VIDYAMANDIR CLASSES
ALPS_ Physics - 2201
Syllabus
Electrostatics, DC-Circuits, Capacitors, Magnetism, EMI, AC-Circuits
* Mark questions are more than one option correct type.
---------------------------------------------------------------------- DAY-1 -----------------------------------------------------------------------
1.
Two positively charged particles of charges q1 and q2 have mass m
each. A uniform electric field having magnitude E exists in positive x
direction as shown in the figure. The given two charged particles are
released from rest at t = 0 as shown in the figure. If position of q1 at
t  2 sec is given by coordinate (+2a, 0) then the x-coordinate of q2 at
[ ]
t  2 sec is : (neglect gravitational interaction between the particles)
(A)
(C)
2.
q1  q2
E  2a
m
q q 
2  1 2  E  2a
 m 
(B)
(D)
q1  q2
E a
m
q q 
2 1 2  E  a
 m 
A cylindrical solid of length L and radius a is having varying resistivity
given by   0 x where  0 is a positive constant and x is measured from
left end of solid. The cell shown in the figure is having emf V and negligible
internal resistance. The electric field as a function of x is best described by:
2V
V
2V
x
x
(A)
(B)
(C)
(D)
x
L2
L2
0 L2
3.
V
L
[ ]
In the figure a capacitor of capacitance 2 F is connected to a cell of
emf 20 volt. The plates of the capacitor are drawn apart slowly to
double the distance between them. The work done by the external
agent on the plates is:
200 J
(A)
(B)
 200 J
(C)
4.
400 J
(D)
400 J
A ring of radius 5m is lying in the x-y plane and carrying current of 1A
in anti-clockwise sense. If a uniform magnetic field B  3iˆ  4 ˆj is
switched on in space, then the co-ordinates of point about which the
loop will have a tendency to lift up is :
(A)
(3, 4)
(B)
(4, 3)
(C)
(3, 0)
(D)
(0, 3)
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[ ]
[ ]
ALPS-2201
VIDYAMANDIR CLASSES
5.
In a gravity free space, a smooth insulating ring of radius R, with a bead having charge q is placed
horizontally in a uniform magnetic field of induction B0 and perpendicular to the plane of ring. Starting
from t = 0, the magnetic field is varying with time as B (t )  B0  t , where  is positive constant. The
contact force between the ring and bead as a function of time is:
[ ]
(A)
(C)
6.
7.
q 2 Rt
(2 B0  t )
m
q 2 Rt
( B0  t )
4m
(B)
(D)
q 2 Rt
(2 B0  t )
4m
4q 2 Rt
(2 B0  t )
m
Four charges are rigidly fixed along the Y axis as shown. A positive charge
approaches the system along the X axis with initial speed just enough to
cross the origin. Then its total energy at the origin is:
(A)
zero
(B)
positive
(C)
negative
(D)
data insufficient
[ ]
A dipole of dipole moment P  2iˆ  3 ˆj  4kˆ is placed at point A(2,  3, 1). The electric potential due to this
dipole at the point B(4,  1, 0) is equal to : (All the parameters specified here are in S.I. units)
(A)
8.
2 109 volts
(B)
2 109 volts (C)
3 109 volts
(D)
3 109 volts [  ]
In the figure shown two long straight wires with the same cross-sections
are arranged in air, parallel to one another. The distance between the
axis of the wire is  times larger then the radius of wire’s cross section.
Capacitance of the wires per unit length would be: (Taken    1 )
(A)
(C)
9.
10.
2  0
ln 
0
ln 
(B)
(D)
 0
2ln 
Information insufficient
A non-conducting sphere of radius R charged uniformly with surface density  rotates with an angular
velocity  about a diametrical axis passing through its centre. Find the magnetic induction due to the
rotating charge at the centre of the sphere.
0R
2
1
0 R
(A)
(B)
(C)
(D)
0 R
0 R
3
3
2
An uncharged capacitor C = 100 F with a resistor R is connected with
A
AC source as shown in the figure. If R is 50  and switch S is closed at t
R
C = 100 F
= 0, the maximum value of (VA  VB) in volts is:
B
(A)
2
100
100
(B)
4
(C)
6
S
16 sin (100 t)
(D)
8
[ ]
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---------------------------------------------------------------------- DAY-2 -----------------------------------------------------------------------
*11.
A point charge q is kept at origin. The space around origin can be considered as non-conducting sphere of
radius, tends to infinity and having continuous charge distribution, whose volume charge density is

r
a
q e
.
4a r 2
Where ‘a’ is a positive constant and ‘r’ is distance of a point from origin. The potential at infinity can be
considered to be zero. Choose the correct options.
[ ]

*12.
(A)
(B)
The total charge of system is zero
The total charge of system is q / 2
(C)
The magnitude of electrostatic field at a distance of r from origin is
qe  r / a
40 r 2
(D)
The magnitude of electrostatic field at a distance of r from origin is
qe r / a
80r 2
Figure shows a potentiometer circuit. The length of potentiometer wire is L and its resistance is 2 R.
Neglect the internal resistance of the cells. Select the correct alternatives.
[ ]
(A)
L

1
6
(B)
When only S 2 is closed,
L

1
2
1
1
(D)
When both S1 and S 2 are closed, 
L 6
L 2
For a RLC series circuit, phasors of current i and applied voltage V  V0 sin t are shown in diagram at
(C)
*13.
When only S1 is closed,
When both S1 and S 2 are closed

[ ]
t  0. Which of the following is/are correct?
(A)
(B)
(C)
(D)

, instantaneous power supplied by source is negative
2
2
From 0  t 
, average power supplied by source is positive
3
5
At t 
, instantaneous power supplied by source is negative
6
If  is increased slightly, angle between the two phasors decreases.
At t 
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*14.
An electrical circuit is shown in the given figure. The resistance of each
voltmeter is infinite and each ammeter is 100  . The charge on the capacitor
of 100 F in steady state is 4mC. Choose correct statements regarding above
circuit.
(A)
(B)
(C)
(D)
Reading of voltmeter V2 is 16V
Reading of ammeter A1 is zero and A2 is 1/25 A
Reading of voltmeter V1 is 40V
EMF of the ideal cell is 66V
[ ]
*15.
Two concentric, coplanar, circular loop of wire, with different
diameter carry current in the same sense as shown in the figure.
Which of the following statement(s) is(are) correct ?
[ ]
(A)
the magnetic force exerted by the outer loop on a short portion of the inner loop is radially outward
(B)
the magnetic force exerted by the outer loop on a short portion of the inner loop is radially inward
(C)
the net magnetic force exerted by the outer loop on a whole inner loop is non-zero and is radially
outward
(D)
the net magnetic force exerted by the outer loop on a whole inner loop is zero
*16.
The diagram shows part of an evacuated tube in which a stream of electrons from an electron gun passes
between a pair of parallel large deflecting plates. The vertical displacement of the electron beam as it leaves
the parallel plates is x. (Do not consider gravity and the electron enters the deflecting region parallel to the
plates)
Which one of A to D below will change the displacement x of the beam as it leaves the parallel plates?
(A)
increasing the accelerating voltage
(B)
increasing the deflecting voltage
(C)
increasing the distance between the electron gun and the deflecting plates
(D)
increasing the distance between the two deflecting plates
[ ]
*17.
A capacitor (without dielectric) is discharging through a resistor. At some instant a dielectric is inserted
between the plates, then:
[ ]
(A)
Just after the insertion of the dielectric, current will decrease
(B)
(C)
(D)
Just after the insertion of the dielectric, charge on capacitor will increase
Just after the insertion of the dielectric, energy stored in the capacitor will decrease
After the insertion of the dielectric, time constant will increase
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*18.
In the circuit shown in the figure
R  50, E1  25 3
volt and
E2  25 6 sin(t ) volt where   100 s1. The switch is closed at t  0 and
remains closed for 14 minutes, then it is opened. Choose the correct options.
(A)
The amount of heat produced in the resistor is 63000 J.
(B)
The amount of heat produced in the resistor is 7000 J.
(C)
If total amount of heat produced is used to heat 3 kg of water at 20°C, the final temperature will be
25°C.
(D)
The value of direct current that will produce same amount of heat in same time through same
resistor will be 1.5 A.
[ ]
*19.
In the figure shown the plates of a parallel plate capacitor have unequal charges. Its capacitance is `C’. P is
a point outside the capacitor and close to the plate of charge –Q. The distance between the plates is `d’
[ ]
Select correct alternatives:
(A)
(B)
(C)
A point charge at point `P’ will experience electric force due to capacitor
3Q
The potential difference between the plates will be
2C
The energy stored in the electric field in the region between the plates is
9Q 2
8C
(D)
*20.
The force on one plate due to the other plate is
Q
2
20 d 2
A hollow, insulating spherical shell has a surface charge distribution placed upon it,
such that the upper hemisphere has a uniform surface charge density  , while the
lower hemisphere has a uniform surface charge density  , as given in the figure.
(A)
(B)
(C)
(D)
The field at all points of x-y plane within the sphere points in the ve z
direction
All points of the x-y plane within the sphere are equipotential
The field at all points on z-axis which are on either side of origin outside
the sphere is in opposite direction
The field at points on z-axis which are on either side of origin inside the sphere are in opposite
direction
[ ]
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---------------------------------------------------------------------- DAY-3 -----------------------------------------------------------------------
*21.
*22.
A series RLC circuit is driven by a generator at frequency 1000 Hz. The inductance is 90.0 mH; capacitance
is 0.500 F ; and the phase constant has a magnitude of 60.0°. (Take 2  10)
[ ]
(A)
Here current leads the voltage in phase
(B)
Here voltage leads the current in phase
80 

(C)
Resistance of circuit is
3
2
 104
(D)
At resonance  
3
The figure shows part of a large network in which potentials of some of the points are shown. Each
capacitor has a capacitance 5F . Which of the following statements is/are true ?
[ ]
(A)
(B)
(C)
From the given information, potential of point O can be determined but that of B cannot be
determined
From the given information, potential of both the points O and B cannot be determined
If charge on capacitor C2 were also specified, potential of point O can be determined but that of B
(D)
cannot be determined
If charge on capacitor C2 where also specified, potentials of both the points O and B can be
determined
*23.
Charge is sprayed onto a large non-conducting belt above the left hand roller.
The belt carries charge with a uniform surface charge density , as it moves
with a speed v between the rollers as shown. The charge is removed by a wiper
at right hand roller. For a point just above the sheet, mark the correct option.
 v
(A)
Magnetic field is 0 , out of the plane of the page, parallel to axis of roller
2
(B)
Magnetic field is 0, out of the plane of the page, perpendicular to axis

(C)
Electric field is
perpendicular to the plane of sheet
20
(D)
If an electron moves parallel to v just above the sheet it will experience an upward magnetic force
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*24.
Volt-ampere (V-I) characteristic of a nonlinear device D and corresponding circuit used are shown in the
adjoining figures. Voltage VB of the battery is made to vary from zero to 30 V and voltage V1 across the
device D, voltage V2 across the 10 resistor and current I supplied by the battery are measured by ideal
voltmeters V1 and V2 and an ideal ammeter A. Which of the following graph/graphs represent correct
relationship?
*25.
(A)
(B)
(C)
(D)
An inductor and two identical capacitors are connected in the circuit as
shown in the figure. Initially capacitor A has no charge and capacitor B
has CV charge. Assume circuit has no resistance at all. At t = 0, switch S
is closed. Then:
2
sec2 and CV  100 mC ]
[Given LC  2
4
  10
(A)
When current in the circuit is maximum, charge on each capacitor is same
(B)
When current in the circuit is maximum charge on capacitor A is twice the charge on capacitor B
(C)
q = 50 (1 + cos 100 t) mC, where q is the charge on capacitor B at time t
(D)
q = 50 (1 – cos 100 t) mC, where q is the charge on capacitor B at time t
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PARAGRAPH FOR QUESTIONS 26 - 28
Figure shows a schematic view of an electrostatic analyzer. It
can sort out charged particles by speed and charge to mass ratio.
Spacecraft use such analyzers to characterize charged particles in
interplanetary space. Two curved metal plates establish an
b
electric field given by E  E0   where E0 and b are positive
r
constants with unit of electric field and length. The field points
toward the centre of curvature and r is distance from centre.
There is no influence of gravity. Proton (charge +e mass ‘m’)
enters along y-axis and exits along x-axis while moving along a
circular path.
26.
27.
Speed with which proton is to be projected ‘v’ and centripetal acceleration of electron ' ac ' is given by
respectively :
[ ]
(A)
v
eE0b
2c  b 
; ac 
E0
m
m  r 
(B)
v
2eE0b
e
b
; ac 
E0  
m
2m  r 
(C)
v
eE0b
2e  b 
; ac  E0  
2m
m r
(D)
v
eE0b
e
b
; ac  E0  
m
m r
Mark the INCORRECT option :
[ ]
(A)
Work done by electric field on proton is zero
eE0b
(B)
If v 
proton may strike outer surface of analyzer
m
2eE0b
(C)
If v 
proton may strike inner surface of analyzer
m
(D)
If an electron is released with zero initial velocity from inner surface of analyzer it will strike outer
surface with velocity v 
28.
2eE0b  b 
n   , where me is mass of electron
me
a
[ ]
Mark the correct option.
(A)
If E0 is made larger then in order to maintain same trajectory, initial speed has to be decreased
(B)
(C)
If proton enters closer to the inner surface it will require smaller speed to follow circular trajectory
It does not matter where the protons enter the device it requires same speed to follow circular
(D)
trajectory
A deuteron (charge +e, mass 2m) will require greater speed as compared to proton to follow
circular trajectory
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PARAGRAPH FOR QUESTIONS 29 -30
One end of a long horizontal fixed track of gauge l and negligible
resistance is connected to a capacitor of capacitance C charged to voltage
V0. The inductance of the assembly is negligible. The system is placed in a
homogeneous, vertical magnetic field of induction B as shown in the
figure. A frictionless conducting rod of mass m and resistance R is placed
perpendicular on to the track. Now the switch is turned from 1 to 2.
29.
(A)
30.
[ ]
What is the maximum velocity of the rod ?
B CV0
m  B 2 2C
(B)
2 B CV0
m  B 2 2C
(C)
B CV0
(D)
2(m  B 2 2C )
None of these
[ ]
Find the minimum charge on the capacitor.
(A)
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B 2 2C 2V0
2m  B 2 2C
(B)
B 2 2C 2V0
m  B 2 2C
(C)
9
2 B 2 2C 2V0
m  B 2 2C
(D)
None of these
ALPS-2201
VIDYAMANDIR CLASSES
---------------------------------------------------------------------- DAY-4 -----------------------------------------------------------------------
31.
In each situation of column -I, some charge distributions are given with all details explained. The
electrostatic potential energy and its nature is given in column -II. Then match situation in column -I with
the corresponding results in column -II
[ ]
Column-I
Column-II
A thin shell of radius a and having a
charge –Q uniformly distributed over its
surface as shown
(P)
1 Q2
in magnitude
80 a
(B)
5a
and having a
2
charge –Q uniformly distributed over its
surface and a point charge –Q placed at
its centre as shown
(Q)
3 Q2
in magnitude
200 a
(C)
A solid sphere of radius a and having a
charge –Q uniformly distributed
throughout its volume as shown.
(R)
2 Q2
in magnitude
50 a
(D)
A solid sphere of radius a and having a
charge –Q uniformly distributed
throughout its volume. The solid sphere
is surrounded by a concentric thin
uniformly charged spherical shell of
radius 2a and carrying charge –Q as
shown
(S)
Positive in sign
(T)
Zero
(A)
A thin shell of radius
32.
A particle enters a space where exists uniform magnetic field B  Bx i  By j  Bz k and uniform electric
field E  Ex i  E y j  Ez k with initial velocity u  u x i  u y j  u z k . Depending on the values of various
components the particle selects a path. Match the entries of column A with the entries of column B. The
component other than specified in column A in each entry are non-zero. Neglect gravity.
[ ]
Column I
Column II
(A)
By  Bz  Ex  Ez  0 ; u  0
(P)
(B)
E  0, ux Bx  u y Bu  uz Bz
(Q) helix with uniform pitch and constant radius
(C)
u  B  0, u  E  0
(R)
cycloid
(D)
u  B , B || E
(S)
helix with variable pitch and constant radius
(T)
straight line
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ALPS-2201
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33.
Consider the circuit shown. The resistance connected between
the junction A and B is 60  including the resistance of the
galvanometer. The switches have no resistance when shorted
and infinite resistance when opened. All the switches are
initially open and they are closed as given in column I. Match
the condition in column I with the direction of current through
galvanometer and the value of the current through the battery
[ ]
in column II.
Column I
34.
Column II
(A)
Only switch S1 is closed
(P)
Current from A to B
(B)
Only switch S 2 is closed
(Q)
Current from B to A
(C)
only switch S3 is closed
(R)
Current through the battery is 12.0 A
(D)
Only switch S 4 is closed
(S)
Current through the battery is 15.6 A
(T)
Current through the Galvanometer is 1.2 A
Two identical capacitors are connected in series, and the combination is
connected with a battery as shown. Some changes in the capacitor 1 are now
made independently after the steady state is achieved, listed in column-I.
Some effects which may occur in new steady state due to these changes on the
capacitor 2 are listed in column-II. Match the changes on capacitor 1 in
[ ]
column-I with corresponding effect on capacitor 2 in column-II.
Column-I
Column-II
(A)
A dielectric slab is inserted
(P)
Charge on the capacitor increases
(B)
Separation between plates increased
(Q)
Charge on the capacitor decreases
(C)
A metal plate is inserted connecting both plates (R)
Energy stored in capacitor increases
(D)
The left plate is grounded
(S)
Energy stored in capacitor decreases
(T)
No change occurs
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35.
A conducting rod (mass m, resistance R) rests on two frictionless and resistanceless rails distant l apart in a
uniform magnetic field B. At t = 0, the rod is at rest and a source of emf E0 is connected to points a and b as
shown below. Match the following columns.
Column I
(A)
(B)
(C)
(D)
36.
Column II
Speed of rod at time t when source gives a constant
current I
Speed of rod at time t when source gives a constant
emf E0
Terminal speed of rod when source gives a constant
current I
(P)

(Q)
E0
Bl
(R)
E0 
B 2l 2t 
1  e

Bl 
mR 
Terminal speed of rod when source gives a constant
emf E0
(S)
E0lBt
mR
Consider a cube of side a  0.1 m placed such that its six faces are given by equations x  0, x  a,
y  0, y   a, z  0 and z  a, placed in electric fied given by E  x2iˆ  yjˆ N /C. The electric flux
crossing out of the cube is ______ × 104 N m2 /C.
[ ]
37.
Consider the potentiometer circuit arranged as in figure. The potentiometer wire AB is 300 cm long. If the
 3E 
jockey touches the wire at a distance of 275 cm from A, then 
 current flows through galvanometer.
 Nr 
Find value of N.
[ ]
38.
A parallel plate capacitor is to be designed which is to be connected across 1 kV potential difference. The
dielectric material which is to be filled between the plates has dielectric constant K  6 and dielectric
strength 107 V/m. For safety, the electric field is never to exceed 10% of the dielectric strength. With such
specifications, if we want a capacitor of capacitance 50 pF, what minimum area (in mm2) of plates is
required for safe working?
1
(use 0 
[ ]
 109 in MKS )
36
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39.
Find current in the branch CD of the circuit (in ampere).
40.
A smooth parabolic wire track defined by relation y 
[ ]
x2
is fixed in x-y plane in a gravity free space as
2a
shown in figure. An electric field E  yiˆ  xjˆ (where  is a constant) exist in the region. A small ring of
a

mass ‘m’, charge ‘q’, which just fits in wire track, is released from rest at position A  a,  . Find speed
2

2m
 a
(in m/s) of the ring when it reaches at point B  a,  if q  2 . All quantities and constants are in SI
2
a


units.
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---------------------------------------------------------------------- DAY-5 -----------------------------------------------------------------------
41.
A variable voltage V  2t is applied across an inductor of inductance L  2H . Find the rate (in J/s) at
which energy stored in inductor is increasing at time t  1s .
[ ]
42.
Two metal spheres of radius R are placed at a very large distance from each
other, and they are connected by a coil of inductance L, as it is shown in the
figure. One of the spheres is loaded with electric charge. At time

t
y0 LR , after closing the switch S, does the charge on this sphere
4
decrease to the half. Then find value of y.
43.
In the circuit shown in figure when S is closed, it is observed that capacitor C receives a charge 120C in
steady state. Find the potential difference VM  VN (in V).
44.
[ ]
A portion of a large network is shown in the figure. Values of the resistances are indicated in the figure and
both the ammeters A1 and A2 are ideal. If reading of the ammeter A1 is 1.0 A, how much will be ammeter
[ ]
A2 read (in ampere)?
45.
A ring of radius 0.1 m is made out of a thin metallic wire of area of cross section 106 m 2 . The ring has a
uniform charge of  coulomb. Find the change in radius of ring (in mm) when a charge of 108 C is placed
at the centre of ring. Given that Young’s modulus of the metal is 2  1011 N / m2 .
[ ]
46.
Figure shows a 5F capacitor on which 100C and 200C charges are given on plates A and B. Find
the amount of heat produced on closing the switch S (in J ) .
[ ]
VMC | Physics
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ALPS-2201
VIDYAMANDIR CLASSES
47.
In figure (a) and (b) two air cored solenoids P and Q have been shown. They are placed near each other. In
figure (a), when IP the current in P, changes at the rate of 5A/s, an emf of 2 mV is induced in Q. The
current in P is then switched off, and a current changing at 2A/s is fed through Q as shown. What emf will
be induced in P (in mV).
[ ]
48.
A 50W, 100V lamp is to be connected to an ac mains of 200V, 50Hz. What capacitor is essential to be put
in series with the lamp (in F ) ?
[ ]
49.
An electron accelerated by a potential difference V = 3 volt first enters into a uniform electric field of a
parallel-plate capacitor whose plates extend over a length l  6 cm in the direction of initial velocity. The
electric field is normal to the direction of initial velocity and its strength varies with time as E  t , where
  3600Vm1s 1 . Then the electron enters into a uniform magnetic field of induction B  109 T .
Direction of magnetic field is same as that of the electric field. Calculate pitch (in cm) of helical path traced
by the electron in the magnetic field. (Mass of electron, m  9  1031 kg )
50.
Two small identical balls lying on a horizontal plane are connected by an ideal spring. One ball is fixed at
point O and the other is free. The oscillation frequency of the free ball is 0 . The balls are now given equal
charges as a result of which the spring length increases two fold. The new frequency of oscillation of the

free ball is  . Find
0
VMC | Physics
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ALPS-2201
VIDYAMANDIR CLASSES
Answer key : ALPS_ Physics – 2201
Electrostatics, DC-Circuits, Capacitors, Magnetism, EMI, AC-Circuits
Day 1
1
2
3
4
5
6
7
8
9
10
C
A
B
A
B
B
B
C
A
D
Day 2
11
12
13
14
15
16
17
18
19
20
AC
ABD
BCD
BC
AD
ABD
ACD
ACD
ABC
AB
Day 3
21
22
23
24
25
26
27
28
29
30
BCD
BD
ACD
ABCD
AC
D
C
C
A
B
Day 4
31
32
33
[A – p s ; B – q s ; C – q s ; D – s]
[A-r; B-q, t; C-t; D-s]
[A-p, s, t ; B-q, r; C-q, t ; D-p]
34
35
36
37
[A-p, r ; B-q, s ; C-p, r ; D-t]
[A – s ; B – r ; C – p ; D – q]
11
32
38
39
40
300
15
2
Day 5
41
42
43
44
45
46
47
48
49
50
1
8
40
2
2.25
2250
0.8
9.2
1.215
1.41
VMC | Physics
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ALPS-2201