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IIT-JEE 2011
PAPER - 1
PART-I PHYSICS
1.
2.
3.
4.
The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å.
The wavelength of the second spectral line in the Balmer series of singly-ionized helium
atom is
(A)
1215 Å
(B)
1640 Å
(C)
2430 Å
(D)
4687 Å
A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball
is rotated on a horizontal circular path about vertical axis. The maximum tension that the
string can bear is 324 N. The maximum possible value of angular velocity of ball (in
radian/s) is
(A)
9
(B)
18
(C)
27
(D)
36
A meter bridge is set-up as shown, to determine an unknown resistance X using a
standard 10 ohm resistor. The galvanometer shows null point when tapping key is at 52 cm
mark. The end corrections are 1 cm and 2 cm respectively for the ends A and B. The
determined value of X is
(A)
10.2 ohm
(B)
10.6 ohm
(C)
10.8 ohm
(D)
11.1 ohm
A 2 F capacitor is charged as shown in the figure. The percentage of its stored energy
dissipated after the switch S is turned to position 2 is
(A)
0%
(B)
20%
(C)
IIT-PAPER –2011
75%
(D)
80%
1
5.
6.
A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr
towards a tall building which reflects the sound waves. The speed of sound in air is 320
m/s. The frequency of the siren heard by the car driver is
(A)
8.50 kHz
(B)
8.25 kHz
(C)
7.75 kHz
(D)
7.50 kHz
5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial
temperature to be T1, the work done in the process is
(A)
7.
9
8
Consider an electric field
area (as shown in
(A)
8.
9.
(B)
RT1
2E0 a
3
2
(C)
RT1
E = E0 xˆ Where
15
8
RT1
(D)
9
2
RT1
is E0 is a constant. The flux through the shaded
the figure) due to this field is
2
(B)
2E a
0
2
(C)
E0 a
2
(D)
E0 a
2
2
SECTION - II (Total Marks : 16)
(Multiple Correct Answer Type)
This section contains 4 multiple choice questions. Each question has four choices (A),
(B), (C) and (D) out of which
ONE OR MORE may be correct.
A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and
radius 'R' (< L) is attached at its center to the free end of the rod. Consider two ways the
disc is attached. ((case A): The disc is not free to rotate about its center and (case B) the
disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane
after being released from the same displaced position. Which of the following statement(s)
is (are) true?
(A)
Restoring torque in case A = Restoring torque in case B
(B)
Restoring torque in case A < Restoring torque in case B
(C)
Angular frequency for case A > Angular frequency for case B
(D)
Angular frequency for case A < Angular frequency for case B
A composite block is made of slabs A, B, C, D and E of different thermal conductivities
(given in terms of a constant K) and sizes (given in terms of length, L) as shown in the
figure. All slabs are of same width. Heat 'Q'
flows only from left to right through the blocks. Then in steady state :
(A)
(B)
Heat flow through A and E slabs are same
Heat flow through slab E is maximum
IIT-PAPER –2011
2
10.
11.
(C)
Temperature difference across slab E is smallest
(D)
Heat flow through C = heat flow through B + heat flow through D
An electron and a proton are moving on straight parallel paths with same velocity. They
enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of
the following statement(s) is/are true?
(A)
They will never come out of the magnetic field region
(B)
They will come out travelling along parallel paths
(C)
They will come out at the same time
(D)
They will come out at different times
A spherical metal shell A of radius RA and a solid metal sphere B of radius RB(< RA) are
kept far apart and each is given charge '+Q'. Now they are connected by a thin metal
wire. Then
inside
EA
=0
Q A > QB
(A)
(B)
(C)
A
B

R
B
R
onsurface
onsurface
EB
E
B
(D)
A
SECTION - III (Total Marks : 15)
(Paragraph Type)
This section contains 2 paragraphs. Based upon one of the paragraph 2 multiple choice
questions and based on the other paragraph 3 multiple choice questions have to be
answered. Each of these questions has four choices (A), (B), (C) and (D) out of which
ONLY ONE is correct.
Paragraph for Questions Nos. 12 and 13
A dense collection of equal number of electrons and positive ions is called neutral plasma.
Certain solids containing fixed positive ions surrounded by free electrons can be treated as
neutral plasma. Let ‘N’ be the number density of free electrons, each of mass ‘m’. When the
electrons are subjected to an electric field, they are displaced relatively away from the
heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about
the positive
ions with a natural angular frequency ‘p’, which is called the plasma frequency. To sustain
the oscillations, a time varying electric field needs to be applied that has an angular
frequency , where a part of the energy is absorbed and
a part of it is reflected. As approaches p, all the free electrons are set to resonance
together and all the energy is reflected. This is the explanation of high reflectivity of metals.
12
Taking the electronic charge as ‘e’ and the permittivity as ‘0’, use dimensional analysis to
determine the correct expression for p
(A)
13.
Ne
mε 0
(B)
mε 0
Ne
(C)
Ne
2
mε 0
(D)
mε 0
Ne
2
Estimate the wavelength at which plasma reflection will occur for a metal having the density
of electrons N = 4 × 1027 m-3. Take 0 10-11 and m = 10-30, where these quantities are in
proper SI units
(A)
800 nm
(B)
600 nm
(C)
300 nm
(D)
200 nm
IIT-PAPER –2011
3
Paragraph for Questions Nos. 14 and 16
Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They
are especially useful in studying the changes in motion as initial position and momentum
are changed. Here we consider some simple dynamical systems in one-dimension. For
such systems, phase space is a plane in which position is plotted along horizontal axis and
momentum is plotted along vertical axis. The phase space diagram is x(t) vs. p(t) curve in
this plane. The arrow on the curve indicates the time flow. For example, the phase space
diagram for a particle moving with constant velocity is a straight line as shown in the figure.
We use the sign convention in which position or momentum upwards (or to right) is positive
and downwards (or to left) is negative.
14.
The phase space diagram for a ball thrown vertically up from ground is
15.
The phase space diagram for simple harmonic motion is a circle centered at the origin. In
the figure, the two circles represent the same oscillator but for different initial conditions,
and E1 and E2 are the total mechanical energies respectively. Then
(A)
16.
E1 = 2E 2
(B)
E1 = E 2
(C)
E1 = 4E2
(D)
E1 = 16E 2
Consider the spring-mass system, with the mass submerged in water, as shown in the
figure. The phase space diagram for one cycle of this system is
IIT-PAPER –2011
4
SECTION - IV (Total Marks : 28)
(Integer Answer Type)
This section contains 7 questions. The answer to each question is a Single-digit integer,
ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in
the ORS.
17.
18.
19.
20.
Steel wire of length 'L' at 40°C is suspended from the ceiling and then a mass 'm' is hung
from its free end. The wire is cooled down from 40°C to 30°C to regain its original length 'L'.
The coefficient of linear thermal expansion of the steel is 10 –5/°C, Young's modulus of steel
is 1011 N/m2 and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then
the value of 'm; in kg is nearly.
[Ans.3]
The activity of a freshly prepared radioactive sample is 10 10 disintegrations per second,
whose mean life is 109s. The mass of an atom of this radioisotope is 10–25 kg. The mass (in
mg) of the radioactive sample is
[Ans.1]
A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure.
The stick applies a force of 2N on the ring and rolls it without sliping with an acceleraton of
0.3 m/s2. The coefficient of friction between the ground and the ring is large enough that
rolling always occurs and the coefficient of friction between the stick and the ring is (P/10).
The value of P is
[Ans. 4]
A block is moving on an inclined plane making an angle 45 with the horizotnal and the
coefficient of friction is . The force required to just it up the inclined plane is 3 times the
force required to just prevent it from sliding down. If we define N = 10 , then N is [Ans. 5]
IIT-PAPER –2011
5
21.
Four point charges, each of +q, are rigidly fixex at the four corners of a square planar soad
film of side ‘a’. The surface tension of the soap film is . The system of charges and planar
1/N
 2

  
film are in equilibrium, and a = k  q
where ‘k’ is a constant. Then N is
[Ans. 3]
22.
A long circular tube of length 10 m and raidus 0.3 m carries a current I along its curved
surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside
the tube with tis axis coinciding with the axis of the tube. The current varies as I = I0 cos
(300 t) where I0 is constant. If the magnetic moment of the loop is N 0 I0 sin (300 t), then ‘N’
is
[Ans. 6]
23.
Four solid spheres each of diameter 5 and mass 0.5 kg are placed with their centers at the
corners of a square of side 4 cm. The moment of inertia of the system about the diagonal of
the square is N 10-4 kg-m2, then N is
[Ans. 9]
1.
6.
11.
16.
(a)
(a)
(a,b,c,d)
(b)
2.
7.
12.
ANSWER-SHEET
IIT- JEE-2011
PAPER - 1
(d)
3.
(b)
(c)
8.
(a,d)
(c)
13.
(b)
IIT-PAPER –2011
4.
9.
14.
(d)
(a,c,d)
(d)
5.
10.
15.
(a)
(b,d)
(c)
6
PART II : PHYSCIS
SECTION – I (Total Marks : 24)
(Single Correct Answer Type)
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.
1.
Which of the field patterns given below is valid for electric field as well as for magnetic field?
2.
3.
4.
(a)
(b)
(c)
(d)
A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a
velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and
bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance
of 100 m from the foot of the post. The velocity V of the bullet is
250 2 m / s
(a)
250 m/s
(b)
(c)
400 m/s
(d)
500 m/s
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured
with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The
reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured
mass of the ball has a relative error of 2 %, the relative percentage error in the density is
(a)
0.9 %
(b)
2.4 %
(c)
3.1 %
(d)
4.2 %
A wooden block performs SHM on a frictionless surface with frequency, 0. The block carries a
charge +Q on its surface. If now a uniform electric field E is switched-on as shown, then the SHM of
the block will be
(a)
of the same frequency and with shifted mean position.
IIT-PAPER –2011
7
5.
6.
of the same frequency and with the same mean position
(c)
of changed frequency and with shifted mean position.
(d)
of changed frequency and with the same mean position.
A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence .
The reflected (R) and transmitted (T) intensities, both as function of , are plotted. The correct sketch
is
(a)
(b)
(c)
(d)
A satellite is moving with a constant speed ‘v’ in a circular orbit about the earth. An object of mass
‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At
the time of its ejection, the kinetic energy of the object is
[ANS. B]
(A)
7.
(b)
1
2
mV
2
(B)
mV
2
(C)
3
2
mV
2
(D)
2mV
2
A long insulated copper wire is closely wound as a spiral of ‘N’ turns. The spiral has inner radius ‘a’
and outer radius ‘b’. The spiral lies in the XY plane and a steady current ‘I’ flows through the wire.
The Z-component of the magnetic field at the centre of the spiral is
(a)
(c)
 0 NI
b
a
In  
2(b-a)
 0 NI
b
In  
2b
a
(b)
(d)
 0 NI
2(b-a)
 0 NI
2b
IIT-PAPER –2011
 b+a 

 b-a 
In 
 b+a 

 b-a 
In 
8
8.
A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x1(t) = A sin
t and x2(t) =  t+ 2  . Adding a third sinusoidal displacement x3(t) = B sin (t + ) brings the mass

3 
to a complete rest. The values of B and are
(a)
2A,
3
4
(b)
A,
(c)
3A,
5
6
(d)
A,
4
3

3
SECTION – II (Total Marks : 16)
(Multiple Correct Answer(s) Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and
(D) out of which ONE OR MORE may be correct.
9.
10.
11.
Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a
string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state
as shown in the figure with a tension in the string. The arrangement is possible only if
(a)
dA < dF
(b)
dB > dF
(c)
dA > dF
(d)
dA + dB = 2dF
A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity
1m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring
at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
1 m/s
(a)
the ring has pure rotation about its stationary CM.
(b)
the ring comes to a complete stop.
(c)
friction between the ring and the ground is to the left.
(d)
there is no friction between the ring and the ground
Which of the following statement(s) is/are correct?
(a)
If the electric field due to a point charge varies as r2.5 instead of r2, then the Gauss
law will still be valid.
(b)
The Gauss law can be used to calculate the field distribution around an electric dipole
(c)
If the electric field between two point charges is zero somewhere, then the sign of the
two charges is the same.
IIT-PAPER –2011
9
(d)
12.
A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a
dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the
resistor and voltage VC across the capacitor are compared in the two cases. Which of the following
is/are true?
(a)
1.
6.
11.
13.
The work done by the external force in moving a unit positive charge from point A at
potential VA to point B at potential VB is (VB VA).
I RA  I BR
(c)
(b)
(c)
(b)
2.
7.
12.
I RA  I BR
(c)
ANSWER-SHEET
IIT- JEE-2011
PAPER - 2
(d)
3.
(c)
(a)
8.
(b)
(bc)
VCA > ICB
4.
9.
(d)
VCA  ICB
(a)
(a,b,d)
5.
10.
(c)
(c)
A series R-C combination is connected to an AC voltage of angular frequency = 500 radian/s. If
the impedance of the R-C circuit is R 1.25 , the time constant (in millisecond) of the circuit is
[Ans. 4 ms]
14.
A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in
free space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are
emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons
emitted from the sphere is A 10z (where 1 < A < 10). The value of ‘Z’ is
[Ans. 7]
15.
A train is moving along a straight line with a constant acceleration ‘a’. A boy standing in the train
throws a ball forward with a speed of 10 m/s, at an angle of 60to the horizontal. The boy has to
move forward by 1.15 m inside the train to catch the ball back at the initial height. The acceleration
of the train, in m/s2, is
[Ans. 5]
16.
A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction
between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An
impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes
to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is
[Ans. 4]
17.
Two batteries of different emfs and different internal resistances are connected as shown. The
voltage across AB in volts is
[Ans. 5]
18.
Water (with refractive index =
4
7
) in a tank is 18 cm deep. Oil of refractive index = lies on water
3
4
making a convex surface of radius of curvature ‘R = 6 cm’ as shown. Consider oil to act as a thin
lens. An object ‘S’ is placed 24 cm above water surface. The location of its image is at ‘x’ cm above
the bottom of the tank. Then ‘x’ is
[Ans. 2]
IIT-PAPER –2011
10
SECTION-IV (Total Marks : 16)
(Matrix-Match Type)
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five
statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or
MORE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements
given q and r, then for the particular question, against statement B, darken the bubbles corresponding to q and r in the
ORS.
19.
One mole of a monatomic gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II give the
characteristics involved in the cycle. Match them with each of the processes given in Column I.
Column I
20.
Column II
(a)
Process A B
(p)
Internal energy decreases
(b)
Process B C
(q)
Internal energy increases.
(c)
Process C D
(r)
Heat is lost
(d)
Process D A
(s)
Heat is gained
(t)
Work is done on the gas
Column I shows four systems, each of the same length L, for producing standing waves. The lowest
possible natural frequency of a system is called its fundamental frequency, whose wavelength is
denoted as f. Match each system with statements given in Column II describing the nature and
wavelength of the standing waves.
Column I
Column II
(a)
Pipe closed at one end
(p)
Longitudinal waves
(b)
Pipe open at both ends
(q)
Transverse waves
(c)
Stretched wire clamped (r)
at both ends
IIT-PAPER –2011
f= L
11

Stretched wire clamped (s)
at both ends and at midpoint
(d)
f= 2L

f= 4L
(t)
Ans.
(a)(p,t)
(b)  (p,s)
(c)  (q, s)
IIT-PAPER –2011
(d)
(q, r)
12