STAGE-1 TEST PAPERS-9 (PHYSICS)
STAGE
TEST PAPERS (PHYSICS)
1
PAPER - 1
Time : 1.00 Hr Max. Marks : 80
GENERAL INSTRUCTIONS
1. There are 23 Questions.
2. In Section I (Total Marks: 21), for each question you will be awarded 3 marks if you darken ONLY the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.
3. In Section Il (Total Marks: 16), for each question you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. There are no negative marks in this section.
4. In Section III (Total Marks: 15), for each question you will be awarded 3 marks if you darken ONLY the bubble corresponding to the correct answer and zero marks if no
bubble is darkened. In all other cases, minus one (-1) mark will be awarded.
5. In Section IV (Total Marks: 28), for each question you will be awarded 4 marks if you darken ONLY the bubble corresponding to the correct answer and zero marks otherwise. There are no negative marks in this section.
SECTION - I (Total Marks : 21)
(Single Correct Answer Type)
This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. 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
2. 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) 9 RT (B) 3 RT
8 1 2 1
(C) 15 RT (D) 9 RT
8 1 2 1
3. Consider an electric field E E0xˆ , where E0 is a constant. The flux through the shaded area (as shown in the figure) due to this field is :
(A) 2E a2 (B)
(C) E a2 (D)
E a2
E0a2
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
5. 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
6. 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
7. A 2F capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is
(A) 0%
(B) 20%
(C) 75%
(D) 80%
SECTION – II (Total Marks : 16)
(Multiple Correct Answers 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.
8. 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
(A) Einside 0
(B) Q > Q
(C) A RB
(D) Eon surface
Eon surface
A A B
B RA A B
9. 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.
10. 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) heat flow through A and E slabs are same
(B) heat flow through slab E is maximum
(C) temperature difference across slab E is smallest
(D) heat flow through C = heat flow through B + heat flow through D.
11. A metal rod of length ‘L’ and mass ‘m’ is pivoted at one end. A thin disk of mass ‘M’ and radius ‘R’ (> diameter of the wire. Then the value of ‘m’ in kg is nearly.
21. The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10–25 kg. The mass (in mg) of the radioactive sample is
22. A long circular tube of length 10 m and radius 0.3 m carries a current 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 its axis coinciding with the axis of the tube. The current varies as = cos (300 t) where is constant. If the magnetic moment of the
loop is N
0 0
0 sin (300 t), then ‘N’ is
23. Four solid spheres each of diameter 5 cm and mass 0.5 kg are placed with their centers at the corners of
a square of side 4cm. The moment of inertia of the system about the diagonal of the square is N × 10–4 kg-m2, then N is
PAPER - 2
Time : 1.00 Hr Max. Marks : 80
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. In Section I (Total Marks: 24), for each question you will be awarded 3 marks it you darken ONLY the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.
3. In Section II (Total Marks: 16), for each queshon you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. There are no negative marks in this section.
4. In Section Ill (Total Marks: 24), for each question you will be awarded 4 marks if you darken ONLY the bubble corresponding to the correct answer and zero marks otherwise. There are no negative marks in this section.
5. In Section IV (Total Marks: 16), for each question you will be awarded 2 marks for each row in which you have darkened ALL the bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. Thus, each question in this section carries a maximum of 8 marks. There are no negative marks in this section.
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. A light ray traveling 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)
2. 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
(A)
1 mV 2
2
(B) mV2
(C) 3 mV 2
2
(D) 2mV2
3. 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 X-Y plane and a steady current flows through the wire. The Z-component of the magnetic field at the center of the spiral is
0N
𝑙 b
0N b a
(A)
2(b a)
n
a
(B) 2(b a) 𝑙n b a
0N 𝑙n b
0N 𝑙n b a
(C) 2b a
(D) 2b
b a
4. A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x (t) = A sin t and
t 2
x (t) = A sin
2
. Adding a third sinusoidal displacement x
3
(t) = B sin (t + ) brings the mass to a
complete rest. The values of B and are
(A) 2A, 3 (B) A, 4
(C)
4 3
3 A, 5 (D) A,
6 3
5. Which of the field patterns given below is valid for electric field as well as for magnetic field?
(A) (B)
(C) (D)
6. 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 initial velocity V of the bullet is
(A) 250 m/s (B) 250 2 m/s
(C) 400 m/s (D) 500 m/s
7. 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%
8. A wooden block performs SHM on a frictionless surface with frequency, . 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.
(B) 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.
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. 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
10. 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) A B (B) A B
R R R R
(C) VA VB (D) VA VB
C C C C
11. 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.
(D) 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).
12. A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/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
(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.
SECTION — III (Total Marks : 24)
(Integer Answer Type)
This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.
13. 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 60º 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
14. 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
15. Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is
4
16. Water (with refractive index = 3 ) in a tank is 18 cm deep.
Oil of refractive index
7 lies on water making a convex
4
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
17. 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 , the time constant (in millisecond) of the circuit is
18. 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
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 in 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 ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.
Column I 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.
20. 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
. 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 at both ends (r) = L
(D) Stretched wire clamped at both ends (s) = 2L and at mid-point
(t) f = 4L
A nswers
PAPER - 1
1. (A) 2. (A) 3. (C) 4. (A) 5. (D)
6. (B) 7. (D) 8. (A),(B),(C),(D) 9. (B),(D) 10. (A),(C),(D)
11. (A),(D) 12. (D) 13. (C) 14. (B) 15. (C)
16. (B) 17. P = 4 18. N = 5 19. N = 3 20. 3
21. 1 22. N = 6 23. N = 9
PAPER - 2
1. (C) 2. (B) 3. (A) 4. (B) 5. (C)
6. (D) 7. (C) 8. (A) 9. (A), (B), (D) 10. (B,C)
11. (C) 12. (C) 13. 5 14. 4 15. 5
16. 2 17. 4 18. 7
19.
(A) – p,r,t; (B) – p,r ; (C) – q,s; (D) – r, t
20.
(A) – p; (B) – p,s; (C) – q,s; (D) – q, r
PAPER - 1
1.
finisident = freflected =
320
320 10 × 8 kHz
fobserved
= 320 10
320
freflected
330
= 8 × 310
= 8.51 kHz 8.5 kHz
2. Number of moles of He = 1
4
Now T (5.6) – 1 = T (0.7) – 1
1 2 / 3
T = T
1 2 8
4T1 = T2
1 R[3T ]
Work done = – nR[T2 T1]
= – 4
1 = – 9 RT
1 2 8 1
3
3. flux = (E0 cos 45°) × area)
= E0 a 2a
= E a2
1 RZ2 1 1
5
2
4.
H 4 9 = R(1)
36
H2
1 RZ2
1 1
3
He 4
16
= R(4) 16
He
He 1 16 5 5
4 3
2
36 27
He =
5 × 6561 = 1215 Å
27
5. T sin = m Lsin 2
324 = 0.5 × 0.5 × 2
324
2 =
=
=
0.5 0.5
18
= 36 rad/sec.
0.5
6. 𝑙1 = 52 + 1 = 53 cm
𝑙2 = 48 + 2 = 50 cm
𝑙1 x
53 x
𝑙 2 R
50 10
x = 10.6
7. Ui =
1 (2)V 2 , V
2
V
common = 5
1 V 2
U = (2 + 8)
f 2 5
2 V 2
Ui Uf 100 = 5
Ui V 2
100
4 100
5
= 80% Ans.
8.
QA + QB = 2Q ...(i)
KQA KQB
...(ii)
RA RB
RA
(i) and (ii) QA = QB R
RA
2Q 2Q RB
& Q 1
B R
= 2Q Q =
B B
1
RA
RB
= A RB
& QA =
2Q RA
RA RB
Q > Q
A QA / 4R2
B QB / 4R2
A
RB
= RA
B
using (ii)
EA = 0
& EB = 0
A B A B (at surface)
9. t
= 2RP
2 mpv 2mp
p v eBv eB
t = (2 2) Re = (2 2)mev (2 2)me
e v
t t
eBv eB
10. A : At steady state, heat flow through A and E are same.
C : T = i × R
‘i’ is same for A and E but R is smallest for E.
T
D : iB = R
B
T
iC = R
C
T
iD = RD
if ic = iB + iD
Hence
1 1 1
RC RB RD
8KA 3KA 5kA
𝑙 𝑙 𝑙
11. torque is same for both the cases.
T = 2
>
<
12.
13. In 1st case amplitude of SHM is a. In 2nd case amplitude of SHM is 2a
1
Total energy =
1
k(amplitude)2
2
E1 = E2 =
k(2a)2
2
1 k(a)2
2
E1 4 E2
Alternative :
Linear momentum P = mv
= m
P2 = m22 (A2 – x2)
P2 + (m)2x2 = m22A2 ...(i)
Equation of circle (bigger)
P2 + x2 = (2a)2
P2 + x2 = 4a2 ...(ii)
Equation of circle (smaller)
P2 + x2 = a2 ...(iii)
Comparing (i) and (ii) Amplitude A = 2a
1
and (m)2 = 1 m2 = m
1 m2(A)2
2
So energy E1 =
=
1 m2(2a)2
2
1 1 (4a2 )
2 m
2a2
=
m
Comparing (i) and (iii)
A = a
(m)2 = 1 m2 = 1
m
So E2 =
1 m2A 2 =
2
1 1 a2 =
2 m
1 a2
2 m2
1 a2
2 m
So E1 4 E
E2 1
= 4E2
14. Linear momentum
P = mv
= m
P2 + m22x2 = m22A2
represents a circle on P–x diagram with radius of circle R = A ( m22 = 1)
of spring mass system remains constant and equal to
Amplitude of oscillation inside liquid will decrease due to viscous force So radius of circular arcs will decrease as position change
Correctly shown in option B
15.
1
T
So only (C) is dimensionally correct
16. For resonance
= =
= 3.2 × 1015
f = 2
= c =
f
3.2 1015
2 3.14
3 108
1 1015
2
1 × 1015
2
600 nm
17. Note : If net force applied by the rod is considered to be 2 N.
2 ...(i)
a
FR – f 'R = 2mR2 R
F – f ' = 2ma = 1.2 ...(ii)
From (i) & (ii)
(1.2 + f ')2 + f '2 = 22
2f '2 + 2.4f ' + 1.44 = 4
f '2 + 1.2f ' + 0.72 – 2 = 0
f '2 + 1.2f ' – 1.28 = 0
f ' =
1.2
1.44 4 (1.28)
2
= 0.6 ±
= –0.6 ±
= 0.68
From eq. (2)
F = 1.88
0.68
= 1.88
= P P = 3.61 4 Ans.
10
5
c c
f – 2 = mR
1.4 – 2 = 2
2
3
5
1.4 – 0.6 = 2µ
0.8 = 2µ
= 0.4 =
P P = 4 Ans.
10
18. F1 =
F2 =
mg
2
F1 = 3F2
1 + = 3 – 3
4 = 2
= 1
2
N = 10
N = 5 Ans.
force
19. Surface Tension = length
2
a2
kq2
= × a × 2
1
2
a = (Some constant)
So N = 3 Ans.
20. F
A
L
= y L
mg y () A
Ay() r 2y()
(103 )2 1011 105 10
m =
Ans. 3
21. N = N e–t
dN
= 1010 = N
g g
() e109 t
= 10
= 3
dt
at (t = 0) 1010 = N
0
10–9
N = 1019
mass of sample = N0
10–25
= N0 (mass of the atom)
= 10–6 kgm
= 10–6 × 103 gm
= 10–3 gm
= 1 mg Ans. 1
22. Flux through circular ring
= ( ni) r2
= 0 r 2
L 0
d
cos 300 t
i = Rdt
r 2
i =
RL
. sin 300 t × 300
r 2.300
= sin 300 t
0 0 RL
M = . r2
2r 4.300
= sin 300 t
0 0 RL
10 104 300
(Take 2 = 10)
= 100 10
N = 6 Ans.
23.
= 2
2 2
2
2 2
= 5 MR
2 + 5 MR
2 + (Mx2) 2
2 2
= 4 MR
+ 2mx2
= 8 MR 2
5
+ 2mx2
8
5 2
= 0.5 2 (0.5) (4 2)10 4
5
= 5 8 × 10–4
= 9 × 10–4 = N × 10–4
So, N = 9 Ans.
PAPER - 2
1. Initially most of part will be transmitted. When > i , all the light
rays will be total internal reflected. So transmitted intensity = 0 So correct answer is (C)
2. Ve =
KE =
2v0
1 mv2 = 1 m 2v 2 = mv 2
2 e 2 0 0
N
dNi
0 b a dx i
0Ni 𝑙n b
3. B 0
= 2(b a) a
2x 2x
4. Velocity of S.H.M. due to combination must be zero
4
So B = A, = 240° = 3
5. True for induced electric field and magnetic field.
6. R = u
20 = V1 and 100 = V2
V1 = 20 m/s , V2 = 100 m/sec.
Applying momentum conservation just before and just after the collision (0.01) (V) = (0.2)(20) + (0.01)(100)
V = 500 m/s
0.5
7. Least count = 50
= 0.01 mm
Diameter of ball D = 2.5 mm + (20)(0.01) D = 2.7 mm
= = 4
M
D 3
vol
3 2
m D
0.01
3
m D
= 2% + 3 2.7 100%
max
= 3.1%
max
8. The frequency will be same f =
but due to the constant qE force, the equilibrium position gets shifted by qE in forward direction. So Ans.
K
will be (A)
9. For equilibrium
dAvg + dBvg = dFvg + dFvg
d =
dA dB
2
Option (D) is correct
to keep the string tight dB > dF and dA < dF
10. Case I Z =
Case II
A V
Z´ < Z
R Z
B V
A B
R Z´ R R
VA VB
R R
So. VA VB
V 2 V 2 V 2
C C R C 0
11. =
Eds =
Kq 4r 2 = q
r 2 0
Wext = q(VB – VA)
Comment : (D) is not crrect answer because it is not given that charge is moving slowly.
12. Friction force on the ring.
13.
T 2usin
g
2 10 3
T = 10 2
1
3 sec
R = ucos . T – 2 aT2
1.15 = 10 × 1
2
3 – 1 a(
2
3 )2
3
2 a = 5 – 1.15
3a = 8.65 – 1.15 = 7.5
2
2
a = 7.5 × 3 5 m/sec2 a = 5 m/sec2
14. = 0.1
1 mu2 = mg × 0.06 +
2
1 kx2
2
1 × 0.18 u2 = 0.1 × 0.18 × 10 × 0.06
2
N
0.4 = 10
N = 4 Ans.
E1 E2
6 3
15.
r1 r2 1 2
1 1 1 1
r1 r2 1 2
15
= 3 = 5 volt Ans.
16.
2 1 2 1
v u
7 1
4v 24
R
7 1
4
6
7 3 1
4v 24 24
2 1
24 12
7 12 V = 21 cm
4
21 7 / 4
OS" 4 / 3
21 7 3
OS" 4 4
OS" = 16
BS" = 2cm
17. W = 500 rad/s
Z =
= R 1.25
1 2
L
+ R2 = R2 (1.25)
1 2 R2
L
+ R2 = R2 +
4
1 R
L 2
2
CR =
2
= 500
sec.
2
= 500
× 103 ms
2 1000
= 500 ms
= 4 ms
18. R = 1cm
f = 4.7 cm
hc
= + eV
1240(ev)(nm) 200(nm)
1240
= 4.7 (eV) + eV
200
e = 4.7 e + eV
6.2 – 4.7 = V V = 1.5 volt
1 Q 4 0 R
(9 × 109)
= 1.5
Ne 1.5
1
100
9 × 1011 Ne = 1.5 ; N =
1.5
= 15 1 108
= 5 108 =
3 16
50 107
48
9 1011 1.6 1019
16 9
Z = 7
19. A B V P const T U (p), (r), (t) B C d 0
P T
d = du +d (p), (r)
C D V T du +ve
d = +ve (q), (s)
D A dw –ve (r), (t) dq –ve
du = 0
20. (A) 4
= L , = 4L,
Sound waves are longitudinal waves
(B) 2 = L , = 2L
Sound waves are longitudinal waves
(C) 2 = L, = 2L
String waves are transverse waves
(D) = L
String waves are transverse waves
STAGE
3
Time : 1.00 Hr
SIMILAR TEST PAPERS (PHYSICS)
PAPER - 1
Max. Marks : 80
GENERAL INSTRUCTIONS
1. There are 23 Questions.
2. In Section I (Total Marks: 21), for each question you will be awarded 3 marks if you darken ONLY the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.
3. In Section Il (Total Marks: 16), for each question you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. There are no negative marks in this section.
4. In Section III (Total Marks: 15), for each question you will be awarded 3 marks if you darken ONLY the bubble corresponding to the correct answer and zero marks if no
bubble is darkened. In all other cases, minus one (-1) mark will be awarded.
5. In Section IV (Total Marks: 28), for each question you will be awarded 4 marks if you darken ONLY the bubble corresponding to the correct answer and zero marks otherwise. There are no negative marks in this section.
SECTION - I (Total Marks : 21)
(Single Correct Answer Type)
This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. A police car with a siren of frequency 8 kHz is moving with uniform velocity 72 km/hr making an angle 60º with the normal towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The beap frequency of the siren heard by the car driver is
(A) 510 Hz. (B) 500 Hz
(C) 750 Hz (D) 1070 Hz
2. 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T1, the change in internal energy and final temperature in the process is :
(A) 9 RT , 3T
2
(B) 9 RT , 4T
8
(C) 15 RT , 4T
8
→
(D) 9 RT , 3T
2
3. Consider an electric field E E0r rˆ , where E0 is a constant, r is
the distance from the origin and rˆ is the radial vector outward from the origin. The flux through the shaded area (a quarter disc of radius 'a' as shown in the figure) due to this field is :
(A) zero (B)
(C) E a2 (D)
E0a3
4
E0a3
6
4. The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The energy corrsponding the wavelength of the second spectral line in the Balmer series of singly ionized helium atom is used for photoelectric emission for metal surface whose work function is 4.2 eV, then the maximum kinetic energy of ejected photoelectron is :
(A) 6 eV (B) 4.2 eV
(C) 10.2 eV (D) 6.2 eV
5. A positively charged ball of mass (m) 0.5 kg and charged 3 C is attached to the end of an insulated string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. There is a uniform vertical upward magnetic field in region B = 107 tesla. The maximum tension that the string can bear is 400N. The maximum possible value of angular velocity of ball (in radian/s) is :
(A) 80 (B) 40
(C) 20 (D) 160
6. 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 point A is found to be at farther distance of 2 cm and point B is also shifted towards the point A by 1 cm. The determined value of ‘X’ is
(A) 10.2 ohm (B) 10.6 ohm
(C) 11.0 ohm (D) 11.5 ohm
7. A 2F capacitor is charged as shown in figure. The percentage change in the electric field inside the 2F capacitor after the switch S is
turned to position 2 is
(A) 80%
(B) 75% (C) –75% (D) –80%
SECTION – II (Total Marks : 16)
(Multiple Correct Answers 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.
8. 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
(A) UFinal UFinal (B) UFinal UFinal
A B A B
(C) PFinal PFinal (D) PFinal PFinal
A B A B
9. An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field into the plane of paper and perpendicular to the velocity. Which of the following statement(s) is/are true?
(A) They will come out with the same angular velocity.
(B) They will come out with same final speed.
(C) Centre of electron's and proton's respective path will be out side and in side the magnetic field region
(D) They will come out at different times.
10. 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) Equivalent thermal conductivity of the composite block is 18 K .
5
(B) Ease of heat flow through slab E is maximum
(C) temperature difference across slab A is largest.
(D) heat flow through C = heat flow through B + heat flow through D.
11. A uniform quarter disc of mass m and radius R is hinged about its centre as shown in figure (I). It is suspended such that it can rotate about horizontal axis. Now a point object of mass m is fixed at the centre of mass of the quarter disc as shown in fig. (II). Now for the small angular displacement about mean position.
() ()
(A) Restoring torque in case () = Restoring torque in case ()
(B) Restoring torque in case () < Restoring torque in case ()
(C) Angular frequency for case () > Angular frequency for case ().
(D) Angular frequency for case (I) < Angular frequency for case (II).
SECTION — III (Total Marks :15)
(Paragraph Type)
This section contains 2 paragraphs. Based upon one of the paragraphs 3 multiple choice questions and based on the other paragraph 2 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 Question Nos. 12 to 14
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/angular momentum are changed. Here we consider some simple dynamical systems in one/two-dimension. For such systems, phase space is a plane in which position or x-coordinate is plotted along horizontal axis and momentum/angular momen- tum about origin is plotted along vertical axis. The phase space diagram is x(t) vs p(t)/L(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. Angular momentum (about origin) direction into the plane of the paper is taken to be positive.
12. The phase space diagram for a ground to ground projectile ball thrown at some angle from ground is :
(A) (B)
(C) (D)
13. The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent two oscillators of masses 4m and m but for different initial conditions, and E1 and E2 are the total mechanical energies respectively. The angular velocities are and respectively
1 2
(A) E1 E2 , 2 = 2 (B) E1 E2 , 2 = 4
(C) E1 2E2 , 2 = 4 (D) E1 4E2 , 1 =
14. Consider the spring-mass system, with the mass submerged in water (always), as shown in the figure. The phase space diagram for one cycle of this
system is :
Momentum
(A) (B)
(C) (D)
Paragraph for Question Nos. 15 and 16
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 elec- trons begin to oscillate about the positive ions with a natural angular frequency ‘ ’, 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 all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.
15. Taking the electronic charge as ‘e’ and the permitlivity as ‘ ’, use dimensional analysis to determine the correct expression for r(maximum displacement from mean position)
e2
(A) 40m2
e2
(B) 0
4m
(C)
0e2
4m2
(D)
16. Estimate the distance at which plasma reflection will occur for angular frequency = 3.2 × 1015, such that one wavelength equals the perimeter of the circle of radius maximum distance (numerically) :
(A) 800 nm (B) 300 nm
(C) 100 nm (D) 200 nm
SECTION – IV (Total Marks : 28)
(Integer Answers Type)
This sections contains 7 questions. The answer to each of the questions 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. A boy is pushing a toy of mass 1 kg and outer radius 0.5 m with a stick as shown in the figure. The stick applies a force of 5 N on the toy at distance 0.25 m from the centre as shown and rolls without slipping with an acceleration of 1.25 m/s2. The coefficient of friction between the ground and the toy is large enough that rolling always occurs and the coefficient of friction between the stick and the toy is (P/4). The value of P is
18. A block is on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is =
0.5. The whole system is rotated as shown in the fig. The maximum angular speed by which system can be rotated about the given axis such that the block remain stationary with respect to incline plane.
19. A soap bubble of radius R is charged with charged density and the surface tension is T. It is found that its
1 2
radius remain constant. Then that surface tension is given by T =
where K is constant . The value of
0
K :
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 energy density stored in the wire is N × 10–5 J where N is :
21. Certain radioactive decay follows the following sequence
A B
3 C
t = 0 N0 0 0
t N1 N2 N3
Then the ratio of N1 to N2 when N2 is maximum is :
22. A long circular tube of length 10 m and radius 0.3 m carries a current along its curved surface as shown. A conducting ring of resistance 0.005 ohm and of radius 0.1 m is bent across its diameter by an angle of 90°
and placed inside the tube as shown. The current varies as =
cos (300 t) where
is constant. If the
magnetic moment of the loop is N sin (300 t), then ‘N’ is
0
23. Four uniform circular disc each of radius 5 cm and mass 0.5 kg are placed with their centers at the
corners of a square of side 4cm as shown. The moment of inertia of the system about the axis passing through the centre of the square and perpendicular to its plane is N × 10–3 kg-m2 where N is :
PAPER - 2
Time : 1.00 Hr Max. Marks : 80
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. In Section I (Total Marks: 24), for each question you will be awarded 3 marks it you darken ONLY the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.
3. In Section II (Total Marks: 16), for each queshon you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. There are no negative marks in this section.
4. In Section Ill (Total Marks: 24), for each question you will be awarded 4 marks if you darken ONLY the bubble corresponding to the correct answer and zero marks otherwise. There are no negative marks in this section.
5. In Section IV (Total Marks: 16), for each question you will be awarded 2 marks for each row in which you have darkened ALL the bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. Thus, each question in this section carries a maximum of 8 marks. There are no negative marks in this section.
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. In Young's double slit experiment the two light waves (from the coherent sources, each having intenisity ) has initial phase difference . The intensity at the point of central maxima which is equidistant from the slits is observed with variation of . The corresponding graph is :
(A) (B)
(C) (D)
2. 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 potential energy of the object (taking potential energy at infinity to be 3 mv2 ) is :
2
(A) 5 mV2
2
(B) –mV2
(C) (C)
1 mV 2
2
(D) 2mV2
3. 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 X-Y plane and a steady current flows through the wire. Now the spiral is bent about the X-axis and rotated by 90° such that half part lies in XY-plane and remaining half part in YZ-plane. The ratio of the magnetic field at the origin in the two cases is :
(A) 1
(B) 1 :
(C) 2 : 1
(D) 1 : 1
4. A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x (t) = A sin t and
t 2 4
x (t) = A sin
2
.A third sinusoidal displacement x
3
(t) = B sin (t +
3 ) is added such that its
average kinetic energy of SHM due to combination of the three displacements is same as its average kinetic energy due to x1(t) only. The values of B is :
(B) A
(C) 2A (D) A
2
5. Which of the field patterns given below is valid for electric field as well as for magnetic field?
() ()
() (IV)
(P) Electric field (Q) Magnetic field
(R) Electric field due to electric dipole (S) Magnetic field due to magnetic dipole
(A) P, P, P,Q, V R, (B) P, P, Q, V R
(C) P, P, Q, V S (D) P, P,Q, P,Q, V R, S
6. 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 some distance left to foot of the post the coefficient of restitution is 0.4 then the initial velocity V of the bullet is :
(A) 250 m/s (B) 500 m/s
(C) 300 m/s (D) 400 m/s
7. The density of a thick disc (circular) is to be determined in an experiment. The diameter and thickness of the disc 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 in both cases. If the measured mass of the disc 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%
8. A block of mass m performs SHM on a frictionless surface with frequency, . Now the setup is taken into the lift whose surface is smooth and block carries a charge +Q, Now if uniform electric field switched on as shown inside the lift, while the lift is accelerating with constant acceleration 'a' as shown. The motion of the
block (spring constant = K, a
2QE ) :
m
d2x
QE
(A) will be SHM is horizontal direction, with shifted mean position and equation is m dt2 Kx
= 0,
K
and freuquency is different
d2x
QE
ma
(B) will be SHM in horizontal with shifted mean position, equation is m dt2
(C) with same mean position, same frequency
(D) with same mean position and different frequency
Kx
K
= 0
2K
1SECTION — 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. 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 dA + dB = 2dF . Now the base of the container is suddenly removed then the tension in the
string will
(A) increase (B) decrease but will be non zero
(C) become zero (D) remain same
10. 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 PAvg (the average power of the circuit) are compared in the two cases. . Which of the following is/are true?
(A) A B (B) A B
R
(C) PA
R
B
Avg
R
(D) PA
R
B
Avg
11. Which of the following statement(s) is/are correct?
→ q
(A) According to Gauss law E .dS
present inside as well as outside it.
, here E is the electric field at the Gaussian surface due to charges
(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.
(D) The work done by the external force in moving slowly a unit negative charge from point A at potential VA to point B at potential VB is (VB — VA).
12. A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/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
(A) The ring has pure rotation about its stationary CM
(B) The ring comes to a complete stop.
(C) The magnitude of impulse on the ball due to the normal force of the ring is 2
(D) There is no friction between the ring and the ground.
3 1 N-s
4
Section — Ill (Total Marks : 24) (Integer Answer Type)
This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.
13. A train is moving along a straight line with constant acceleration 5 m/s2 . Two boys facing each other standing in the train. One boy throws a ball forward with a speed of 10m/s at an angle of 60° to the horizontal. At the
1 1
same instant the second boy throws another ball towards the first boy at an angle
tan
to the
2
horizontal, both receive the ball thrown by the other at the same time. Then the speed of the second ball is x × 103 cm/s. Then x is :
14. 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 such that it acquire a velocity 0.4 m/sec. The total distance covered by the block before it comes to complete rest is N cm, where N is :
15. Two batteries of different emfs of different internal resistances and load resistance R are connected as
shown. The value of R for which the power dissipated across it is maximum is
4
2 . The N is :
N
7
16. Water (with refractive index = 3 ) in a tank is 18 cm deep. Oil of refractive index 4 lies on water making a convex surface of radius of curvature ‘R = 6 cm’ as shown. Consider oil to act as a thin lens and the bottom of tank is silvered. An object ‘S’ is placed x cm above oil surface. The final image coincides with the object
then x is :
17. The time constant for the circuit shown is NRC , where N is :
2
18. 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
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 in 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 ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. For the process D to A we have PV2 = constant. Match them with each of the processes given in Column I.
Column I 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.
20. Column I shows four systems, each of the same length L, for producing standing waves. The second overtone frequency whose wavelength is denoted as . 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 at both ends (r) = 2L 3
(D) Stretched wire clamped at both ends (s) = 4L 5
and at mid-point
(t) = L
3
A nswers
PAPER - 1
1. (A) 2. (B) 3. (A) 4. (A) 5. (C)
6. (B) 7. (D) 8. (A),(D) 9. (B), (C), (D)
10. (A), (B), (D) 11. (B), (D) 12. (C) 13. (B) 14. (B)
15. (A) 16. (C) 17. 3 18. = 3 rad/s 19. 2
20. 2 21. 3 22. N = 4 23. 2
PAPER - 2
1.
(C)
2.
(A)
3.
(A)
4.
(C)
5.
(A)
6. (C) 7. (C) 8. (B) 9. (C) 10. (B,C)
11. (A, C) 12. (C) 13. 3 14. 6 15. 3
16. 8 17. 2 18. 7
19. (A) – r,t , (B) – p,r (C) – s, (D) – q, s, t 20. (A) – p,s , (B) – p,r (C) – q,r, (D) – q, t
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