INTERNAL TEST

IIT – JEE 2023

PHASE – VI
IIT-2012 (P1)
DATE: 10.10.2022
SET–B
Time: 3 hours Maximum Marks: 210
INSTRUCTIONS:
A. General
1. This booklet is your Question Paper containing 60 questions.
2. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and
electronic gadgets in any form are not allowed to be carried inside the examination hall.
3. Fill in the boxes provided for Name and Enrolment No.
4. The answer sheet, a machine-readable Objective Response (ORS), is provided separately.
5. DO NOT TAMPER WITH / MULTILATE THE ORS OR THE BOOKLET.
B. Filling in the OMR:
6. The instructions for the OMR sheet are given on the OMR itself.
C. Question paper format:
7. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part
consists of three sections.
8. Section I contains 10 multiple choice questions. Each question has four choices (A), (B),
(C) and (D) out of which ONLY ONE is correct.
9. Section II contains 5 multiple choice questions. Each question has four choices (A), (B),
(C) and (D) out of which ONE or MORE are correct.
10. Section III contains 5 questions. The answer to each question is a single digit integer,
ranging from 0 to 9 (both inclusive).
D. Marking Scheme
11. 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.
12. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s)
corresponding 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.
13. 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 answers in this section.

Don’t write / mark your answers in this question booklet.

If you mark the answers in question booklet, you will not be allowed to continue the exam.

NAME:

ENROLLMENT NO.:

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 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 square loop of wire of side l is placed inside a large square loop of wire of side L (L >> l). The loop
are coplanar and their centre coincide. The mutual inductance of the system is proportional to
(A) l / L (B) (C) (D)

2. A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of
the coil. The radius of the coil changes as shown in figure. The graph of induced emf in the coil is
represented by
Y

O
t(s)
Y
Y

e e
(A) (B)

O O
1 2 t 1 2 t
Y Y

e e
(C) (D)

O O
1 2 t 1 2 t

3. A particle having charge q enters a region of uniform magnetic field


B (directed inwards) and is deflected a distance x after travelling a
distance y. The magnitude of the momentum of the particle is
qBy qBy
(A) (B)
2 x
qB  y 2  qBy 2
(C)   x (D)
2  x  2x

Space for rough work

4. A conducting wire of length '  ' is placed on a rough horizontal surface, where a uniform horizontal
magnetic field B perpendicular to the length of the wire exists. Least values of the force required to move
the rod when a current ‘I’ is established in the rod are observed to be F1 and F2 (  F1 ) for the two possible
directions of the current through the rod respectively. Find coefficient of friction between the rod and the
surface.
F F F F
(A)   1 2 (B)   1 2
2BIL BIL
F1  F2 F1  F2
(C)   (D)  
BIL 2BIL

5. A long solenoid contains another coaxial solenoid (whose radius R is half

of its own). Their coils have the same number of turns per unit length and
initially both carry no current. At the same instant currents start increasing
linearly with time in both solenoids. At any moment the current flowing in
the inner coil is twice as large as that in the outer one and their directions
are the same. As a result of the increasing currents a charged particle,
initially at rest between the solenoids, starts moving along a circular
trajectory. What is the radius r of the circle?
R
(A) r = R (B) r  2R (C) r  (D)r = 2 R
2

6. A straight wire of mass m can slide on two parallel plastic rails kept in a horizontal plane with a separation
d. The coefficient of friction between the wire and the rails is  . If the wire carries a current i, what
minimum magnetic field should exist in the space in order to slide the wire on the rails
mg
(A) magnitude of minimum magnetic field to slide the wire on the rail is
id 1   2 
mg
(B) magnitude of minimum magnetic field to slide the wire on the rail is
id 1   2 
(C) magnitude of minimum magnetic field to slide the wire on the rail is Bil

(D) magnitude of minimum magnetic field to slide the wire on the rail is mg

Space for rough work

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7. A current I flowing a cylindrical wire of radius R is uniformly
distributed over its cross – section. The energy stored in a co–axial
cylindrical volume near its centre per unit length is.

0I2 0I2
(A) 1  n2 (B)
8 8
 I2  I2
(C) 0 1  4n2 (D) 0
16 16

8. A conducting rod PQ of length  = 2 m is moving at a

–1
speed of 2 ms making an angle of 30 with its length. A
uniform magnetic field B = 2T exists in a direction
perpendicular to the plane of motion. Then
(A) VP  VQ  8V (B) VP  VQ  4V
(C) VQ  VP  8V (D) VQ  VP  4V

9. Two wires AO and OC carry equal currents i as shown in figure.

A
One end of both the wire extends to infinity. Angle AOC is  . The
magnitude of magnetic field at a point P on the bisector of these
two wires at a distance r from point O is 
P

O
C

 
0 i  1  cos 
 i   i   2 0 i   
(A) 0 cot   (B) 0 cot   (C) (D) sin  
2 r 2 4 r 2  4 r  2 
2 r sin  
2

Space for rough work

10. In the figure, shown electrical network at t  0 , key was placed on (1)
till the capacitor get fully charged. Key is placed on (2) at t  0 .
Determine the time when the energy in both capacitor and inductor
will be same for the first time.

 
(A) LC (B) LC (C) 2 LC (D) None of these
2 4

SECTION – II: Multi 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 may be is correct.

11. A circuit consisting of a constant emf ‘E’ , a self – inductance ‘L’

and a resistance ‘R’. Graph of current with time t is as shown by
curve ‘a’ in the figure. When one or more parameters E, R & L
are changed, the curve ‘ b’ is obtained. The steady state current
is same in both the cases. Then, it is possible that

(A) E & R are kept constant and L is increased

(B) E & R are kept constant and L is decreased
(C) E & R are both halved and L is kept constant
(D) E & R are doubled and L is constant.

12. Switch S is closed at t = 0, I10 is the current supplied by battery just after closing the switch S. Q1, Q2 and
Q3 are the charges on the capacitors of 10 F, 20 F and 30 F in steady state respectively. I20 is the
current supplied by battery in the circuit at steady state. Choose the correct statement(s).

(A) I10 > I20 (B) I10 < I20 (C) Q1 < Q2 < Q3 (D) Q1 < Q3 < Q2

Space for rough work

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13. Consider a region of cylindrical magnetic field, changing with time at the rate x. A triangular conducting
loop PQR is placed in the field such that mid point of side PQ coincides with axis of the magnetic field
region. PQ = 2  , PR = 2  . The emf induced in the sides PQ, QR, PR of the loop respectively are.

x 2 3x 2 3 2 x 2
(A) x 2 ,0, x2 (B) 0, , (C) 0, x 2 , x 2 (D) 0, x ,
2 2 2 2

14. The conductor AB of mass 1 kg is sliding over two parallel

conducting rails separated by a distance of 1 m and is in a region

 
of inward uniform magnetic filed B0  0.1 kˆ . At time t=0, AB is
projected towards right with speed v 0 .
t

(A) The velocity of AB as a function of time is given as v  v 0 e 600

v0
(B) The velocity of rod becomes at t  600n  2 
2
v0
(C) The induced current is A at t= 600 n  2 
120
t
v  
(D) The induced emf as a function of time is given as  0  e 600
 10 

15. A vertical conducting ring of radius R falls vertically in a

horizontal magnetic field of magnitude B. The direction of B
is perpendicular to the plane of the ring. When the speed of
the ring is v,
(A) no current flows in the ring
. (B) A and D are at the same potential
(C) C and E are at the same potential
(D) the potential difference between A and D is 2BRv, with D
at a higher potential

Space for rough work

 SECTION – III: Integer Answer Type
This section contains 5 questions. The answer to each of the questions is a single–digit integer, ranging from 0
to 9 (both inclusive).

16. A uniform magnetic field of intensity B = B0 sin (t) directed into the plane of the paper exists in the
cylindrical region of radius r. A loop of wire with a resistance R = 5 is folded in the form of an equilateral
triangle of side length 2r and is placed as shown in the figure. The maximum potential drop in the wire AB
r 2B0 
is Volts. Find n.
n

17. The network shown in Figure is part of a complete circuit. I

A B
If at a certain instant the current (I) is 5A, and is 1 5mH
3 15 V
decreasing at a rate of 10 A/s. then (VB – VA) is 5x Volts.
Find x.

18. A uniform magnetic field exists in region which forms an equilateral triangle of side a. The magnetic field is
perpendicular to the plane of the triangle. A charge q enters into this magnetic field perpendicularly with
speed v along perpendicular bisector of one side and comes out along perpendicular bisector of other side.
The magnetic induction in the triangle is
2mv 2
. Find x .
 
x qa

Space for rough work

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19. A ring of radius r and total resistance R is made of wire of uniform cross– section. It is placed in a uniform
magnetic field of induction B directed parallel to the plane of the ring. You have an ideal battery of
electromotive force  . you should connect this battery between two points on the ring to obtain maximum
force on the ring
krB
the maximum force is . Then find k.
R

20. A cylindrical cavity of diameter a exists

inside a cylinder of diameter 2a as shown in
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.
12

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.

O OH
+ + 3+
21. + (X)
(ii) H 3O H + Li and Al salts
4 LiAlH4 4
(ether)
major
Value of X is ________
(A) 1 (B) 2 (C) 3 (D) 4

Space for rough work

22. Which of these compounds form imine derivative with aldehydes and ketones?
(A) NH2OH only (B) NH2 — NH2 only
(C) NH2 — CO — NH — NH2 only (D) all A,B,C

23. Which of the following molecules cannot undergo periodic oxidation?

Me
OH OH OH
Me OH
(A) (B) (C) (D)
OH OH O
Me OH
Me

24. Which of the following compound(s), having molecular formula C4H8O, gives following results
Reaction with
Br2/CCl4 Na metal Chromic acid Lucas reagent

Compound X Decolorizes Bubbles Orange to Green Veryvery slow reaction
Compound X will be
HO
H2C
(A) H3C (B)
O
H3C OH
O OH
(C) (D) H3C
CH2

25. Collision theory of Arrhenius is mainly applicable for

(A) uni molecular reaction (B) bi molecular reaction
(C) tri molecular reactions (D) ter molecular reactions

26. In which of the following conditions, the increase in the rate of reaction will be the maximum?
Ea Teperature rise
(A) 40 KJ/mol 200 K – 210 K
(B) 80 KJ/mol 300 K – 310 K
(C) 90 KJ/mol 300 K – 320 K
(D) Rate is independent of activation energy value

Space for rough work

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27. An organic compound (A) on reduction gives a compound (B) which on reaction with CHCl3 and NaOH
form (C). The compound (C) on catalytic reduction gives N–methyl aniline. The compound (A) is

(A) NO2 (B) C N

O
(C) C NH2 (D) NH2

28. Consider the following reaction

+
K2Cr2O 7, H
A O O

The substance A cannot be

NH2 OH

(A) (B)

NH2 NH2
OH NH2

(C) (D)

OH CH3

29. For a reaction at T1 = 2000K, Eact was 20 KJ/mol, at same temperature if catalyst makes Eact = 2kJ/mol,
then rate constant increases.
(A) 12 times (B) 100 times (C) 2 times (D) 3 times

30. C3H6 Cl2  A  

Hydrolysis
 C3H6 O B 
‘B’ gives Iodoform test if A is :
(A) 1,1-dichloro propane (B) 1,2-dichloro propane
(C) 1,3-dichloro propane (D) 2,2-dichloro propane

Space for rough work

 SECTION – II: Multi 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 may be is correct.

31. A new carbon-carbon bond formation is possible in

(A) Cannizzaro reaction (B) Friedel-Crafts alkylation
(C) Clemmensen reduction (D) Reimer-Tiemann reaction

32. Which of the following compounds will give ethyl alcohol on reduction with LiAIH4?
(A) Acetic Anhydride (B) Acetyl Chloride (C) Acetamide (D) Ethyl Ethanoate

1
33. For a reaction A  2B, rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the
2
expression.
d  A  1 d B  d A  1 d B 
(A)   (B)  
dt 2 dt dt 4 dt
d  A  1 d B  1 d  A  d B 
(C) 2  (D)  2
dt 2 dt 2 dt dt

34. Phenol 

HNO
 P 
2 tautomerism
Q
Q  Phenol 
H2O 
H2SO4
X 
Indo phenol
NaOH
 SodiumYsalt of , then the colour of
Indo Phenol

(A) X is blue (B) X is red (C) Y is blue (D) Y is red

35. For a reaction X  Y, the rate law is

1/2
Rate = k[A] which of the following statements are correct
(A) Half life of the reaction is inversely proportion to the initial concentration.
(B) Half life of the reaction is directly proportional to the square root of the initial concentration.
(C) The rate constant of the reaction is constant at a particular temperature for this reaction.
(D) On increasing the concentration of the reactant 9 times ,the rate of reaction increases by 3 times

Space for rough work

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 SECTION – III: Integer Answer Type
This section contains 5 questions. The answer to each of the questions is a single–digit integer, ranging from 0
to 9 (both inclusive).

36. O
O
This compound can react with a maximum “Z” moles of CH3MgBr, then “Z” is ?
O
HO
O

37. The number of hydroxyl group(s) in the product Q is

H+ KMnO 4 / OH
OH P Q
 0 °C
H
H3C CH3

38. The concentration of R in the reaction R  P was measured as a function of time and the following data is
obtained :
[R] (molar) 1.0 0.75 0.40 0.10
t(min.) 0.0 0.05 0.12 0.18
The order of the reaction is

39. For a first order reaction nA  B whose concentration Vs time curve is as shown in the figure. If half life
for the reaction is 24 minutes. Find out the value of n.
B
concentration

A
20 48 72
Time (min)

Space for rough work

40.
O O
hot KMnO4 || ||
C12 H16 
 H 3C  C  CH 3  HO  C  C  C  OH
|| ||
O O
 A
1mole   2mole   2mole 
Number of  bonds present in A.

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.

x2 y2
41. If the normal at the point P (  ) to the ellipse   1 intersects it again at the point Q  2  , then
14 5
cos  
(A) -2/3 (B) 2/3 (C) -6/7 (D) 6/7

x2 y2
42. If C is the centre of the hyperbola 
 1 and the tangent at any point P on this hyperbola meets the
a2 b 2
straight line bx  ay  0 and bx  ay  0 in the point Q and R respectively, then CQ  CR is equal to
(A) a2  b2 (B) a2  b2 (C) b2 / a2 (D) a2 / b2

43. If a chord 4y =3x-48 subtends an angle  at the vertex of the parabola y 2  64x then tan  =
10 13 20 16
(A) (B) (C) (D)
9 9 9 9

44. The length of the chord 4y = 3x + 8 of the parabola y2  8x is

320 320 80 640
(A) (B) (C) (D)
7 9 9 7

Space for rough work

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45. Set of values of m for which chord of the circle x 2  y 2  4 having slope m touches the parabola y2  4x
is
 2 1  2 1 
(A)  ,   , (B) ( , 1)U(1,  )
 2   2 
   
(C) (-1, 1) (D)  ,  

1
46. x 3
(x  1)1/ 3
3
dx is equal to

1 _ 3 2/3 –3 –2/3
(A)  (1  x 3 )2 / 3  C (B) –(1 + x ) +C (C) –(1 + x ) +C (D) none of these
2

1 
47. An ellipse has eccentricity 1/2 and one focus at the point p  ,1 . Its one directrix is the common tangent
2 
2 2 2 2
nearer to the point P, to the circle x + y = 1 and the hyperbola x - y = 1. The equation of the ellipse in
the standard form, is
(x  1/ 3)2 (y  1)2 (x  1/ 3)2 (y  1)2
(A)  1 (B)  1
1/ 9 1/ 12 1/ 9 1/ 12
(x  1/ 3)2 (y  1)2 (x  1/ 3)2 (y  1)2
(C)  1 (D)  1
1/ 9 1/ 12 1/ 9 1/ 12

48. A line y = 2x + 5 intersects a hyperbola only at a point (–2, 1). The equation of one of its asymptotes is 3x
+ 2y + 1 = 0. If hyperbola passes through a point (–1, 0), then the equation of hyperbola is
2 2 2 2
(A) 6x + xy – 2y + 35x – 21y + 29 = 0 (B) 6x + xy – 2y – 35x – 21y + 29 = 0
2 2
(C) 6x + xy – 2y + 35x – 21y – 29 = 0 (D) none of these


ln x  1  x 2 dx = a 1  x
49. If x 1 x 2
2
 
ln x  1  x 2  bx  c then

(A) a = 1, b = –1 (B) a = 1, b = 1
(C) a = –1, b = 1 (D) a = – 1, b = –1

50. An isosceles triangle is inscribed in the parabola y 2  4ax with its base as the line joining the vertex and
 
positive end of the latus rectum of the parabola. If at 2 , 2at is the vertex of the triangle then
2 2 2
(A) 2t  8t  5  0 (B) 2t  8t  5  0 (C) 2t  8t  5  0 (D) 2t 2  8t  5  0

Space for rough work

 SECTION – II: Multi 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 may be is correct.

51. A line touches 9x 2  9y 2  8 and y 2  32x whose equation is

(A) 9x + 3y – 8 = 0 (B) 9x – 3y + 8 = 0 (C) 9x + 3y + 8 = 0 (D) 9x – 3y – 8 = 0

 x  h   y  k   p lx  my  n  represents
2 2 2
52.
1 1
(A) a parabola if p  (B) an ellipse if 0  p 
l2  m 2 l2  m2
1
(C) a hyperbola if p  2 (D) a circle if p = 0
l  m2

53. If e1 and e2 be the eccentricities of two conics s1 = 0 and s2 = 0 such that e12  e 22  3 , then
s1 = 0 and s2 = 0 can be
(A) both hyperbola (B) both ellipse
(C) a parabola and an ellipse (D) a parabola and a hyperbola

The line 2x – y = 1 intersect the parabola y  4x at the points A and B and the normals at A and B
2
54.
intersect each other at the point G. If a third normal to the parabola through G meets the parabola at C
then which of the following statement(s) is/are correct.
(A) sum of the abscissa and ordinate of the point C is –1
(B) the normal at C passes through the lower end of the latus rectum of the parabola
(C) centroid of the triangle ABC lies at the focus of the parabola
(D) normal at C has the gradient –1

Normal at point P  x1, y1  , not lying on x–axis, to the hyperbola x  y  a meets x–axis at
2 2 2
55.
A and y–axis at B. IF O is origin then
(A) Circumcentre of triangle OAB is P
(B) Slope of OP + slope of AB = 0
(C) Slope of OP = slope of AB
(D) Locus of centroid of triangle OAB is rectangular hyperbola

Space for rough work

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 SECTION – III: Integer Answer Type
This section contains 5 questions. The answer to each of the questions is a single–digit integer, ranging from 0
to 9 (both inclusive).

56. A circle is drawn whose centre is on x–axis and it touches y–axis. If no part of the circle lies outside the
parabola y  8x, then maximum possible radius of the circle is
2

Normal at the point P to the parabola y  4x, intersects the circle with SP as diameter at Q also.
2
57.
If PQ =2 units(given that point S is focus of the given parabola), then find the abscissa of point P.

x2 y2
58. A circle intersects an ellipse   1 precisely at there points A, B, C as shown in the figure. AB is a
a 2 b2
diameter of the circle and is perpendicular to the major axis of the ellipse. If the eccentricity of the ellipse is
4 17
, find the length of the diameter AB given that a  .
5 2

x2 y2
59. 
P is a point in first quadrant lying on the ellipse  1, tangent at point P meets x–axis at T. S1 is a
a 2 b2
focus lying on positive x–axis. If PTS1  45 and S1PT  60 , find the square of reciprocal of
eccentricity of the ellipse

60. Let y  3x  8 be the equation of tangent at the point (7, 13) lying on a parabola whose focus is at
 1,  1 . If the length of latus rectum of the parabola is k, then the value of k 2  ,
(where [.] denote greatest integer function), is

Space for rough work