Solved papers for JEE Main & Advanced AIEEE Solved Paper-2006

AIEEE Solved Paper-2006 Total Questions - 55

1) The Kirchhoff's first law\[(\Sigma i=0)\]and second law\[(\Sigma iR=\Sigma E)\], where the symbols have their usual meanings, are respectively based on AIEEE Solved Paper-2006

A)

Conservation of charge, conservation of momentum

B)

Conservation of energy, conservation of charge

C)

Conservation of momentum, conservation of charge

D)

Conservation of charge, conservation of energy

View Answer
2) Needles\[{{N}_{1}},{{N}_{2}}\]and\[{{N}_{3}}\]are made of a ferromagnetic, a paramagnetic and a diamagnetic substance, respectively. A magnet when brought close to them will AIEEE Solved Paper-2006

A)

Attract\[{{N}_{1}}\]and\[{{N}_{2}}\]strongly but repel\[{{N}_{3}}\]

B)

Attract\[{{N}_{1}}\]strongly, \[{{N}_{2}}\]weakly and repel\[{{N}_{3}}\] weakly

C)

Attract\[{{N}_{1}}\]strongly, but repel\[{{N}_{2}}\]and\[{{N}_{3}}\]weakly

D)

attract all three of them

View Answer
3) A material B has twice the specific resistance of A. A circular wire made of B has twice the diameter of a wire made of Then, for the two wires to have the same resistance, the ratio \[{{l}_{B}}/{{l}_{A}}\] respective lengths must be AIEEE Solved Paper-2006

A)

1

B)

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

C)

       \[\frac{1}{4}\]

D)

       2

View Answer
4) In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a AIEEE Solved Paper-2006

A)

helix

B)

       straight line

C)

ellipse

D)

       circle

View Answer
5) An electric dipole is placed at an angle of \[30{}^\circ \]to a non-uniform electric field. The dipole will experience AIEEE Solved Paper-2006

A)

a translational force only in the direction of the field

B)

a translational force only in a direction normal to the direction of the field

C)

a torque as well as a translational force

D)

a torque only

View Answer
6) A particle located at\[x=0\]at time\[t=0\], starts moving along the positive x-direction with a velocity v that varies as \[v=\alpha \sqrt{x}\]. The displacement of the particle varies with time as AIEEE Solved Paper-2006

A)

\[{{t}^{2}}\]

B)

                       \[t\]

C)

       \[{{t}^{1/2}}\]

D)

       \[{{t}^{3}}\]

View Answer
7) A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is\[4\text{ }m{{s}^{-1}}\]. The kinetic energy of the other mass is AIEEE Solved Paper-2006

A)

144 J

B)

                       288 J

C)

       192 J

D)

       96 J

View Answer
8) A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed\[v\text{ }m{{s}^{-1}}\]. The velocity of sound in air is \[300\,m{{s}^{-1}}\]. If the person can hear frequencies up to a maximum of 10000 Hz, the maximum value of v up to which he can hear the whistle is AIEEE Solved Paper-2006

A)

\[15\sqrt{2}m{{s}^{-1}}\]

B)

       \[15/\sqrt{2}m{{s}^{-1}}\]

C)

       \[15m{{s}^{-1}}\]

D)

       \[30\,m{{s}^{-1}}\]

View Answer
9) A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of \[45{}^\circ \]with the initial vertical direction is AIEEE Solved Paper-2006

A)

\[Mg(\sqrt{2}+1)\]

B)

\[Mg\sqrt{2}\]

C)

       \[\frac{Mg}{\sqrt{2}}\]

D)

       \[Mg(\sqrt{2}-1)\]

View Answer
10) A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time the particle goes up is AIEEE Solved Paper-2006

A)

\[-0.5J\]

B)

       \[-1.25\,J\]

C)

       1.25 J

D)

       0.5 J

View Answer
11) The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is AIEEE Solved Paper-2006

A)

0.01s

B)

       10s

C)

       0.1s

D)

       100s

View Answer
12) Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy? AIEEE Solved Paper-2006

A)

\[\frac{1}{6}s\]

B)

                       \[\frac{1}{4}s\]

C)

       \[\frac{1}{3}s\]

D)

       \[\frac{1}{12}s\]

View Answer
13) Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on earth, at a distance r from the sun.

A)

\[4\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}\]

B)

\[\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}\]

C)

       \[r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/4\pi {{r}^{2}}\]

D)

     \[{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}\] where, \[{{r}_{0}}\] is the radius of the earth and a is Stefan's constant.

View Answer
14) Which of the following units denote the dimensions\[[M{{L}^{2}}/{{Q}^{2}}],\]where 0 denotes the electric charge? AIEEE Solved Paper-2006

A)

\[Wb/{{m}^{2}}\]

B)

       henry (H)

C)

       \[H/{{m}^{2}}\]

D)

       Weber (Wb)

View Answer
15) A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes up to 2 m height further, find the magnitude of the force. Consider\[g=10\text{ }m/{{s}^{2}}\]. AIEEE Solved Paper-2006

A)

4N

B)

                       16N

C)

       20N

D)

       22N

View Answer
16) A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is AIEEE Solved Paper-2006

A)

105 Hz

B)

     1.05 Hz

C)

       1050 Hz

D)

       10.5 Hz

View Answer
17) Consider a two particle system with particles having masses\[{{m}_{1}}\]and\[{{m}_{2}}\]. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position? AIEEE Solved Paper-2006

A)

\[\frac{{{m}_{2}}}{{{m}_{1}}}d\]

B)

                       \[\frac{{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}d\]

C)

       \[\frac{{{m}_{1}}}{{{m}_{2}}}d\]

D)

       \[d\]

View Answer
18) A player caught a cricket ball of mass 150 g moving at a rate of 20 m/s. If the catching process is completed in 0.1 s, the force of the blow exerted by the ball on the hand of the player is equal to AIEEE Solved Paper-2006

A)

150N

B)

3N

C)

30N

D)

       300N

View Answer
19) In a common-base mode of a transistor, the collector current is 5.488 mA for an emitter current of 5.60 mA. The value of the base current amplification factor (P) will be AIEEE Solved Paper-2006

A)

49

B)

                       50

C)

       51

D)

       48

View Answer
20) A thermocouple is made of two metals, Antimony and Bismuth. If one junction of the couple is kept hot and the other is kept cold, then an electric current will AIEEE Solved Paper-2006

A)

flow from Antimony to Bismuth at the hot junction

B)

flow from Bismuth to Antimony at the cold junction

C)

not flow through the thermocouple

D)

flow from Antimony to Bismuth at the cold junction

View Answer
21) The threshold frequency for a metallic surface corresponds to an energy of 6.2 eV and the stopping potential for a radiation incident on this surface is 5V. The incident radiation lies in AIEEE Solved Paper-2006

A)

ultraviolet region

B)

infrared region

C)

visible region

D)

X-ray region

View Answer
22) An alpha nucleus of energy \[\frac{1}{2}m{{v}^{2}}\]bombards a heavy nuclear target of charge \[Ze\]. Then, the distance of closest approach for the alpha nucleus will be proportional to AIEEE Solved Paper-2006

A)

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

B)

       \[1/m\]

C)

       \[1/{{v}^{4}}\]

D)

       \[1/Ze\]

View Answer
23) The time taken by a photoelectron to come out after the photon strikes is approximately AIEEE Solved Paper-2006

A)

\[{{10}^{-4}}s\]

B)

                       \[{{10}^{-10}}s\]

C)

       \[{{10}^{-16}}s\]

D)

       \[{{10}^{-1}}s\]

View Answer
24) When\[_{3}L{{i}^{7}}\]nuclei are bombarded by protons and the resultant nuclei are\[_{4}B{{e}^{8}},\] the emitted particles will be AIEEE Solved Paper-2006

A)

alpha particles

B)

      beta particles

C)

                       gamma photons

D)

       neutrons

View Answer
25) The current I drawn from the 5 V source will be AIEEE Solved Paper-2006

A)

0.33 A

B)

                       0.5 A

C)

       0.67 A

D)

0.17 A

View Answer
26) The energy spectrum of \[\beta \]-particles [number N(E) as a function of \[\beta \]-energy E] emitted from a radioactive source is AIEEE Solved Paper-2006

A)



B)

C)



D)



View Answer
27) In a series resonant LCR circuit, .the voltage across R is 100 V and\[R=1k\,\Omega \]. With\[C=2\mu F\]. The resonant frequency\[\omega \] is 200 rad/s. At resonance, the voltage across L is AIEEE Solved Paper-2006

A)

\[2.5\times {{10}^{-2}}V\]

B)

\[40\,V\]

C)

       \[250\,V\]

D)

       \[4\times {{10}^{-3}}\,V\]

View Answer
28) The resistance of a bulb filament is\[100\text{ }\Omega \].at a temperature of\[100{}^\circ C\]. If its temperature coefficient of resistance is\[0.005/{}^\circ C,\]its resistance will become\[200\,\Omega \]. at a temperature of AIEEE Solved Paper-2006

A)

\[300{}^\circ C\]

B)

       \[400{}^\circ C\]

C)

       \[500{}^\circ C\]

D)

       \[200{}^\circ C\]

View Answer
29) Two insulating plates are both uniformly charged in such a way that the potential difference between them is\[{{V}_{2}}-{{V}_{1}}=20\,V\] (i.e., plate 2 is at a higher potential). The plates are separated by\[d=0.1\text{ }m\]and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2? \[(e=1.6\times {{10}^{-19}}C,{{m}_{0}}=9.11\times {{10}^{-31}}kg)\] AIEEE Solved Paper-2006

A)

\[2.65\times {{10}^{6}}\text{ }m/s\]

B)

       \[7.02\times {{10}^{12}}\text{ }m/s\]

C)

\[1.87\times {{10}^{6}}m/s\]

D)

\[32\times {{10}^{-19}}m/s\]

View Answer
30) In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency \[\omega \] in a magnetic field B. The maximum value of emf generated in the coil is AIEEE Solved Paper-2006

A)

\[NABR\,\omega \]

B)

       \[NAB\]

C)

       \[NABR\]

D)

       \[NAB\,\omega \]

View Answer
31) A solid which is not transparent to visible light and whose conductivity increases with temperature is formed by AIEEE Solved Paper-2006

A)

ionic bonding

B)

covalent bonding

C)

van der Waals' bonding

D)

metallic bonding

View Answer
32) The refractive index of glass is 1.520 for red light and 1.525 for bin l light. Let\[{{D}_{1}}\]and\[{{D}_{2}}\]be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then, AIEEE Solved Paper-2006

A)

\[{{D}_{1}}<{{D}_{2}}\]

B)

\[{{D}_{1}}={{D}_{2}}\]

C)

\[{{D}_{1}}\]can be less than or greater than\[{{D}_{2}}\] depending upon. The angle of prism

D)

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

View Answer
33) If the ratio of the concentration of electrons to that of holes in a semiconductor is\[\frac{7}{5}\]and the ratio of currents is \[\frac{7}{4}\], then what is the ratio of their drift velocities? AIEEE Solved Paper-2006

A)

\[\frac{5}{8}\]

B)

       \[\frac{4}{5}\]

C)

       \[\frac{5}{4}\]

D)

       \[\frac{4}{7}\]

View Answer
34) In a Wheatstone?s bridge, three resistances P, Q and R are connected in the three arms and the fourth arm is formed by two resistances\[{{S}_{1}}\]and\[{{S}_{2}}\]connected in parallel. The condition for the bridge to be balanced will be AIEEE Solved Paper-2006

A)

\[\frac{P}{Q}=\frac{2R}{{{S}_{1}}+{{S}_{2}}}\]

B)

\[\frac{P}{Q}=\frac{R({{S}_{1}}+{{S}_{2}})}{{{S}_{1}}{{S}_{2}}}\]

C)

       \[\frac{P}{Q}=\frac{R({{S}_{1}}+{{S}_{2}})}{2{{S}_{1}}{{S}_{2}}}\]

D)

       \[\frac{P}{Q}=\frac{R}{{{S}_{1}}+{{S}_{2}}}\]

View Answer
35) The flux linked with a coil at any instant t is given by \[\phi =10{{t}^{2}}-50t+250\] The induced emf at\[t=3\text{ }s\]is AIEEE Solved Paper-2006

A)

\[-190V\]

B)

     \[-10V\]

C)

       \[10V\]

D)

       \[190V\]

View Answer
36) A long solenoid has 200 turns/cm and carries a current i. The magnetic field at its centre is \[6.28\,\times {{10}^{-2}}\,Wb/{{m}^{2}}\]. Another long solenoid has 100 turns/cm and it carries a current\[i/3\]. The value of the magnetic field at its centre is AIEEE Solved Paper-2006

A)

\[1.05\times {{10}^{-2}}Wb/{{m}^{2}}\]

B)

\[1.05\times {{10}^{-5}}Wb/{{m}^{2}}\]

C)

\[1.05\times {{10}^{-3}}Wb/{{m}^{2}}\]

D)

\[1.05\times {{10}^{-4}}Wb/{{m}^{2}}\]

View Answer
37) The circuit has two oppositely connected ideal diodes in parallel. What is the current flowing in the circuit? AIEEE Solved Paper-2006

A)

1.71 A

B)

       2.00 A

C)

       2.31 A

D)

       1.33A

View Answer
38) In the following, which one of the diodes is reverse biased? AIEEE Solved Paper-2006

A)

B)

C)

D)

View Answer
39) The anode voltage of a photocell is kept fixed. The wavelength \[\lambda \] of the light falling   on the cathode is gradually changed. The plate current I of the photocell varies as follows AIEEE Solved Paper-2006

A)

B)



C)



D)



View Answer
40) If the binding energy per nucleon in\[_{3}^{7}Li\]and\[_{2}^{4}He\]nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction \[P+_{3}^{7}Li\to 2_{2}^{4}He\] energy of proton must be AIEEE Solved Paper-2006

A)

28.24 MeV

B)

       17.28 MeV

C)

       1.46 MeV

D)

39.2 MeV

View Answer
41) An electric bulb is rated\[220\text{ }V-100\text{ }W\]The power consumed by it when operated on 110 V will be AIEEE Solved Paper-2006

A)

75 W

B)

40 W

C)

       25 W

D)

       50 W

View Answer
42) The 'rad' is the correct unit used to report the measurement of AIEEE Solved Paper-2006

A)

the ability of a beam of gamma ray photons to produce ions in a target

B)

the energy delivered by radiation to a target

C)

the biological effect of radiation

D)

the rate of decay of a radioactive source

View Answer
43) A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency\[\omega \]. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time AIEEE Solved Paper-2006

A)

at the mean position of the platform

B)

for an amplitude of \[g/{{\omega }^{2}}\]

C)

for an amplitude of\[{{g}^{2}}/{{\omega }^{2}}\]

D)

at the highest position of the platform

View Answer
44) Four point masses, each of value m, are placed at the corners of a square ABCD of side \[l\]. The moment of inertia of this system about an axis passing through A and parallel to BD is AIEEE Solved Paper-2006

A)

\[2m{{l}^{2}}\]

B)

\[\sqrt{3}\,m{{l}^{2}}\]

C)

                       \[3\,m{{l}^{2}}\]

D)

       \[\,m{{l}^{2}}\]

View Answer
45) A force of \[-F\hat{k}\] acts on O, the origin of the coordinate system. The torque about the point \[(1,-1)\]is AIEEE Solved Paper-2006

A)

\[F(\hat{i}-\hat{j})\]

B)

       \[-F(\hat{i}+\hat{j})\]

C)

       \[F(\hat{i}+\hat{j})\]

D)

       \[-F(\hat{i}-\hat{j})\]

View Answer
46) The potential energy of a 1 kg particle free to move along the x-axis is given by \[V(x)=\left( \frac{{{x}^{4}}}{4}-\frac{{{x}^{2}}}{2} \right)J\] The total mechanical energy of the particle is 2 J. Then, the maximum speed (in m/s) is AIEEE Solved Paper-2006

A)

\[3/\sqrt{2}\]

B)

       \[\sqrt{2}\]

C)

       \[1/\sqrt{2}\]

D)

       2

View Answer
47) A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity\[\omega \]. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity\[\omega '\]is equal to AIEEE Solved Paper-2006

A)

\[\frac{\omega (m+2M)}{m}\]

B)

       \[\frac{\omega (m-2M)}{(m-2M)}\]

C)

\[\frac{\omega m}{(m+M)}\]

D)

       \[\frac{\omega m}{(m+2M)}\]

View Answer
48) A wire elongates by\[l\,mm\] when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm) AIEEE Solved Paper-2006

A)

\[l\]

B)

       \[2l\]

C)

zero

D)

       \[l/2\]

View Answer
49) An inductor\[(L=100mH)\], a resistor\[(R=100\,\Omega )\] and a battery\[(E=100\,V)\]are initially connected in series as shown in the figure. After a long time, the battery is disconnected after short circuiting the points A and B. The current in the circuit 1 ms after the short circuit is AIEEE Solved Paper-2006

A)

\[1/e\,A\]

B)

\[e\text{ }A\]

C)

                       \[0.1A\]

D)

       \[1\,A\]

View Answer
50) Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire, the in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B is AIEEE Solved Paper-2006

A)

4 : 1

B)

                     1 : 2

C)

       2 : 1

D)

       1 : 4

View Answer
51) Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature \[{{T}_{0}},\] while box B contains one mole of helium at temperature (7/3)\[{{T}_{0}}\]. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases,\[{{T}_{f}}\]in terms of\[{{T}_{0}}\]is AIEEE Solved Paper-2006

A)

\[{{T}_{f}}=\frac{3}{7}{{T}_{0}}\]

B)

\[{{T}_{f}}=\frac{7}{3}{{T}_{0}}\]

C)

       \[{{T}_{f}}=\frac{3}{2}{{T}_{0}}\]

D)

       \[{{T}_{f}}=\frac{5}{2}{{T}_{0}}\]

View Answer
52) The work of 146 kJ is performed in order to compress one kilo mole of a gas adiabatically and in this process, the temperature of the gas increases by\[7{}^\circ C\]. The gas is \[(R=8.3\,J\,mo{{l}^{-1}}{{K}^{-1}})\] AIEEE Solved Paper-2006

A)

diatomic

B)

triatomic

C)

a mixture of monatomic and diatomic

D)

monatomic

View Answer
53) If the lattice constant of this semiconductor is decreased, then which of the following is correct? AIEEE Solved Paper-2006

A)

All \[{{E}_{c}},{{E}_{g}},{{E}_{v}}\] increase

B)

\[{{E}_{c}}\]and\[rms\]increase, but\[{{E}_{g}}\]decreases

C)

\[{{E}_{c}}\]and \[{{E}_{v}}\]decrease, but\[{{E}_{g}}\]increases

D)

All \[{{E}_{c}},\,{{E}_{g}},\,{{E}_{v}}\] decrease

View Answer
54) The \[rms\] value of the electric field of the light coming from the sun is 720 N/C. The average total energy density of the electromagnetic wave is AIEEE Solved Paper-2006

A)

\[4.58\times {{10}^{-6}}J/{{m}^{3}}\]

B)

       \[6.37\times {{10}^{-9}}J/{{m}^{3}}\]

C)

       \[81.35\times {{10}^{-12}}J/{{m}^{3}}\]

D)

\[3.3\times {{10}^{-3}}J/{{m}^{3}}\]

View Answer
55) If the terminal speed of a sphere of gold (density\[=19.5\text{ }kg/{{m}^{3}}\]) is 0.2 m/s in a viscous liquid (density\[=1.5\text{ }kg/{{m}^{3}}\]), find the terminal speed of a sphere of silver (density =10.5\[kg/{{m}^{3}}\]) of the same size in the same liquid. AIEEE Solved Paper-2006

A)

0.4 m/s

B)

      0.133 m/s

C)

       0.1 m/s

D)

       0.2 m/s

View Answer