Fiitjee Aiits Open Jee Mains

FIITJEE JEE (Main)-2019
OPEN TEST
ALL INDIA INTEGRATED TEST SERIES
Time Allotted: 3 Hours Maximum Marks: 360
 Pl ea s e r ea d t h e i n s t r u c t i o n s c a r ef u l l y. Yo u a r e a l l o t t ed 5 m i n ut es
s p ec i f i c a ll y f o r t h i s p u r p o s e.
 Yo u a r e n o t a ll o wed t o l ea v e t h e E xa m i n at i o n Ha ll b ef o r e t h e en d o f
t h e t es t .
INSTRUCTIONS
A. General Instructions
1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Parts.
3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.
4. Each part has only one section: Section-A.
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be
provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic
devices, in any form, are not allowed.
B. Filling of OMR Sheet

1. Ensure matching of OMR sheet with the Question paper before you start marking your answers
on OMR sheet.
2. On the OMR sheet, darken the appropriate bubble with black pen for each character of your
Enrolment No. and write your Name, Test Centre and other details at the designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.
C. Marking Scheme For All Three Parts.

1. Section-A (01 – 30, 31 – 60, 61 – 90) contains 90 multiple choice questions which have only one
correct answer. Each question carries +4 marks for correct answer and –1 mark for wrong
answer.
Name of the Candidate
Enrolment No.
FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942
website: www.fiitjee.com
AIITS-OT-PCM-JEE(Main)/19 2
Useful Data
PHYSICS
Acceleration due to gravity g = 10 m/s2

Planck constant h = 6.6 1034 J-s
Charge of electron e = 1.6  1019 C
Mass of electron me = 9.1  1031 kg
Permittivity of free space 0 = 8.85  1012 C2/N-m2
Density of water water = 103 kg/m3
Atmospheric pressure Pa = 105 N/m2
Gas constant R = 8.314 J K1 mol1
CHEMISTRY
Gas Constant R = 8.314 J K1 mol1
= 0.0821 Lit atm K1 mol1
= 1.987  2 Cal K1 mol1
Avogadro's Number Na = 6.023  1023
Planck’s constant h = 6.625  1034 Js
= 6.625  10–27 ergs
1 Faraday = 96500 coulomb
1 calorie = 4.2 joule
1 amu = 1.66  10–27 kg
1 eV = 1.6  10–19 J
Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,

N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16,
Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25,
Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33,
Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56,
Pb=82, U=92.
Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16,
F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32,
Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59,
Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108,
Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.
3 AIITS-OT-PCM-JEE(Main)/19
Physics PART – I
SECTION – A
(One Options Correct Type)
This section contains 30 multiple choice questions. Each question has four choices (A), (B), (C) and
(D), out of which ONLY ONE option is correct.
1. Two projectiles are thrown from the same point simultaneously with initial speeds u1 and
u2 at angles 1 and 2 with horizontal respectively If u1 sin 1 = u2 sin 2, then path of one
projectile as seen from other will be
(A) A parabola (B) A vertical straight line
(C) A horizontal straight line (D) none of above
2. In order to calculate the speed of sound in nitrogen gas at 300 K, you are given that the
gas is diatomic. You will also need to know only the
(A) density of the gas at 300 K, and the mass of one mole of the nitrogen
(B) pressure of the gas at 300 K
(C) molecular weight of nitrogen and the universal gas constant
(D) characteristic gas constant for nitrogen
3. A spring of force constant k is cut into two pieces such that one piece is double the
length of the other. Then the long piece will have a force constant of
2 3
(A) k (B) k
3 2
(C) 3k (D) 6k
4. The bob hanging from a light string is projected horizontally with a

speed u0. In the subsequent upward motion of the bob in vertical
plane 
(A) A negative amount of work has been done by tension on the bob.
(B) A positive amount of work has been done by gravity on the bob.
(C) The tension in the string and speed of bob both may become zero
at an instant. m u0
(D) None of these.
Space for Rough work
5. For a system in equilibrium as shown in figure elongation in spring

will be
2mg mg k
(A) (B)
k k
mg mg
(C) (D)
2k 3k
m
6. A simple pendulum has time period T = 2s in air. If the whole arrangement is placed in a
1
nonviscous liquid whose density is times the density of bob. The time period of the
2
simple pendulum in the liquid will be
2
(A) s (B) 4 s
2
(C) 2 2 s (D) 4 2 s
7. A gas bubble from an explosion under water oscillate with a period T proportional to pa
db Ec where p is the static pressure, d is the density and E is the total energy of
explosion. The values of a, b, c are
(A) a = 0, b = 1, c = 2 (B) a = 1, b = 2, c = 1
(C) a = 5/6, b = -1/2, c = ½ (D) a = -5/6, b = 1/2, c = 1/3
8. A heavy disc is thrown on a horizontal surface with an initial linear velocity of v0. It will
start pure rolling when its linear velocity becomes
v 2v 0
(A) 0 (B)
2 3
3v 0 5v 0
(C) (D)
5 7
9. A string of length 1m and linear mass density 0.01 kg m–1 is stretched to a tension of 100
N. When both ends of the string are fixed, the three lowest frequencies for standing
wave are f1, f2 and f3. When only one end of the string is fixed, the three lowest
frequencies for standing wave are n1, n2 and n3. Then
(A) n3 = 5n1 = f3 = 125 Hz (B) f3 = 5f1 = n2 = 125 Hz
f f
(C) f3 = n2 = 3f1 = 150 Hz (D) n2 = 1 2 = 75 Hz
2
-1 -1
10. Two identical blocks each of mass 1 kg are join together 3ms 5ms
with a compressed spring. The system at any time after
releasing is moving with unequal speed in the opposite
direction as shown in figure. Choose the correct statement
(A) it is not possible
(B) whatever may be the speed of the blocks the centre of mass will remain stationary
(C) the centre of mass of the system is moving with a velocity of 2ms-1
(D) the centre of mass of the system is moving with a velocity of 1 ms-1
11. A U tube of uniform cross section is kept in a vertical position. A liquid of mass m and
density d is filled in one of its limbs. This liquid will oscillate in this tube with time period T
given by
m ma
(A) T  2 (B) T  2
gda gd
m m
(C) T  2 (D) T  2
g 2agd
12. A liquid is filled in a spherical container of radius R till a height

h. At this position the liquid surface at the edges is also
horizontal. The contact angle is R R
R h
(A) 0 (B) cos1  
 R  h
hR R h
(C) cos1   (D) sin1  
 R   R 
13. A firecracker exploding on the surface of a lake is heard as two sounds a time interval t
apart by a man on a boat close to water surface. Sound travels with a speed u in water
and a speed v in air. The distance from the exploding firecracker to the boat is (u > v)
uvt t(u  v)
(A) (B)
uv uv
t(u  v) uvt
(C) (D)
uv uv
14. A sphere of mass m and radius r slips on a rough horizontal =vo/2r
plane.
vo
At some instant it has translational velocity vo and rotational O
velocity about the centre vo/2r. Find the velocity of bottom most
point A of the sphere. x(ve) A +x 
(A) vo/2 in +ve x-direction.
(B) vo/2 in ve x-direction.
(C) zero.
(D) vo in +ve x-direction.
15. In order to shift a body of mass m from a circular orbit of radius 2R to a higher orbit of
radius 4R around the earth, (Where R is radius and M is mass of earth) the work done
on the body is
GMm GMm
(A) (B)
8R 2R
GMm GMm
(C) (D)
4R R
16. For a given process with an enclosed one mole of 2

P (N/m )
monoatomic ideal gas, the variation of its pressure (P) with
2 B
its volume (V) is as shown in the graph AB. If the
temperature of the gas at A is (To )K, then,
A
(A) the temperature at B = (2To)K 1
(B) the temperature at B = (3To)K 3
V (m )
(C) the work done by gas from A to B is 1.5 J 0 1 2
(D) the change in the internal energy of the gas is 9RTo.
17. A tank with vertical walls is mounted so that its base is at a height H above the horizontal
ground. The tank is filled, with water to a depth h. A hole is punched in the side wall of
the tank at a depth x below the water surface. To have maximum range of emerging
stream, the value of x is (h > H)
Hh H
(A) (B)
2 2
h Hh
(C) (D)
2 2
18. A boat carrying a number of large stone piece is floating in a water tank. What will
happen to the water level if the stones are unloaded into the water?
(A) rises
(B) falls
(C) remains unchanged
(D) rises till half the number of stones are unloaded and then being to fall
19. An open organ pipe of length L vibrates in second harmonic mode. The pressure
vibration is maximum
(A) at the two ends
(B) at a distance L/4 from either end inside the tube
(C) at the mid-point of the tube
(D) none of these
20. A body of mass m is falling freely through a height h from the top of a tower. The velocity
just before touching the ground is  3 / 2 gh . The work done by air drag is
mgh mgh
(A)  (B) 
4 4
(C) zero (D) none of these
21. A man holds an umbrella at 300 with vertical to keep himself dry. He then runs at a
speed of 10 ms-1 and find the raindrops are hitting him vertically. Speed of the raindrops
wrt earth is
(A) 20ms1 (B) 10ms1
(C) 10 3ms1 (D) 20ms1
22. An insect of mass m crawls along the hanging thread with an

g
acceleration a  . The reaction offered by ground on the block of
2
mass 2 m is: a
g
2
(A)
3mg
2
(B) mg  m
mg
(C) 2mg (D) 2m
2
23. A cubical frame is made by connecting 12 identical uniform

E F
conducting rods as shown in the figure. In the steady state
the temperature of junction A is 1000 C while that of the G is
A B
00 C . Then, a
(A) H will be Hotter than B 0
0C
(B) Temperature of F is 400 C H G
(C) Temperature of D is 66.670 C D a C
(D) Temperature of E is 500 C
24. What change in surface energy will be noticed when a drop of radius R splits up into
1000 droplets of radius r, surface tension of T?
(A) 4R2 T (B) 7 R 2T
(C) 16 R 2T (D) 36 R2 T
25. A train of mass M is moving on a circular track of radius R with constant speed v. The
length of train is half the perimeter of track. The linear momentum of the train will be
(A) 0 (B) 2M/
(C) MvR (D) Mv
26. The force exerted by a liquid density , on the wall of the dam b
of width b, as shown in the figure, Atmospheric pressure is P0.
 gh  h
(A)  P0   bh (B) P0  gh  bh
 2 
  gh   P  gh 
(C)  P0   bh (D)  0  bh
 3   2 
27. A uniform disc of radius R lies in the x – y plane, with its centre at origin moment of
inertia about z – axis is equal to its moment of inertia about line y = x + c. The value of c
will be –
R R
(A)  (B) 
2 2
R
(C) (D) – R
4
28. The velocity of a particle is   0  gt  ft 2 . If its position is x =0 at t =0, then its

displacement after unit time (t =1) is :
(A) 0  g / 2  f (B) 0  2g  3f
(C) 0  g / 2  f / 3 (D) 0  g  f
29. A car accelerates from rest with a constant acceleration  on a straight road. After
gaining a velocity  the car moves with the same velocity for some-time. Then the car
decelerated to rest with a retardation  . If the total distance covered by the car is equal
to S, the total time taken for its motion is
S   1 1 S  
(A)     (B)  
 2    
   S   
(C)    (D)    
   2 
30. In order to do work :

(A) force must act at any angle to the displacement
(B) Force may not act along the same direction as is the displacement
(C) must act along the direction of displacement
(D) must act normal to the direction of displacement
Chemistry PART – II
SECTION – A
31. XeF4 is planar whereas CCl4 is tetrahedral because

(A) in XeF4, Xe is sp2 hybridised and C is sp3 hybridised in CCl4.
(B) Xe is sp3d2 hybridised in XeF4 but due to the presence of two lone pairs of electrons,
the shape is planar whereas in CCl4, C is sp3 hybridised.
(C) in both XeF4 and CCl4, the central atom is sp3 hybridised.
(D) Xe is a noble gas whereas C is a non-metal.
32. In an experiment, 50 ml of 0.1M solution of a salt reacted with 25 ml of 0.1 M solution of

sodium sulphite. The half equation for the oxidation of sulphite ion is:
2
SO3(aq)  H2O  SO24(aq)
 
 2H(aq)  2e 
If the oxidation number of the metal in the salt was 3, what would be the new oxidation
number of the metal?
(A) 0 (B) 1
(C) 2 (D) 4
33. The compound most likely to decolourise a cold solution of alkaline potassium
permanganate is
(A) H2C  CH2 (B)
CH3
(C) (D) H3C
CH3
34. Which one of the following compounds will give in the presence of peroxide a product
different from that obtained in the absence of peroxide?
(A) 1-butene HCl (B) 1-butene, HBr
(C) 2-butene, HCl (D) 2-butene, HBr.
35. Of the following transitions in hydrogen atom, the one which gives an absorption line of
lowest frequency is
(A) n = 1 to n = 2 (B) n = 3 to n = 8
(C) n = 2 to n = 1 (D) n = 8 to n = 3
36. Each of the following pair contains species with the same geometry EXCEPT
(A) P O34 , S O 24 (B) NH4 , BF4
(C) CO2, C2H2 (D) N2O, NO2
37. A reaction mixture containing H2, N2 and NH3 has partial pressures 2 atm, 1 atm and 3


atm respectively at 725 K. If the value of Kp for the reaction, N2(g) + 3H2(g) 
 2NH3(g)
is 4.28  10–5 atm–2 at 725 K, in which direction the net reaction will go ?
(A) Forward
(B) Backward
(C) No net reaction
(D) Direction of reaction cannot be predicted.
38. 10 L of aqueous solution contains 0.1 mole of each of NaCl, CH3COONa and
CH3COOH. What is the pH of the solution?
[Ka of CH3COOH = 10–5]
(A) 3 (B) 6
(C) 4 (D) 5
39. A solution of HCl is diluted so that its pH changes by 0.3. How does concentration of H+
ion change?
(A) 0.5 times of initial value (B) 0.3 times of initial value
(C) 10–3 times increases (D) None
40. If for two gases of molecular weights MA and MB at temperature TA and TB, TAMB = TBMA,
then which property has the same magnitude for both the gases.
(A) density (B) pressure
(C) KE per mole (D) Urms
41. Assuming that air is 79% by mole of N2, 20% O2 and 1% Ar, the density of air at 25°C
and 1 atm is
(A) 1.18 g/lit (B) 1.08 g/lit
(C) 1.28 g/lit (D) 1.0 g/lit.
42. SiO2  HF  X  Y
HF
 Z
Compound (Z) in the above reaction is:
(A) SiF4 (B) H2SiF4
(C) H2SiF6 (D) H2SiF3
43. Pyrosilicate ion is:

(A) SiO22 B) SiO42
(C) Si2O76 D) Si2O77
44. Arrange the following in decreasing order of E2 reaction:

Cl Cl Cl
Cl Cl Cl Cl Cl Cl
Cl Cl Cl Cl Cl Cl
Cl Cl Cl
(X ) (Y) (Z)
(A) X > Y > Z (B) X > Z > Y
(C) Z > X > Y (D) Y > X> Z
45. OH
H
 P, P is

HO
OH
[info there is interconversion between the given compounds


CH2  ]
(A) (B)
(C) (D)
46. For the reaction equilibrium


2NOBr  g  
 2NO  g  Br2  g
P K
If PBr2 at equilibrium and P is total pressure. The ratio P is equal to
9 P
1 1
(A) (B)
9 81
1 1
(C) (D)
27 3
47. Which of the following is not correct?

(A) G is zero for a reversible reaction
(B) G is positive for a spontaneous reaction
(C) G is negative for a spontaneous reaction
(D) G is positive for a non-spontaneous reaction
48. The first ionisation enthalpies of Na, Mg, Al and Si are in the order:
(A) Na < Mg > Al < Si (B) Na > Mg > Al > Si
(C) Na < Mg < Al < Si (D) Na > Mg > Al < Si
49. The types of hybrid orbitals of nitrogen in NO2 ,NO3 and NH4 respectively are expected to
be
(A) sp, sp3 and sp2 (B) sp, sp2 and sp3
2 3
(C) sp , sp and sp (D) sp2, sp3 and sp
50. Which molecule/ion out of the following does not contain unpaired electrons?
(A) N2 (B) O2
(C) O 22 (D) B2
51. In each of the following total pressure set-up at equilibrium is assumed to be equal and
is 1 atm. With equilibrium constants Kp given as K1, K2 & K3 for I, II & III equilibria
respectively, which of the following is correct ?
I. CaCO3(s)  CaO(s) + CO2(g), K1
II. NH4HS(s)  NH3(g) + H2S(g), K2
III. NH2CO2NH4(s)  2NH3(g) + CO2(g), K3
(A) K1 = K2 = K3 (B) K1 < K2 < K3
(C) K3 < K2 < K1 (D) None of these
52. Under the same reaction conditions, initial concentration of 1.386 mol. dm–3 of a
substance becomes half in 40 seconds and 20 seconds through first order and zero
[K 1 ]
order kinetics, respectively. Ratio of the rate constants for first order (K1) and zero
[K 0 ]
order (K0) of the reaction is :
(A) 0.5 mol–1 dm3 (B) 1.0 mol. dm–3
(C) 1.5 mol. dm–3 (D) 2.0 mol–1. dm3
53. Solubility of AgCl in water, 0.01M CaCl2, 0.01M NaCl and 0.05M AgNO3 are S1, S2, S3
and S4 respectively then.
(A) S1  S2  S3 < S4 (B) S1 > S3 > S2 > S4
(C) S1 > S2 = S3 > S4 (D) S1 > S3 > S4 < S2
H2 O Heat  Na2 CO3

54. SiCl4   (A)   (B) Heat
(C). The compound (C) is;
(A) SiO2 (B) Si
(C) SiC (D) Na2SiO3
55. Aluminium chloride exists as a dimmer, Al2Cl6, in solid state as well as in solution of non-
polar solvents such as benzene. When dissolved in water, it gives :
3
(A) Al3  3Cl (B)  Al H2O 6   3Cl
3
(C)  Al  OH6   3HCl (D) Al2O3  6HCl
56. Borax is used as a cleaning agent because on dissolving in water, it gives;

(A) alkaline solution (B) acidic solution
(C) bleaching solution (D) neutral solution
57. A mixture of two gases is formed when an organic acid heated with conc.H2SO4. When
the gaseous mixture is passed through KOH solution, one gas is absorbed. The
unabsorbed gas combines with chlorine and forms a poisonous gas. The organic acid
and the two gases evolved with conc. H2SO4 are respectively:
(A) CH3COOH, CO2, CO (B) oxalic acid, CO2, CO
(C) HCOOH, CO, H2O (D) none of these
58. An inorganic compound (A) made of two most occurring elements in the earth’s crust
and used in building construction when made to react with carbon, forms a poisonous
gas (B) which is most stable hetero diatomic molecule. Compounds (A) and (B) are
(A) SiO2, CO2 (B) SiO2, CO
(C) SiO2, N2 (D) CaO, CO2
59. A reaction, 2A  3B takes place according to first order kinetics. The time in which the
concentration of reactant and product become equal is (k = 4.6 × 10–2 min–1), (log 5 =
0.7; log 3 = 0.48; log 2 = 0.3)
(A) 11 min (B) 15 min
(C) 9 min (D) 25 min
60. A vessel contains H2 and H2S gases at a partial pressures of 1 and 2 atm respectively at
certain temperature then the reaction, 8 H2S (g)  8H2(g) + S8(s) occurs. It is found
 nH   nH S 
that  2   2  (n represents no of moles). Then identify the correct
 nH2S  at equilibrium  nH2  at time,t 0
value of the given property :
(A) KP = 1/256
(B) KP = 256
(C) At equilibrium the volume of the gaseous mixture is doubled when provided with
frictionless piston
(D) KP = KC = 320
Mathematics PART – III
SECTION – A
61. 
Find number of integral values of a for which equation loge x 2  5x  loge  x  a  3  
has exactly one solution
(A) 4 (B) 5
(C) 6 (D) 1
62. If a and b are real number such that 3a  4b  25 then the minimum value of a 2  b2 is
equal to
(A) 1 (B) 5
(C) 25 (D) not defined
x
63. Equation of a circle is x 2  y 2  r 2 which has two chords y  0 and y 
. In smaller
3
sector between chords a circle of radius unity touches the chords and the circle
internally, then r is
(A) 1  2  6 (B) 2  3
(C) 1  2  6 (D) 1  2  6
64. In parabola y 2  4x, two shortest normal chords are diagonals of a quadrilateral, then
area of quadrilateral is
(A) 24 2 (B) 18 2
(C) 72 2 (D) 36 2
x2 y2
65. Equation of an ellipse E1   1, then equation of ellipse E2 whose foci are ends of
16 9
minor axis of E1 and which passes through foci of E1 is
x2 y2 x2 y2
(A)  1 (B)  1
7 16 16 7
x2 y2 x2 y2
(C)  1 (D)  1
9 16 7 9
66. A circle passes through (3, 4) and (10, 11) then length of tangent to this circle from (2, 3)
is
(A) Variable (B) 8
(C) 4 2 (D) 4
2 2 2 2
67. Let P(x, y) be a variable point such that  x  1   y  2   x  5   y  5  4
represent a hyperbola then eccentricities of conjugate hyperbola is

5 4
(A) (B)
4 3
5 3
(C) (D)
3 2
t 6  8t 4
68. If ,  are roots of x 2  5x  8  0 and tn  n  n then is
5t 5
(A) 5 (B) 4
(C) 8 (D) 1
69. If 4x 2  y 2  45 and x 2  4y 2  5 are orthogonal then the value of  is

1 1
(A) (B)
9 3
(C) 9 (D) 18
70. The value of sin3 10o  sin3 50o  sin3 70o is equal to
3 3
(A) (B)
2 4
3 3
(C) (D)
4 8
71. 
The number of solution of the equation 16 sin5 x  cos5 x  11 sin x  cos x  in the 
interval 0, 2 is
(A) 6 (B) 7
(C) 8 (D) 9
H1  2 H20  3
72. If H1,H2 ,....H20 are 20 harmonic means between 2 and 3 then  
H1  2 H20  3
(A) 20 (B) 21
(C) 40 (D) 38
73. The coefficient of x r  0  r  n  1 in the expansion of

n 1 n2 n 3 2 n 1
 x  3   x  3  x  2    x  3   x  2  ......   x  2  is

(A) n Cr 3n  2n  
(B) n Cr 3nr  2nr 
(C) n
C 3
r
r
 2nr  (D) None of these
z2
74. If z lies on the circle z  2i  2 2 then the value of arg   is equal to
 z  2
 
(A) (B)
3 4
 
(C) (D)
6 2
 
75. If z  2  i  z sin   arg z  then locus of z is
4 
(A) a pair of straight lines (B) circle
(C) parabola (D) ellipse
76. In a decagon find number of points of intersection of diagonals which will lie inside the
decagon if no three diagonals are concurrent
(A) 35 C2 (B) 10 C2  8C2
(C) 9 C6 (D) 10
C4
77. Let y be an element of the set A  1,2,3,5,6,10,15,30 and x1, x 2 , x3 be positive integer
such that x1x 2 x 3  y then the number of positive integral solutions of x1. x 2 . x 3  y is
(A) 64 (B) 27
(C) 81 (D) none of these
78. 7 people leave their bag outside the temple and returning after working the deity picked
one bag each at random. In how many ways at least one and at most three of them get
their correct bags?
(A) 3 C3 .9  7 C5 .44  7C1.265 (B) 7 C6 .265  7C3 .9  7C5 .44
(C) 7 C5 .9  7C2 .44  7C1.265 (D) none of these
1
79. If 2a  3c  2b  and a, b, c, > 0 then maximum value of term independent of x in the
5
1 1 25
  
expansion of  abx  cx  is
2 3
 
25 25 25
(A) C10 (B) C15  35 
35 35
25  1  25  1 
(C) C15   (D) C10  
 35   25 
80. If 4a2  b2  2c 2  4ab  6ac  3bc  0 , then family of lines ax  by  c  0 is concurrent

at one or the other of the two points whose coordinate are
 1  1
(A)  1,   or  2,  1 (B)  1,  1 or  2,  
 2  2
1  1 
(C)  2, 2  or  ,  1 (D) (1, 2) or  ,  1
2  2 
 1 1  1 1  1 
81. The sum of the infinite series 1   1       1   2   2   ..... is
 2  3   2 2  3 
12 9
(A) (B)
5 5
8 5
(C) (D)
5 3
82. The inverse of the compound proposition p   q  r    q  p  is

(A)  ~ p   q ~ r     ~ q ~ p  (B)  ~ p   ~ q ~ r     ~ q ~ p 
(C)  ~ p   ~ q  r     ~ q ~ p  (D)  ~ p   ~ q ~ r     ~ q ~ p 
83. A lamp post standing at a point A on a circular path of radius ‘r’ subtends an angle  at
some point B on the path and AB subtends an angle of 45o at any other point on the
path, the height of the lamp post is
r
(A) tan  (B) 2r tan 
2
r
(C) 2 r cot  (D) cot 
2
84. By mathematical induction 11n 2  122n 1 is divisible by

(A) 132 (B) 133
(C) 233 (D) 11
85. If , ,  are roots of x 3  2x 2  3x  4  0 then the value of  22  2  2   2 2 is

(A) –7 (B) –5
(C) –3 (D) 0
86. If a,a1,a 2 ,.....a 2n ,b are in A.P and g,g1,g2 ,........g2n ,b are in G.P. and h is the H.M. of a
a  a 2n a 2  a 2n 1 a  an 1
and b, then 1   .....  n is equal to
g1g2n g2 g2n 1 gn gn 1
n
(A) nh (B)
h
2n
(C) 2nh (D)
h
87. Normals are drawn from a point P to y 2  4x . The slopes of the normals are m1,m2 ,m3 .
If locus of P with m1m2   is part of y 2  4x , then  is
(A) 2 (B) 1
(C) 4 (D) none of these
88. If e and e1 are the eccentricities of the curves xy  2y  3x  2  0 and

x 2  y 2  6x  4y  1  0 respectively then e2  e12 is
(A) 1 (B) 4
(C) 6 (D) 9
n
89. 
If 5  2 6   I  f, n,I  N and 0  f  1, then I is
1 1
(A) f (B) f
f 1 f
1 1
(C) f (D) f
1 f 1 f
 1 2 1 3 1 4
90. If S  sin  sin  sin  sin  .......... then S =
3 2 3 3 3 4 3

(A) 0 (B)
3
 
(C) (D)
2 6

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FIITJEE JEE (Main)-2019

B. Filling of OMR Sheet

C. Marking Scheme For All Three Parts.

Name of the Candidate

Acceleration due to gravity g = 10 m/s2

Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,

4. The bob hanging from a light string is projected horizontally with a

Space for Rough work

5. For a system in equilibrium as shown in figure elongation in spring

Space for Rough work

12. A liquid is filled in a spherical container of radius R till a height

Space for Rough work

14. A sphere of mass m and radius r slips on a rough horizontal =vo/2r

16. For a given process with an enclosed one mole of 2

Space for Rough work

Space for Rough work

22. An insect of mass m crawls along the hanging thread with an

23. A cubical frame is made by connecting 12 identical uniform

Space for Rough work

28. The velocity of a particle is   0  gt  ft 2 . If its position is x =0 at t =0, then its

30. In order to do work :

Space for Rough work

31. XeF4 is planar whereas CCl4 is tetrahedral because

32. In an experiment, 50 ml of 0.1M solution of a salt reacted with 25 ml of 0.1 M solution of

(A) H2C  CH2 (B)

Space for Rough work

Space for Rough work

43. Pyrosilicate ion is:

44. Arrange the following in decreasing order of E2 reaction:

Space for Rough work

46. For the reaction equilibrium

Space for Rough work

47. Which of the following is not correct?

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H2 O Heat  Na2 CO3

56. Borax is used as a cleaning agent because on dissolving in water, it gives;

Space for Rough work

Space for Rough work

Mathematics PART – III

Space for Rough work

represent a hyperbola then eccentricities of conjugate hyperbola is

69. If 4x 2  y 2  45 and x 2  4y 2  5 are orthogonal then the value of  is

Space for Rough work

73. The coefficient of x r  0  r  n  1 in the expansion of

Space for Rough work

Space for Rough work

80. If 4a2  b2  2c 2  4ab  6ac  3bc  0 , then family of lines ax  by  c  0 is concurrent

82. The inverse of the compound proposition p   q  r    q  p  is

Space for Rough work

84. By mathematical induction 11n 2  122n 1 is divisible by

85. If , ,  are roots of x 3  2x 2  3x  4  0 then the value of  22  2  2   2 2 is

88. If e and e1 are the eccentricities of the curves xy  2y  3x  2  0 and

Space for Rough work

Space for Rough work

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