Sec: SR.

IIT_*CO-SC(MODEL-A) Date: 19-09-21

Time: 3HRS Max. Marks: 186

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

19-09-21_SR.STAR CO-SUPER CHAINA(MODEL-A)_JEE-ADV_GTA-1_SYLLABUS

PHYSICS: TOTAL SYLLABUS

CHEMISTRY: TOTAL SYLLABUS

MATHEMATICS: TOTAL SYLLABUS

Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
TIME:3HRS IMPORTANT INSTRUCTIONS Max Marks: 186

PHYSICS
+Ve - Ve No.of Total
Section Question Type
Marks Marks Qs marks
One of More Correct Options Type
Sec – I (Q.N : 1 – 8) +4 -1 8 32
(partial marking scheme) (+1)
Questions with Numerical Value Type
Sec – II (Q.N : 9 – 14) (e.g. 6.25, 7.00, ‐0.33, ‐.30, 30.27, ‐1 +3 0 6 18
27.30)
Matrix Matching Type
Sec – III (Q.N : 15 – 18) (Each match consist of 2 questions)
+3 -1 4 12
Total 18 62

CHEMISTRY
+Ve - Ve No.of Total
Section Question Type
Marks Marks Qs marks
One of More Correct Options Type
Sec – I (Q.N : 19 – 26) +4 -1 8 32
(partial marking scheme) (+1)
Questions with Numerical Value Type
Sec – II (Q.N : 27 – 32) (e.g. 6.25, 7.00, ‐0.33, ‐.30, 30.27, ‐ +3 0 6 18
127.30)
Matrix Matching Type
Sec – III (Q.N : 33 – 36) (Each match consist of 2 questions)
+3 -1 4 12
Total 18 62

MATHEMATICS
+Ve - Ve No.of Total
Section Question Type
Marks Marks Qs marks
One of More Correct Options Type
Sec – I (Q.N : 37 – 44) +4 -1 8 32
(partial marking scheme) (+1)
Questions with Numerical Value Type
Sec – II (Q.N : 45 – 50) (e.g. 6.25, 7.00, ‐0.33, ‐.30, 30.27, ‐ +3 0 6 18
127.30)
Matrix Matching Type
Sec – III (Q.N : 51 – 54) (Each match consist of 2 questions)
+3 -1 4 12
Total 18 62

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
PHYSICS Max.Marks:62
SECTION – I
(MULTIPLE CORRECT CHOICE TYPE)
This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer,
out of which ONE OR MORE is/ are correct.
Marking scheme +4 for correct answer , 0 if not attempted and -1 in all other cases.
1. A rectangular vessel of dimension  l  b  h  and mass M contains a liquid of density  .
The vessel has an orifice at its bottom at a distance c from the rear wall as shown in the
figure.

A) The maximum volume of the water that can be stored when the vessel is accelerated
is hcb / 2

B) The maximum volume of the water that can be stored when the vessel is accelerated
is hlb / 2

C) Force F that must be applied when maximum water stored is  M  hcb / 2 hg / c

D) Force F that must be applied when maximum water stored is  M  hcb / 2 lg / c

2. Consider a rope of mass 4m and length 4  R on a fixed rough pulley of radius R as

shown in the figure. The rope is in equilibrium. Length of vertical hanging parts is
shown in the figure.

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
A) Torque of tension force about O on pulley is 4 mgR

B) Torque of normal force between rope and pulley on pulley about O is zero

C) Torque of friction force between rope and pulley on pulley about O is mgR

D) Torque of friction force between rope and pulley on pulley about O is zero

3. A ray OP of monochromatic light is incident at angle 600 on the face AB of prism

ABCD near its vertex B as shown. The refractive index of the material of the prism is

3 . Then, it follows that

A) The ray gets totally internally reflected at face CD

B) The ray emerges through face AD

C) The angle between the incident ray and the emergent ray is 1200

D) The angle of incidence of the ray with face AD is 300

4. Remote objects are viewed through a converging lens with a focal length F  9 cm placed
at a distance a  36 cm in front of the eye. Assume that the radius r of the pupil is
approximately 1.5 mm . Choose the correct options.

A) The minimum radius of the screen that should be placed behind the lens so that the
entire field of view is covered is 0.5 mm

B) The minimum radius of the screen that should be placed behind the lens so that the
entire field of view is covered is 1.0 mm

C) The screen must be placed in the plane S with its centre at point B

D) The screen must be placed perpendicular to the plane S with its centre at point B

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
5. A rod OA of length l is rotating (about end O ) over a conducting ring in crossed
magnetic field B with constant angular velocity  as shown in the figure.

3B 2
A) Current flowing through the rod is
4R

3B 23
B) Magnetic force acting on the rod is
4R

3B 2 4
C) Torque due to magnetic force acting on the rod is
8R

D) magnitude of external force that acts perpendicularly at the end of the rod to maintain
3B 23
the constant angular speed is
8R

6. Two point monochromatic and coherent sources of light of wavelength  are placed on
the dotted line in front of an infinite screen. The source emit waves in phase with each
other. The distance between S 1 and S 2 is d while their distance from the screen is much
larger. Then

3
A) If d is , at O minima will be observed
2

11  3
B) If d is , then intensity at O will be of maximum intensity
6 4

C) If d is 3 , O will be a maxima

7 3
D) If d is , the intensity at O will be of maximum intensity
6 4
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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P

stopping potential V0  and   is shown in the figure.

1
7. The graph between the

 1 ,  2 and  3 are work functions. Which of the following is/are correct ?

A) 1 :  2 :  3  1: 2 : 4

B) 1 :  2 :  3  4 : 2 :1
hc
C) tan  
e
D) ultraviolet can be used to emit photoelectrons from metal 2 and metal 3 only
8. A large plate with uniform surface charge density  is moving with constant speed v as
shown in the figure. The magnetic field at a small distance from plate is

0 v
A) 0 v in magnitude B) in magnitude
2
C) perpendicular to plate D) parallel to plate

SECTION – II
(Numerical Value Answer Type )
This section contains 6 questions. The answer to each question is a Numerical values comprising of positive
or negative decimal numbers (place value ranging from Thousands Place to Hundredths place).
Eg: 1234.56, 123.45, -123.45, -1234.56, -0.12, 0.12 etc.
Marking scheme : +3 for correct answer, 0 in all other cases.
9. From the top of tower of height 80 m , a body projected with velocity 50 m / s at an angle
of inclination of 370 . If mass of the body is m  0.01 kg and acceleration due to gravity is
10 m / s 2 , then find power (in watts) supplied by gravitational force on the body seven

second after the projection.

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
10. A wall is inclined to a horizontal surface at an angle of 1200 as shown. A rod AB of
length L  0.75 m is sliding with its two ends A and B on the horizontal surface and on
the wall respectively. At the moment angle   200 (see figure), the velocity of end A is
VA  1.5 m / s towards right. Calculate the angular speed of the rod at this instant. [Take

cos 400  0.766 ].

11. A room is in shape of a cube. A heavy ball ( B ) is suspended at the centre of the room
tied to three inextensible strings as shown. String BA is horizontal with A being the
centre point of the wall. Find the ratio of tension in the string BA and BC .

12. A 20 mm diameter copper pipe is used to carry heated water. The external surface of the
pipe is at T  800 C and its surrounding is at T0  200 C . The outer surface of the pipe
radiates like a black body and also loses heat due to convection. The connective heat loss
per unit area per unit time is given by h T  T0  where h  6W  m2 K  . Calculate the total
1

heat lost by the pipe in unit time for one meter of its length.

13. A spool has the shape shown in figure. Radii of inner and outer cylinders are R and
2R respectively. Mass of the spool is 3m and its moment of inertia about the shown axis

is 2mR 2 . Light threads are tightly wrapped on both the cylindrical parts. The spool is
placed on a rough surface with two masses m1  m and m 2  2m connected to the strings

as shown. The string segment between spool and the pulleys P1 and P2 are horizontal.
The centre of mass of the spool is at its geometrical centre. System is released from rest.

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
What is minimum value of coefficient of friction between the spool and the table so that
it does not slip ?

14. In the arrangement shown in the figure A is an equilateral wedge and the ball B is
rolling down the incline XO . Find the velocity of the wedge (of course, along OY ) at the
moment velocity of the ball is 10 m / s parallel to the incline XO

SECTION-III
(MATCHING LIST TYPE)
This section contains 4 questions, each having two matching lists (List-1 & List-II). The options for the correct
match are provided as (A), (B),(C) and (D) out of which ONLY ONE is correct.
Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.
Answer Q.15 and Q.16 by appropriately matching the lists based on the information
given in the paragraph.
In a thermodynamic process on an ideal monoatomic gas, the infinitesimal heat absorbed
by the gas is given by T  X , where T is temperature of the system and X is the
infinitesimal change in a thermodynamic quantity X of the system. For a mole of
3 T   v 
monoatomic ideal gas X  R n    R n   .
2  TA   vA 

Here, R is gas constant, V is volume of gas, TA and VA are constants.

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
15. If the process carried out on one mole of monoatomic ideal gas is as shown in figure in
1
0 0 
the PV diagram with PV RT0 . The correct match is
3

The List – I below gives some quantities involved in a process and List – II gives some
possible values of these quantities
List - I List - II
(I) Work done by the system in process 1  2  3 (P) 1 RT n2
0
3
(II) Change in internal energy in process 1  2  3 (Q) 1
RT0
3
(III) Heat absorbed by the system in process 1  2  3 (R) RT0
(IV) Heat absorbed by the system in process 1  2 (S) 4
RT0
3
(T) 1
RT0  3  n2 
3
(U) 5
RT0
6
A) I  Q, II  S , III  R, IV  U B) I  S , II  R, III  Q, IV  T
C) I  Q, II  R, III  P, IV  U D) I  Q, II  R, III  S , IV  U
16. If the process carried out on one mole of monoatomic ideal gas is as shown in the TV -
1
0 0 
diagram with PV RT0 . The correct match is
3

The List – I below gives some quantities involved in a process and List – II gives some
possible values of these quantities.

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
List - I List - II
(I) Work done by the system in process 1  2  3 (P) 1
RT0 n2
3
(II) Change in internal energy in process 1  2  3 (Q) 1
RT0
3
(III) Heat absorbed by the system in process 1  2  3 (R) RT0

(IV) Heat absorbed by the system in process 1  2 (S) 4

RT0
3
(T) 1
RT0  3  n2 
3
(U) 5
RT0
6

A) I  P, II  R, III  T , IV  P B) I  P, II  R, III  T , IV  S
C) I  S , II  T , III  Q, IV  U D) I  P, II  T , III  Q, IV  T
Answer Q.17 and Q.18 by appropriately matching the lists based on the information
given in the paragraph.
A musical instrument is made using four different metal strings, 1,2,3 and 4 with mass

per unit length  , 2 , 3 and 4 respectively. The instrument is played by vibrating the

strings by varying the free length in between the range L 0 and 2L 0 . It is found that in

string- 1(  ) at free length L 0 and tension T0 the fundamental mode frequency is f0 .

17. List – I gives the above four strings while List – II lists the magnitude of some quantity.
List - I List - II
(I) String – 1 (  ) (P) 1
(II) String – 2 ( 2 ) (Q) 1/2
(III) String – 3 ( 3 ) (R) 1/ 2

(IV) String – 4 ( 4 ) (S) 1/ 3

(T) 3/16
(U) 1/16

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
If the tension in each string is T0 , the correct match for the highest fundamental
frequency in f 0 units will be

A) I  Q, II  S , III  R, IV  P B) I  P, II  R, III  S , IV  Q
C) I  P, II  Q, III  T , IV  S D) I  Q, II  P, III  R, IV  T
3L 0 5 L 0 7L
18. The length of the strings 1,2,3 and 4 are kept fixed at L 0 , , and 0 , respectively.
2 4 4

Strings 1,2,3, and 4 are vibrated at their 1st , 3rd , 5th and 14th harmonics, respectively

such that all the strings have same frequency. The correct match for the tension in the

four strings in the units of T0 will be

List – I gives the above four strings while List – II lists the magnitude of some quantity.

List - I List - II
(I) String – 1 (  ) (P) 1
(II) String – 2 ( 2 ) (Q) 1/2
(III) String – 3 ( 3 ) (R) 1/ 2

(IV) String – 4 ( 4 ) (S) 1/ 3

(T) 3/16
(U) 1/16
A) I  P, II  R, III  T , IV  U B) I  P, II  Q, III  T , IV  U
C) I  T , II  Q, III  R, IV  U D) I  P, II  Q, III  R, IV  T

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
CHEMISTRY Max.Marks:62
SECTION – I
(MULTIPLE CORRECT CHOICE TYPE)
This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer,
out of which ONE OR MORE is/ are correct.
Marking scheme +4 for correct answer , 0 if not attempted and -1 in all other cases.
19. The ground state energy of hydrogen atom is 13.6eV . Consider an electronic state 

of He  whose energy, azimuthal quantum number and magnetic quantum number are
3.4 eV , 2 and 0 respectively. Which of the following statement(s) is (are) true for the
state ?
A) It is a 4d state
B) It has 2 angular nodes
C) It has 3 radial nodes
D) The nuclear charge experienced by the electron in this state is less then 2e, where ‘e’
is the magnitude of the electronic charge.
20. Among the following, the correct statement(s) is (are)
A) Al  CH 3 3 has the three-centre two-electron bonds in its dimeric structure.

B) BH 3 has the three-centre two-electron bonds in its dimeric structure.

C) AlCl3 has the three-centre two-electron bonds in its dimeric structure.
D) The Lewis acidity of BCl3 is greater than that of AlCl3 .
21. An ideal gas in a thermally insulated vessel at internal pressure  P1 , Volume  V1 and
absolute temperature  T1 expands irreversibly against zero external pressure, as shown
in the diagram. The final internal pressure, volume and absolute the temperature of the
gas are P2 ,V2 and T2 , respectively. For this expansion,

 
A) q  0 B) T2  T1 2 2  PV
C) PV 1 1 2 2  PV
D) PV 1 1

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
22. Copper is purified by electrolytic refining of blister copper. The correct statement(s)
about this process is (are)
A) Impure Cu strip is used as cathode
B) Acidified aqueous CuSO4 is used as electrolyte
C) Pure Cu deposits at cathode
D) Impurities settle as anode-mud
23. When O2 is adsorbed on a metallic surface, electron transfer occurs from the metal to O2.
The TRUE statement(s) regarding this adsorption is (are)
A) O2 is physisorbed
B) Heat is released
C) Occupancy of  2* p of O2 is increased

D) Bond length of O2 is increased

24. The pair(s) of ions where BOTH the ions are precipitated upon passing H2S gas in
presence of dilute HCl , is (are)
A) Ba 2 , Zn 2 B) Bi 3 , Fe3 C) Cu 2 , Pb 2 D) Hg 2 , Bi 3
25. For ‘invert sugar’, the correct statement(s) is (are)
(Given: Specific rotations of (+)-sucrose, (+)-maltose, L     -glucose and L     -

fructose in aqueous solution are 660 , 1400 , 520 and 920 , respectively)
A) ‘Invert sugar’ is prepared by acid catalyzed hydrolysis of maltose
B) ‘Invert sugar’ is an equimolar mixture of D     -glucose and D     -fructose

C) Specific rotation of ‘invert sugar’ is 200

D) On reaction with Br2 water, ‘invert sugar’ forms saccharic acid as one of the
products.
26. Which of the following can decolourise brown colour of bromine water?
OH NH 3

A) B) C) D)

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
SECTION – II
(Numerical Value Answer Type )
This section contains 6 questions. The answer to each question is a Numerical values comprising of positive
or negative decimal numbers (place value ranging from Thousands Place to Hundredths place).
Eg: 1234.56, 123.45, -123.45, -1234.56, -0.12, 0.12 etc.
Marking scheme : +3 for correct answer, 0 in all other cases.
27. The amount of water produced (in g) in the oxidation of 1 mole of rhombic sulphur by
conc. HNO3 to a compound with the highest oxidation state of sulphur is __ (Given

data: Molar mass of water  18 g mol 1 , gram atomic weight of sulphur  32g )
238 206
28. 92 U is known to undergo radioactive decay to form 82 Pb by emitting alpha and beta

particles. A rock initially contained 68  106 g of 238

92 U . If the number of alpha particles
238 206
that it would emit during its radioactive decay of 92 U to 82 Pb in three half-lives is

Z  1018 , then what is the value of ‘Z’?

29. An acidified solution of 0.05 M Zn 2 is saturated with 0.1 M H 2 S . What is the

minimum molar concentration (M) of H  required to prevent the precipitation of ZnS?

Use K sp  ZnS   1.25  1022 and overall dissociation constant of H 2 S ,

K NET  K1K 2  1  1021 .

30. Total number of cis N  Mn  Cl bond angles (that is, Mn  N and Mn  Cl bonds in

cis position) present in a molecule of cis   Mn  en 2 Cl2  complex is ___

 en  NH 2CH 2CH 2 NH 2 
31. A saturated solution in AgA  K sp  3  1014  and AgB  K sp  1014  has conductivity of

375  1010 Scm 1 and limiting molar conductivity of Ag  and A are 60 Scm 2 mol 1 and

80 Scm 2 mol 1 respectively. The what will be the limiting molar conductivity of ‘B’ (in

Scm 2 mol 1 )
32. The packing percentage for equilateral triangular rods stacked as shown below is

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
SECTION-III
(MATCHING LIST TYPE)
This section contains 4 questions, each having two matching lists (List-1 & List-II). The options for the correct
match are provided as (A), (B),(C) and (D) out of which ONLY ONE is correct.
Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.
Answer Q.33 and Q.34 by appropriately matching the lists based on the information
given in the paragraph.
In the List-I some reactions are given. In the List-II some points related to the
mechanism and products of relations of List-I given.
List – I List – II

 CH 3 3 C  O  CH 3 
HI
(I)  
 aq
(P) Unimolecular path

O OCH 3
C
Ph Ph
(II) 
conc . H 2 SO4 (Q) Bimolecular path

Ph
O OH

Aromatic electrophilic
(III) O  
conc . H 2 SO4
(R)
substitution

O
O
  OH  conc
(IV) CH 3  C   (S) Product is coloured (in
O  C  CH 3 3 acidic or basic medium)

(T) Acyl-Oxygen cleavage

(U) Alkyl oxygen cleavage

33. Which of the following option has correct combinations considering the List-I and List-
II.
A) I – Q B) II – P,R,S,T C) I – P,S,U D) II – Q,T
34. Which of the following option has correct combinations.
A) III – P,T B) IV – P,U C) IV – P,T D) III – R,S

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Narayana IIT Academy 19-09-21_SR.IIT_*CO-SC(MODEL-A)_JEE-Adv_GTA-1_Q’P
Answer Q.35 and Q.36 by appropriately matching the lists based on the information
given in the paragraph.
List-I includes staring materials and reagents of selected chemical reactions. List-II gives
structures of compounds that may be formed as intermediate products and /or final
products from the reactions of List-I.
List – I List – II

(I) (P)

(II) (Q)

(III) (R)

(IV) (S)

(T)

(U)

35. Which of the following options has correct combination considering List-I and List-II?
A) I – Q,T,U B) II – P,S,T C) II – P,S,U D) I – S,Q,R
36. Which of the following options has correct combination considering List-I and List-II?
A) III – S,R B) IV – Q,U C) III – T,U D) IV – Q,R

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MATHEMATICS Max.Marks:62
SECTION – I
(MULTIPLE CORRECT CHOICE TYPE)
This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer,
out of which ONE OR MORE is/ are correct.
Marking scheme +4 for correct answer , 0 if not attempted and -1 in all other cases.
2 x  1  4 x  5  3x  1
37. The number of real values of x satisfying the equation;    are
 3   6  2

greater than or equal to { [.] denotes greatest integer function}:

A) 7 B) 8 C) 9 D) 10
38. Let f ( x) be twice differentiable function such that f ''( x)  0 in [0, 2]. Then
A) f (0)  f (2)  2 f (c) , for atleast one c, c  (0, 2)
B) f (0)  f (2)  2 f (1)
C) f (0)  f (2)  2 f (1)

D) 2 f (0)  2 f (2)  3 f  
2
3

39. A triangle has sides 6, 7, 8. The line through its incentre parallel to the shortest side is
drawn to meet the other two sides at P and Q. The length of the segment PQ is
30 25 36
A) equal to B) greater than C) less than D) equal to 5
7 7 7
40. The differentiable function y  f ( x) has a property that the chord joining any two points
A  x1 , f ( x1 )  and B  x2 , f ( x2 )  always intersects y-axis at  0, 2x1 x2  . Given that f (1)  1,
then
1
A) f ( x) is a polynomial B) maximum value of f ( x) is
8
C) f (2)  6 D) f (2)  6
41. Which of the following statement(s) is/are correct ?
A) The number of quadratic equations having real roots which remain unchanged even
after squaring their roots is 3.
B) The number of solutions of the equation tan 2  tan 3  0 , in the interval  0,   is
equal to 6.
2 x1 128 x32 x3
C) For x1 , x2 , x3  0, the minimum value of  2  2 2 equals 24.
x2 x2 4 x1 x3
D) The locus of the mid-points of chords of the circle x 2  y 2  2 x  6 y  1  0 , which are
passing through origin is x 2  y 2  x  3 y  0 .

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42. For  ABC , if 81  144a  16b  9c  144abc, (where notations have their usual meaning),
4 4 4

then
A) a  b  c B) A  B  C
3 3
C) Area of  ABC  D) Triangle ABC is right angled
8
43. A consignment of 15 record players contain 4 defectives. The record players are
selected at random, one by one and examined. The one examined is not put back. Then
A) Probability of getting exactly 3 defectives in the examination of 8 record players is
4 11
C3 C5
15
.
C8

8
B) Probability that 9th one examined is the last defective is .
197
C) Probability that 9th examined record player is defective, given that there are 3
1
defectives in first 8 players examined is .
7
8
D) Probability that 9th one examined is the last defective is .
195
44. Let a, b, c, d be non zero distinct digits. The number of 4 digit numbers abcd such that
ab  cd is even is divisible by

A) 3 B) 4 C) 7 D) 11
SECTION – II
(Numerical Value Answer Type )
This section contains 6 questions. The answer to each question is a Numerical values comprising of positive
or negative decimal numbers (place value ranging from Thousands Place to Hundredths place).
Eg: 1234.56, 123.45, -123.45, -1234.56, -0.12, 0.12 etc.
Marking scheme : +3 for correct answer, 0 in all other cases.
z2 z2 z2
45. Let z1 , z2 , z3 be complex numbers such that z1  z2  z3  1 and 1  2  3  1  0 .
z2 z3 z1 z3 z1 z2

Find the number of elements in the range of z1  z2  z3 .

2
46. Find the absolute value of  tan A tan 2 A   tan 2 A tan 4 A   tan 4 A tan A  , where A  .
7

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1 n 1 n
x x
47. Let I n   dx and J n   dx n  2012, n  N if the matrix A   aij  3  3 , where
0
x 2012
1 0
x 2013
1

I  I j, i  j  J 2016 j  J j 3 , i  j
aij   2012i and the matrix B  bij  3  3 , where bij   . Find
 0, i j  0, i j

the value of trace  A1   det  B 1  .

 
2
48. The value of the definite integral 1  x 3  3 x 2  2 x dx is
0

Let f ( x) be continuous function such that f (0)  1 and f ( x)  f    x  R, then

x x
49.
7 7
f (42) 

50. Rectangle ABCD has area 200. An ellipse with area 200 passes through A and C and
P
has foci at B and D. Let perimeter of the rectangle ABCD is P, then 
10
SECTION-III
(MATCHING LIST TYPE)
This section contains 4 questions, each having two matching lists (List-1 & List-II). The options for the correct
match are provided as (A), (B),(C) and (D) out of which ONLY ONE is correct.
Marking scheme: +3 for correct answer, 0 if not attempted and -1 in all other cases.
Answer Q.51 and Q.52 by appropriately matching the lists based on the information
given in the paragraph.
If y  x  1 is axis of parabola, y  x  4 is tangent of same parabola at its vertex and
y  2 x  3 is one of its tangent, then

Column – I Column – II
If equation of directrix of parabola is
i) P) 9
ax  by  29  0 , then a  b 
a 2
If length of latus rectum of parabola is where
b Q) 18
ii)
a and b are relatively prime natural numbers, then
ab 
Let extremities of latus rectum are  a1 , b1  and
iii)  a2 , b2  , then  a1  b1  a2  b2   R) 23
(where [.] denotes greatest integer function)
If equation of parabola is a  x  y  1  b  x  y  4 
2

iv) where a and b are relatively prime natural S) 37

numbers then a  b 

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51. Which of the following is correct ?
A) i – Q B) ii – p C) iii – S D) iv – R
52. Which of the following incorrect ?
A) iv – S B) i – Q C) ii – P D) iii – P
Answer Q.53 and Q.54 by appropriately matching the lists based on the information
given in the paragraph.
Column – I Column – II
If eccentricity of conjugate hyperbola of the given

 x  1   y  2    x  5   y  5 3
2 2 2 2
i) hyperbola P) 8

is e ' then value of 8e ' is

x2 y 2
If area of the ellipse   1 inscribed in a
16 b 2
ii) Q) 12
A
square of side length 5 2 is A then equal to


Any chord of the conic x 2  y 2  xy  1 passing

iii) through origin is bisected at a point (p, q) then R) 10
 p  q  12  equals
Length of the shortest chord of the parabola
iv) y 2  4 x  8 which belong to the family of lines S) 7
1    y     1 x  2 1     0 , is
T) 9

53. Which of the following is the correct combination ?

A) i – R, iii – P B) iii – R, ii – Q C) ii – Q, iii – Q D) i – S, iv – T
54. Which of the following is incorrect combination ?
A) ii – Q, i – R B) iii – Q, iv – P C) iv – P, ii – Q D) i – T, iii – S

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