

View Answer
205) 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)

       \[0{}^\circ \]

View Answer
206) 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

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207) 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

View Answer
208) 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)

       \[\frac{2}{{{e}^{2}}}\]

View Answer
209) 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)

\[(f+f'){{m}^{2}}=ff'n\]

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210) 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

View Answer
211) 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)

       \[2:1\]

View Answer
212) 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

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213) 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

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214) 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\[\lambda \]

View Answer
215) 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)

       \[\frac{2H}{A-B}\]

View Answer
216) 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)

       \[\frac{e-1}{\sqrt{e}}\]

View Answer
217) 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

View Answer
218) 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)

       \[\frac{u}{3}\]

View Answer
219) 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]

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220) 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

View Answer
221) 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)

\[-f(x)\]

View Answer
222) 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 \[\alpha \]

View Answer
223) 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)

       \[a\pi \]

View Answer
224) 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

View Answer
225) 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)

\[3{{a}^{2}}-10ab+3{{b}^{2}}=0\]

View Answer