STAGE-1TEST PAPERS-10 (PHYSICS)
STAGE
TEST PAPERS (PHYSICS)
1
PAPER - 1
Time : 1.00 Hr Max. Marks : 70
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded in this section.
3. For each question in Section II, you will awarded 4 marks If you darken ALL the bubble (s) correspoding to the correct answer (s) ONLY . In all other cases zero (0)marks will be awarded. No negative marks will be awarded for incorrect answers in this section.
4. For each question In Section III, You will be awarded 4 marks if you darken the bubble corresponding to the correct answer ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect anwers in this section.
SECTION - I
Single Correct Answer Type
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and
(D) out of which ONLY ONE is correct.
1. A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed . If the angular
momentum of the system, calculated about O and P are denoted by LO
and LP respectively, then
(A) LO and LP do not vary with time.
(B) LO varies with time while LP remains constant.
(C) LO remains constant while LP varies with time.
(D) LO and LP both vary with time.
2. A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
(A) – 280.0 cm. (B) 40.0 cm. (C) 21.5 cm. (D) 13.3 cm.
3. A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed , as shown in the figure. At time, t = 0, a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system
remains throughout. The magnitude of the torque (| → |) on the system about O, as a function of time is best
represented by which plot ?
(A) (B)
(C) (D)
4. A mixture of 2 moles of helium gas (atomic mass = 4 amu), and 1 mole of argon gas (atomic mass = 40 amu)
vrms(helium)
is kept at 300 K in a container. The ratio of the rms speeds
rms
(argon) is :
(A) 0.32 (B) 0.45 (C) 2.24 (D) 3.16
5. Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference X. A proton is released at rest midway between the two plates. It is found to move at 45° to the vertical JUST after release. Then X is nearly
(A) 1 × 10–5 V (B) 1 × 10–7 V (C) 1 × 10–9 V (D) 1 × 10–10 V
6. Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is
(A) T (D) 974 T
7. A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency
rad / s . Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of
3
45º as shown in the figure. Point P is at a horizontal distance of 10 cm from O. If the pebble hits the block at t = 1s, the value of v is (take g = 10 m/s2)
(B)
51m / s
(C)
52 m / s
(D)
53 m / s
8. Young’s double slit experiment is carried out by using green, red and blue light, one color at a time. The fringe widths recorded are G, R and B, respectively. Then
(A) G > B > R (B) B > G > R (C) R > B > G (D) R > G > B
9. Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface
→
charge density. The variation of the magnitude of the electric field E(r) and the electric potential V(r) with the distance r from the centre, is best represented by which graph?
(A) (B)
(C) (D)
Y 4MLg
10. In the determination of Young’s modulus
ld2
by using Searle’s method, a wire of length L = 2 m
and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension 𝑙 = 0.25 mm in the length of the wire is observed. Quantities d and 𝑙 are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to
the maximum probable error of the Y measurement
(A) due to the errors in the measurements of d and 𝑙 are the same.
(B) due to the error in the measurement of d is twice that due to the error in the measurement of 𝑙.
(C) due to the error in the measurement of 𝑙 is twice that due to the error in the measurement of d.
(D) due to the error in the measurement of d is four time that due to the error in the measurement of 𝑙.
SECTION - II
Multiple Correct Answer(s) Type
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
11. Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields → E ˆj and → B ˆj . At time t = 0, this charge has velocity → in the x-y plane, making an
E 0 B 0 v
angle with x-axis. Which of the following option(s) is(are) correct for time t > 0 ?
(A) If = 0°, the charge moves in a circular path in the x-z plane.
(B) If = 0°, the charge undergoes helical motion with constant pitch along the y-axis.
(C) If = 10°, the charge undergoes helical motion with its pitch increasing with time, along the y-axis.
(D) If = 90°, the charge undergoes linear but accelerated motion along the y-axis.
12. A cubical region of side a has its centre at the origin. It encloses three fixed point charges, –q at (0, –a/4, 0),
+ 3q at (0, 0, 0) and –q at (0, +a/4, 0). Choose the correct option(s).
(A) The net electric flux crossing the plane x = +a/2 is equal to the net electric flux crossing the plane x = –a/2.
(B) The net electric flux crossing the plane y = +a/2 is more than the net electric flux crossing the plane y = –a/2.
q
(C) The net electric flux crossing the entire region is 0 .
(D) The net electric flux crossing the plane z = +a/2 is equal to the net electric flux crossing the plane x = +a/2.
13. A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe.
(A) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.
(B) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is open.
(C) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.
(D) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.
14. A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle with the horizontal. A horizontal force of 1 N on the block through its center of mass as shown in the figure. The block remains
stationary if (take g = 10 m/s2)
(A) = 45°
(B) > 45° and a frictional force acts on the block towards P.
(C) > 45° and a frictional force acts on the block towards Q.
(D) < 45° and a frictional force acts on the block towards Q.
15. For the resistance network shown in the figure, choose the correct option(s).
(A) The current through PQ is zero.
(B) I1 = 3 A.
(C) The potential at S is less than that at Q.
(D) I2 = 2 A.
SECTION - III
Integer Answer Type
This section contains 5 question. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).
16. A circular wire loop of radius R is placed in the x-y plane centered at the origin O. A square loop os side a (a
<< R) having two turns is placed with its center at a = 3 R along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of 45° with respect to the z-axis. If the mutual
0a2
inductance between the loops is given by 2p / 2 R , then the value of p is
17. An infinitely long solid cylinder of radius R has a uniform volume charge density . It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field
23R
at the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression 16k0 .
The value of k is
18. A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Brogle wavelength (in units of fm) of the proton at its start is :
(take the proton mass, mp
= (5/3) × 10–27 kg, h/e = 4.2 × 10–15 J.s/C ;
1
40
= 9 × 109 m/F ; 1 fm = 10–15 m)
19. A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P
IP
is IO and IP, respectively. Both these axes are perpendicular to the plane of the lamina. The ratio IO to the nearest integer is :
20. A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the
magnetic field at the point P is given by N
aJ, then the value of N is :
12 0
PAPER - 2
Time : 1.00 Hr Max. Marks : 66
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. In Section I (Total Marks: 24), for each question 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) Mark will be awarded.
3. In Section ll (Total Marks: 18), contain three paragraphs each describing theory. There are six multiple choice questions relating to three paragraph with two questions from each paragraph. For each question you will be awarded 3 marks if you give the correct answer and zero marks if no answer is given. In all other cases, minus one (-1) mark will be awarded.
4. In Section Ill (Total Marks: 24), for each question you will be awarded 4 marks if you give the correct answer(s) ONLY and zero marks otherwise. There are no negative marks in this section.
SECTION - I
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 loop carrying current lies in the x-y plane as shown in the
figure. the unit vector kˆ is coming out of the plane of the paper. the mag
netic moment of the current loop is :
2 ˆ
(A) a2kˆ
2kˆ
(B)
1a k
2 ˆ
(C)
1a
(D) (2 1)a k
2. A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
(A) more than half filled if
is less than 0.5 (B) more than half filled if
is less than 1.0
(C) half filled if
is less than 0.5 (D) less than half filled if
is less than 0.5
3. An infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current
→
density along is length. The magnitude of the magnetic field, B
axis is best represented by :
(A) (B)
as a function of the radial distance r from the
(C) (D)
4. Consider a disc rotating in the horizontal plane with a constant angular speed about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i)
they land back on the disc before the disc completed
1 rotation.
8
(ii) their range is less than half disc radius, and (iii) remains constant throughout . Then
(A) P lands in the shaded region and Q in the unshaded region
(B) P lands in the unshaded region and Q in the shaded region
(C) Both P and Q land in the unshaded region
(D) Both P and Q land in the shaded region
5. A student is performing the experiment of Resonance Column. The diameter of the column tube is 4cm . The distance frequency of the tuning for k is 512 Hz. The air temperature is 38°C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top and of the Resonance column. When first
resonance occurs, the reading of the water level in the column is
(A) 14.0 (B) 15.2 (C) 16.4 (D) 17.6
6. In the given circuit, a charge of +80 C is given to the upper plate of the 4F capacitor. Then in the steady state, the charge on the upper plate of the 3F capacitor is :
(A) +32 C
(B) +40 C
(C) +48 C
(D) +80 C
7. Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed . The disc are in the same horizontal plane.At time t = 0 , the points P and Q are facing each other as shown in the figure. The relative speed between the two points P
and Q is vr. as function of times best represented by
(A) (B)
(C) (D)
8. Two moles of ideal helium gas are in a rubber balloon at 30° C .The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35°C.The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)
(A) 62J (B) 104 J (C) 124 J (D) 208 J
SECTION – II
Paragraph Type
This section contains 6 multiple choice questions relating to three paragraphs with two questions on each paragraph. Each question has four choices (A), (B) (C) and (D) out of which ONLY ONE is correct.
Paragraph for Questions 9 and 10
The - decay process, discovered around 1900, is basically the decay of a neutron (n), In the laboratory, a proton (p) and an electron (e–) are observed as the decay products of the neutron. therefore, considering the decay of a neutron as a tro-body dcay process, it was predicted theoretically that thekinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has a
continuous spectrum. Considering a three-body decay process, i.e. n p + e– + e , around 1930, Pauli
explained the observed electron energy spectrum. Assuming the anti-neutrino ( e ) to be massless and possessing negligible energy, and neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8 × 106 eV. The kinetic energy carried by the proton is only the recoil energy.
9. What is the maximum energy of the anti-neutrino ?
(A) Zero (B) Much less than 0.8 × 106 eV
(C) Nearly 0.8 × 106 eV (D) Much larger than 0.8 × 106 eV
10. If the anti-neutrino had a mass of 3eV/c2 (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron ?
(A) 0 K 0.8 × 106 eV (B) 3.0 eV K 0.8 × 106 eV
(C) 3.0 eV K < 0.8 × 106 eV (D) 0 K < 0.8 × 106 eV
Paragraph for Question 11 and 12
Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring
material, then by Snells' law, sin1 n2 , it is understood that the refracted ray bends towards the normal.
sin2 n1
But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the
c
refractive index of the medium is given by the relation, n =
where c is the speed of electromag-
netic waves in vacuum, v its speed in the medium, and are negative, one must choose the negative root
r r
of n. Such negative refractive index materials can now be artificially prepared and are called meta-materials. They exhibit significantly different optical behavior, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.
11. Choose the correct statement.
(A) The speed of light in the meta-material is v = c|n|
c
(B) The speed of light in the meta-material is v = | n |
(C) The speed of light in the meta-material is v = c.
(D) The wavelength of the light in the meta-material ( ) is given by =
|n|, where
is the wavelength of
the light in air.
m m air
air
12. For light incident from air on a meta-material, the appropriate ray diagram is :
(A) (B)
(C) (D)
Paragraph for Q. No. 13-14
The general motion of a rigid body can be considered to be a combination of (i) a motioon --- centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through center of mass. These axes need not be stationary. Consider, for example, a thin uniform welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure. Where disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed , the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass the disc about the z-axis, and (ii) a rotation of the disc through an instanta- neous vertical axis pass through its centre of mass (as is seen from the changed orientation of points P and Q). Both the motions have the same angular speed in the case.
Z
Q
Y
X
Now consider two similar systems as shown in the figure: case (a) the disc with its face ver--- and parallel to x-z plane; Case (b) the disc with its face making an angle of 45° with x-y plane its horizontal diameter parallel to x-axis. In both the cases, the disc is weleded at point P, and systems are rotated with constant angular speed about the z-axis.
Z
Z
Y Y
X
Case (a)
X
Case (b)
13. Which of the following statement regarding the angular speed about the istantaneous axis (passing through the centre of mass) is correct?
(A) It is
2 for both the cases (B) it is for case (a); and
for case (b).
(C) It is for case (a); and 2 for case (b) (D) It is for both the cases
14. Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?
(A) It is vertical for both the cases (a) and (b).
(B) It is vertical for case (a); and is at 45° to the x-z plane and lies in the plane of the disc for case (b)
(C) It is horizontal for case (a); and is at 45° to the x - z plane and is normal to the plane of the disc for case (b).
(D) It is vertical of case (a); and is at 45° to the x - z plane and is normal to the plane of the disc for case (b).
SECTION – III
Multiple Correct Answer(s) Type
This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
15. Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane form the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement (s) is (are) correct?
(A) Both cylinders P and Q reach the ground at the same time
(B) Cylinder P has larger linear acceleration than cylinder Q.
(C) Both cylinder Q reaches the ground with same translational kinetic energy.
(D) Cylinder Q reaches the ground with larger angular speed.
16. A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement (s) is (are) :
(A) the emf induced in the loop is zero if the current is constant.
(B) The emf induced in the loop is finite if the current is constant.
(C) The emf induced in the loop is zero if the current decreases at a steady rate.
(D) The emf induced in the loop is finite if the current decreases at a steady rate.
17. In the given circuit, the AC source has = 100 rad/s. considering the inductor and capacitor to be ideal, the correct choice (s) is(are)
(A) The current through the circuit, is 0.3 A
(B) The current through the circuit, is 0.3 A.
(C) The voltage across 100 resistor = 10 V
(D) The voltage across 50 resistor = 10V
18. Six point charges are kept at the vertices of a regular hexagon of side L and centre O, as shown in the figure. Given that K =
1 q
40 L2 ,
which of the following statement (s) is (are) correct ?
(A) the elecric field at O is 6K along OD
(B) The potential at O is zero
(C) The potential at all points on the line PR is same
(D) The potential at all points on the line ST is same.
19. Two spherical planets P and Q have the same uniform density , masses M
and MQ, an surface areas A and
4A, respectively. A spherical planet R also has unfirom density and its mass is (M
+ MQ) . The escape
velocities from the planets P, Q and R, are VP, VQ and VR respectivley. Then
(A) VQ
> VR
> VP
(B) VR
> VQ
> VP
(C) VR/VP
= 3 (D) VP
1
/VQ = 2
20. The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed /2. The ring and disc are separated by frictionless ball bearings. The system is in the x- z plane. The point P on the inner disc is at distance R from the origin, where OP makes an angle of 30º with the horizontal. Then with respect to the horizontal surface,
(A) the point O has linear velocity 3R ˆi .
(B) the point P has a linear velocity 11 R ˆ +
4
(C) the point P has linear velocity 13 R ˆ –
4
3 R ˆ
4
3 R ˆ
4
(D) The point P has a linear velocity 3
R ˆ +
1 R ˆ .
A nswers
PAPER - 1
1. (C) 2. (B) 3. (B) 4. (D) 5. (C) 6. (C) 7. (A)
8. (D) 9. (D) 10. (A) 11. (C,D) 12. (A,C,D) 13. (B,D) 14. (A,C)
15. (A,B,C,D) 16. P = 7 17. K = 6 18. 7 fm 19. 3 20. N = 5
PAPER - 2
1. (B) 2. (D) 3. (D) 4. (A) 5. (B) 6. (C) 7. (A)
8. (D) 9. (C) 10. (D) 11. (B) 12. (C) 13. (D) 14. (A)
15. (D) 16. (A, C) 17. (A, C) 18. (A, B, C) 19. (B, D) 20. (A, B)
PAPER - 1
1.
magnitude and direction of LO remains constant
Magnitude of LP remains constant but direction of LP changes.
1 ( 1) 1 1
2. f1 R1 R2
1 (1.5 1) 1
1
f1 14
1 0.5
f1 14
1 (1.2 – 1) 1 – 1
f2 – 14
1 0.2
f2 14
1 1 1
f f1 f2
= 0.5 0.2
14 14
1 0.7
f 14
1 7 1
v 140 40
= 1 1
20 40
1 2 1
v 40
v = 40 cm
3. L = [m(vt)2] +
m𝑙2
3
L = mv2t2 +
m𝑙2
3
So = dL dt
t
= 2mv2t
straight line passing through (0, 0)
vRms
4. He
vRms
=
3.16
Ar
5.
mg = qE
1.67 × 10–27 × 10 = 1.6 × 10–19 ×
X = 1.67 109 V
1.6
X = 1 × 10–9 V
X 0.01
6.
In steady state energy absorbed by middle plate is equal to energy released by middle plate.
A(3T)4 – A(T’)4 = A(T’)4 – A(2T)4
(3T)4 – (T’)4 = (T’)4 – (2T)4 2(T’)4 = (16 + 81) T4
97 1/ 4
T’ = T
2
7. Time of flight for projectile
2usin
T = g
2usin45 g
= 1 sec.
= 1 sec.
D
8. = d
u =
u = m/s
VIBGYOR increase
> >
So
> G
> B
9.
10. d = 𝑙 =
0.5
100 mm
y =
y
4MLg
𝑙d2
𝑙 d
y max 𝑙
+ 2 d
error due to 𝑙 measurement
𝑙 0.5 /100 mm
𝑙 0.25 mm
2 0.5
error due to d measurement 2
d 100
0.5 /100
d 0.5 mm 0.25
So error in y due to 𝑙 measurement = error in y due to d measurement
11.
If = 0° then due to magnetic force path is circular but due to force qE
() q will have accelerated motion
along y–axis. So combined path of q will be a helical path with variable pitch so (A) and (B) are wrong.
If = 10° then due to vcos, path is circular and due to qE and vsin, q has accelerated motion along y-axis so combined path is a helical path with variable pitch (C) is correct.
If = 90° then F
= 0 and due to qE0
motion is accelerated along y-axis. (D)
12. Position of all the charges are symmetric about the planes x = a
2
them will be same.
and x =
a . So net electric flux through
2
Similarly flux through y = a
2
is equal to flux through y =
a .
2
= qin 3q q q q
0 0 0
By symmetry flux through z =
a is equal to flux through x = a 2 2
13. At open end phase of pressure wave charge by so compression returns as rarefraction. While at closed end phase of pressure wave does not change so compression return as compression.
14.
f = 0, If sin = cos = 45° f towards Q, sin > cos > 45° f towards P, sin < cos < 45°
15. Due to input and output symmetry P and Q and S and T have same potential.
Req =
6 12
18
= 4
= 12 = 3A
1 4
12
=
3
2 6 12
2 = 2 A
VA – VS = 2 × 4 = 8V VA – VT = 1 × 8 = 8V
VP = VQ Current through PQ = 0 (A)
VP = VQ
V > V
(C)
I1 = 3A (B)
I2 = 2A (D)
16. B =
B =
0iR2
2(R2 X2 )3/ 2
0iR2
2(R2 3R2 )3/ 2
0iR2
= 2(4R2 )3 /2
0iR2
= 2.23.R3
0i 16R
= NBA cos45°
= 2 0i a2 1
16R 2
0ia2
M = i
2
M 27 / 2 R =
P = 7
. R2
0a2
2P / 2R
17. E1 =
0 .2R
4 R3
E2 =
1 .
40
. .
3 8
(2R)2
E – E =
R .R
1 2 40
R
0 .24 4
1
= 4
1
0
24
23R
= 960
23R
= 16K0
K = 6
18.
9 109 120ee p2
10 1015 = 2m
h
p
2 h2
p 2
5 10
10
9 109
12e2 = h
2
(120) (3)10–27+15+9 2 = (4.2)2 × 10–30
2 4.2 4.2 1030
360 103
= 42 42 1029
360
= 72 ×10–30
= 7×10–15 m
= 7 fm
19.
I0 =
(4m) (2R)2 2
– 3 mR2 = mR2 [8 –
2
3 ] =
2
13 mR2
2
3 mR2
2 2
11 2 37 2
IP =
(4m) (2R)2 –
2 2
37
m[(2R)
R ]
= 24 mR2 – mR
2
= 2 mR
IP 2
37 3
IO 13
2
= 13
Ans. 3
20.
B oJa oJa
1 2 12
oJa 1 1 5 oJa 50aJ N
2
6 2
12 =
12 aJ
N = 5
a 2
1. Area = a2 + 4 2
2
= a2 +
a2
2
PAPER - 2
A = 1 a2 kˆ
2
2 ˆ
M = A =
1a k
2.
Let outer volume of shell is V0 Let inner volume of shell is Vi
Let volume of water inside the shall is v.
1Vg + (V – V )g = 1V0 g [Equlibrium]
C
V +
0
(V0
i 2
V0
– Vi) = 2
C (V0
– Vi) =
V0 V
V0 V
2
C =
if <
2
V0 Vi
1
2
V0 V 1
2 <
V0 Vi 2
V0 – V <
2
–V < – Vi
2
V0 – Vi 2 2
V > Vi so (D)
2
3.
Case-I x < R
2
|B| = 0
Case-II
R x R 2
→ →
B.d𝑙 0I
2
R 2
|B| 2x =
x
J
0
2
|B| =
0J 2 2
2x
Case-III x > R
→ →
B. d𝑙
= I
2
R 2
|B| 2x =
R
J
|B| =
0J 2x
0
3 R2
4
2
|B| = so
30JR2
8x
4.
To reach the unsheded partion particle P needs to travel horizontal range greater than R sin 45º or (0.7 R) but
its range is less than R . So It will fall on shaded partion.
2
Q is near to origin,its velocity will be nearly along QR so its will fall in unshaded partion. So, (A)
V
5. 4(𝑙 e)
= f 𝑙 + e =
V 𝑙 =
4f
V e 4f
here e = (0.6)r = (0.6) (2) = 1.2 cm
336 102
so 𝑙 =
4 512
–1.2 = 15.2 cm
6. q3 =
C3 .Q
C2 C3
3 3
q3 =
3 2
× 80 = 5
× 80
= 48 C
7.
v = |2 v sin )|
= |2v sin t)|
8. Q = nC T
f R R
= 2
T
= 2 3 R R × 5
2
= 2 ×
5 × 8.31 × 5
2
= 208 J
9. KE
max
of –
Q = 0.8 × 106 eV
KEP KE KE = Q KEP is almost zero When KE 0
10.
then KE Q – KEP
Q
O KE Q KEP KE
O KE Q
11. n = c v
for metamaterials
c
v = | n |
12. Meta material has a negative refractive index
sin =
n1 sin1 n2
n is negative
negative
15. IP > IQ
aP =
aQ =
gsin IP mR2
gsin IQ mR2
1
aP < aQ
V = u + at t a
t P > tQ
V2 = u2 + 2as v a V
1
< VQ
Translational K.E. =
mV2 KE
2 TP
< KETQ
V = R V <
16.
() = 0 for all cases so induced emf = 0
17. C = 100 F, 1
C
1
= (100)(100 106 )
X = 100 , X = L = (100) (.5) = 50
Z1 = Z2 =
= 50 2
= 100 2
=
= 20 sin t
i1 = i1 =
sin (t + /4)
1 sin (t + /4)
5
I2 =
sin (t – /4)
I =
= (.2)
1
= 5 =
(I)rms = =
= 10
10
0.3 A
(V100)rms = (I1)rms) × 100
0.2
= × 100 =
2
= 10 V
0.4
V50)rms =
× 50
= = 10 V
18.
E0 = 6 K (along OD) V0 = 0
Potential on line PR is zero
Ans. (A), (B), (C)
19. Ves = = = R
Ves R
Sarface area of P = A = 4R 2
Surface area of Q = 4A = 4 R 2
R = 2Rp
mass R is MR = MP + MQ
4 R3 = 4 R3 + 4 R3
3 R 3 P 3 Q
R 3 = R 3 + R 3
R P Q
= 9R 3
R = 91/3 R R > R
Q
> RP
Therefore VR > VQ > VP
VR
= 91/3 and
P
VP 1
VQ = 2
20.
V0 = 3R ˆi
V = (3R – R
2
R
cos 60º) ˆi + 2
sin 60 kˆ
= 11R ˆi 3R kˆ
4 4
STAGE
SIMILAR TEST PAPERS (PHYSICS)
3
PAPER - 1
Time : 1.00 Hr Max. Marks : 70
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded in this section.
3. For each question in Section II, you will awarded 4 marks If you darken ALL the bubble (s) correspoding to the correct answer (s) ONLY . In all other cases zero (0)marks will be awarded. No negative marks will be awarded for incorrect answers in this section.
4. For each question In Section III, You will be awarded 4 marks if you darken the bubble corresponding to the correct answer ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect anwers in this section.
SECTION I
Single Correct Answer Type
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and
(D) out of which ONLY ONE is correct.
1. A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed . If the angular momentum of the system, calculated about O, P and Q are denoted by
→
LO , LP and LQ respectively, then
→
(A) LO , LP and LQ do not vary with time.
→
(B) LO varies with time while LP and LQ remains constant.
→
(C) LO remains constant while LP and LQ varies with time.
→
(D) LO , LP and LQ all varies with time.
2. A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 2 Both the curved surfaces are of the same radius of curvature R = 15 cm. one surface of this lens is silvered. For this bi-convex lens, for an object distance of 6 cm, the image distance will be
(A) – 3 cm. (B) – 6 cm. (C) +3 cm. (D) + 6 cm.
3. A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed , as shown in the figure. At time, t = 0, a small insect starts from O and moves with constant acceleration a with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the
system remains throughout. The magnitude of the torque (| → |) on the system about O, as a function of
time is best represented by which plot ?
(A) (B)
(C) (D)
4. A mixture of 2 moles of hydrogen gas (atomic mass = 2 amu), and 1 mole of argon gas (atomic mass = 40
Vrms (hydrogen)
amu) is kept at 300 K in a container. The ratio of the rms speeds
Vrms (argon)
is :
(A) 0.32 (B) 4 (C) 3 (D) 4.47
5. Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference X. A proton is released at rest midway between the two plates. It is found to move at 37° to the vertical JUST after release. Then X is nearly
(A) .75 × 10–5 V (B) .75 × 10–7 V (C) .75 × 10–9 V (D) 1.33 × 10–10 V
6. Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 4T respectively. The temperature of the middle (i.e. second) plate under steady state condition is
1
(A) 65 4 T
1
272 4
1
272 4
1
132 4
2
(B) T
4
(C) T
2
(D) T
2
7. A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency
rad / s . Simultaneously at t = 0, a small pebble is projected with speed v from point O at an angle of
3
45º as shown in the figure. If the pebble hits the block at t = 1s, the value of v is (take g = 10 m/s2)
(B)
51m / s
(C)
52 m / s
(D)
53 m / s
8. Young’s double slit experiment is carried out by using yellow, red and violet light, one colour at a time. The
fringe widths recorded are , and , respectively. Then
y R v
(A) y > v > R (B) v > y > R (C) R > v > y (D) R > y > v
9. Consider a solid non conducting sphere of radius R with its centre at the origin, carrying uniform positive
→
volume charge density. The variation of the magnitude of the electric field E(r)
with the distance r from the centre, is best represented by which graph?
(A) (B)
and the electric potential V(r)
(C) (D)
Y 4MLg
10. In the determination of Young’s modulus
ld2
by using Searle’s method, a wire of length L = 2 m
and diameter d = 0.25 mm is used. For a load M = 2.5 kg, an extension 𝑙 = 0.25 mm in the length of the wire is observed. Quantities d and 𝑙 are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 200. The contributions to
the maximum probable error in measurement of Y.
(A) due to the errors in the measurements of d and 𝑙 are the same.
(B) due to the error in the measurement of d is twice that due to the error in the measurement of 𝑙.
(C) due to the error in the measurement of 𝑙 is twice that due to the error in the measurement of d.
(D) due to the error in the measurement of d is four time that due to the error in the measurement of 𝑙.
SECTION II
Multiple Correct Answer(s) Type
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
11. Consider the motion of a negative point charge in a region where there are simultaneous uniform electric and
magnetic fields → E ˆj and → B ˆj . At time t = 0, this charge has velocity → in the x-y plane, making an
E 0 B 0 v
angle with x-axis. Which of the following option(s) is(are) correct for time t > 0 ?
(A) If = 0°, the charge moves in a circular path in the x-z plane.
(B) If = 0°, the charge undergoes helical motion with constant pitch along the y-axis.
(C) If = 10°, the charge undergoes helical motion with its pitch first decreases than increases with time, along the y-axis.
(D) If = 90°, the charge undergoes linear but first deceletrated than accelerated motion along the negative y-axis.
12. A cubical region of side a has its centre at the origin. It encloses three fixed point charges, –q at (0, –a/4, 0),
+ 2q at (0, 0, 0) and –q at (0, +a/4, 0). Choose the correct option(s).
(A) The net electric flux crossing the plane x = +a/2 is equal to the net electric flux crossing the plane x = –a/2.
(B) The net electric flux crossing the plane y = +a/2 is equal to the net electric flux crossing the plane y = –a/2.
(C) The net electric flux crossing the entire surface of cube is zero.
(D) The net electric flux crossing the plane z = +a/2 is equal to the net electric flux crossing the plane x = +a/2.
13. When a wave pulse travelling in a string is reflected from a rigid wall to which string is tied as shown in figure. For this situation two statements are given below.
(1) The reflected pulse will be in opposite orientation of incident pulse due to a phase change of
radians
(2) During reflection the wall exerts a force on string in upward direction For the above given two statements choose the correct option given below.
(A) Only (1) is true (B) Only (2) is true (C) Both are true (D) Both are wrong
14. A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle with the horizontal.
A horizontal force of 3 N on the block through its center of mass as shown in the figure. The block remains stationary if (take g = 10 m/s2)
(A) = 60°
(B) > 60° and a frictional force acts on the block towards P.
(C) > 60° and a frictional force acts on the block towards Q.
(D) < 60° and a frictional force acts on the block towards Q.
15. For the resistance network shown in the figure, choose the correct option(s).
(A) The current through PQ is zero.
(B) I1 =
48 A.
11
(C) The current through ST is zero
(D) I2
= 18 A.
11
Section III : Integer Answer Type
This section contains 5 question. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).
16. A circular wire loop of radius R is placed in the x-y plane centered at the origin O. A square loop of side
a (a << R) having one turn is placed with its center at 3 R along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of 60° with respect to the z-axis. If the mutual
0a2
inductance between the loops is given by , then the value of p is
2p R
17. An infinitely long solid cylinder of radius R has a uniform volume charge density . It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field
at the point P, which is at a distance 3R
4
The value of k is
65R
from the axis of the cylinder, is given by the expression 27k0 .
18. partical is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Brogle wavelength (in units of fm) of the
partical at its start is fm then find value of p :
(take the proton mass, mp
= (5/3) × 10–27 kg, h/e = 4.2 × 10–15 J.s/C ;
1
40
= 9 × 109 m/F ; 1 fm = 10–15 m)
19. A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P
is I
and I , respectively. Both these axes are perpendicular to the plane of the lamina. The ratio IP is p 3 .
O P IO 13
Find value of p :
20. A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the
magnetic field at the point P is given by
N 0 aJ, then the value of N is :
24
PAPER - 2
Time : 1.00 Hr Max. Marks : 66
GENERAL INSTRUCTIONS
1. There are 20 Questions.
2. For each question in Section I and Section II , you will be awarded 3 marks if you darken the bubble corresponding to the correct answer ONLY and zero (0) marks if no bubbles are darkend. In all other cases, minus one (–1) mark will be awarded in these sections.
3. For each question in Section III, you will be awarded 4 marks If you darken ALL the bubble (s) correspond- ing to the correct answer (s) ONLY In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect answer (s) in this section.
SECTION - I
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 loop carrying current lies in the x-y plane as shown in the figure. the unit vector kˆ is coming out of the plane of the paper. the magnetic moment of the current loop is :
2 ˆ
2 ˆ 2
(A) a2kˆ
(B) 4
1 a k
(C)
1a k
(D) (2 1)a kˆ
2. A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in
water in one-third submerged state. If is the relative density of the material of the shell with respect to
water, then the correct statement is that the shell is
(A) more than one-third filled if is less than 1/3
(B) more than one-third filled if is less than 1.0
(C) one-third filled if is less than 1/3
(D) less than one-third filled if is less than 1/3
3. An infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a total current I which is uniformly distributed along its length. Also a thin wire carrying same current I in opposite direction
→
is placed along the axis of cylinder. The magnitude of the magnetic field, B
distance r from the axis is best represented by :
(A) (B)
as a function of the radial
(C) (D)
4. A thin string is wrapped several times around a cylinder kept on a rough horizontal surface. A boy standing at a distance 𝑙 from the cylinder draws the string towards him as shown in figure. The cylinder rolls without slipping. The length of the string passed through the hand of the boy while the cylinder reaches his hand is
(A) 𝑙 (B*) 2𝑙 (C) 3𝑙 (D) 4𝑙
5. A student is performing the experiment of Resonance Column. The diameter of the column tube is 4cm . The resonating frequency of the tuning fork is 512 Hz. The air temperature is 38°C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top and of the Resonance column. When second resonance occurs, the reading of the water level in the column is
(A) 48.0 (B) 15.2 (C) 49.0 (D) 17.6
6. In the given circuit, a charge of +80 C is given to the upper plate of the 4F capacitor. Then in the steady state, the charge on the upper plate of the 3F capacitor is :
(A) +32 C (B) +40 C (C) +48 C (D) +80 C
7. Two identical discs of same radius R are rotating about their axes in same directions with the same constant angular speed . The disc are in the same horizontal plane.At time t = 0 , the points P and Q are facing each other as shown in the figure. The relative speed between the two points P
and Q is vr. as function of times best represented by
(A) (B)
(C) (D)
8. One mole of ideal helium gas and one mole of argon gas are in a rubber balloon at 30° C .The balloon is fully expandable and can be assumed no energy is required for its expansion. The temperature of the gas in the balloon is slowly changed to 35°C.The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)
(A) 62J (B) 104 J (C) 124 J (D) 208 J
SECTION – II : Paragraph Type
This section contains 6 multiple choice questions relating to three paragraphs with two questions on each paragraph. Each question has four choices (A), (B) (C) and (D) out of which ONLY ONE is correct.
Paragraph for Questions 9 and 10
A radio nuclide with half life T = 69.31 second emits -particles of average kinetic energy E = 11.25 eV. At an instant concentration of -particles at distance, r = 2 m from nuclide is n = 3 × 1013 per m3.
9. Calculate number of nuclei in the nuclide at that instant.
(A) 9.6 × 1022 (B) 9.6 × 1020 (C) 4.8 × 1022 (D) None
10. If a small circular plate is placed at distance r from nuclide such that -particles strike the plate normally and come to rest, calculate pressure experienced by the plate due to collision of -particle.
(Mass of -particle = 9 × 10–31 kg) (log 2 = 0.693)
(A) 1.08 × 10–4 N/m2 (B) 2.16 × 10–4 N/m2 (C) 1.08 × 10–3 N/m2 (D) None
Paragraph for Question 11 and 12
Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring
material, then by Snells' law, sin1 n2 , it is understood that the refracted ray bends towards the normal.
sin2 n1
But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the
c
refractive index of the medium is given by the relation, n =
where c is the speed of electromag-
netic waves in vaccum, v its speed in the medium, and are negative, one must choose the negative root
r r
of n. Such negative refractive index materials can now be artificially prepared and are called meta-materials. They exhibit significantly different optical behavior, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.
11. Choose the correct statement.
(A) The speed of light in the meta-material is v = c|n|
c
(B) The speed of light in the meta-material is v < | n |
(C) The speed of light in the meta-material is v = c.
(D) The wavelength of the light in the meta-material ( ) is given by m air
, where
is the wavelength
of the light in air.
m | n |
air
12. Let the x-z plane be the boundary between two transparent media. Media with y 0 is air has refractive
index 1 and meidum II which is meta material with y 0 has refractive index of magnitude . A ray of light
in medium 1 given by the vector of refracted ray in medium 2.
→ ˆi ˆj incident on the plane of seperation. Then unit vector in the direction
(1)
3 ˆi 1 ˆj
(B*)
3 ˆi 1 ˆj
(C)
3 ˆi 1 ˆj
(D) None
2 2 2 2 2 2
Paragraph for Q. No. 13-14
The general motion of a rigid body can be considered to be a combination of (i) a motion of centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through center of mass. These axes need not be stationary. Consider, for example, a thin uniforming ring welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure. Where disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed , the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass the disc about the z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis pass through its centre of mass (as is seen from the changed orientation of points P and Q). Both the motions have the same angular speed in the case.
Z
Q
Y
X
Now consider two similar systems as shown in the figure: case (a) the disc with its face vertical and parallel to x-z plane; Case (b) the ring with its face making an angle of 45° with x-y plane its horizontal diameter parallel to x-axis. In both the cases, the ring is weleded at point P, and systems are rotated with constant angular speed about the z-axis.
13. Let ring has mass m and radius r then its magnitude of anguler momentum about z axis in case (a) is
mr 2
(A) mr2 (B)
2
2
(C) md2
(D) m(d2 + r2)
14. Which of the following statements about the kinetic energy is correct?
(A) It is same for both the cases (a) and (b). (B) It is more for case (a)
(C) It is more for case (b) (D) nothing can be said
SECTION – III
Multiple Correct Answer(s) Type
This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
15. Two solid cylinders P and Q of same mass and same radius are released frorm top of an inclined plane of same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Friction is just sufficient for pure rolling of solid sphere then Which statement (s) is (are) correct?
(A) Both cylinders P and Q reach the ground at the same time
(B) Cylinder P has larger linear acceleration than cylinder Q.
(C) Both cylinder Q reaches the ground with same translational kinetic energy.
(D) Cylinder Q reaches the ground with larger angular speed.
16. Two current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it wires are at right angle to each other and in the plane of loop then, The correct statement (s) is (are) :
(A) the emf induced in the loop is zero if the current is constant.
(B) The emf induced in the loop is finite if the current is constant.
(C) The emf induced in the loop is zero if the current decreases at a steady rate.
(D) The emf induced in the loop is finite if the current decreases at a steady rate.
17. In the given circuit, the AC source has = 100 rad/s. considering the inductor and capacitor to be ideal, the correct
choice (s) is(are)
(A) The current through the circuit, is 0.56 A
(B) The current through the circuit, is 0.3
(C) The voltage across 50 resistor = 20 V
(D) The voltage across 50 resistor = 10V
2 A.
18. Six point charges are kept at the vertices of a regular hexagon of side L
1 q
and centre O, as shown in the figure. Given that K = 40 L2 , which of the following statement (s) is (are) correct ?
(A) the elecric field at O is 8K along OD
(B) The potential at O is zero
(C) The potential at all points on the line PR is same
(D) The potential at all points on the line ST is same.
19. Two spherical planets P and Q have the same uniform density , masses M
and MQ, and surface areas A
and 9A, respectively. A spherical planet R also has uniform density and its mass is (M
+ MQ) . The escape
Speed from the planets P, Q and R, are VP, VQ and VR respectivley. Then
1
(A) VQ > VR > VP (B) VR > VQ > VP (C) VR/VP = 3 (D) VP /VQ = 3
20. The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed and (ii) an inner disc of radius 2R rotating clockwise with angular speed . The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at distance R from the origin, where OP makes an angle of 30º with the horizontal. Then with respect to the horizontal surface,
(A) the point O has linear velocity 3R ˆi .
(B) the point P has a linear velocity 7 R ˆi – 3 R kˆ
2 2
(C) the point P has linear velocity 7 R ˆi + 3 Rkˆ
2 2
3 3 1
(D) The point P has a linear velocity 2 R ˆi + R kˆ .
2
A nswers
PAPER - 1
1. (C) 2. (B) 3. (D) 4. (D) 5. (C) 6. (C) 7. (A)
8. (D) 9. (D) 10. (B) 11. (C,D) 12. (A,B,C,D) 13. (A)
14. (A,C) 15. (A,B,D) 16. P = 5 17. K = 8 18. p = 8 19. 2 20. N = 3
PAPER - 2
1. (B) 2. (A) 3. (D) 4. (B) 5. (A) 6. (C) 7. (B)
8. (D) 9. (A) 10. (A) 11. (D) 12. (B) 13. (C) 14. (C)
15. (A) 16. (A,C) 17. (A,C) 18. (A,B,C) 19. (B,D) 20. (A,B)
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