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

AIEEE Solved Paper-2005 Total Questions - 75

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

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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

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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

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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)

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

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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)

       \[2\,\Omega \]

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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)

       \[200\,\Omega \]

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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

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