JEE MAIN - Physics (2006)

1
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
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(A)
$$4.58 \times {10^{ - 6}}\,J/{m^3}$$
2
The circuit has two oppositively connected ideal diodes in parallel. What is the current following in the circuit?

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(B)
$$2.00$$ $$A$$
3
In the following, which one of the diodes is reverse biased?
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(D)
4
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 $${\rm I}$$ of the photocell varies as follows
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(B)
5
If the lattice constant of this semiconductor is decreased, then which of the following is correct?
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(C)
$${E_c}$$ and $${E_v}$$ decrease, but $${E_g}$$ increases
6
An inductor $$(L=100$$ $$mH)$$, a resistor $$\left( {R = 100\,\Omega } \right)$$ and a battery $$\left( {E = 100V} \right)$$ 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
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(A)
$$1/eA$$
7
Needles $${N_1}$$, $${N_2}$$ and $${N_3}$$ are made of ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will
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(B)
attract $${N_1}$$ strongly, $${N_2}$$ weakly and repel $${N_3}$$ weakly
8
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
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(B)
straight line
9
A long solenoid has $$200$$ turns per $$cm$$ and carries a current $$i.$$ The magnetic field at its center is $$6.28 \times {10^{ - 2}}\,\,\,Weber/{m^2}.$$ Another long solenoid has $$100$$ turns per $$cm$$ and it carries a current $${i \over 3}$$. The value of the magnetic field at its center is
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(A)
$$1.05 \times {10^{ - 2}}\,\,Weber/{m^2}$$
10
Which of the following units denotes the dimension $${{M{L^2}} \over {{Q^2}}}$$, where $$Q$$ denotes the electric charge?
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(B)
Henry $$(H)$$
11
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
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(D)
$$N.A.B.$$$$\omega $$
12
In a series resonant $$LCR$$ circuit, the voltage across $$R$$ is $$100$$ volts and $$R = 1\,k\Omega $$ with $$C = 2\mu F.$$ The resonant frequency $$\omega $$ is $$200$$ $$rad/s$$. At resonance the voltage across $$L$$ is
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(C)
$$250$$ $$V$$
13
The flux linked with a coil at any instant $$'t'$$ is given by
$$\phi = 10{t^2} - 50t + 250$$
The induced $$emf$$ at $$t=3s$$ is
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(B)
$$-10$$ $$V$$
14
The refractive index of a glass is $$1.520$$ for red light and $$1.525$$ for blue 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,
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(A)
$${D_1} < {D_2}$$
15
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
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(A)
ultra-violet region
16
An alpha nucleus of energy $${1 \over 2}m{v^2}$$ bombards a heavy nuclear target of charge $$Ze$$. Then the distance of closest approach for the alpha nucleus will be proportional to
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(C)
$${1 \over {{v^2}}}$$
17
An alpha nucleus of energy $${1 \over 2}m{v^2}$$ bombards a heavy nuclear target of charge $$Ze$$. Then the distance of closest approach for the alpha nucleus will be proportional to
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(C)
$${1 \over {{v^2}}}$$
18
The time taken by a photoelectron to come out after the photon strikes is approximately
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(B)
$${10^{ - 10}}\,s$$
19
If the ratio of the concentration of electrons to that of holes in a semiconductor is $${7 \over 5}$$ and the ratio of currents is $${7 \over 4},$$ then what is the ratio of their drift velocities?
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(C)
$${5 \over 4}$$
20
When $${}_3L{i^7}$$ nuclei are bombarded by protons, and the resultant nuclei are $${}_4B{e^8}$$, the emitted particles will be
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(C)
gamma photons
21
If the binding energy per nucleon in $${}_3^7Li$$ and $${}_2^4He$$ nuclei are $$5.60$$ $$MeV$$ and $$7.06$$ $$MeV$$ respectively, then in the reaction $$$p + {}_3^7Li \to 2\,{}_2^4He$$$
energy of proton must be
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(B)
$$17.28$$ $$MeV$$
22
The resistance of bulb filmanet is $$100\Omega $$ at a temperature of $${100^ \circ }C.$$ If its temperature coefficient of resistance be $$0.005$$ per $$^ \circ C$$, its resistance will become $$200\,\Omega $$ at a temperature of
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(B)
$${400^ \circ }C$$
23
If the terminal speed of a sphere of gold (density $$ = 19.5\,\,kg/{m^3}$$) is $$0.2$$ $$m/s$$ in a viscous liquid (density $$ = 1.5\,\,kg/{m^3}$$, find the terminal speed of a sphere of silver (density $$ = 10.5\,\,kg/{m^3}$$) of the same size in the same liquid
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(C)
$$0.1$$ $$m/s$$
24
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 $$mm$$)
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(A)
$$l$$
25
The work of $$146$$ $$kJ$$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $${7^ \circ }C.$$ The gas is $$\left( {R = 8.3J\,\,mo{l^{ - 1}}\,{K^{ - 1}}} \right)$$
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(A)
diatomic
26
Where r₀ is the radius of the Earth and $$\sigma $$ is Stefan's constant.
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(B)
$$\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}$$
27
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 contains one mole of helium at temperature $$\left( {{7 \over 3}} \right){T_0}.$$ 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
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(C)
$${T_f} = {3 \over 2}{T_0}$$
28
A force of $$ - F\widehat k$$ acts on $$O,$$ the origin of the coordinate system. The torque about the point $$(1, -1)$$ is
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(C)
$$F\left( {\widehat i + \widehat j} \right)$$
29
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?
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(A)
$${1 \over 6}s$$
30
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
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(A)
$$0.01$$ $$s$$
31
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
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(A)
$$105$$ $$Hz$$
32
An electric dipole is placed at an angle of $${30^ \circ }$$ to a non-uniform electric field. The dipole will experience
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(C)
a torque as well as a translational force
33
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 then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $$A$$ and $$B$$ is
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(C)
$$2:1$$
34
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 $$d=0.1$$ $$m$$ 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 $$2$$?
$$\left( {e = 1.6 \times {{10}^{ - 19}}\,C,\,\,{m_e} = 9.11 \times {{10}^{ - 31}}\,kg} \right)$$
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(A)
$$2.65 \times {10^6}\,m/s$$
35
A thermocouple is made from 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
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(D)
flow from Antimony to Bismuth at the cold junction
36
An electric bulb is rated $$220$$ volt - $$100$$ watt. The power consumed by it when operated on $$110$$ volt will be
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(C)
$$25$$ Watt
37
In a Wheatstone's bridge, three resistance $$P, Q$$ and $$R$$ 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
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(B)
$${P \over Q} = {{R\left( {{S_1} + {S_2}} \right)} \over {{S_1}{S_2}}}$$
38
The current $${\rm I}$$ drawn from the $$5$$ volt source will be
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(B)
$$0.5$$ $$A$$
39
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 $$\omega ' = $$
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(D)
$${{\omega m} \over {\left( {m + 2M} \right)}}$$
40
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
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(A)
t²
41
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
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(D)
$$Mg\left( {\sqrt 2 - 1} \right)$$
42
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 upto $$2$$ $$m$$ height further, find the magnitude of the force. (consider $$g = 10\,m/{s^2}$$).
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(D)
$$22$$ $$N$$
43
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $$\omega .$$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
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(B)
for an amplitude of $${g \over {{\omega ^2}}}$$
44
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 $$0.1s,$$ the force of the blow exerted by the ball on the hand of the player is equal to
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(C)
$$30$$ $$N$$
45
A particle of mass $$100g$$ 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
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(B)
$$-1.25J$$
46
The total mechanical energy of the particle is $$2J.$$ Then, the maximum speed (in $$m/s$$) is
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(A)
$${3 \over {\sqrt 2 }}$$
47
A bomb of mass $$16kg$$ at rest explodes into two pieces of masses $$4$$ $$kg$$ and $$12$$ $$kg.$$ The velocity of the $$12$$ $$kg$$ mass is $$4\,\,m{s^{ - 1}}.$$ The kinetic energy of the other mass is
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(B)
$$288$$ $$J$$
48
Consider a two particle system with particles having masses $${m_1}$$ and $${m_2}$$. If the first particle is pushed towards the center of mass through a distance $$d,$$ by what distance should the second particle is moved, so as to keep the center of mass at the same position?
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(C)
$${{{m_1}} \over {{m_2}}}d$$
49
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 $$\omega ' = $$
Përgjigju
(D)
$${{\omega m} \over {\left( {m + 2M} \right)}}$$