@bohring Bot × @JEE Tests 07 04 24 OSR STAR CO SC JEE ADV 2021

Sec: OSR.
IIT_*CO-SC Date: 07-04-24

Time: 3HRS Max. Marks: 180
Name of the Student: ___________________ H.T. NO:
07-04-24_OSR.STAR CO-SUPER CHAINA_JEE-ADV_GTA-4(P2)_SYLLABUS
PHYSICS: TOTAL SYLLABUS
CHEMISTRY: TOTAL SYLLABUS
MATHEMATICS: TOTAL SYLLABUS

Narayana IIT Academy 07-04-24_OSR.IIT_*CO-SC_JEE-Adv_GTA-4(P2)_Q’P
TIME: 3HRS IMPORTANT INSTRUCTIONS Max Marks: 180
MATHEMATICS
+Ve - Ve No.of Total
Section Question Type
Marks Marks Qs marks
Questions with Multiple Correct Choice
Sec – I (Q.N : 1 – 6) +4 -2 6 24
(partial marking scheme) (+1,0)
Questions with Comprehension Type With
Sec – II (Q.N : 7 – 12) Numerical value type +2 0 6 12
(3 Comprehensions – 2 + 2 + 2 = 6Q)
Questions with Comprehension Type
Sec – III (Q.N : 13 – 16) +3 –1 4 12
(2 Comprehensions – 2 + 2 = 4Q)
Sec – IV (Q.N : 17 – 19) Questions with Non-Negative Integer type +4 0 3 12
Total 19 60
PHYSICS
Sec – I (Q.N : 20 – 25) +4 -2 6 24
Sec – III (Q.N : 32 – 35) +3 –1 4 12
Total 19 60
CHEMISTRY
Sec – I (Q.N : 39 – 44) +4 -2 6 24
Sec – III (Q.N : 51 – 54) +3 –1 4 12
Total 19 60
OSR.IIT_*CO-SC Page. No. 2

MATHEMATICS MAX.MARKS: 60
SECTION - 1 (Maximum Marks : 24)
This section contains SIX (06) questions.
Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is
(are) correct option(s).
For each question, choose the correct option(s) to answer the question.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all) the correct option(s) is (are) chosen.
Partial Marks: +3 If all the four options are correct but ONLY three options are chosen.
Partial Marks: +2 If three or more options are correct but ONLY two options are chosen, both of which are
correct options.
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct
option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks: -2 In all other cases.
n 1
2 sin  sin 2  x 
1. In   dx, n  Z then
 2
x
n
2
 
In In 1  I8 n 4 I n
A) 2 B)  C) n0
 D) n0
2
I n4 I n4 2 I0 3 I0
  
2. A parallelopipped is formed using 3-non coplanar vectors a , b , c with fixed magnitudes
angles between any of the vector with normal of the plane determined by the other two is
1 1 1
 y
 and the volume of parallelopped is T and its surface area is y. If    4       
T  a b c 
 
then
3 21
A) cos 2   cos   B) sin 2   sin 4  
4 16
3 2 3 5
C) cos 2   cos   D) sin 2   sin 4  
4 16
3. Z1 , Z 2 , Z 3 are 3 non-zero distinct points satisfying Z  1  1 and Z 22  Z1Z 3 then
Z3  Z 2  Z2 1   Z2 
A) is purely imaginary B) arg    2 arg  
Z2  Z3  2  Z3  1   Z3 
 Z2 1   Z3  1 1 1 1 1 1
C) arg    2 arg   D)     
 Z1  1   Z1  Z 2 Z 3 Z1 Z 2 Z1 Z 3

4. Let f :    and g :    be two functions f ( x)  x  x 2  1 , g ( x)  x   x 2  1 . Where
| .| is modulus function and [.] = G.I.F., then which of the following options are true ?
A) f is discontinuous exactly at 5 points of [1, 2]
B) g is discontinuous exactly at 5 points of [1, 2]

1 1
2 2
1
C)   f ( x)  g ( x)  dx  2
1
D)   f ( x)  g ( x)  dx  1
1
2 2
5. The lengths of two perpendicular tangents from a point to a parabola are 3 and 4 then
length of latus rectum of parabola is
125 144 576 125

A) B) C) D)
144 125 125 576
6. The first term of an infinite G.P. is 21. The 2nd term and sum of the series are both
positive integers. All possible values of 2nd term are
A) 12 B) 14 C) 18 D) 20

This section contains TWO (3) Paragraphs. Based on each paragraph, there are 2 questions.
The answer to each question is a NUMERICAL VALUE.
For each question, enter the correct numerical value of the answer using the mouse and the on-screen virtual
numeric keypad in the place designated to enter answer. If the numerical value has more than two decimal
places truncate/round- off the value to TWO decimal places.
Full Marks: +2 If ONLY the correct numerical value is entered as answer.
Zero Marks: 0 In all other cases.
Question Stem for Question Nos. 7 and 8:
1
A( Z 0 )  ai, B ( Z1 )   bi, C ( Z 2 )  1  ci, a, b, c  R .
2
W1 represents Z when A, B, C are non collinear.
W2 represents Z when A, B, C are collinear where

Z  Z 0 cos 4 t  2 Z1 cos 2 t . sin 2 t  Z 2 sin 4 t (t  R ) .
7. If b  a (a, b  R  ) then number of points of intersection of W2 with Z  t  ibt 2 (t  R) is __

8. If b  a (a, b  R  ) then number of points of intersection of W2 with the curve
Z  t  ib t 2 (t  R ) is ________

Let f : R  R be a function defined as f ( x)  3x 5  25 x 3  60 x  5 and
 max  f (t ) : 4  t  x ; 4  x  0

g ( x)   min  f (t ) : 0  t  x ; 0  x  2
 f ( x)  16 ; x2

9. Total number of points at which y  f ( x) and y  g ( x) is non differentiable in [4, ) is _
10. If f ( x)    0 has exactly 3 distinct real roots then number of integral values of   ____

A person repeatedly tosses a fair dice. He gets two points for a throw of a perfect square
and one point otherwise. Let Pn denote the probability that he reaches a score of exactly
n then
P10  P9
11.  ______
P8  P9
12. lim Pn  _______

n 

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is the correct answer. For
each question, choose the option corresponding to the correct answer.
Negative Marks: –1 In all other cases.
Let X  1, 2, 3 . A number is selected from the set X with replacement and this process
is repeated 1100 times for each i, i  1, 2, 3 . Let f (i ) represent the number of times the
number i is selected. Also let S denote the total sum of 1100 numbers selected. If
S 3  162 f (1) . f (2) . f (3) then
13. Harmonic mean of f (1), f (2), f (3) is _______
A) 100 B) 200 C) 300 D) 400

14. There are f (1) red balls, f (2) blue balls, f (3) white balls, X green balls. (balls of same
colour are identical). The balls are arranged in a row such that no two balls of same
colour are consecutive. Let X 1 and X 2 both minimum and maximum values of X
respectively for which above arrangement is possible then X 1  X 2  ______
A) 1000 B) 1100 C) 1200 D) 1300
dy
Let y  f ( x) be a solution of  4 x ( y  2) with f (0)  2 and
dx
 x x 
g ( x)  max 1     , sin x, x  1  , h( x)  log e x [.]  G.I .F .
 2 2 
15. Area enclosed by y  f ( x), y  g ( x) and y-axis.

A) 1 B) 2 C) 3 D) 4
16. Area bounded by the curve y  f ( x), y  h( x) and the y-axis is
3e
A) e B) e2 C) D) e2  1
2

This section contains THREE (03) questions. The answer to each question is a NON-NEGATIVE INTEGER
For each question, enter the correct integer corresponding to the answer using the mouse and the on-screen
virtual numeric keypad in the place designated to enter answer.
17. If  2sin 2 x  2 3 sin x cos x  1  9  4 cos 2 x  4 cos x   40 . The number of values of x in
[0, 20] is ________

x 1 y  3 z
18. Let F be the foot of perpendicular from P(1, 2,  3) on the line L :   . Given
2 2 1
Q( x1 , y1 , z1 ) and R( x2 , y2 , z2 ) are points at a distance 3 units from F on the line L. Then
1  2 2 2
 
24  i 1
xi  yi2   zi   

19. Tangents are drawn from any point on the straight line y  x  8 to the auxiliary circle of
x 2  16 y 2  16 . If A and B are points of contact of these tangents and P, Q are
corresponding points of A and B on the ellipse respectively. If locus of mid point of PQ
is x 2   y 2   x   y  0 then       ________

PHYSICS MAX.MARKS: 60
correct options.
option.
20. A uniform metal rod (AB) of mass m and length L is lying on a rough incline. The
inclination of the incline is  and coefficient of friction between the rod and the incline
is  . Choose the correct options.
A) If temperature increases the rod expands. However, there is a point P on the rod
which does not move. The distance of this point from the lower end of the rod is
L  tan  
1 .
2   
B) If the temperature falls the rod contracts. Once again there is a point Q which does
L  tan  
not move. The distance of Q from the lower end of the rod is 1
2   
C) Repeated expansion and contraction cause the rod to slide down
D) Repeated expansion and contraction will not cause the rod to slide down
21. A plank of mass m0 and length  moving with velocity v0 on a smooth horizontal
surface passes under a stationary hopper. Sand spills from the hopper at a constant rate
of  kg / s , falls through height h onto the plank and sticks to it. Let v be the
instantaneously velocity of plank, choose the correct option(s).

A) Horizontal component of force exerted by falling sand on the plank is proportional to

v.
B) Vertical component of force exerted by falling sand on the plank is proportional to

h
C) Acceleration of the plank is proportional to v

 
D) Velocity of the plank after it completely passes from under the hopper is v0 e m0 v0
.
22. The radii of a spherical capacitor are equal to a and b(b  a) . The space between the two
spherical shells is filled with a dielectric of dielectric constant K and resistivity  . At
t = 0, the inner sphere is given a charge q0 . Choose the correct option(s).
t

 K0
A) Charge q on the inner sphere as a function of time is given by q  q0 e
B) The charge on the inner sphere will become zero almost instantly
C) After a long time, the charge on the outer sphere will become q0
D) The total amount of heat generated during the redistribution of charge will be given
q2
by H     0
1 1
 a b  8 0

23. In the figure there are four arcs carrying positive or negative charge all of them have
same magnitude of charge density  . Choose the correct statement(s).
A) The net dipole moment for the given charge distribution is 4 5 R 2
B) The resultant electric field at the center and at any point on the axis passing through
point O and perpendicular to the plane of arcs are opposite in direction
C) If a uniform electric field is switched on perpendicular to the plane then the charge
distribution starts rotating about x-axis
D) Potential at the center of the given charge distribution is zero
24. A stationary homogenous sphere of radius R and mass M is gently placed on the
conveyor belt moving with a constant velocity v0 towards the east. After a time t from
the instant the sphere was placed on the belt, it starts pure rolling and its CM moves with
a velocity v relative to the ground. Coefficient of kinetic friction is k .
2v0 2v0 2v0 2v0

A) t  B) t  C) v  D) v 
5 k g 7k g 5 7

25. An ideal monoatomic gas is taken from state A (pressure P, volume V) to state B
(pressure P/2, volume 2V) along a straight line in the P  V diagram as shown in figure.
Then, choose the correct options.
A) The work done by the gas in the process A to B exceeds the work that would be done
by it if the system were taken from A to B along the isotherm
B) In going from A  B the volume of gas where nature of process changes from
15
endothermic to exothermic is V
8
C) In the P – T diagram, the path AB becomes a part of a parabola
D) In going from A to B, the temperature T of the gas first decreases to a minimum and
then increases

A monochromatic light of wavelength  is incident on two slits S1 and S2 made on x-
axis. The mid point of the line S1S2 is considered as origin and ‘d’ is the distance
between the two slits which are symmetric about y-axis. The interference pattern is
observed on a plate of mass M which is acting as a screen. The screen is attached to one
end of a vertical spring of spring constant ‘k’ and the other end of spring is attached with
the ground. Spring is massless and screen always remains in horizontal plane. The
distance between the plane of slits and the screen is D  D  d  . Assuming S1 and S2 are
coherent in nature. At t  0, screen is released and spring is in its natural length. It is
Mg
given that M  1 kg , k  1 N / m, D  , g  10 m / s 2 , d  200  . The x co-ordinate (in cm)
k
of the first order maxima on the screen as a function of time is given by   1  2 cos t  .
26. The value of 1 is _______.
27. The value of 2 is _______.

A galvanometer is used as an ammeter and a voltmeter. The range of the voltmeter can
be changed to n times its original value with the help of a 27  multiplier. The range of
the same galvanometer when used as an ammeter can be changed to n times its original
value using a 3 shunt. Power dissipated by the galvanometer when giving a full-scale
reading is 9  104W .
28. The resistance of the coil (in  ) is ________.
29. The full scale deflection current (in mA) is _______.

Figure shows block A of mass 0.2kg sliding to the right over a frictionless elevated
surface at a speed of 10m/s. The block undergoes a collision with stationary block B,
which is connected to a non deformed spring of spring constant 1000 Nm 1 . The
coefficient of restitution between the blocks is 0.5. After the collision, block B oscillates
in SHM with a period of 0.2. Block A eventually slides off the opposite end of the
elevated surface, landing a distance ‘d’ from the base of that surface after falling height
5m. (use  2  10; g  10 m / s 2 )

30. Amplitude of the SHM as being executed by block B spring system is 2.5 x cm, where x
is ____.
31. The distance ‘d’ (in m) will be equal to _________.

Rogowski coil: The coil shown in the figure, called Rogowski coil, is used in electrical
measurements. The coil consists of a toroidal conductor wrapped around a circular
return cord. The coil can be used to measure amplitude of alternating current or value of
direct current in a wire. The coil is simply clipped around the wire. Measured value of
emf across the ends of the coil gives value of current amplitude, in case a.c. is flowing
through the wire. To measure direct current, ends of the coil are connected to ballistic
galvanometer. Current in the wire is switched off and amount of charge crossing the
loop is measured by the ballistic galvanometer. This value of charge is used to calculate
value of direct current in the wire.

32. Number of turns per unit length of the coil, area of each loop in the coil, resistance of the
coil, are n, S and R respectively. Current flowing through the wire crossing the plane of
the coil is i . A ballistic galvanometer is connected across the ends of the coil and the
current is switched off, charge that flows through the coil is measured to be Q. The
correct relation is
0 nSi 0 nSi 0 nSi 1 0 nSi

A) 1 B) 2 C)  D) 1
QR QR QR 2 Q2 R
33. Consider two current carrying wires carrying currents i1 and i2 in opposite directions.
Both the wires are perpendicular to the plane of the coil. Wire carrying currents i1 and i2
are respectively at a distance 0.5 r and 1.5 r from the centre of the coil. Reading of
ballistic galvanometer depends on [ r : mean radius of the coil]
i1 i1  i2
A) i1 B) i1  i2 C) D)
2 2

A cube of wood of side 1m and density 500 kg / m3 is dipped in a tank of water (density
1000 kg / m3 ). We want of push the cube to the bottom of the tank. The depth of the
water in tank is 1m, as shown figure. The cross section of the base of tank is 2m  2m
and the water does not spill out as the cube is pushed down.
34. As the cube is pushed down in the tank:
A) The force required to push it down increases continuously.
B) The force required to push it down decreases continuously.
C) The force required to push it down increases and then becomes constant.
D) The force required to push it down decreases and then becomes constant.

35. The minimum work required to be done by the person pushing the cube to the base of
the tank is
A) 1250 J B) 2500 J C) 1875 J D) 625 J

36. Two radioactive samples A1 and A2 having half life 3 years and 2 years respectively
have been decaying for many years. Today the number of atoms in the sample A1 is
twice the number of atoms in the sample A2 . Both the samples had same number of
atoms X years ago, calculate X.
37. A thin plano-convex lens acts like a concave mirror of radius of curvature 20cm when its
plane surface is silvered. The radius of curvature of the curved surface (in cm) if index
R
of refraction of its material is 1.5 will be ‘R’, then  ___
2
38. A thin metallic wire of mass per unit length 0.02kg/m is clamped at three points A, B
and C and a block of weight 50 N is suspended from the wire as shown. The length
AC = 25 cm and the length CB  26 cm . If both segments (AC and CB) of the wire are
made to vibrate in their fundamental modes, the number of beats heard per second (to
the nearest integer) is _________.

CHEMISTRY MAX.MARKS: 60
correct options.
option.
39. Which of the following is (are) correct.
A)  NiCl4  is paramagnetic while  Ni(CO)4  is diamagnetic though both are tetrahedral.

2
B) The colour of Ti ( H 2O)6  is pale yellow.

3
C)  Fe( H 2O)6  is strongly paramagnetic whereas  Fe(CN )6  is weakly paramagnetic.

3 3
D) Co( NH 3 )6  is an inner orbital complex whereas  Ni ( NH 3 )6  is an outer orbital

3 2
complex.
40. Which of the following transition metals are having more melting point than ‘Tc’
A) Rh B) V C) Mo D) Re
41. Choose the correct statement(s) regarding given reaction scheme.

A)
B)
C)
D)
42. Which of the following combinations would result in the formation of a buffer solution.
A) NH 3  NH 4Cl
B) CH 3COOH  NaOH in 2 : 1 molar ratio
C) NH 3  HCl in 2 : 1 molar ratio
D) CH 3COOH  NaOH in 1 : 2 molar ratio
43. The correct order of electron affinity of the elements/ions is/are
A) O  Se B) F   Cl  C) P  N D) Ne  Ar
44. What is true about ice ?
A) Its density is more than water
B) It is good conductor of heat
C) It is electrical insulator (poor conductor)
D)  f H ice0  0

Phosphorous when treated with excess of chlorine forms compound ‘X’. This ‘X’ when
reacts with phosphorous pentoxide form a product ‘Y’.
45. The number of SP3 hybridized atoms present in one molecule of the product formed
when ‘Y’ is dissolved in excess of hot water.
46. In the following reaction oxidation state of ‘Z’ is

As a result of the isobaric heating by  T  72 K , one mole of a certain ideal gas obtains
an amount of heat Q  1.598 kJ .
47. The |work| performed by the gas is ________ J.
48. The increment of its internal energy is _________ kJ.

A volume of 100 ml of 0.1 M  H 3 PO4 solution is titrated with 0.5M  NaOH solution till
the second equivalence point. Then 10 ml of 0.5 M HCl solution is mixed in the resulting
solution. The dissociation constants of H 3 PO4 are 103 , 108 and 1013 .
49. pH at the second equivalence point is ________
50. pH of the solution after adding HCl is _______

P
major
1)conH2SO4(3hr)/1000C
2)NaOH(excess)
3)Br2(1eq)/H2O
4)H3O+/
OH
1)NaNO2,dilHCl 1)NaOH/CO2
S 2)dilHNO3 2)H+ Q
major major
Br2(1eq)/CS2
273K
R
major
51. P and R are

A) Identicals B) Chain isomers C) Positional isomers D) Functional isomers
52. Which of the following is more acidic.
A) P B) R C) Q D) S
Concentration cell is one in which anode and cathode of a voltaic cell is mode of same
electrode.
Ex: A | AC n || AC n | A

1 2
C1  C2 to have some emf in the cell. Now consider the cell.
Pt  Cl2  | NaCl || AgCl | Cl2 ( Pt )

P1 C P2
K sp AgCl is 1012

53. If P1  P2 , required condition so that the above cell has positive emf is
A) C  106 M B) C  106 M C) P1  P2  1 atm
D) Emf of the cell cannot be found as it is not a concentration cell
54. If C  106 which of the following conditions will give positive emf.
A) P1  P2 B) P1  P2 C) P1  P2 D) None

55. The value of (Y - X) in the following reaction.
56. ‘X’ is the number of essential amino acids of the following.
Glycine, Leucine, Glutamic acid, Aspartic acid, Lysine, Serine, Cysteine, Methionine,
Tyrosine, Phenyl alanine, Proline.
‘Y’ is the number of D-sugars of the following structural formula.
CHO  CHOH  CHOH  CHOH  CHOH  CH 2OH
Then (X+Y) / 2 is
57. The total number of unpaired electrons present in N 2 , O22 , N 22 are _____

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Sec: OSR.

IIT_*CO-SC Date: 07-04-24

Name of the Student: ___________________ H.T. NO:

07-04-24_OSR.STAR CO-SUPER CHAINA_JEE-ADV_GTA-4(P2)_SYLLABUS

PHYSICS: TOTAL SYLLABUS

CHEMISTRY: TOTAL SYLLABUS

MATHEMATICS: TOTAL SYLLABUS

OSR.IIT_*CO-SC Page. No. 2

3. Z1 , Z 2 , Z 3 are 3 non-zero distinct points satisfying Z  1  1 and Z 22  Z1Z 3 then

OSR.IIT_*CO-SC Page. No. 3

A) f is discontinuous exactly at 5 points of [1, 2]

B) g is discontinuous exactly at 5 points of [1, 2]

125 144 576 125

SECTION - 2 (Maximum Marks : 12)

W1 represents Z when A, B, C are non collinear.

W2 represents Z when A, B, C are collinear where

7. If b  a (a, b  R  ) then number of points of intersection of W2 with Z  t  ibt 2 (t  R) is __

OSR.IIT_*CO-SC Page. No. 4

9. Total number of points at which y  f ( x) and y  g ( x) is non differentiable in [4, ) is _

Question Stem for Question Nos. 11 and 12:

12. lim Pn  _______

SECTION - 3 (Maximum Marks : 12)

13. Harmonic mean of f (1), f (2), f (3) is _______

A) 100 B) 200 C) 300 D) 400

OSR.IIT_*CO-SC Page. No. 5

15. Area enclosed by y  f ( x), y  g ( x) and y-axis.

SECTION - 4 (Maximum Marks : 12)

17. If  2sin 2 x  2 3 sin x cos x  1  9  4 cos 2 x  4 cos x   40 . The number of values of x in

[0, 20] is ________

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C) Repeated expansion and contraction cause the rod to slide down

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A) Horizontal component of force exerted by falling sand on the plank is proportional to

B) Vertical component of force exerted by falling sand on the plank is proportional to

C) Acceleration of the plank is proportional to v

t = 0, the inner sphere is given a charge q0 . Choose the correct option(s).

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A) The net dipole moment for the given charge distribution is 4 5 R 2

D) Potential at the center of the given charge distribution is zero

2v0 2v0 2v0 2v0

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SECTION - 2 (Maximum Marks : 12)

26. The value of 1 is _______.

27. The value of 2 is _______.

Question Stem for Question Nos. 28 and 29:

28. The resistance of the coil (in  ) is ________.

29. The full scale deflection current (in mA) is _______.

Question Stem for Question Nos. 30 and 31:

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31. The distance ‘d’ (in m) will be equal to _________.

SECTION - 3 (Maximum Marks : 12)

OSR.IIT_*CO-SC Page. No. 12

0 nSi 0 nSi 0 nSi 1 0 nSi

Question Stem for Question Nos. 34 and 35:

34. As the cube is pushed down in the tank:

A) The force required to push it down increases continuously.

B) The force required to push it down decreases continuously.

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A) 1250 J B) 2500 J C) 1875 J D) 625 J