SR IIT STAR BATCH-II & CO SC N120
Time: 3 Hrs
Date: 12-03-22
Max. Marks: 300
PTM-2
PHYSICS
MAX.MARKS: 100
SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer,
out of which ONLY ONE option can be correct.
Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.
1.
Two parallel long wires A and B carry currents i1 and i2   i1  . When i1 and i2 are in the same
direction, the magnetic field at a point mid way between the wires is 10T . If i2 is reversed, the field
2.
becomes 30T . The ratio i1 / i2 is
1) 1
2) 2
3) 3
4) 4
Two long current carrying thin wires, both with current I , are held by insulating threads of length L
and in equilibrium as shown in the figure, with threads making an angle  with the vertical. If wires
have per unit length mass  then, the value of I is (g= gravitational acceleration)

L
I
1) 2sin 
3) 2
3.
4.
 gL
0 cos
I
2) sin
 gL
tan 
0
4)
 gL
0 cos
 gL
tan
0
A voltmeter of resistance 20000 reads 5 volt. To make it read 20 volt, the extra resistance required
is
1) 40000 in parallel
2) 60000 in parallel
3) 60000 in series
4) 40000 in series
A rigid square loop of side a and carrying current I 2 is lying on a horizontal surface near a long current
I1 carrying wire in the same plane as shown in figure. The net force on the loop due to the will be
I2
I1
a
a
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1) repulsive and equal to
0 I1I 2
2
0 I1I 2
3
II
4) repulsive and equal to 0 1 2
4
2) attractive and equal to
3) Zero
5.
A conducting circular loop is placed in a uniform magnetic field, B=0.025T with its plane perpendicular
to the field. the radius of the loop is made to shrink at a constant rate of1 mm s 1 . the induced emf when
the radius is 2 cm, is:
1) 2V
6.
2) V

V
2
4) 2V
A rod of length 6 m is rotated about the axis passing through the point C and parallel to the magnetic
field lines with angular velocity 4 radian/second. If B=0.5T, the potential difference across the ends of
the wire is
x x x x x x x xB
a
x x
x
x x x
2m
x x x
1) 2 V
7.
3)
c x x x x xb
x x x x x
4m
x x x x x
2) 6 V
3) 12 V
4) zero

A conducting rod AC of length 4l is rotated about a point ‘O’ in a uniform magnetic field B directed into
the paper. AO = l and OC = 3l. Then

B
T O
X
X
A
C
X
X
X
B l 2
7
9
2) VO  VC  B l 2
3) V A  VC  4 B l 2
4) VC  V0  B l 2
2
2
2
In the LCR series circuit given below, what will be the reading of the voltmeter
1) VA  VC 
8.
9.
1) 200 V
2) 300 V
3) 400 V
4) 900 V
The variation of EMF with time for four types of generators are shown in the figures. Which amongst
them can be called AC?
E
E
(d)
1) a and d
t
t
(b)
2) a,b,c and d
SR.IIT_BATCH-II &CO-SC -120
3) a and b
4) only a
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10. If the apparent value of dip at a place in two perpendicular vertical planes are respectively 300 and 450,
then the true angle of dip at that place is
1) cot-1(2)
11.
3) cot 1
2) tan-1(2)
 3
4) cot 1
 5
If the B-H curves of two samples of P and Q of iron are as shown below, then which one of the following
statements is CORRECT ?
1) Both P and Q are suitable for making permanent magnet
2) P is suitable for making permanent magnet and Q for making electromagnet
3) P is suitable for making electromagnet and Q is suitable for permanent magnet
4) Both P and Q are suitable for making electromagnets
12.
The radius of a hollow metallic sphere is 'R'. If the P.D between it's surface and a point at a distance 3R
from it's centre is V then the electric field intensity at a distance 3R from it's centre is
1)
13.
V
2R
V
3R
3)
V
4R
4)
V
6R
Two concentric spheres of radii r1 and r2 carry charges q1 and q 2 respectively. If the surface charge
density
1)
14.
2)
  is same for both spheres, the electric potential at the common centre will be
 r1
0 r2
2)
 r2
0 r1
3)

 r1  r2 
0
4)

 r1  r2 
0
Figure shows a potentiometer circuit. The length of wire is 10 m and its resistance is 1 . The balancing
length is
9
10V
A
J
B
0.5V
1) 5 m
15.
2) 6 m
3) 8 m
4) Not possible
Two particles each of mass m are placed at points P and Q as shown in the figure. R is the mid-point of
PQ = l. The gravitational force on the third particle of mass m placed at point S on the perpendicular
bisector of PQ is
SR.IIT_BATCH-II &CO-SC -120
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Gm2
1) 2
l
16.
16Gm 2
2)
5l2
3)
16Gm 2
5 5l 2
4 2Gm 2
4)
5l 2
Calculate the temperature at which the oxygen molecules will have the same rms velocity as the
hydrogen molecules at 150ºC. Molecular weight of oxygen is 32 and that of hydrogen is 2
1) 2495ºC
17.
2) 4495ºC
3) 6495ºC
4) 8495ºC
A spherical solid ball of volume V is made of a material of density ρ1 . It is falling through a liquid of
density ρ 2 ρ 2 < ρ1  . Assume that the liquid applies a viscous force on the ball that is proportional to the
square of its speed υ , i.e., Fviscous = -kυ2 k > 0 . The terminal speed of the ball is
1)
18.
Vg 1  2 
k
2)
Vg1
k
3)
Vg1
k
4)
Vg 1  2 
k
Find the radius of the soap bubble if 44  10 6 J of work is done in blowing the soap bubble?
(Surface tension of soap solution = 7  10 2 Nm 1 )
19.
1) 2mm
2) 4 mm
3) 5 mm
4) 8 mm
Three rods of same dimensions are arranged as shown in figure. They have thermal conductivities K 1 , K 2
and K 3 . The points P and Q are maintained at different temperatures for the heat to flow at the same rate
along PRQ and PQ then which of the following option is correct
1
2
1) K 3  (K 1  K 2 )
20.
2) K 3  K1  K 2
3)
K3 
K1 K 2
K1  K 2
4)
K 3  2(K 1  K 2 )
A thermodynamic system is taken through the cycle PQRSP process. The net work done by the system is
1) 20 J
2) – 20 J
SR.IIT_BATCH-II &CO-SC -120
3) 400 J
4) – 374 J
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SECTION-II
(NUMERICAL VALUE ANSWER TYPE)
This section contains 10 questions. The answer to each question is a Numerical value. If the Answer in the
decimals , Mark nearest Integer only. Have to Answer any 5 only out of 10 questions and question will be
evaluated according to the following marking scheme:
Marking scheme: +4 for correct answer, -1 in all other cases.
21.
A very high frequencies, the effective impedance of the given circuit will be_________ 
22.
An ac circuit has an inductor and a resistor of resistance R in series, such that XL  3R . Now, a
capacitor is added in series such that X C  2R . The ratio of new power factor with the old power factor
of the circuit is
5 :x . The value of x is_________
23.
Two circuits are shown in the figure (a) & (b). At a frequency of____rad/s the average power dissipated
in one cycle will be same in both the circuits.
24.
In an LCR a series circuit, an inductor 30 mH and a resistor 1 are connected to an AC source of
angular frequency 300 rad/s. The value of capacitance for which, the current leads the voltage by 450 is
1
 103 F . Then the value of x is__________
x
25.
In a series LR circuit, power of 400 W is dissipated from a source of 250 V, 50 Hz. The power factor of
the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in series to
 n 
the L and r. Taking the value C as   F, then value of ‘n’ is_________
 3 
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26.
A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed
of 50 rad s 1 in a uniform horizontal magnetic field of 3.0 10 2 T . The maximum emf induced the coil
will be______ 103 volt (rounded off to the nearest integer)
27.
A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 10 5 T with its plane
perpendicular to the field initially. It is rotated at constant angular speed about an axis along the
diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2s. The
maximum value of EMF induced  in V  in the coil will be close to the integer_____.
28.
In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke
current changes uniformly from 0.25A to 0 in a duration of 0.025 ms. The self-inductance of the choke
(in mH) is estimated to be_____.
29.

A circular conducting coil of radius 1m is being heated by the change of magnetic field B passing
perpendicular to the plane in which the coil is laid. The resistance of the coil is 2 . The magnetic
field is slowly switched off such that its magnitude changes in time as
B
4
t 

 103 T  1 


 100 
The density dissipated by the coil before the magnetic field switched off completely is E =_____mJ.
30.
A galvanometer coil has 500 turns and each turn has an average area of 3 104 m 2 . If a torque of 1.5
Nm is required to keep this coil parallel to a magnetic field when a current of 0.5A is flowing through
it, the strength of the field (in T) is_____
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CHEMISTRY
MAX.MARKS: 100
SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its
answer, out of which ONLY ONE option can be correct.
Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.
31
 B  g  at equilibrium , the partial pressure of B is found to be 1/4 of the
For a reaction A  g  
 B is
partial pressure of A. The value of G 0 of the reaction A 
1)RT ln 4
32
2)  RT ln 4
3) RT log 4
4)  RT log 4
Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of
Y. If molecular weight of X is A, then molecular weight of Y is
1) 3.3A
33
2) 2A
3)3A
4) A
Which of the following are the uses of lithium
1)Electrochemical cells
2)To make tetra ethyl lead
3)Liquid metal is used as a coolant in fast breed nuclear reactions
4) LiOH is used in manufacture of soft soap
34
How many moles of NaOH is must be removed from one litre of aqueous solution to change its pH
from 12 to 11
1) 0.009
35
2)0.01
3)0.02
4)0.1
Which one is wrong regarding Boric acid
1) Exists in polymeric form due to inter- molecular hydrogen bonding
2)is used in manufacturing of optical glasses
3) is a tri- basic acid
4)with borax, it is used in the preparation of a buffer solution
36
37
The Lewis acid nature of BX 3 follows the order:
1) BF3  BCl3  BBr3  BI3
2) BF3  BCl3  BBr3  BI 3
3) BCl3  BF3  BBr3  BI3
4) BF3  BBr3  BCl3  BI 3
Which of the following is in correct for group 14 elements?
1)The stability of dihalides are in the order CX 2  SiX 2  GeX 2  SnX 2  PbX 2
2)The ability to form p  p multiple bonds among themselves increases down the group
3)The tendency for catenation decreases down the group
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4)They all form oxides with the formula MO2
38
Choose the reactions which would not liberate nitrogen gas ?

1) NH 4 NO3 


2) NH 3  CuO 


3) NH 3  excess   Cl2 


4) NH 4 Cl  NaNO2 

39
H 3 PO2 is a good reducing agent due to :
1)one P  OH bonds 2) one P  H bond
3)two P  H bonds 4)two P  OH bonds
40
A 5L vessel contains 2.8 g of N 2 , only when heated to 1800 K,30% molecules are dissociated into
atoms
1)Total no of moles of N in the container will be 1
2)Total no . of molecules in the container will be close to 0.4211023
3) Total no of moles in the container will be 0.098
4)Pressure in the container decreased
41
When 20 g of naphthoic acid  C11 H 8O2  is dissolved in 50 g of benzene  K f  1.72 K kg mol 1  , a
freezing point depression of 2K is observed. The van’s Hoff factor  i  is :
1)0.5
42
2)1
3)2
4)3
Which of the following expression is not true
1)  H    OH    K w for a neutral solution at all temperature
2)  H    K w and OH    K w for an acidic solution
3)  H    K w and OH    K w for an alkaline solution
4)  H    OH    107 M for an neutral solution at all temperatures
43
Which of the following compound having number of p  p bond is equal to d  p bonds
1) SO2
44
2) SO3
3) O3
4) POCl3
Which one of the following compounds contain   C1  C4 glycosidic linkage
1)Lactose
2)Surcose
SR.IIT_BATCH-II &CO-SC -120
3)Maltose
4)Amylose
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45
Sodium carbonate can be manufactured by Solvay’s process but potassium carbonate cannot be
prepared by this method because
1) K 2CO3 is more soluble
2) K 2CO3 is less soluble
3) KHCO3 is more soluble than NaHCO3
4) KHCO3 is less soluble than NaHCO3
46
Which of the following hydride is not ionic
1) CaH 2
47
2) BaH 2
3) SrH 2
4) BeH 2
Which reaction does not produce ammonia
1) NH 4 I  KOH 


2) N 2  3 H 2 

Fe / Mo

3)  NH 4 2 Cr2O4 

4) Mg 3 N 2  HCl  aq  

48
49
50
Column-I
Column-II
(a) Dry ice
(p) Used as sealant
(b) silicone
(q) Used as non- stick coating
( c) Carborundum
(r) Used as refrigerant
(d) Teflon
(s) Used as abrasive for cutting
Which of the following is correct matching
1) a-r b-q c-s d-p
2) a-r b-p c-s d-q
3) a-r b-s c-q d-p 4) a-s b-p c-s d-r
Disproportionation products of H 3 PO2 on heating are:
1) H 3 PO3  PH 3
2) H 3 PO3  H 3 PO4 3) PH 3  H 3 PO4
Noradrenaline is a/an
1) antidepressant
2) antihistamine
3) neurotransmitter
4) only PH 3
4) antacid
SECTION-II
(NUMERICAL VALUE ANSWER TYPE)
This section contains 10 questions. The answer to each question is a Numerical value. If the Answer in the
decimals , Mark nearest Integer only. Have to Answer any 5 only out of 10 questions and question will be
evaluated according to the following marking scheme:
Marking scheme: +4 for correct answer, -1 in all other cases.
51
Assuming that Ba  OH  2 is completely ionized in aqueous solution under the given conditions the
concentration of H 3O  ions in 0.005 M aqueous solution of Ba  OH  2 at 298 K is …… 1012 mol L1
52
The number of significant figures in 50000.020  103 is ……..
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53
 C  D is 100. Starting with an
The equilibrium constant K C at 298 K for the reaction A  B 
equimolar solution with concentrations of A,B,C and D all equal to 1M, the equilibrium concentration
of D is …… 102 M (Rounded off to the nearest integer )
54
Electromagnetic radiation of wavelength 663 nm is just sufficient to ionize the atom of metal A. The
ionization energy of metal A in kJ mol 1 is ……(Rounded off to the nearest integer )
 h  6.63  1034 J  s , c  3.00  108 ms 1 , N A  6.02 10 23 mol 1 
55
A system does 200J of work and at the same time absorbs 150J of heat . The magnitude of the change
in internal energy is …….. J
56
A co-ordination complex has the formula PtCl4 .2 KCl . Electrical conductance measurement indicate
the presence of three ion in one formula unit. Treatment with AgNO3 produces no precipitate of AgCl .
What is the co-ordination number of Pt in this complex
57
In the sulphur estimation, 0.471 g of an organic compound gave 1.44g of barium sulphate. The
percentage of sulphur in the compound is …….. %
(Atomic mass of Ba=137 u) (Rounded off to the nearest integer )
58
5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature
becomes 200 K. If CV  28 JK 1 moI 1 , Calculate U  kj  for this process. ( R  8.0 JK 1 moI 1 )
59
For the reaction , A( g )  B ( g ), the value of the equilibrium constant at 300 K and 1 atm is equal to
100.0. the value of  r G for the reaction at 300 K and 1 atm in J moI 1 is –xR, where x is …… (
Rounded off to the nearest integer) ( R  8.31 J moI 1 K 1 and In10  2.3)
60
3
Ti ( H 2O)6 
absorbs light of wavelength 498 nm during a d-d transition . The octahedral splitting
energy for the above complex is …… 10 19 J (Round off to the nearest intger)
 h  6.626  1034 Js, c  3  108 ms 1 
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MATHEMATICS
MAX.MARKS: 100
SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its
answer, out of which ONLY ONE option can be correct.
Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.
61.
62.
63.
Suppose A, B are two points on 2x-y+3=0 and P (1, 2) is such that PA = PB. Then the mid point of AB
is
 1 13 
 7 9 
 7 9 
 7 9 
1)  , 
2)  , 
3)  , 
4)  , 
 5 5
 5 5
5 5 
 5 5 
Let P (1, 1) and Q (3, 2) be given points. The point R on the x-axis such that PR + PQ minimum is
5 
3 
1)  , 0 
2) (2, 0)
3) (3, 0)
4)  , 0 
3 
2 
the equation of the pair of lines passing through the origin whose sum and product of slopes are
respectively the arthemetic mean and geometric mean of 4 and 9 is
1) 12x 2  13xy  2y 2  0
2) 12x 2  13xy  2y 2  0
3) 12x 2  15xy  2y 2  0
64.
65.
4) 12x 2  15xy  2y 2  0
If the pair of lines 2x 2  3xy  y 2  0 makes angles 1 and 2 with X-axis then tan  1  2  
1
1
1
1) 1
2)
3)
4)
2
3
4
If the centroid of an equilateral triangle is (1, 1) and one of its vertices is (-1, 2) then, equation of its
circumcircle is
1) x 2  y2  2x  2y  3  0
2) x 2  y2  2x  2y  3  0
3) x 2  y 2  4x  6y  9  0
66.
4) x 2  y2  x  y  5  0

To the circle x 2  y 2  8x  4y  4  0 tangent at the point  
is
4
1) x  y  2  4 2  0
2) x  y  2  4 2  0
3) x  y  2  4 2  0
67.
68.
69.
70.
71.
4) x  y  2  4 2  0
If the tangent at P on the circle x 2  y2  a 2 cuts two parallel tangents of the same circle at A and B
then PA.PB =
1) a
2) a2
4) 2a
4) 2a2
The triangle formed by the common tangents of the circles x 2  y 2  2x  0 and x 2  y 2  6x  0 is
1) An isosceles triangle
2) An equilateral triangle
3) A scalene triangle
4) A right angled triangle
 5
If  0,  is a centre of similitude for the circles x 2  y 2  6x  2y  1  0 and x 2  y 2  2x  6y  9  0 ,
 2
then the length of the common tangent of the circles through it is
1) 6
2) 3
3) 2
4) 1
2
The point on the parabola y  x  7x  2 which is closest to the line y  3x  3 is
1) (2, 8)
2) (2, -8)
3) (-2, 8)
4) (- 2, - 8)
The distance between a focus and one end of minor axis of an ellipse is
1) Length of minor – axis
2) Length of major – axis
3) Distance between the foci
4) Length of semi major axis
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72.
x 2 y2
The eccentricity of the hyperbola 2  2  1 which passes through the poi8nts (3, 0) and 3 2, 2 is
a
b

15
2
1)
73.

C
4) 2

2) BC
3) 
4) U
Let R be the relation on the set of all lines in a plane defined by  1 ,  2   R  1 ||  2 then R is
1) Reflexive
75.
13
2
3)
Let A and B be two sets then  A  B   A C  B 
1) A C
74.
13
3
2)

2) Symmetric
3) Transitive
4) Equivalence
 0, if x is rational
f x  
 x, if x is irrational
 0, if x is irrational
. Then f – g is
gx  
x, if x is rational
76.
1) One one and into
2) neither one-one nor onto
3) many one and onto
4) one – one and onto

1 x
dx 
x
3
1) 4 1  x   c
2)
4
3
3
1  x 
a
77.
If f(x) is intergrable on [0, a] then
c
3)
3
4
3
1  x 
c
4)
4
3
4)
a
2
1  x 
2
c
f x
 f  x   f  a  x  dx 
0
1) 0
78.
79.
80.
2) 1
3) a
dy
 elog x is
dx
2
1) 2y  x  c
2) y  x 2  c
3) y 2  x  c
4) xy  x 2  c
One side of an equilateral triangle is 3x + 4y = 7 and its vertex is (1, 2). Then the length of the side of
the triangle is
4 3
3 3
8 3
4 3
1)
2)
3)
4)
17
16
15
15
The rectangle formed by the pair of lines 2hxy + 2gx + 2fy + c = 0 with the coordinate axes has the area
equal to
fg
gh
fg
hf
1) 2
2) 2
3) 2
4)
h
h
f
g
The solution of
SR.IIT_BATCH-II &CO-SC -120
Page. No. 12
Narayana IIT Academy
SECTION-II
(NUMERICAL VALUE ANSWER TYPE)
This section contains 10 questions. The answer to each question is a Numerical value. If the Answer in the
decimals , Mark nearest Integer only. Have to Answer any 5 only out of 10 questions and question will be
evaluated according to the following marking scheme:
Marking scheme: +4 for correct answer, -1 in all other cases.
1
 cos2 x 1  4 tan 2 x  dx
81.
If
82.
1  2 tan x
 c, then 4k is______
1  2 tan x
dy x  y  1
If f(x) is an I. F of

then 2f(1) value is……..
dx
x 1
9x
  1   2 
 1995  
If f  x   x
then 2  f 
f 
  .....f 
   _____
9 3
 1996  
  1996   1996 
 k.log
83.
84.
85.
86.
87.
88.
89.
90.
the number of points on the line 3x + 4y = 5 which are at a distance of sec 2   2 cos ec 2,   R from
the point (1, 3) is.
If the orthocentre of the triangle formed by 2x  3y  1  0, x  2y  1  0, ax  by  1  0 is at the origin
ba
then

4
The tangent to the circle x 2  y 2  4x  2y  k  0 at (1, 1) is x – 2y + 1 = 0 then k =
A parabola with vertex (2, 3) and axis parallel to the y - axis passes through (4, 5). Then its length of
latusrectum is.
The angle subtended by double ordinate of length 8a of the parabola y 2  4ax at its vertex is
 12 
The length of subtangent corresponding to the point  3,  on the ellipse is 16/3. Then it’s
 5
eccentricity is.
If 5x 2  y 2  20 represents a rectangular hyperbola, then  is equal to.
SR.IIT_BATCH-II &CO-SC -120
Page. No. 13