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JEE-MAIN_2013 MODEL
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry
and Maths having 30 questions in each part of equal weightage. Each question is
allotted 4 (four) marks for correct response.
4. Candidates will be awarded marks as stated above in instruction No. 4 for correct
response of each question. (1/4) (one fourth) marks will be deducted for indicating
incorrect response of each question. No deduction from the total score will be
made if no response is indicated for an item in the answer sheet.
5. There is only one correct response for each question. Filling up more than one
response in any question
will be treated as wrong response and marks for wrong response will be deducted
accordingly as per instructions 5 above
PHYSICS1. In an experiment to measure the length of a rod by four different instruments, the
measurement are reported asA)200.0 cm B)20 cm C)20.00 cm D)0.2000 cm
From the above data, we can infer that
A) All measurements have same accuracy B) A has least accuracy
C) B has least accuracy D) D has least accuracy
2. Which of the following plots correctly represents variation of the magnitude of radial
acceleration | | Ra with time t for a particle projected at t = 0 with speed 0v at an angle
θ above the horizontal?
A) B)
C) D)
3. In the given figure, a smooth parabolic wire track lies in the vertical plane(x-y plane).
The shape of track is defined by the equation (where a is constant). A ring of mass m
which can slide freely on the wire track, is placed at the position A(a, a). The track is
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C) 1 2 33
mgT T T D) 1 1 2 2 3 3T T T l l l
8. A block of mass 2 kg is to be lifted with constant velocity by applying force F down
the rope that passes over a pulley having coefficient of friction µ . The pull required is
A) 22geπµ
B) 2g C) 2geπµ D) 42geπµ
9. A chain of mass per unit length λ and length 1.5 m rests on a fixed smooth sphere of
radius 2 R π m such that A end of chain is at the top of sphere while the other end is
hanging freely. Chain is held stationary by a horizontal thread PA. The tension in the
thread is
A)1 2
2gλ
π
B)
2
2g
πλ
π
C)
2gλ
π
D) None of these
10. Figure shows a disc of mass M and radius R hinged at the centre. A small ball of mass
2
M is attached to point P with a thread of length 2R and held at rest at position shown.
Now, the balls is released to fall under gravity with what angular speed the disc starts
turning when the string becomes taut?
A)
2
g
R
B) g
R
C) R
g
D)2g
R11. A particle is projected from ground with speed u such that the horizontal range is R
and maximum height is H. The angular velocity of the particle about the point of projection, when it is at the highest point of its trajectory is
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A) 2 2 2 24 16
HRu
R H R H B)
2 2 2 24
4 16
HRu
R H R H
C) 2 2 2 2
8
4 16
HRu
R H H R D)
2 216
uR
H R H
12. Two identical discs of mass M and radius R are in contact with each other on smooth
horizontal surface. The disc A is fixed while B start rolling on circular path such thatthere is no slipping. The disc B makes one revolution around A in T time. Calculate
kinetic energy of the disc B.
A)2 2
2
16 M R
T
π B)2 2
2
3 MR
T
π C)2 2
2
24 MR
T
π D)2 2
2
12 MR
T
π
13. In the case of geostationary satellite, the
A) Rotation of the earth and the revolution of the satellite need not to be about
common axis
B) Rotation of the earth and revolution of the satellite will be in opposite directionsC) Angular velocity of the earth’s rotation and angular velocity of revolution of the
satellite will be equal and be in the same directionD) Angular velocity of the earth’s rotation and angular velocity of revolution of the
satellite will not be equal14. A rectangular container of base dimensions 2 1m m and height 0.5 m is filled with
water upto height of 0.2m. The mass of the empty container is 1 kg. The coefficient of
friction between container and plane is 0.5. The container is placed on the plane
inclined at 450
to the horizontal. The angle of the water surface to the horizontal is
A) 11
tan2
B) 1tan 2 C) 11
tan3
D) 1tan 3
15. The frequency of first overtone of a closed organ pipe of length L is f 1. A hole is made
at a distance
6
Lfrom the closed end. Now the frequency of first overtone of open pipe
is f 2. Then1
2
f
f is
A)4
5B)
5
4C)
8
5D)
5
8
16. One end of a string of length L is tied to ceiling of lift accelerating upwards with an
acceleration 3g. The other end of the string is free. The linear mass density of string
varies linearly from 0 to λ from bottom to top. Then correct statement for wave
travelling in string
A) Wave speed is increasing as it travels from bottom to top
B) Acceleration of wave on string is uniform
C) Time taken by pulse to reach from bottom to top will be2 L
g
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D) All of these
17. Statement-I: A planet may orbit around a star either in orbit P or orbit Q. The speed
of a planet at O is same for both orbits. AndStatement-II: The radius vector of point O from the sun is same for both orbit
P and Q.
[Note: Centre of circle consider with focus of the ellipse]
A) Statement-1 is True, Statement-2 is True; Statement -2 is a correct explanation for
Statement-1.
B) Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct
explanation for Statement-1.C) Statement -1 is True, Statement-2 is False.
D) Statement -1 is False, Statement-2 is True.18. P-V diagram of ideal gas is as shown in figure. Work done by the gas in the process
ABC is
A) 0 02PV B) 0 04PV C) 0 0PV D) 0 03PV
19. One mole of ideal gas whose adiabatic exponent4
3γ undergoes process
1200P
V
then change in internal energy of gas when volume changes from 32m to 34m is
A) 400 J B) 800 J C) 1200 J D) None of these
20. A capacitor is initially connected to a battery of EMF 3 V after a long time. At t = 0,
switch is thrown to B state. Now charge on capacitor at any instant is given by
A) / 2 t RC q C V V e B) / 2 t RC q C V V e
C) /2
2
t RC
q C V V e
D)
2 /
2
t RC
q C V V e
21. Consider the diagrams shown. Work done in transferring wire from position(1) to
position (2) is W1. Work done in transferring the wire from position (3) to position (4)
is W2 then
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A) 1
2
1W W
B) 2
1
1W W
C) 1 2 0W W D) 1W is positive, 2W is zero
22. A particle of mass m and charge q enters a region of magnetic field (as shown) with
speed v. There is a region in which the magnetic field is absent, as shown. The particleafter entering the region collides elastically with a rigid wall. Time after which the
velocity of particle becomes anti parallel to its initial velocity is
A) 42
m
qBπ B) 2
m
qBπ C) 2
4
m
qBπ D) 2 3
4
m
qBπ
23. Consider a wire of non-uniform cross-section. If the area of cross-section at point A is
double of the area of cross-section at point B. What is ratio of heat energy dissipated
in a unit volume at points A and B?
A)
1
2B)
2
1C)
1
4D)
4
1
24. Image in convex mirror, of the image of rod PQ in the plane mirror, is(radius of
curvature of mirror is 60 cm).
A) Virtual, erect and 6 cm long B) Real, inverted and 3 cm long
C) Virtual, erect and 3 cm long D) Real, inverted and 6 cm long
25. White light is used for double slit interference, for how many wavelengths, we get
maximum at point P shown here on the screen?
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A) 1 B) 2 C) 3 D) 726. When a monochromatic point source of light is at distance of 0.2 m from aphotoelectric cell, the cut off voltage and saturation current are respectively 0.6 V and
18 mA. If same source is placed 0.6 m away from photoelectric cell then
A) Stopping potential will be 0.2 volt B) Stopping potential will be 0.6 volt
C) Saturation current will be 6 mA D) Saturation current will be 4 Ma
27. The dependence of nuclear force on distance between nucleons is not known precisely,
but approximate variation is shown graphically. From graph which of following
statements cannot be concluded?
A) Nuclear force is repulsive for separation less than 0.5 fermi
B) Nuclear force is attractive for separation less than 0.5 fermi
C) Nuclear force is attractive for separation more than 0.5 fermi
D) Nuclear force is negligible when separation between nucleon is more than 10 fermi28. A point source of light is placed directly above an opaque sphere of radius y placed on
a horizontal surface
A) For2
3
y x , radius of shadow formed on horizontal surface is 2y
B) For x y , radius of the shadow formed on horizontal surface is 3 y
C) For2
3
y x and for surrounding medium having refractive index 3 , radius of
shadow formed on horizontal surface is 2y
D) For x = y and for surrounding medium having refractive index 3 , radius of the
shadow formed on horizontal surface is 2 y
29. Consider a hypothetical atom with single electron. In this atom, when an electron de-excites from energy level n x to 2n , wavelength λ of the radiation emitted is
given by2
24
Ax
xλ
(where A is a constant). Choose the correct alternatives.
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A) Least energetic photon emitted during such a transition will have wavelength 1.8 A
B) Most energetic photon emitted in such a transition will have wavelength A
C) Ionization potential of the atom in its ground state is1.8
hc
eA
D) Ionization potential of the atom in its first excited state is hc
eA
30. Choose the correct alternative.A) K α wavelength emitted by an atom of atomic number Z = 21 is λ , then
K α wavelength emitted by an atom of atomic number Z = 31 is4
9
λ
B) Half life of a radioactive substance is 5 years. Probability that a nucleus decays in
10 years is3
4
C) Mass number of a nucleus is always greater than its atomic number
D) Gamma rays are emitted due to nuclear de-excitation
CHEMISTRY31. Among the following hydroxides the one with lowest value of Ksp at ordinary
temperature.
A) 2
Ba OH B) 2
Mg OH C) 2
Ca OH D) 2
Be OH
32. Which of the following pairs can be distinguished by action of heat
1) 2 3 3 Na CO and CaCO 2) 2 2 2 2.6 .6 MgCl H O and CaCl H O 3) 3 32Ca NO and NaNO
A) 1 and 2 B) 1,2 and 3 C) 1 and 3 D) 1 only
33. 0200
2 6 3.2 C
g B H NH X Y
Number of double bonds in X.A) 3 B) 2 C) 4 D) 1
34.0200
3 4
C H PO X Y . The hybridization of ‘P’in X and Y.
A) 2 2sp and sp B) 3sp and sp C) 2sp and sp D) 3sp and no hybridization
35. H2SO4 is used to dry which of the following gases?
A) H2S B) CO2 C) NH3 D) all of these
36. Lowest boiling point is associated withA) HF B) HCl C) HBr D) HI
37. 2 2 2 23 2SiO H F X H O . During the formation of ‘X’ an intermediate product ‘Y’ is
formed. Hybridization of central atom in X and Y respectively
A) 3 2 2,sp d sp B) 3 3,sp d sp C) 3 2 3,sp d sp D) 3 3 2,sp d sp d
38. The percentage by volume of C3H8 in a mixture of C3H8, CH4 and CO is 36.5.
Calculate the volume of CO2 produced when 100 ml of the mixture is burnt in excessof O2A) 173 mL B) 253 mL C) 168 mL D) 223 mL
39. A complex is prepared by mixing CoCl3 and NH3. 0.1M solution of the complex was
found to freeze at 00.372 C . The formula of the complex is (molal depression constant
of water = 1.86 0 / C m )
A) 3 36Co NH Cl B) 3 25Co NH Cl Cl C) 3 24Co NH Cl Cl D) 3 33Co NH Cl
40. Magnetic moment of 3
6Cr CN
ion if it is a inner orbital complex.
A) 5.92 B.M B) 1.73 B.M C) 2.828 B.M D) 3.9 B.M
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41.
3CH
OH O
H
X
The product ‘X’ is
A)
3CH
OH O B)
3CH
OH HO
C)
3CH
O D)
3CH
O
42.
N
O
2 Br
Fe The Major Product formed is
A)
N
O
Br
B)
N
O
Br
C)
N
O
Br D)
N
OBr
43.
3CH
HOBr ' ' X
. No. of atoms undergoing tetrahedral hybridization in X.
A) 7 B) 6 C) 8 D) 9
44. 2
3
Hg
H Ph C C CH A
. (A) is
A)
Ph
O
3 H C B)
Ph
O
3 H C
C)
Ph
3 H C
OH
D)
Ph
3 H C
OH
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45. Which of the following readily undergo SN1
mechanism
A) 3CH Br B)
Br
C)
3CH
Br
D)
2 2CH CH Br
46. The appropriate reagent for the following transformation
3CH
O
HO HO
A) / Zn Hg HCl B) 2 2 / NH NH OH
C) 2 / H Ni D) 2 4 / / H Pd BaSO Quinoline
47. What is the shortest wavelength line in the Paschen series of 2 Li ion ?
A) 9
RB)
9
RC)
1
RD)
9
4
R
48. A certain hydrate has the formula 4 2. MgSO xH O .A quantity of 54.2 g of the compound
is heated in an oven to drive off the water .If the steam generated exerts a pressure of
24.8 atm in a 2.0 L container at 0120 C , calculate x.
A) 2 B) 5 C) 6 D) 7
49. Poly caprolactum is
A) Nylon 6,6 B) Perlon-L C) Dacron D)Glyptal50. Calculate 0 f H for 4UBr from the
0G of reaction and the 0S values of U (s),
( )2 4( ) Br l and UBr s are 50.3,152.3,242.6 (J / K – mol) respectively
0 12 42 ; 788.6 ;U S Br l UBr s G kJ mole
A) -822.1 kJ/mol B) -841.2 kJ/mol C) -775.6 kJ/mol D) -804.3 kJ/mol51. The equilibrium constant Kc for the reaction
4 22P g P gƒ
Is 1.4 at 4000C. Suppose that 3 moles of 4P g and 2 moles of 2P g are mixed in 2 litre
container at 0400 C . What is the value of reaction quotient (Q)?
A)3
2B)
2
3C) 1 D) 4/3
52. 20
amino group is present in
A) Tyrosine B) Lysine C) Proline D) Serine53. In the following reaction A B C , rate constant is 0.001 1 Ms . If we start with 1 M
of A then conc.of A and B after 10 minutes are respectively:
A) 0.5 M , 0.5 M B) 0.6 M , 0.4 M
C) 0.4 M , 0.6 M D) 0.2M, 0.8 M
54. The radioactive decay211 207
83 81 Bi Tl , takes place in 100 L closed vessel at0
27 C .Starting with 2 moles of 21183 1/ 2 130sec Bi t , the pressure development in the vessel
after 520 sec will be :
A) 1.875 atm B) 0.2155 atm C) 0.4618 atm D) 4.618 atm
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55. a pK of 4 NH is 9.26. Hence, effective range for 4 4 NH OH NH Cl buffer is about pH :
A) 8.26 to 10.26 B) 4.74 to 5.74
C) 3.74 to 5.74 D) 8.26 to 9.26
56. Which of the following is most soluble in water ?
A) 393 4 2 6 10sp Ba PO K B) 167 10sp ZnS K
C) 38
3 6 10spFe OH K
D)
18
3 4 1.8 10sp Ag PO K
57. A 100.0 mL dilute solution of Ag is electrolyzed for 15.0 minutes with a current of
1.25 mA and the silver is removed completely. What was the initial Ag ?
A) 12.32 10 B) 42.32 10 C) 32.32 10 D) 41.16 10
58. The Nernst equation 0 / ln E E RT nF Q indicates that the Q will be equal to
equilibrium constant cK when
A) 0 E E B) / 1 RT nF C) E = zero D) 0 1 E
59. Which of the following expressions is correct in case of a CsCl unit cell
(edge length, a)?
A) c ar r a B) / 2c ar r a C) 3 / 2c ar r a D) / 2c ar r a
60. On adding 3 AgNO solution into KI solution , a negatively charged colloidal sol is
obtained when they are in :
A) 50 ml of 0.1 M 3 AgNO + 50 ml of 0.1 M KI
B) 50 ML of 0.1 M 3 AgNO + 50 ml of 0.2 M KI
C) 50 ML of 0.2 M 3 AgNO + 50 ml of 0.1 M KI
D) 50 ML of 0.2M 3 25 mL 0.4 M KI AgNO
MATHEMATICS
61. If 2 y f x ax bx c ,where a, b and c are real numbers such that 2 4 0b ac ,then
A) 0ac x R
B) 0,af x x R
C) The shortest distance from the curve y= f x to the x -axis is2
4
4
b acd
a
D) All of the above
62. If I is the incentre of ABC with inradius r, circum radius R, then ( AI )( BI )(CI ) is
equal to
A) 22r R B) 24r R C) 38r D) 32 R
63. The number of roots of the equation 7
1
sin 7k
kx
sin 4 x in the interval 0,2π is
A) 3 B) 5 C) 7 D) 9
64. The fractional part of x ,
where 6 6 6 6
3 2 1 3 2 1 3 2 1 3 2 1 x
A) 0 B) 3 2 C) 3 2 3 D) 1 2 3
65. If
x = fractional part of x , then
12
sin 2 1lim x
x
x x
is equal to
A) 0 B) 1
C) does not exists D) 9
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66. Consider y f x such that 3 1 7 111 1 3 5 7 f x x x x x , then
A) 1,5 x are the local minima of y f x
B) 1,5 x are the local maxima of y f x
C) 3,7 x are not the local minima of y= f x
D) 3,7 x are the local maxima of y= f x
67. If
2 2
cos sin
2 sin cos sin cos
x x dx
x x x
=
1
1tan log
1
f x A f x B C
f x
, then
A) A= 3B B) sin cos
13
x x f x
C) 2 29 1 A B D) A= -2B68. Statement – I The value of the integral
/3
/ 6 1 tan
dx
x
π
π is equal to / 6π
Statement – II b b
a a f x dx f a b x dx
A) Statement I is true; Statement II is true ; Statement II is a correct explanation for
Statement I.B) Statement I is true; Statement II is true ; Statement II is not a correct explanation
for Statement I.
C) Statement I is true; Statement II is false
D) Statement I is false ; Statement II is true.
69. The number of roots of the equation 1 1 3sin sin 1
2
x x π is equal to
A) 0 B) 1 C) 2 D) 6
70. The number of solutions of sin cos tanθ θ θ in 0,π is
A) 0 B) 1 C) 2 D) 4
71. Area of the quadrilateral formed from tangents and normals drawn on the extremities
of the latusrectum of the parabola 2 4 y ax is
A) 2a B) 22a C) 24a D) 28a
72. The shortest distance between the line y x and the hyperbola2 2
19 4
x y is
A) 32
B) 23
C) 52
D) 9
73. The area of the parallelogram formed by the lines 1 x y
a b and the directrices of the
ellipse2 2
2 21
x y
a b with eccentricity , e and a, b being positive is
A)2
ab
eB)
2
4ab
eC)
2
2ab
eD)
2
9ab
e
74. One of the tangents drawn from the origin to the circle 2 2
6 6 18 x y are
A) 2 3 y x B) 2 3 y x C) y x D) y x 75. If 1 2,h h and 3 0h are in HP and
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1 2 2 3 3 1
2 3 3 1 1 2
3 1 1 2 2 3
h h h h h h
h h h h h h
h h h h h h
, then
A) is always positive B) is always negative
C) is positive, if 2h is negative D) is negative, if 3h is positive
76. There are 5 men and 5 women in a party. In how many ways can 5 dancing pairs be
selected ? ( each dancing pair consists of 1 man and 1 woman)A) 120 B) 44 C) 32 D) 10
77. In a party, there are 6 husband – wife pairs .Dance couples are formed randomly
choosing one man and one woman. The probability that H j
dances with7
W i, given
that H i
dances with , 1, 2, 3, 4, 5, 6W i j i j
A)265
720B)
1
265C)
10
265D)
263
500
78.
3
1/ 3
log x
x dx is equal toA) 0 B) log 3 C) 2 log 3 D) 1
79. Let / 2 / 2, 1a e e b eπ π π and /42c eπ , then
A) ac C) ab
80. The order and degree of the differential equation
1/3 2/3 13 2
3 20
d y d y dy
dx dx dx
are,
respectively.
A) 3, 3 B) 3, 6 C) 3, 9 D) 4, 4
81. If , f x g x and h x are continuous function, thrice differentiable and each satisfythe differential equation
2
20
d y y
dx , then find 1 xφ , where
1 1 1
2 2 2
f x g x h x
x f x g x h x
f x g x h x
φ (here, ,k k f x g x and k h x are the k th
derivatives of
, f x g x and h x , respectively)
A) 0 B) f x g x h x
C) 1 1 1 f x g x h x D) 182. The incentre of the triangle formed by the lines xy=0 and 1
3 4
x y is (h,k) , then
A) (h ,k ) lies on the line x+y = 12
B) (h ,k ) lies on the line x-y =10
C) (h ,k ) lies on the circle 2 2 12 x y
D) (h ,k ) lies on the circle 2 2
4 5 25 x y
83. If the lines1 1 1
2 3 4
x y z and
3
1 2 1
x y k z intersects , then k is equal to
A) 32
B) 92
C) 92
D) 32
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