STAGE-1-Test Paper-8 Physics
Time : 1.00 Hr Max. Marks : 84
GENERAL INSTRUCTIONS
1. There are 28 Questions.
2. For each question in Section–I, you will be awarded 3 marks if you give the correct answer and
zero mark if no answer is given. In all other cases, minus one (–1) will be awarded.
3. For each question in Section–II, you will be awarded 3 marks if you give the correct answer and zero mark if no answer is given. Partial marks will be answered for partially correct answers. No negative marks will be awarded in this Section.
4. For each question in Section–III, you will be awarded 3 marks if you give the correct answer and
zero mark if no answer is given. In all other cases, minus one (–1) will be awarded.
5. For each question in Section–IV, you will be awarded 3 marks if you give the correct answer and
zero mark if no answer is given. No negative marks will be awarded for in this Section.
SECTION - I
Single Correct Choice Type
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. A block of mass m is on inclined plane of angle . The coefficient of friction between the block and the plane is and tan > . The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P1 = mg(sin – cos) to P2 = mg(sin + cos), the
frictional force f versus P graph will look like :
(A) (B)
(C) (D)
2. A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner
radius 3R. The work required to take a unit mass from point P on its axis to infinity P
is:
4R
(A)
2GM 4
7R
5
(B) 2GM 4
7R
5 3R
4R
(C) GM (D) 2GM
1
4R 5R
3. Consider a thin square sheet of side L and thickness t, made of a material of resitivity . The resistance between two opposite faces, shown by the shaded areas in the figure is:
(A) directly proportional to L (B) directly proportional to t
(C) independent of L (D) independent of t
4. A real gas behaves like an ideal gas if its
(A) pressure and temperature are both high (B) pressure and temperature are both low
(C) pressure is high and temperature is low (D) pressure is low and temperature is high
5. Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R100, R60 and R40, respectively, the relation between these resistance is :
(A)
1
R100
1
R 40
1
R60
(B) R100
= R40
+ R60
(C) R100
> R60
> R40
(D) (D)
1
R100
1
R60
1
R40
6. To verify Ohm's law, a student is provided with a test resistor RT, a high resistance R1, a small resistance R2, two identical galvanometers G1 and G2, and a variable voltage source V. The correct circuit to carry out the
experiment is :
(A) (B)
R1
(C) (D)
7. An AC voltage source of variable angular frequency and fixed amplitude V connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When is increased :
(A) the bulb glows dimmer (B) the bulb glows brighter
(C) total impedence of the circuit is unchanged (D) total impedence of the circuit increases
8. A thin flexible wire of length L is connected to two adjacent fixed points carries a current in the clockwise direction, as shown in the figure. When system is put in a uniform magnetic field of strength B going into the plane of paper, the wire takes the shape of a circle. The tension in the wire is :
BL
(A) BL (B)
(C)
BL 2
(D)
BL 4
SECTION - II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.
9. One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P0. Choose the correct option(s) from the following :
(A) Internal energies at A and B are the same (B) Work done by the gas in process AB is P0V0 πn 4
(C) Pressure at C is P0 (D) Temperature at C is T0
4 4
10. A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60ΒΊ (see figure). If the refractive index of the material
of the prism is , which of the following is (are) correct?
(A) The ray gets totally internally reflected at face CD
(B) The ray comes out through face AD
(C) The angle between the incident ray and the emergent ray is 90ΒΊ
(D) The angle between the incident ray and the emergent ray is 120ΒΊ
11. A few electric field lines for a system of two charges Q1 and Q2 fixed at two different points on the x-axis are shown in the figure. These lines suggest that :
(A) |Q1| > |Q2|
(B) |Q1 | < |Q2|
(C) at a finite distance to the left of Q1 the electric field is zero
(D) at a finite distance to the right of Q2 the electric field is zero
12. A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true ?
(A) Error T in measuring T, the time period, is 0.05 seconds
(B) Error T in measuring T, the time period, is 1 second
(C) Percentage error in the determination of g is 5%
(D) Percentage error in the determination of g is 2.5%
13. A point mass of 1kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses ?
(A) Total momentum of the system is 3 kg ms–1
(B) Momentum of 5 kg mass after collision is 4 kg ms–1
(C) Kinetic energy of the centre of mass is 0.75 J
(D) Total kinetic energy of the system is 4 J
SECTION–III
Paragraph Type
This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice questions and based upon the second 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. 14 to 16
When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx2, it performs simple
harmonic motion. The corresponding time period is proportional to
m , as can be seen easily using
k
dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx2 and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = x4 ( > 0) for |x| near the origin and becomes a constant equal to V0 for |x| X0 (see figure)
14. If the total energy of the particle is E, it will perform periodic motion only if :
(A) E < 0 (B) E > 0 (C) V0 > E > 0 (D) E > V0
15. For periodic motion of small amplitude A, the time period T of this particle is proportional to :
(A) A
(B)
(C) A
(D)
16. The acceleration of this particle for |x| > X0 is :
V0
(A) proportional to V0 (B) proportional to mX0
(C) proportional to
(D) zero
Paragraph for Question Nos. 17 to 18
Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature TC(0). An interesting property of superconductors is that their critical temperature becomes smaller than TC (0) if they are placed in a magnetic field, i.e., the critical temperature TC (B) is a function of the magnetic field strength B. The dependence of TC
(B) on B is shown in the figure.
17. In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B1 (solid line) and B2 (dashed line). If B2 is larger than B1, which of the following graphs shows the correct variation of R with T in these fields?
(A) (B)
(C) (D)
18. A superconductor has TC (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its TC decreases to 75
K. For this material one can definitely say that when :
(A) B = 5 Tesla, TC (B) = 80 K (B) B = 5 Tesla, 75 K < TC (B) < 100 K
(C) B = 10 Tesla, 75 K < TC (B) < 100 K (D) B = 10 Tesla, TC (B) = 70 K
SECTION–IV
Integer Type
This Section contains 10 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.
19. A piece of ice (heat capacity = 2100 J kg–1 ΒΊC–1 and latent heat = 3.36 × 105 J kg–1) of mass m grams is at
–5 ΒΊC at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice- water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is :
20. A stationary source is emitting sound at a fixed frequency f0, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f0. What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is 330 ms–1.
21. The focal length of a thin biconvex lens is 20cm. When an object is moved from a distance of 25cm in front
m25
of it to 50cm, the magnification of its image changes from m25 to m50. The ratio m50 is :
22. An -particle and a proton are accelerated from rest by a potential difference of 100V. After this, their
p
de-Broglie wavelength are and p respectively. The ratio , to the nearest integer, is :
23. When two identical batteries of internal resistance 1 each are connected in series across a resistor R, the rate of heat produced in R is J1. When the same batteries are connected in parallel across R, the rate is J2. If J1 = 2.25 J2 the value of R in is :
24. Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperature T1 and T2 respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?
2x – 6t –
25. When two progressive waves y1 = 4 sin (2x – 6t) and y2 = 3 sin
are superimposed, the
amplitude of the resultant wave is :
26. A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is 4.9 × 10–7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s–1. If the Young's modulus of the material of the wire is n × 109 Nm–2, the value of n is :
27. A binary star consists of two stars A (mass 2.2 MS) and B ( mass 11 MS) where Ms is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is :
28. Gravitational acceleration on the surface of a planet is
6 g, where g is the gravitational acceleration on the
11
2
surface of the earth. The average mass density of the planet is 3
times that of the earth. If the escape speed
on the surface of the earth is taken to be 11 kms–1, the escape speed on the surface of the planet in kms–1 will be :
PAPER - 2
Time : 1.00 Hr Max. Marks : 79
GENERAL INSTRUCTIONS
1. There are 19 Questions.
2. For each question in Section–I : you will be awarded 5 marks if answer is correct and zero mark
if no answer is given. In all other cases, minus two (–2) mark will be awarded.
3. For each question in Section–II : you will be awarded 3 marks if answer is correct and zero mark if no answer is given. No negative marks will be awarded for incorrect answers in this Section.
4. For each question in Section–III : you will be awarded 3 marks if answer is correct and zero mark if no answer is given. In all other cases, minus one (–1) mark will be awarded.
5. For each question in Section–IV : you will be awarded 2 marks for each row in which you give the correct answer(s). Thus, each question in this section carries a maximum of 8 marks. There is no negative marks awarded for incorrect answer(s) in this Section.
SECTION - I
Single Correct Choice Type
This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and
(D) out of which ONLY ONE is correct.
1. A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is
(A) Virtual and at a distance of 16 cm from mirror
(B) Real and at distance of 16 cm from the mirror
(C) Virtual and at a distance of 20 cm form the mirror
(D) Real and at a distance of 20 cm from the mirror
2. A uniformly charged thin spherical shell of radius R carries uniform
surface charge density of per unit area. It is made of two hemi- F F spherical shells, held together by pressing them with force F (see
figure). F is proportional to
(A)
1 2R2
0
(B)
1 2R
0
1 2 1 2
(C) 0 R (D) 0 R2
3. A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F (t) in the x direction. The force F (t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is :
(A) 4.50 J (B) 7.50 J
(C) 5.06 J (D) 14.06 J
4. A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is 320 ms–1, the mass of the string is :
(A) 5 grams (B) 10 grams
(C) 20 grams (D) 40 grams
5. A vernier calipers has 1 mm marks on the main scale. It has 20 equal division on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is :
(A) 0.02 mm (B) 0.05 mm
(C) 0.1 mm (D) 0.2 mm
6. A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of
strength 81 105 Vm–1. When the field is switched off, the drop is observed to fall with terminal velocity
7
2 × 10–3 m s–1. Given g = 9.8 m s–2, viscosity of the air = 1.8 × 10–5 Ns m–2 and the density of oil = 900 kg m–3, the magnitude of q is :
(A) 1.6 × 10–19 C (B) 3.2 × 10–19 C
(C) 4.8 × 10–19 C (D) 8.0 × 10–19 C
SECTION - II
(Integer Type)
This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.
7. To determine the half life of a radioactive element, a student plots a graph of πn dN(t) versus t. Here dN(t)
dt dt
is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor f p after 4.16 years, the value of p is :
8. Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed
25
to move from 3
m to 50
7
m in 30 seconds. What is the speed of the object in km per hour.
9. A large glass slab ( = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R.
10. At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V?
[Take : πn 5 = 1.6, πn 3 = 1.1]
1
11. A diatomic ideal gas is compressed adiabatically to 32
of its initial volume. If the initial temperature of the
gas is Ti (in Kelvin) and the final temperature is aTi, the value of a is :
SECTION - III
Paragraph Type
This section contains 2 Paragraphs. Based upon the first paragraph 3 multiple choice questions have to be answered. Each of these question has four choice (A), (B), (C) and (D) out of which ONLY ONE is correct.
Paragraph for questions 12 to 14.
When liquid medicine of density is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
12. If the radius of the opening of the dropper is r; the vertical force due to the surface tension on the drop of radius R (assuming r << R) is :
(A) 2rT (B) 2RT
(C)
2r 2T R
(D)
2R2T
r
13. If r = 5 ×10–4 m, = 103 kgm–3, g = 10 ms–2,T = 0.11 Nm–1, the radius of the drop when it detaches from the dropper is approximately :
(A) 1.4 × 10–3 m (B) 3.3 ×10–3 m
(C) 2.0 × 10–3 m (D) 4.1 ×10–3 m
14. After the drop detaches, its surface energy is :
(A) 1.4 ×10–6 J (B) 2.7 ×10–6 J
(C) 5.4 ×10–6 J (D) 8.1 × 10–6 J
Paragraph for questions 15 to 17
The key feature of Bohr’s theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr’s quantization condition.
15. A diatomic molecule has moment of inertia . By Bohr’s quantization condition its rotational energy in the nth level (n = 0 is not allowed) is :
(A)
2
2 2
(B)
2
2
n 8 n 8
2
(C) n 2
2
(D) n 2
8 8
16. It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule
is close to
4 1011 Hz. Then the moment of inertia of CO molecule about its centre of mass is close to
(Take h = 2 × 10–34 J s )
(A) 2.76 × 10–46 kg m2 (B) 1.87 × 10–46 kg m2
(C) 4.67 × 10–47 kg m2 (D) 1.17 × 10–47 kg m2
17. In a CO molecule, the distance between C (mass = 12 a.m.u.) and O (mass = 16 a.m.u.),
where 1 a.m.u. =
5 1027
3
kg, is close to : (1 a.m.u. =
5 1027
3
kg) :
(A) 2.4 × 10–10 m (B) 1.9 × 10–10 m
(C) 1.3 × 10–10 m (D) 4.4 × 10–11 m
SECTION - IV
(Matrix - 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) in Column-II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question against statement B,darken the bubbles corresponding to q and r in the ORS.
18. Two transparent media of refractive indices 1 and 3 have a solid lens shaped transparent material of refractive index 2 between them as shown in figures in column ΞΞ. A ray traversing these media is also shown in the figures. In Column Ξ different relationships between 1, 2 and 3 are given. Match them to the ray diagrams shown in Column ΞΞ.
Column Ξ Column ΞΞ
(A) 1 < 2 (p)
(B) 1 > 2 (q)
(C) 2= 3 (r)
(D) 2 > 3 (s)
(t)
19. You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column ΞΞ. When a current (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage V1 and V2. (indicated in circuits) are related as shown in Column Ξ. Match the two
Column Ξ Column ΞΞ
(A) 0,V1 is proportional to (p)
(B) 0,V2 > V1 (q)
(C) V1= 0, V2 = V (r)
(D) 0,V2 is proportional to (s)
(t)
A nswers
PAPER - 1
1. (A) 2. (A) 3. (C) 4. (D) 5. (D)
6. (C) 7. (B) 8. (C) 9. (A, B) 10. (A, B,
C)
11. (A, D) 12. (A, C) 13. (A, C) 14. (C) 15. (B)
16. (D) 17. (A) 18. (B) 19. 8 gm 20. 7
21. 6 22. 3 23. 4 24. 9 25. 5
26. 4 27. 6 28. 3
PAPER - 2
1. (B) 2. (A) 3. (C) 4. (B) 5. (D)
6. (D)
sec 7. 8 8. 3 9. 6 10. t = 2
11. a = 4 12. (C) 13. (A) 14. (B) 15. (D)
16. (B) 17. (C) 18. (A) – p,r ; (B) – q,s,t ; (C) – p,r,t ; (D) – q, s
19. (A) – r,s,t ; (B) – q,r,s,t ; (C) – p,q ; (D) – q,r,s,t
As per given conditions, there will be no steady state in circuit ‘p’, so it should not be considered in options of ‘c’.
(A) – r,s,t ; (B) – q,r,s,t ; (C) – q ; (D) – q,r,s,t
STAGE SOLUTIONS TO TEST PAPERS (PHYSICS)
2
1.
P1 = mgsin – mgcos
P2 = mgsin + mgcos
Initially block has tendency to slide down and as tan > , maximum friction mgcos will act in positive direction. When magnitude P is increased from P1 to P2, friction reverse its direction from positive to negative and becomes maximum i.e.mgcos in opposite direction.
2. Wext = U – UP
Wext = 0 – – –
Gdm x
.1
Wext = G
7R2
2rdr
2 2
2GM
= 2
rdr
Let 16 R2 + r2 = z2 rdr = z dz
Then
16R r 7R
P
Wext =
2GM
7R2
2GM
zdz =
z
2GM
7R2
4R
[Z]
Wext =
7R2
3R
Wext =
2GM
7R2
2R – 5R
Wext =
2GM
7R2
– 5.
l
3. R = A
L
R = tL = t
Independent of L.
4. At low pressure and high temperature inter molecular forces become ineffective. So a real gas behaves like an ideal gas.
V 2
5. 100 = R'100
1
R'100
100
= V2
where R’100 is resistance at any temperature corresponds to 100 W
60 =
V 2
R'60
1
R'60
60
= V 2
40 =
V 2
R'40
1
R'40
40
= V 2
From above equations we can say
1
R'100
1
> R'60 >
1
R'40 .
So, most appropriate answer is option (D).
6. To verify Ohm's law one galvaometer is used as ammeter and other galvanometer is used as voltameter. Voltameter should have high resistance and ammeter should have low resistance as voltameter is used in parallel and ammeter in series that is in option (C).
7. irms =
when increases, irms increases so the bulb glows brighter
8.
d
2Tsin 2 = dlB 2T
= RdlB ( 2R = L R =
L
2 )
2
T = BR = BL .
2
9.
f
U = 2 nRT, where f,n,R are constants. Also temperature T is same at A & B.
UA = UB
Also, WAB = nRT0 πn V = nRT0 πn
4V0 V
= nRT0 πn4 = P0V0 πn4
i 0
So, answers are (A) & (B).
10. By refraction at face AB :
1.sin60ΒΊ =
So, r1 = 30ΒΊ
. sinr1
This shows that the refracted ray is parallel to side BC of prism. For side 'CD' angle of incidence will be 45ΒΊ, which can be calcu- lated from quadrilateral PBCQ.
By refraction at face CD :
sin45ΒΊ = 1 sinr2
So, sin r2 =
which is impossible. So, there will be T.I.R. at face CD.
Now, by geometry angle of incidence at AD will be 30ΒΊ. So, angle of emergence will be 60ΒΊ. Hence, angle between incident and emergent beams is 90ΒΊ
11.
From the diagram, it can be observed that Q1 is positive, Q2 is negative.
No. of lines on Q1 is greater and number of lines is directly proportional to magnitude of charge. So, |Q1| > |Q2|
Electric field will be zero to the right of Q2 as it has small magnitude & opposite sign to that of Q1 .
12. Since, t = nT. So, T = t n
Now, t = n T
40
= 20
or T = 2 sec.
t T
and t = T
1 T
So, 40 = 2
T = 0.05
Time period, T = 2
So,
T = 1 g
or g
= 2 T
T 2 g g T
g
So, percentage error in g = g × 100
= 2 T
T
× 100 = – 2 0.05
2
× 100 = 5%.
13.
Since collision is elastic, so e = 1
Velocity of approach = velocity of separation So, u = v + 2 (i)
By momentum conservation : 1 × u = 5v – 1 × 2
u = 5v – 2
v + 2 = 5v – 2
So, v = 1 m/s
and u = 3 m/s
Momentum of system = 1 × 3 = 3 kgm/s Momentum of 5kg after collision = 5 × 1 = 5 kgm/s
1
m u 2 1
1 3 2
So, kinetic energy of centre of mass =
(m + m ) 1 =
(1 + 5)
= 0.75 J
Total kinetic energy =
2 1
1 × 1 × 32 = 4.5 J.
2
2 m1 m2 2
6
14. When 0 < E < V0 there will be acting a restoring force to perform oscillation because in this case particle will be in the region |x| x0 .
15. V = x4
T.E. =
2 =
1 m2A2 = A4 (not strictly applicable just for dimension matching it is used)
2
2A2
m
16. F = dU dx
as for |x| > x0 V = V0 = constant
dU
dx = 0 F = 0.
17. As the magnetic field is greater, the critical temperature is lower and as B2 is larger than B1. Graph ‘A’ is correct.
18. For B = 0 TC = 100 k
B = 7.5 T TC = 75 k
For B = 5T 75 < TC < 100
19. S = 2100 J kg–1 ΒΊC–1 L = 3.36 × 105 J kg–1
420 = m S + (1) × 10–3 × L
420 = m s(5) + 3.36 × 102
1
420 – 336 = m(2100) × 5 m = 125
× 1000 = 8 gm.
20. Let speed of cars are v1 and v2
v
frequency received by car f =
1 v v
f
1 0
v v1 v
frequency reflected by car f =
v
v v
f
1 0
v v 2 v v1
f = f2’ – f2 = v v
v v
f
1 0
(v v2 )(v v1 ) (v v1)(v v2 )
f =
(v v1)(v v2 ) 0
f =
2v(v 2 v1) f0 (v v1)(v v2 )
2(v 2 v1) f0
v
Given
2(v 2 v1) f0 v
1.2
= 100 f0
v2
– v1
= 7.126
Answer in nearest integer is 7.
21. When object distance is 25.
1 1 1
v – u = f
1 1 1
v – (–25) = 20
v 100
v = 100 cm.
m25 = u
= – 25
= – 4.
When object distance is 50.
1 1
v – (–50)
1
= 20
u = 100 cm
3
m50 =
100
3
– 50
2
= – 3
m25
m50
–4
= – 2
= 6.
Alternate : 3
f
m25
m50
20 25
= f
20 50
30
= 5 = 6
P2
22. P1 =
E =
2m
P =
2mE
or E = qV}
P =
P
=
=
p
The ratio , to the nearest integer, is equal to 3.
23.
2
i = 2 R
2 2
J1 =
2 R
eq
1 1
= 1 1 =
1 1
1 2
2 2
req = 2
i = 1
= 2R 1
J2 = 1 2R R
R
2
9 2 2
9 2 2
Given J1 = 4
J2
2 R
R = 4
1 2R
2
2 R
3
= 1 2R
2 + 4R = 6 + 3R R = 4.
24. Given that (m)B = 3(m)A
1
T
so, TA = 3TB
E1 = 4 (6)2 T 4 = 4(6)2 (3T )4
A B
E2 = 4 (18)2 T 4
E1
E2 = 9.
25. Aeq =
Aeq =
42 32 2(4)(3)cos
2
Aeq = 5.
26. n =
y =
F / A
π / π
F
π =
yA
π }
n = =
= 140 n = 4.
27.
A
2.2 Ms
5d
c.m. B
d
6 6 11 M
5d 5d d d
Total angular
momentum about
c.m.
(2.2M ) (11M )
Angular
momentum of
B about
c.m. =
(11M
) d d
= 6.
s 6 6
(G) 4 R3
GM
28. g =
R2
=
R2
; g R
Given, =
Ve = = Ve R
V1
e
Ve
V1
e
Ve 22
Ve = 3 km/hr.
PAPER - 2
1.
First image,
1 1 = 1
v u f
1 1 = 1
v 30 15
v = 30, image in formed 20 cm behind the mirror.
Second image, by plane mirror will be at 20 cm infront of plane mirror.
For third image,
1 1
v 10
1 1
v 10
1
= 15
1 =
15
3 2 5
30 = 30
v = 6 cm
Ans. Final image is real & formed at a distance of 16 cm from mirror.
2.
Electrostatics repulsive force ; F
ele
2
20
2
; F = F
ele =
2R2
20
3. Fdt p
1 × 4 × 3 – 1 × 1.5 × 2 = p – 0
2 2 f
9
pf = 6 – 1.5 = 2
K.E. = p =
2m
81
4 2 2
;K.E. = 5.06 J Ans.
4. Fundamental frequency of close organ pipe =
V1
4π1
Second harmonic frequency of string =
2V2
2π 2
So,
V1
4π1 =
V2
π 2
320
= 4 0.8
1
= 0.5
50
2500 =
1
= 50 =
m 0.5
m = 10 gm.
Main scale
5.
0
0 10
20 VSD = 16 MCD
1 VSD = 0.8 MSD
Least count = MSD – VSD
= 1 mm – 0.8 mm
= 0.2 mm
6. In equilibrium, mg = qE
In absence of electric field, mg = 6rv
qE = 6qrv
m = 4 Rr3d. = qE
3
4 qE 3 qE
3 6v
d = g
After substituting value we get, q = 8 × 10–19 C Ans.
7. dN
dt
dN dt
πn
= N
= N0e–t
= –t + πn(N0)
y = mx + c m = –
= 1 [slope by graph = 1 ]
2 2
πn2
T =
= 2 × 0.693 = 4.16
n
n = 3 = no. of half life. p = 23 = 8. Ans.
8. R = 20 m, f = 10 m
For mirror,
1 1 1
1 1 1
V U f
25 / 3 U1 10
1 1 3
U1 10 25
1
= 50
U1
= – 50 cm
1 1
50 / 7 U2
= 1
10
1 1
U2 = 25
U2
= –25 cm
25 5
So, speed =
= 30 m/sec. = 6 m/sec.
5 18
& in km/hr = 6 × 5
= 3 km/hr.
R
9. tanC = 8
............(i)
5 3
3 sinC = 1.sin90ΒΊ sinC = 5
C = 37ΒΊ
3 R
4 = 8
R = 6 cm.
10. Equation of charging of capacitor,
V = V 1 et / ReqCeq
Ceq = 2 + 2 = 4 F
Req = 1 M
t
4 = 101 e 106410 6
e–t/4 = 0.6
et/4 = 5
3
t = πn 5 – πn 3 t = 0.5 × 4
4
t = 2 sec. Ans.
11. For adiabatic process,
TV–1 = constant
V 1
T = T1 1
2 V2
T = T 327 1
2 1 5
T2 = 4T1 a = 4 Ans.
12.
Due to surface tension, vertical force on drop = F = T2r sin = T2r r
v R
T2r 2
=
R
13. Equating forces on the drop :
T2r 2
R
= 4 R3g 3
(Assume drop as a complete sphere)
3Tr 2 1/ 4
3 0.11 25 108 1/ 4
2g
2 103
10
= 14.25 × 10–4 m = 1.425 × 10–3 m
14. Surface energy of the drop
U = TA = 0.11 × 4 (1.4 × 10–3)2 = 2.7 × 10–6 J
nh
15. = 2
Rotational kinetic energy =
1 2 =
2
1 n2h2
2 42
n2h2
= 82
16. hf = change in rotational kinetic energy (f = frequency)
3h2
hf = 82
3h 3 2 1034
= 82f = 2 4 11 = 0.1875 × 10–45
8 10
= 1.875 × 10–46 kg m2 .
17.
m1r1 = m2r2 12r1 = 16r2
r1 4
r1 = 4
r2 3
4
r1 = 7 π ; r2
π 7
= 3 r = 3 4 π = 3 π
4 1 4 7 7
4 2
3 2
Now, = m r 2 + m r 2 = m1
π
+ m
π
1 1 2 2
7
2 7
π = = 0.128 × 10–9 m = 1.28 × 10–10 m
18. (A)
2 = 3
As there is no deviation. As the light bends towards normal in denser medium 2 > 1
p – A & C
(B)
As light bends away from normal
2 < 1
& 3 < 2
q – B & D
(C)
2 = 3 (As no deviation)
2 > 1 (As light bends + towards normal) r – C & A
(D)
2 < 1
3 < 2
As light bends away from normal s – B, D
(E)
2 = 3 As no deviation of light
2 < 1 As light bend away from normal t – C & B
18. (p)
As is steady state current
V1 = 0 ; = 0
Hence, V2 = V
So , answer of P C (q)
In the steady state ;
d
V1 = 0 as dt = 0
V2 = V = R or V2 and V2 > V1 So , answer of q B, C, D
(r)
Inductive reactance XL = L
XL = 6 × 10–1
and resistance = R = 2
So, V1 = XL
and V2 = R
Hence, V2 > V1 So, Answer of r A,B,D
(s)
Here, V1 = XL, where, XL = 6 × 10–1
104
Also, V2 = XC, where, XC = 3
So, V2 > V1
V1
V2
So, answer of s A,B,D
(t)
Here, V1 = R, where, R = 1000 , XC =
104
104
3
V2 = XC , where, XC =
3
So, V2 > V1 and V1
V2
So, answer of t A,B,D
Ans. (A) – r,s,t ; (B) – q,r,s,t ; (C) – p,q ; (D) – q,r,s,t Note : For circuit ‘p’ :
Ldi q
di d2i dq
d2i
1 dq
V – dt
C = 0 or CV = CL dt
+ q or 0 = LC dt2 dt or
dt 2 LC dt
So, i = i0 sin
t 0
As per given conditions, there will be no steady state in circuit ‘p’. So it should not be considered in options of ‘c’.
Ans. (A) – r,s,t ; (B) – q,r,s,t ; (C) – q ; (D) – q,r,s,t
Time : 1.00 Hr Max. Marks : 84
GENERAL INSTRUCTIONS
1. There are 28 Questions.
2. For each question in Section–I, you will be awarded 3 marks if you give the correct answer and zero mark if no answer is given. In all other cases, minus one (–1) will be awarded.
3. For each question in Section–II, you will be awarded 3 marks if you give the correct answer and zero mark if no answer is given. Partial marks will be answered for partially correct answers. No negative marks will be awarded in this Section.
4. For each question in Section–III, you will be awarded 3 marks if you give the correct answer and
zero mark if no answer is given. In all other cases, minus one (–1) will be awarded.
5. For each question in Section–IV, you will be awarded 3 marks if you give the correct answer and
zero mark if no answer is given. No negative marks will be awarded for in this Section.
SECTION - I
Single Correct Choice Type
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. A block is kept on a incline plane whose angle of inclination can be changed. The coefficient of friction between the incline and the block is . As the angle is varied from = 0 to = /2, the frictional force f versus angle graph will look like
f f
mg mg
(A) (B)
(C) (D)
2. Four rings of radii R, 2R, 3R and 4R are made of wires of linear mass
densities 2 ,
5Ξ» ,
10Ξ» and
17Ξ» respectively. They are placed
concentric and in the same plane. The work required to move a unit mass from point P on the axis at a distance R from the common centre of the rings to infinity is:
(A) 20ΟGΞ»
(B) G.2 Ο Ξ»
(C) – 20ΟGΞ»
(D) – G.2 Ο Ξ»
3. Consider a square sheet of side a and thickness b. The resistance between two opposite square faces is
(A) directly proportional to a (B) directly proportional to b
(C) inverse proportaional to of a (D) independent of a
4. A gas deviates from an ideal behavior if :
(A) its pressure is low and temperature is high (B) it follows assumptions of kinetic theory of gases
(C) for one mole of a gas [PV/RT –1] = 0. (D) Pressure is high and temperature is low.
5. There are three bulbs having rating 100 W, 60 W and 40 W at voltage 220 volt. If their resistance are R100, R60 and R40, respectively, the relation between there resistance is.
(A)
1
R100
1
R 40
1
R60
(B) R100
= R40
+ R60
(C) R100 > R60 > R40 (D) R100 =
6. For the verification of Ohm's law, a student has made the connection as shown. R1and R2 are the effective resistances of the galvanometers G1 and G2 respectively. For best result
(A) R1 = R, R2 >> R (B) R1 << R, R2 >> R
(C) R1 >> R, R2 << R (D) R1 << R, R2 = R1.
7. An AC voltage source of variable angular frequency and fixed amplitude V is connected in series with a inductor of inductance L and an electric bulb of resistance R (capacitance zero). When is increased :
(A) the bulb glows dimmer (B) the bulb glows brighter
(C) total impedance of the circuit is unchanged (D) total impedance of the circuit increases
8. A light flexible wire (with ends joined) of nonconducting material has posi- tive charge q uniformly distributed it placed in uniform magnetic field B. The wire takes a circular shape of radius R when rotated in the magnetic field with
angular velocity . The tension in the wire is :
BqR
(A)
(B) (B)
BqR 2
2BqR
(C) BqR (D)
SECTION - II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.
9 One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. its volume at A is V0. choose the correct option (s) from the following
(A) Internal energies at A and C are the same
(B) volume at B is 4 V0
(C) workdone by the gas in the process AB is 12P0 . V0
(D) Temperature at B is 4T0
10. A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 45ΒΊ (see figure). If the refractive index of
the material of the prism is , which of the following is (are) correct ?
(A) The ray gets totally internally reflected at face CD.
(B) The ray comes out through face AD undeviated.
(C) The angle between the incident ray and the emergent ray is 45ΒΊ.
(D) The angle between incident ray and the emergent ray is 120ΒΊ.
11. A few electric field lines for a system of two charges Q1 and Q2 fixed at two different points on the x-axis are shown in the figure. These lines suggest that.
(A) Q1 is negative
(B) Q2 is positive
(C) The electric field at a some finite distance right of Q2 is zero.
(D) The electric potential at some finite distance right of Q2 is zero
12. A student uses a simple pendulum of length π to determine g, the acceleration due to gravity. He measures the length π with a tape of least count 1 cm and finds the length as 100 cm. He uses a stop-watch with the least count of 1 sec for this and records 20 seconds for 10 oscillations. For this observation, which of the
following statement(s) is (are) true ?
(A) Error T in measuring T, the time period, is 0.1 seconds
(B) Error T in measuring T, the time period, is 1 second
(C) Percentage error in the determination of g is 11%
(D) Percentage error in the determination of g is 9%
13. A point mass of 1kg collides elastically with a point mass of 5 kg moving with speed 1 m/s in the same direction. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is (are) correct for the system of these two masses ?
(A) Total momentum of the system is
21 kg ms–1
2
(B) The speed of 5 kg mass after collision is 5 ms–1
2
(C) Kinetic energy in centre of mass frame is nearly 8.4 J.
(D) Total kinetic energy of the system in laboratory frame is nearly 15.1 J.
SECTION–III
Paragraph Type
This section contains 2 paragraphs. Based upon the first paragraph 3 multiple choice questions and based upon the second 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. 14 to 16
When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx2, it performs simple
harmonic motion. The corresponding time period is proportional to
m , as can be seen easily using
k
dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different
from kx2 and its total energy is such that the particle does not escape
to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = |x|3 ( > 0) for |x| near the origin and becomes a constant for |x| x0 (see figure)
14. If the total energy of the particle is E, it will not move to infinity only if :
(A) E < 0 (B) E > 0
(C) |x0|3 > E > 0 (D) E > |x0|3
15. For periodic motion of small amplitude A, the time period T of this particle is proportional to :
(A)
(C) A
(B)
(D)
16. The acceleration of this particle for |x| < x0 is :
(A) proportional to x2 (B) proportional to x
(C) proportional to x3 (D) zero
Paragraph for Question Nos. 17 to 18 Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is
lowered below a critical temperature TC(0). An interesting property of
superconductors is that their critical temperature becomes smaller than TC (0) if they are placed in a magnetic field, i.e., the critical temperature TC
(B) is a function of the magnetic field strength B. The dependence of TC (B)
on B is shown in the figure.
17. In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for three different magnetic fields B1 (solid line) ,B2 (dashed line) and B3 (thick line). If B3 > B2 > B1 , which of the following graphs shows the correct variation of R with T in these fields?
(A) (B)
(C) (D)
18. The magnetic field increases beyond the value B0 . Select the correct statement :
(A) The material will behave as a superconductor at high temperature.
(B) Material will not behave as a superconductor unless temperature is below certain non-zero value.
(C) Material will not behave as a superconductor at all.
(D) Material will behave as a superconductor at negative absolute temperature.
SECTION–IV
Integer Type
This Section contains 10 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.
19. A piece of ice (heat capacity = 2100 J kg–1 ΒΊC–1 and latent heat = 3.36 × 105 J kg–1) of mass m grams is at
–10 ΒΊC at atmospheric pressure. It is given 840 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 2 gm of ice has melted. Assuming there is no other heat exchange in the process find the value of m :
20. Two cars are moving in the same direction perpendicular to a wall with speed v1 and v2. One is moving towards the wall and the other away from it. They blow horns of frequency f0 each. The difference of frequencies observed by the drivers of the cars of its own echo is 1% of f0. The cars are moving at constant speeds much smaller than the speed of sound 333 m/s. Find the sum of speeds of two cars (in Km per hour) to nearest integer.
21. The focal length of a thin biconvex lens is 30 cm. When an object is moved from a distance of 40 cm in front
m40
of it to 120 cm, the magnification of its image changes from m40 to m120. Find the ratio m120 :
22. An -particle and a 16O nucleus are accelerated from rest by a potential difference of 100V. After this, their
Ξ»o
de-Broglie wavelengths are and o respectively. Find the ratio :
Ξ±
23. When three identical batteries of internal resistance 1 each are connected in series across a resistor R, the rate of heat produced in R is J1. When the same batteries are connected in parallel across R, the rate is J2. If J1 = 4 J2 find the value of R in :
24. Two spherical bodies A (radius 4 cm) and B (radius 32 cm) are at temperatures T1 and T2 respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 2000 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?
2x – 6t – 2Ο
25. When two progressive waves y1 = 4 sin (2x – 6t) and y2 = 4 sin
are superimposed, find the
amplitude of the resultant wave :
26. A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is 3.2 × 10–7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 160 rad s–1. If the Young's modulus of the material of the wire is n × 109 Nm–2, find the value of n :
27. A binary star consists of two stars A (mass 2 MS) and B ( mass 12 MS) where Ms is the mass of the Sun. They are separated by a distance d and are rotating about their centre of mass, which is stationary. The ratio of the kinetic energy of star A to that of star B :
1
28. Gravitational acceleration on the surface of an astronomical body is 6 g, where g is the gravitational acceleration
25
on the surface of the earth. The average mass density of the planet is 36
times that of the earth. If the
escape speed on the surface of the earth is taken to be 11 kms–1, find the escape speed on the surface of the astronomical body in kms–1 to the nearest integer :
PAPER - 2
Time : 1.00 Hr Max. Marks : 79
GENERAL INSTRUCTIONS
1. There are 19 Questions.
2. For each question in Section–I : you will be awarded 5 marks if answer is correct and zero mark
if no answer is given. In all other cases, minus two (–2) mark will be awarded.
3. For each question in Section–II : you will be awarded 3 marks if answer is correct and zero mark if no answer is given. No negative marks will be awarded for incorrect answers in this Section.
4. For each question in Section–III : you will be awarded 3 marks if answer is correct and zero mark if no answer is given. In all other cases, minus one (–1) mark will be awarded.
5. For each question in Section–IV : you will be awarded 2 marks for each row in which you give the correct answer. Thus, each question in this section carries a maximum of 8 marks. There is no negative marks awarded for incorrect answer(s) in this Section.
SECTION - I
Single Correct Choice Type
This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and
(D) out of which ONLY ONE is correct.
1. A biconvex lens of focal length 15 cm is infront of a plane mirror. The distance between the lens and the mirror is 40 cm. A small object is kept at a distance of 20 cm from the lens. The final image is
(A) Virtual and at a distance of 20 cm from mirror
(B) Real and at distance of 60 cm from the lens
(C) Virtual and at a distance of 20 cm from the lens
(D) Real and at a distance of 20 cm from the mirror
2. A uniformly charged thin spherical shell of radius R carries uniform surface charge density of per unit area. It is divided in two parts by a plane at a distance R/2 from the centre of the shell. The minimum force F required to hold the two parts is :
1 2 2
2R2
(A) 0
(B)
20
3 2R2 2
(C) 8 0 (D) 20
3. A block of mass 9 kg is free to move along the x-axis. Initially it is at rest and from t = 0 onwards it is subjected to a time-dependent force F (t) in the x direction. The force F (t) varies with time t as shown in the figure. The kinetic energy of the block after 6 sec onds is :
(A) 15 J (B) 450 J
(C) 225 J (D) 12.5 J
4. A hollow pipe of length 0.85 m is closed at one end. At its open end a 0.5 m long uniform string fixed at both ends is vibrating in its fourth harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the string is 50 N and the speed of sound is 340 ms–1, the mass of the string is :[Sound]
(A) 5 grams (B) 10 grams
(C) 20 grams (D) 40 grams
5. A vernier calipers has 1 mm marks on the main scale. It has 40 equal divisions on the Vernier scale which match with 36 main scale divisions. For this Vernier calipers, the least count is :
(A) 0.02 mm (B) 0.05 mm
(C) 0.1 mm (D) 0.2 mm
6. A small spherical drop of oil carrying charge +3e (e = electronic charge) is balanced in still air with vertical uniform electric field of strength E = 12 × 105 Vm–1. When the field strength is doubled, the drop is observed to rise with terminal velocity v = 1.0 × 10–3 ms–1.Given, g = 10 ms–2, coefficent of viscosity of the a i r
1.6 × 10–5 Nsm–2, the density of oil is :
(A) 200 kg-m–3 (B) 400 kg-m–3
(C) 500 kg-m–3 (D) 900 kg-m–3
SECTION - II
(Integer Type)
This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.
7. To determine the half life of a radioactive element, a student plots a graph of πn dN(t) versus t. Here dN(t)
dt dt
is the rate of radioactive decay at time t. The time of 10.4 years is n half lives. Find the nearest integral value of n.
8. Image of an object approaching a convex mirror of radius of curvature 50 m along its optical axis is observed
50
to move from 3
m to 25
2
m in 18 seconds. What is the speed of the object in km per hour.
9. A large glass slab ( = ) is placed over a point source of light on a plane surface. The light emerges out
from the top surface of the slab in a radius 1.41 cm. Find the thickness of the slab (in cm) to nearest integer.
10. At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. At what time (in milli seconds) does the voltage across them become 2.5 V?
11. A monoatomic ideal gas is compressed adiabatically so that its pressure becomes 32 times its initial value. If its temperature increases a times initial value, find the value of a.
SECTION - III
Paragraph Type
This section contains 2 Paragraphs. Based upon the first paragraph 3 multiple choice questions have to be answered. Each of these question has four choice (A), (B), (C) and (D) out of which ONLY ONE is correct.
Paragraph for questions 12 to 14.
When liquid medicine of density is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
12. Let π be the length of small element of the contact of the drop and the dropper. The inter molecular force between the two is :
(A) 2rT (B) π.T
T.2Οr 2
(C) 2π.T (D)
R
13. If F be the force due to surface tension, the maximum radius of the liquid drop formed is R. Then the best relation is :
(A) F =
4 R3..g (B) F × r = 4 R3..g
3 R 3
(C) F =
4 R3..g (D) F × r = 4 r3..g
3 R 3
14. After the drop detaches, the shape of the drop is (neglect the effect of gravity on the drop shape) :
(A) spherical as surface area is minimum
(B) spherical as surface area is maximum
(C) approximately cylindrical as surface area is minimum
(D) approximately cylindrical as surface area is maximum
Paragraph for questions 15 to 17
To explain the discreate spectrum of hydrogen atom Bohr introduced the concent of quantization of angular momentum of the electron revolving around a proton. We want to see the same effect of quantization if applied on the Earth revolving around the Sun. We will assume that the Sun is at rest and of point size and there is no effect of other planets on the motion of the Earth. Let m be mass of the Earth revolving with speed vn in nth orbit of radius rn around the Sun of mass M. The angular momentum of Earth in nth orbit is
h
Ln = n 2 , h = Planck's constant, n = Positive integer.
The energy of an orbit is the total kinetic energy plus gravitational potential energy of the Earth-Sun system. Take gravitational potential energy to be zero when the separation is .
[Useful data : G = (6.67 × 10–11) Nm2/Kg2 ; h = 6.63 × 10–34 Js ; M = mass of the Sun = 2 × 1030 Kg; m = Mass of the Earth = 6 × 1024 Kg, radius of Earth orbit = 1.5 ×1011 m]
15. The energy of the nth orbit of the earth is :
2Ο 2G2M2m3
2Ο2G2M2m3
(A) En =
n2h2
(B) En =
n2h2
(C) En =
4Ο2G2M2m3
n2h2
(D) En = 0
16. The radius of the first 'Bohr orbit' for the Earth is :
(A) 10–138 m (B) 10–10 m
(C) 108 m (D) 1011 m
17. The 'Principal quantum number' n corresponding to the present orbit of the Earth is :
(A) 1 (B) 5
(C) 1074 (D) 10
SECTION - IV
(Matrix - 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) in Column-II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question
against statement B, darken the bubbles corresponding to q and r in the ORS.
18. Two transparent media of refractive indices 1 and 3 have a solid lens shaped transparent material of refractive index 2 between them as shown in figures in column ΞΞ. A ray traversing these media is also shown in the figures. The dotted line shows the line passing through the centre of curvature on the second (left) face of refraction. In Column Ξ different relationships between 1, 2 and 3 are given. Match them to the ray diagrams shown in Column ΞΞ.
Column Ξ Column ΞΞ
(A) 1 < 2 (p)
(B) 1 > 2 (q)
(C) 2= 3 (r)
(D) 2 > 3 (s)
(t)
19. You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first three circuits) or an AC voltage source of 50 Hz frequency (the next two circuits) in different
ways as shown in Column ΞΞ. In DC circuit, the current is the current in the circuit after t = πn2 × , where
is time constant for corresponding circuit. In AC circuit, the current is the rms value after steady state is reached.
Column Ξ Column ΞΞ
(A) V1 > V2 (p)
(B) V1 = V2 (q)
(C) V1= V (r)
(D) V1= V2 =
V (s)
2
(t)
A nswers
PAPER - 1
1. (D) 2. (A) 3. (B) 4. (D) 5. (A)
6. (C) 7. (A) 8. (B) 9. (A)(B)(C)(D)
10. (A)(B)(C) 11. (A) (B)(C)(D) 12. (A)(C) 13. (A)(C) 14. (C)
15. (B) 16. (A) 17. (A) 18. (C) 19. 8 gm
20. 6 21. 9 22. 4 23. 5 24. 4
25. 4 26. 8 27. 6 28. 2
PAPER - 2
1.
(B)
2.
(C)
3.
(D)
4.
(D)
5.
(C)
6. (A) 7. 5 8. 5 9. 2 10. t = 7 ms
11. a = 4 12. (B) 13. (A) 14. (A) 15. (A)
16. (B) 17. (C)
18. (A) – q,s,t ; (B) – p,q,r,s ; (C) – p ; (D) – p,q, r, t
19. (A) – p,s ; (B) – q,r,t ; (C) – s ; (D) – q,r
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