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Sec: SR.IIT_*CO-SC(MODEL-A,B&C) Date:15-01-24

Time: 3HRS Max. Marks: 300

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

15-01-24_SR.STAR CO-SUPER CHAINA(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_SYLLABUS

PHYSI CS: TOTAL SYLLABUS

CHEM I STRY: TOTAL SYLLABUS

M ATHEM ATI CS: TOTAL SYLLABUS

M I STAKES
SUBJECT JEE JEE TOTAL
SYLLABUS Q'S EXTRA SYLLABUS Q'S Q'S

M ATHS

PHYI SCS

CHEM I STRY
 Yashpatil TG~ @bohring_bot
Narayana IIT Academy
PHYSICS
15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
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 answ er, 0 if not attempted and -1 if not correct.

1. The rms value of the emf given by E(in volt) = 8sin t   6 cos t  is

1) 5 2 V 2) 7 2 V 3) 10 V 4) 10 2 V
2. A ball is spun with angular acceleration   6t 2  2t where t is in second and  is in
rads 2 . At t  0 , he ball has angular velocity of 10 rads 1 and angular position of 4 rad.

The most appropriate expression for the angular position of the ball is
3 t4 t3 2t 4 t 3 t3
A) t 4  t 2  10t B)   10 t  4 C)   10 t  12 D) 2t   5t  4
4

2 2 3 3 6 2
3. A block of mass 2 kg moving on a horizontal surface with speed of 4 ms 1 enters a rough
surface ranging from x  0.5 m to x  1.5 m . The retarding force in this range of rough
surface is related to distance by F  kx where k  12 Nm1 . The speed of the block as it
just crosses the rough surface will be
A) zero B) 1.5 ms 1 C) 2.0 ms 1 D) 2.5 ms 1
4. A current is made of two components given by i1  4 2 sin t ( A) and i2 = 3A. A hot wire
ammeter measures the current as –
A) 3A B) 4 2 C)7A D) 5A
5. Water falls from a 40 m high dam at the rate of 9  104 kg per hour. Fifty percentage of
gravitational potential energy can be converted into electrical energy. Using this hydro
electric energy number of 100 W lamps that can be lit is
(Take g  10 ms 2 )
A) 25 B) 50 C) 100 D) 18
6. Two objects of equal masses placed at certain distance from each other attracts each
other with a force of F. If one-third mass of one object is transferred to the other object,
then the new force will be
2 16 8
A) F B) F C) F D) F
9 9 9

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Yashpatil TG~ @bohring_bot
Narayana IIT Academy 15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
A charged particle is released form rest in a region of steady and uniform electric and
magnetic field which are parallel to each other. The particle will move in –
A) straight line B) circle C) helix D) cycloid
8. A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure.
It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat
during CA. A work of 50 J is done on the gas during the part BC. The internal energy
of the gas at A is 1560 J. The work done by the gas during the part CA is

A) 20 J B) 30 J C) -30 J D) -60 J
9. What will be the effect on the root mean square velocity of oxygen molecules if the
temperature is doubled and oxygen molecule dissociates into atomic oxygen?
A) The velocity of atomic oxygen remains same
B) The velocity of atomic oxygen doubles
C) The velocity of atomic oxygen becomes half
D) The velocity of atomic oxygen becomes four times
10. If the series limit wavelength of Lyman series for hydrogen atom is 912 Å, then the series
limit wavelength for Balmer series of hydrogen atom is –
A) 912 Å B) 1824 Å C) 3648 Å D) 456 Å
11. Two junction diodes one of Germanium (Ge) and other of silicon (Si) are connected as
shown in figure to a battery of emf 12 V and a load resistance 10 k . The germanium
diode conducts at 0.3 V and silicon diode at 0.7 V. When a current flows in the circuit, the
potential of terminal Y will be

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Narayana IIT Academy 15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P

A)12 V B)11 V C)11.3 V D)11.7 V

12. The space inside a straight current carrying solenoid is filled with a magnetic material
having magnetic susceptibility equal to 1.2  105 . What is fractional increase in the
magnetic field inside solenoid with respect to air as medium inside the solenoid ?
A) 1.2  105 B) 1.2  103 C) 1.8  103 D) 2.4  105
13. Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A
in the same direction. If the force of attraction per meter of each wire is 2  106 N , then
the value of x is approximately.
A) 1 B) 2.4 C) 1.4 D) 2
14. Two sounding bodies producing progressive waves given by y1  4sin  400 t  and

y2  3sin  404 t  , where t is in seconds, are situated near the ears of a person. The person

will hear
4
1) 2 beats per second with intensity ratio between maxima and minima.
3
2) 2 beats per second with intensity ratio 49 between maxima and minima.
3) 4 beats per second with intensity ratio 7 between maxima and minima.
4
4) 4 beats per second with intensity ratio between maxima and minima.
3
15. An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field
vibrating y-direction has maximum magnitude of 60 Vm 1 . Choose the correct equations
for electric and magnetic fields if the EM wave is propagating in vacuum.
 
A) E y  60sin   103  x  3  108 t  ˆj Vm 1 , Bz  2sin   103  x  3  108 t  kˆ T
4  4 
 
B) E y  60sin   103  x  3  108 t   ˆj Vm1 , Bz  2  107 sin   103  x  3  108 t   kˆ T
4  4 

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Narayana IIT Academy

15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P

C) E y  2  107 sin   103  x  3  108 t  ˆj Vm 1 , Bz  60sin   103  x  3  108 t   kˆ T
4  4 
 
D) E y  2  107 sin   104  x  4  108 t   ˆj Vm 1 , Bz  60sin   10 4  x  4  108 t  kˆ T
4  4 

16. In young’s double slit experiment performed using a monochromatic light of wavelength
 , when a glass plate    1.5 of thickness x  is introduced in the path of the one of the

interfering beams, the intensity at the position where the central maximum occurred
previously remains unchanged. The value of x will be
A) 3 B) 2 C) 1.5 D) 0.5
17. Let K1 and K 2 be the maximum kinetic energies of photo-electrons emitted when two
monochromatic beams of wavelength 1 and 2 , respectively are incident on a metallic
surface. If 1  32 then
K2 K2 K2 K1
A) K1  B) K1  C) K1  D) K 2 
3 3 3 3
18. A massless rod is suspended by two identical strings AB and CD of equal length. A block
of mass m is suspended from point O such that BO is equal to ‘x’. Further, it is observed
that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2nd harmonic
frequency in CD. Then, length of BO is
A C

B O D
L

A) L/5 B) 4L/5 C) 3L/4 D) L/4

19. A solid sphere of mass M, radius R and having moment of inertia about an axis passing
through the centre of mass I, is recast into a disc of thickness t, whose moment of inertia
about an axis passing through its edge and perpendicular to its plane remains I. Then,
radius of the disc will be
2R 2 4R R
A) B) R C) D)
15 15 15 4

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Narayana IIT Academy 15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
20. A system of binary stars of masses mA and mB are moving in circular orbits of radii rA and
rB respectively. If TA and TB are the time periods of revolution of masses mA and mB

respectively, then
3/2
T r 
A) A   A  B) TA  TB  if rA  rB 
TB  rB 

C) TA  TB  if mA  mB  D) TA  TB
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 Answ er any 5 only out of 10 questions and question will be
evaluated according to the following marking scheme:
Marking scheme: + 4 for correct answ er, -1 in all other cases.
21. A student in the laboratory measures thickness of a wire using screw gauge. The
x
readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is %.
121
The value of x is _____
22. A zener of breakdown voltage VZ  8V and maximum zener current, I ZM  10 mA is
subjected to an input voltage Vi  10V with series resistance R  100  . In the given
circuit RL represents the variable load resistance. The ratio of maximum and minimum
value of RL is ______

23. In a Young’s double slit experiment, an angular width of the fringe is 0.350 on a screen
placed at 2m away for particular wavelength of 450 nm. The angular width of the
1
fringe, when whole system is immersed in a medium of refractive index 7/5, is . The

value of  is ______
24. A 60W monochromatic point source radiating equally in all directions in vacuum. The
amplitude of electric field in S.I units at a distance of 2m from the source is…

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 Yashpatil TG~ @bohring_bot
Narayana IIT Academy 15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
a
25. All resistances in figure are 1  each. The value of current ‘I’ is A . The value of a is
5

26. A capacitor C1 of capacitance 5  F is charged to a potential of 30 V using a battery.

The battery is then removed and the charged capacitor is connected to an uncharged
capacitor C2 of capacitance 10  F as shown in figure. When the switch is closed charge
flows between the capacitors. At equilibrium, the charge on the capacitor C2 is
________  C .

27. A convex lens of focal length 40 cm is held coaxially 12 cm above a concave mirror of
focal length 18 cm. An object held x cm above the lens gives rise to an image coincident
with it. The x is equal to

x cm

12 cm

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Narayana IIT Academy
28.
15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
A liquid of density 750 kgm flows smoothly through a horizontal pipe that tapers in
3

A1
cross-sectional area from A1  1.2  102 m 2 to A2  . The pressure difference between
2
the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is
_______  103 m3 s 1 .
29. A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed
horizontal axle as shown in figure. A block with mass m = 2kg hangs from a massless
cord that is wrapped around the rim of the disc. During the fall of the block, the cord
does not slip and there is no friction at the axle. The tension in the cord is _______ N.

30. A car covers AB distance with first one-third at velocity v1 ms 1 , second one-third at
v2 ms 1 and last one-third at v3 ms 1 . If If v3  3v1 , v2  2v1 and v1  11 ms 1 then the average

velocity of the car is ______ ms 1 .

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 Yashpatil TG~ @bohring_bot
Narayana IIT Academy
CHEMISTRY
15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
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 answ er, 0 if not attempted and -1 if not correct.
31. Compound A contains 8.7% Hydrogen, 74% Carbon and 17.3% Nitrogen. The
molecular formula of the compound is,
Given : Atomic masses of C, H and N are 12, 1 and 14 amu respectively.
The molar mass of the compound A is 162 g mol 1 .
A) C4 H 6 N 2 B) C2 H 3 N C) C5 H 7 N D) C10 H14 N 2
32. Consider the following statements:
(A) The principal quantum number ‘n’ is a positive integer with values of ‘n’ = 1, 2, 3,
……
(B) The azimuthal quantum number ' l ' for a given ‘n’ (principal quantum number) can
have values as ' l ' = 0, 1, 2, ….. n
(C) Magnetic orbital quantum number ' ml ' for a particular ' l ' (azimuthal quantum
number) has (2l  1) values
(D) For  1/ 2 are the two possible electron spin states
(E) For l  5, there will be a total of 9 orbitals
Which of the above statements are correct ?
A) (A), (B) and (C) B) (A), (C), (D) and (E)
C) (A), (C) and (D) D) (A), (B), (C) and (D)
33. In the structure of SF4 , the lone pair of electrons on S is in.
A) equatorial position and there are two lone pair – bond pair repulsions at 900
B) equatorial position and there are three lone pair – bond pair repulsion at 900
C) axial position and there are three lone pair – bond pair repulsion at 900
D) axial position and there are two lone pair – bond pair repulsion at 900
34. The pH of a buffer solution changes from 6.20 to 6.17 when 0.003 mole of acid is added
to 500 mL of the buffer. The buffer capacity of the system is, therefore,
A) 0.1 B) 0.3 C) 0.2 D) 0.4

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35.
15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
Mole fraction of a non electrolyte in aqueous solution is 0.07. If Kf is 1.86° mol–1 kg,
depression in f.p,  Tf is,
A) 0.26° B) 1.86° C) 0.13° D) 7.78°
36. Match List-I with List-II.
List-I (Oxide) List-II (Nature)
(A) Cl2O7 (I) Amphoteric
(B) Na2 O (II) Basic
(C) Al2O3 (III) Neutral
(D) N 2O (IV) Acidic
Choose the correct answer from the options given below:
A) (A) – (IV), (B) – (III), (C) – (I), (D) – (II)
B) (A) – (IV), (B) – (II), (C) – (I), (D) – (III)
C) (A) – (II), (B) – (IV), (C) – (III), (D) – (I)
D) (A) – (I), (B) – (II), (C) – (III), (D) – (IV)
37. Among the following species identify the isostructural pairs: NF3 , NO 3 – , BF3 ,

H 3 O  , HN 3

A) [NF3 , NO 3 – ] and  BF3 , H 3 O   B)  NF3 , HN 3  and  NO3 – , BF3 

C)  NF3 , H 3O   and  NO3 – , BF3  D)  NF3 , H 3O   and  HN 3 , BF3 

32. Zieglar-Natta catalyst is-

A) R3Al B) TiCl4 C) R3Al + TiCl4 D) R3B + TiCl2
39. Among the following, basic oxide is
A) SO3 B) SiO2 C) CaO D) Al2O3
40. Maltose is made up of
A)  –D-glucose B) D-fructose
C)  –D-Glucose and  –D-glucose D) Glucose and fructose
41. Which of the following oxoacids of sulphur contains “S” in two different oxidation
states ?
A) H 2 S 2O3 B) H 2 S2O6 C) H 2 S2O7 D) H 2 S2O8

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Narayana IIT Academy 15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P

42. Given the following reaction at equilibrium N 2 g   3H 2 g   2 NH 3 g  . Some inert

gas is added at constant Volume predict which of the following facts will be affected?

A) More of NH 3 g  is produced B) less of NH 3 g  is produced

C) No affect on the degree of advancement of the reaction at equilibrium

D) K P of the reaction is increased

43. The correct IUPAC name of the following compound is

A) 4-methyl-2-nitro-5-oxohept-3-enal B) 4-methyl-5-oxo-2-nitrohept-3-enal
C) 4-methyl-6-nitro-3-oxohept-4-enal D) 6-formyl-4-methyl-2-nitrohex-3-enal
44. The major product (P) of the given reaction is
(where, Me is CH 3 )

A) B)

C) D)

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Narayana IIT Academy 15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
(i ) Cl2 , 
A 
(ii ) CN 

45. 4-Bromophenyl acetic acid
(iii ) H2O / H 

In the above reaction ‘A’ is

A) B)

C) D)

  
46. The hybridisation of orbitals of N-atom in NO3 , NO2 and NH 4 are respectively:-
3 2 2 3 2 3
D) sp , sp, sp
2 3
A) sp, sp , sp B) sp , sp , sp C) sp, sp , sp
47. With respect to the following reaction, consider the given statements:

(A) o-Nitroaniline and p-nitroaniline are the predominant products

(B) p-Nitroaniline and m-nitroaniline are the predominant products
(C) HNO3 acts as an acid
(D) H 2 SO4 acts as an acid
A) (A) and (C) are correct statements B) (A) and (D) are correct statements
C) (B) and (D) are correct statements D) (B) and (C) are correct statements
H2 Na, liq. NH 3
48. B  R  C  C  R  A
Lindlar
A and B are geometrical isomers :-
A) A is trans, B is cis B) A and B both are cis
C) A and B both are trans D) A is cis, B is trans
SR.IIT_*CO-SC Page. No. 12
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Narayana IIT Academy
49.
15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
When sugar ‘X’ is boiled with dilute H 2 SO4 in alcoholic solution, two isomers ‘A’ and
‘B’ are formed. ‘A’ on oxidation with HNO3 yields saccharic acid where as ‘B’ is
laevorotatory. The compound ‘X’ is
A) Maltose B) Sucrose C) Lactose D) Starch
50. The correct name for the complex [Cr(NH3)6] [Co(C2O4)3] is
A) Hexaamminechromium (III) trioxalatocobalt (III)
B) Hexaamminechromate (III) trioxalatocobaltate (III)
C) Hexaamminechromium (III) trioxalatocobaltate (III)
D) Hexaamminechromate (III) trioxalatocobalt (III)

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 Answ er any 5 only out of 10 questions and question will be
evaluated according to the following marking scheme:
Marking scheme: + 4 for correct answ er, -1 in all other cases.
51. 100 g of an ideal gas is kept in a cylinder of 416 L volume at 270 C under 1.5 bar
pressure. The molar mass of the gas is _________ g mol 1 . (Nearest integer)
(Given : R  0.083 L bar K 1 mol 1 )
52. For combustion of one mole of magnesium in an open container at 300 K and 1 bar
pressure, C H   601.70 kJ mol 1 , the magnitude of change in internal energy for the
reaction is ________ kJ. (Nearest integer)
(Given : R  8.3 J K 1 mol 1 )
53. The number of radial nodes present in 3p orbital is
54. No. of moles of neutrons present in 36g of H2O
55. How many liters of water must be added to 1 liter of an aqueous solution of HCl with a
P H of 1 to create an aqueous solution with P H of 2
4 3 3 2 3
56.  Fe  CN  6  ,  Fe  CN 6  , Ti  CN 6  ,  Ni  CN  4  , Co  CN 6 

Among the given complexes, number of paramagnetic complexes is ______

57. (a) CoCl3 .4 NH 3 (b) CoCl3 . 5 NH 3 (c) CoCl3 . 6 NH 3 and (d) CoCl ( NO3 )2 . 5 NH 3
Number of complex(es) which will exist in cis-trans form is/are _______

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Narayana IIT Academy 15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
The complete combustion of 0.492 g of an organic compound containing ‘C’, ‘H’ and
‘O’ gives 0.793 of CO2 and 0.442 g of H 2O . The percentage of oxygen composition in
the organic compound is ______ (nearest integer)
59. When phenol reacts with bromine water, the major product contains number of bromine
atom(s).

60. Calculate G 0  KJ / mol  at 1270 C for a reaction with K eq  105 (Nearest integer)

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 answ er, 0 if not attempted and -1 if not correct.
61. Let R1  (a, b)  N  N : a  b  13 and R2  (a, b)  N  N : a  b  13 . Then on N :

A) Both R1 and R2 are equivalence relations

B) Neither R1 nor R2 is an equivalence relation
C) R1 is an equivalence relation but R2 is not
D) R2 is an equivalence relation but R1 is not
62. Let f ( x) be a quadratic polynomial such that f (2)  f (3)  0 . If one of the roots of
f ( x )  0 is 1 , then the sum of the roots of f ( x )  0 is equal to :

11 7 13 14
A) B) C) D)
3 3 3 3
63. The number of ways to distribute 30 identical candies among four children C1 , C2 , C3 and
C4 so that C2 receives atleast 4 and atmost 7 candies, C3 receives atleast 2 and atmost 6

candies, is equal to
A) 205 B) 615 C) 510 D) 430
11

The term independent of x in the expansion of 1  x  3 x   x 3  2  , x  0 is

5 1
64. 2 3

2 5x 

7 33 39 11
A) B) C) D)
40 200 200 50

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65.
15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
If n arithmetic means are inserted between a and 100 such that the ratio of the first mean
to the last mean is 1 : 7 and a  n  33, then the value of n is
A) 21 B) 22 C) 23 D) 24
66. A die is rolled 5 times. The probability there are at least two equal numbers among the
outcomes obtained is
A) 319/324 B) 49/54 C) 13/18 D) 4/9
  
67. Let f : R  R be a differentiable function such that f    2, f    0 and f '    1
4 2
  2    
 
and let g ( x )  x  f '(t )sec t  tan t sec t f (t )  dt for x   ,  . Then lim g ( x) is equal to
 /4

4 2  
x  


 2

A) 2 B) 3 C) 4 D) 3
68. Let f : R  R be a continuous function satisfying f ( x)  f ( x  k )  n, for all x  R where
4 nk 3k

k  0 and n is a positive integer. If I1  

0
f ( x)dx and I 2  
k
f ( x ) dx , then

A) I1  2 I 2  4nk B) I1  2 I 2  2nk C) I1  nI 2  4n 2 k D) I1  nI 2  6n 2 k
1
69. The area of the bounded region enclosed by the curve y  3  x   x  1 and the x-axis
2

is
9 45 27 63
A) B) C) D)
4 16 8 16

70.
2


Let x  x( y) be the solution of the differential equation 2 y e x / y dx  y 2  4e x / y dy  0 such
2


that x(1)  0 . Then, x(e) is equal to
A) e log e (2) B) e log e (2) C) e 2 log e (2) D) e 2 log e (2)
71. Let the slope of the tangent to a curve y  f ( x) at  x, y  be given by 2 tan x  cos x  y  . If
 /2

the curve passes through the point  , 0  , then the value of  y dx is equal to
4  0

   
A)  2  2   B) 2  C)  2  2   D) 2 
2 2 2 2

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72.
15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
Let a triangle be bounded by the lines L1 : 2 x  5 y  10; L2 : 4 x  3 y  12 and the line L3 ,
which passes through the point P(2, 3), intersects L2 at A and L1 at B. If the point P
divides the line-segment AB, internally in the rtio 1 : 3, then the area of the triangle is
equal to
110 132 142 151
A) B) C) D)
13 13 13 13
73. Let a  0, b  0. Let e and  respectively be the eccentricity and length of the latus
x2 y2
rectum of the hyperbola   1 . Let e ' and  ' respectively be the eccentricity and
a2 b2
11 11
 and  e '   ' , then
2
length of the latus rectum of its conjugate hyperbola. If e 2 
14 8
the value of 77 a  44b is equal to
A) 100 B) 110 C) 120 D) 130
 
74. Let a   iˆ  2 ˆj  kˆ and b  2iˆ   ˆj  kˆ , where   R . If the area of the parallelogram
 
whose adjacent sides are represented by the vectors a and b is 15  2  4  , then the
   2
value of 2 a 2   a . b  b is equal to

A) 10 B) 7 C) 9 D) 14
75. If vertex of a parabola is  2,  1 and the equation of its directrix is 4 x  3 y  21 , then the

length of its latus rectum is

A) 2 B) 8 C) 12 D) 16
Sn
76. If cos1  cos 2  cos 3  .........  cos n  Sn . That lt 
n  n
A) 1 B) 2
C) does not exists D) 0
77. The probability that a randomly chosen one-one function from the set a, b, c, d  to the

set 1, 2, 3, 4, 5 satisfies f  a   2 f  b   f  c   f  d  is

1 1 1 1
A) B) C) D)
24 40 30 20

 
The value of lim 6 tan  tan 1 
n
1
78.   is equal to
 r  3r  3  
2
n 
 r 1

A) 1 B) 2 C) 3 D) 6
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 
15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P

79. If x  3iˆ  6 ˆj  kˆ, y  iˆ  4 ˆj  3kˆ, and z  3iˆ  4 ˆj  12kˆ, then the magnitude of the scalar
  
projection of x  y on z is:
A) 12 B) 15 C) 14 D) 13
5 3 
80. If cot   1 and sec    , where     and     , then the value of tan    
3 2 2
and the quadrant in which    lies, respectively are
1
A)  and IVth quadrant B) 7 and Ist quadrant
7
1
C) 7 and IVth quadrant D) and Ist quadrant
7
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 Answ er any 5 only out of 10 questions and question will be
evaluated according to the following marking scheme:
Marking scheme: + 4 for correct answ er, -1 in all other cases.
x  6 y 1 z  2
81. Let the image of the point P 1, 2, 3 in the line L :   be Q. Let R  ,  ,  
3 2 3
be a point that divides internally the line segment PQ in the ratio 1 : 3. Then the value of
22       is equal to ______

82. Suppose a class has 7 students. The average marks of these students in the mathematics
examination is 62, and their variance is 20. A student fails in the examination if he/she
gets less than 50 marks, then in worst case, the number of students can fail is
_________.

83. The number of real solutions of the equation log 7  x  2   6  x is

84. Standard deviation of two distributions are same and their arithmetic means are 30 and

25 respectively. If their coefficient of variation is v1 and v 2 , then 6v1  5v2 is equal to

If ax  bx  6  0 does not have two distinct real roots, where a  R , b  R , then

2
85.

the least value of 3a  b is m , then m is

86. If the system of linear equations 2 x  3 y    5,  x  5 y    1, where  ,  ,   R has

infinitely many solutions, then the value of 9  3  5 is equal to _______.

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Narayana IIT Academy 15-01-24_SR.IIT_* CO-SC(MODEL-A,B&C)_JEE-MAIN_GTM-17(N)_Q’P
1  i 1 
87. Let A   where i  1 . Then, the number of elements in the set
 i 0 

n 1, 2,....., 100 : A

n
 A is ______.

88. Sum of squares of modulus of all the complex numbers z satisfying z  iz 2  z 2  z is

equal to ___
89. Let S  1, 2, 3, 4 . Then the number of elements in the set { f : S  S  S : f is onto and

f (a, b)  f (b, a )  a  (a, b)  S  S} is _____

90. The number of divisors of the form 4n  2n  0 of the integer 240 is

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