COLLEGE NAME

JEE MAINS MODEL PRACTICE TEST

GRAND TEST - 2
Exam Date : ............................ Max. Marks: 300
INSTRUCTIONS
1. The question paper consists of three subjects (Physics 1 to 25; Chemistry 26 to 50 and Mathematics 51 to 75).
2. All questions are Multiple Choice questions with single correct answer only and each question has four choices
(1), (2), (3) and (4) out of which ONLY ONE is correct. Each question carries +4 for Correct Option and –1 for
Wrong Option.
3. No Negative Marks for Numerical Value Questions.

PHYSICS
 
01. An expression is given by 2
 Fv  2 .
t x
Find dimension formula for [] (here ‘t’ is time, ‘F’ is force, ‘v’ is velocity and ‘x’ is distance.

1) []  M1L2 T 3 2) []  M1L2T 3 3) []  M1L2 T 3 4) []  M3L1T 3

P
02. One mole of an ideal gas at temperature T1 expends according to the law  a (constant). The
V2
work done by the gas till temperature of gas becomes T2 is

1 1 1 1
1) R(T2  T1 ) 2) R(T2  T1 ) 3) R(T2  T1 ) 4) R(T2  T1 )
2 3 4 5
03. Equivalent resistance between point A and B is
2R
1) R 2) R/2 2R
R R
R

3) 3R/11 4) R/11 A B
R

R
7
04. For a prism, A  60 ,   . Find the minimum possible angle of incidence, so that the light ray
3
is refracted from the second surface. Also find max .
1) 60° 2) 50° 3) 40° 4) 30°
05. A composite slab consists of two slabs A and B of different materials but of the same thickness
placed one on top of the other. The thermal conductives of A and B are k 1 and k2 respectively. A
steady temperature difference of 12°C is maintained across the composite slab. If k1  k 2 / 2 , the
temperature difference across slab A will be

1) 4°C 2) 8°C 3) 12°C 4) 16°C

1
SPACE FOR ROUGH WORK
06. A large number of byllets are fired in all directions with the same speed v. What is the maximum
area on the ground on which these bullets with spread ?

v 4 v 3 v 2 v 8
1) 2) 3) 4)
g2 g2 g2 g2
07. A gasoline engine in a large truck takes in 10 kJ of heat and does 2000 J of mechanical work per
cycle. Find the thermal efficiency of engine.
1) 20% 2) 40% 3) 60% 4) 10%

08. Consider a long straight uniform cylinder of radius R. A direct current of density J flows along the
length of cylinder. A cylindrical cavity of radius r is carved out from the cylinder as shown in
figure. For this situation mark the correct statement(s). [The axis of cavity and cylinder are not
coinciding]

r
O'
B
O

1) Magnetic field intensity in the cavity is uniform and non-zero

2) Magnetic field intensity in the cavity is uniform and zero
3) Magnetic field intensity in the cavity is non uniform
4) Magnetic field intensity in the cavity can’t be determined
09. A beam of natural light falls on a system of 6 polaroids, which are arranged in succession such that
each polaroid is turned through 30° with respect to the preceding one. The percentage of incident
intensity that passes through the system will be
1) 100% 2) 50% 3) 30% 4) 12%
10. Each of the bulb shown in figure is having resistance of 3 . Each of the bulb can withstand a
maximum current of 2A without getting fuse. The maximum power the circuit can dissipate for
proper functioning is

1) 72 W 2) 22 W 3) 4 W 4) none of these
11. Two blocks ‘A’ and ‘B’ each of mass ‘m’ are placed on a smooth horizontal surface. Two horizontal
force F and 2F are applied on the block A and B respectively as shown in figure. The block A does
not slide on block B. Then the normal reaction acting between the two blocks is: (A and B are
smooth)
A B

F m m 2F

30°

F
1) F 2) F/2 3) 4) 3F
3
2
SPACE FOR ROUGH WORK
12. A 4.0 kg block is suspended from the ceiling of an elevator through a string having a linear mass
density of 19.2  103 kg / m . Find the speed (with respect to the string) with which a wave pulse can
proceed on the string if the elevator accelerate up at the rate of 2.0ms –2. Take g  10ms2 .
1) 50ms–1 2) 60ms–1 3) 40ms–1 4) 70ms–1
13. A current carrying wire AB of length 2a is placed near to an infinite long current carrying wire as
shown in figure. The magnetic force experienced by wire AB is

I
 I2 8 50I2
1) 0 n 2) n3
8 5 8 A 37°
I
a

50I2  13  0I2  13 
3) n   4) n  
8  5 8  5 

14. Electrons in a hydrogen like atom (Z  3) make transitions from fourth excited state to 3rd excited
state and from 3rd to 2nd excited state. The resulting radiation are incident on a metal plate to
eject photoelectrons. The stopping potential for photoelectron ejected by shorter wave-length is
3.95 V. The stopping potential for the photoelectrons ejected by longer wavelength is
1) 2.0 V 2) 0.75 V 3) 0.6 V 4) None
15. The permeability of substance is 6.28  10 4 wb / A  m susceptibility ?
1) 499 2) 599 3) 199 4) 299
16. Block of mass m 2 is in equilibrium and at rest. The mass m1 moving with velocity u vertically
downwards collides with m2 and sticks to it. Find the energy of oscillation.

1  m12u2 m22 g2  1  m12u2 m22 g2 

1) 2    2) 2   
 m1  m2 k2   m2  m1 k2 
m1

u
1  m22u2 m12 g2  1  m22u3 m12 g 3 
3) 2    4) 2   
 m2  m1 k2   m2  m1 k2  m2

17. A particle of mass 10 gm is placed in a potential field given by V  (50x 2  100)J / kg . The frequency
of oscillation in cycle/sec is
10 5 100 50
1) 2) 3) 4)
   
18. A rod ACD bent in shape shown is moving in the x-y plane with a velocity vi . The magnetic field in
the region is B  k as shown in the figure. What will be the emf induced between points A and D
0
(along the path ACD) as a function of x coordinate of point A.
y
B vL2 B vL2 C
1) 0 2) 0
2 4 L
B
2 45°
2B0 vL A D
3) 0 4)
3
x 3
SPACE FOR ROUGH WORK
 19. A radioactive material consists of nuclides of 3 isotopes which decay by   emission,   emission
and deuteron emission respectively. The decay constant for these three isotopes are 4 , 2 & 
respectively. At t  0 , probability of getting,  ,  and deuteron from radio nuclide are equal. If the
probability of  emission at t  1600 s s is n / 13 , then find the value of ‘n’.

1 1 1 1
1) 2) 3) 4)
13 18 20 19
20. Find the average value of current shown graphically, from t  0 to t  2 sec .

i
(Amp)
10

0 1 2
t(sec)

1) 2 Amp 2) 5 Amp 3) 4 Amp 4) 1 Amp

NUMERICAL VALUE QUESTIONS:
21. A plank of area of cross-section A and mass m is half immersed in liquid 1 of density  and half in
liquid 2 of density 2 . What is period of osculation of the plank if it is slightly depressed downwards.


1
2
2

m m 3m m
1) 2 2)  3) 2 4) 2
Ag Ag 2Ag 3Ag
22. Two thin wire rings each having a radius R are placed at a distance ‘d’ apart with their axes coinciding.
The charges on the two rings are  q and q . The potential difference between the centres of the
two rings is

q 1 1  qR q 1 1 
1) zero 2) 4     3) 4  d2 4) 2   
0 R R 2  d2  0 0 R R 2  d2 
23. During the propagation of electromagnetic waves in a medium
1) electric energy density is equal to the magnetic energy density
2) both electric and magnetic energy densities are zero
3) electric energy density is double of the magnetic energy density
4) electric energy density is half of the magnetic energy density
24. In a common base circuit, the current gain is 0.96. If the base current is 60 A , find the emitter
current and collector current.
1) 1.44 mA 2) 1.55 mA 3) 1.66 mA 4) 1.45 mA

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SPACE FOR ROUGH WORK
25. The KE of a particle is equal to the energy of a photon. The particle moves at 5 percent of the
speed of light. The ratio of the photon wavelength to the De-Broglie wavelength of particle is [No
need to use relativistic formula for particle]
1) 40 2) 4 3) 2 4) 80
CHEMISTRY
25 X 4 = 100M
26. Ammonium carbamate when heated to 200°C gives a mixture of NH3 and CO2 vapour with a
density of 13. What is the degree of dissociation of ammonium carbamate ?
3 1
1) 2) 3) 2 4) 1
2 2
27. Match the column I with column II and mark the appropriate choice.
Column-I Column-II
OH OH OH
CH3
1) Anhyd.A C 3
CH3C CS 2
 p) Decarboxylation

CH3

OH OH
CHO
CHC 3
2) 
aq. NaOH
 q) Friedel - Crafts reaction

OH OH
COOH
3) NaOH
  r) Reimer - Tiemann reaction
CO , H
2

OH OH

COOH

4) CaO
2NaOH 

 s) Kolbe’s reaction

1) 1-p. 2-q; 3-r; 4-s 2) 1-q. 2-r; 3-s; 4-p 3) 1-r. 2-s; 3-p; 4-q 4) 1-s. 2-r; 3-q; 4-p

CH 3

28. The major product formed in the following reaction is CH3  C  CH2Br 
CH3 O
CH3OH

CH3 CH3
CH3
CH3  C  CH3
1) CH3  C  CH2OCH3 2) CH3  CH  CH2CH3 3) CH3  C  CH2 4)
H OCH3
OCH3

29. According to Bohr’s model, if the kinetic energy of an electron in 2nd orbit of He  is x, then what
should be the ionisation energy of the electron revolving in 3rd orbit of M5 ion (assuming as one
electron species)
1) x 2) 4x 3) x/4 4) 2x
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SPACE FOR ROUGH WORK
30. Which of the following reactions will not give a primary amine ?
Br2 /KOH LiAH4 LiAH4 LiAH4
1) CH3CONH2   2) CH3CN  3) CH3NC  4) CH3CONH2 
31. Which of the following polymers is not correctly matched ?
1) Formation of dacron - Step growth polymerisation
2) Formation of polytetrafluoroethene - Step growth polymerisation
3) Formation of polytene - Chain growth polymerisation in presence of
benzoyl peroxide
4) Formation of polyacrylonitrile - Chain growth polymerisation in presence of
peroxide
HCN Hydrolysis HI
32. Glucose    Y 
Heat
 Z . Identify Z
1) 2-Iodoheptane 2) Heptane-2-ol 3) 2-Iodohexane 4) Heptanoic acid
33. Which of the following is not a true statement about the detergents ?
1) Anionic detergents are sodium salts of sulphonated long chain alcohols hydrocarbons
2) Cationic detergents are quarternary ammonium salts of amines with acetates, chlorides or bromides
as an ions
3) Non-ionic detergents do not contain any ion in their constitution
4) Detergents containing branched hydrocarbon chains are biodegradable
34. Select correct statement for BrF5 .
1) All fluorine atoms are in same plane
2) Four fluorine atoms and Br atom is in same plane
3) Four fluorine atoms are in same plane
4) It has all F  Br  F bond angles at 90°
35. Sometimes it is possible to separate two sulphide ores by adjusting the proportion of oil to water or
by using depressants. When a depressant NaCN is added to an ore containing ZnS and PbS, what is
the correct observation ?
1) NaCN prevents PbS from coming to the froth but allows ZnS to come with froth.
2) NaCN prevents ZnS from coming to the froth but allows Pbs to come with froth.
3) NaCN prevents frothing of both ZnS and PbS hence no froth is formed.
4) NaCN does not act as depressant hence a mixture of PbS and ZnS is found in froth.
36. Fill in the blanks with appropriate choice. Bond order of N2 is P while that of N2 is Q. Bond order of O2
is R while that of O 2 is S N  N bond distance T , when N2 changes to N2 and when O2 changes to O2 ,
the O  O bond distance U .
P Q R S T U
1) 2 2.5 2.5 1 increases decreases
2) 2.5 3 2 1.5 decreases increases
3) 3 2 1.5 1 increases decreases
4) 2.5 3 2.5 2 increases decreases
37. Fill in the blanks:
(i) Ca 3P2  6HC  3CaC 2  .....p.....
(ii) P4  3NaOH  3H 2O  .....q.....  3NaH2 PO2
(iii) PH4I  KOH  KI  H2O  .....r..... p, q and r respectively are

6
SPACE FOR ROUGH WORK
 1) PH3 H3PO3 , PI3 2) PH3 , PH3 , PH3 3) PC 3 H3PO4 , PH3 4) PC 5 , PH3 P4O6
38. Which of the following pairs of isomers is not correctly matched with its type of isomerism ?
1) [Cr(NH3 )6 ][Cr(CN)6 ] and [Cr(NH3 )4 (CN)2] [Cr(NH3 )2 (CN)4 ] – Coordination isomerism
2) [Co(NH3 )5 NO2 ] C 2 and [Co(NH3 )5 ONO] C 2 – Linkage isomerism
3) [Co(py)2 (H2O)2 C 2 ]C and [Co(py )2 (H2O) C 3 ] H2O – Coordination isomerism
4) [Pt(NH3 )4 Br2 ] C 2 and [Pt(NH3 )4 C 2] Br2 – Ionisation isomerism
39. Select the incorrect option.
1) Sodium peroxide dissolves in water giving H2O 2 and NaOH
2) Both LiNO3 and NaNO3 on heating separately decompose and each liberates two gases NO2 and
O2
3) Solvay process can not be used for the manufacture of potassium hydrogen carbonate
4) Alkali metals are prepared only by the electrolysis of their fused chlorides
40. Which is the correct sequence in the following properties. For the correct order mark (T) and for the
incorrect order mark (F):
a) Acidity order : SiF4  SiC 4  SiBr4  SiI4 b) Melting point : NH3  SbH3  AsH3  PH3
c) Boiling point : NH3  SbH3  AsH3  PH3 d) Dipole moment order : NH 3  SbH 3  AsH 3  PH 3
1) FTFT 2) TFTF 3) FFTT 4) FFTF
41. An ideal gas does work on it surroundings when it expands by 2.5 L against external pressure 2
atm. This work done is used to heat up 1 mole of water at 293 K. What would be the final
temperature of water in kelvin if specific heat for water is 4.184 Jg -1K–1 ?
1) 300 2) 600 3) 200 4) 1000
42. Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure p i and temperature
T1 are connected through a narrow tube of negligible volume as shown in the figure below. The
temperature of one of the bulbs is then raised to T2. The final pressure pf is

T1 T1 T1 T2
p i, V p i, V V p f, V
pf,

 T1T2   T1   T2   T1T2 
1) pi  T  T  2) 2pi  T  T  3) 2pi  T  T  4) 2pi  T  T 
 1 2   1 2   1 2   1 2 

43. An aromatic compound (X) (C8H8O) gives positive 2,4-DNP test. It gives a yellow precipitate of
compound (Y) on reaction with iodine and sodium hydroxide solution. (X) does not give Tollens’
test on oxidation under drastic conditions. It gives a carboxylic acid (Z) (C7H6O 2 ) . (Z) is also formed
with (Y) during the reaction. (X), (Y) and (Z) respectively are
1) C6H5COCH3 , CHI3 , C6H5COOH 2) CH3COCH3 , CHI3 , CH3COOH
3) C6H5COCH3 , CHI3 , CH3COOH 4) CH3CHO , CHI3 , C6H5COOH
44. Which will act as a buffer solution ?
1) 200 m N /10 NaOH  100 m N / 20 HC 2) 100 m 0.1 N NaOH  100 m 0.1 N HC
3) 100 m 0.1 N NaOH  50 m 0.2 N CH 3COOH 4) 100 m 0.1 N NaOH  150 m 0.1 N HCN
7
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 alcohol NaNH2
45. Identify X and Y in the following reaction. H2C  CH2  KOH  X  Y

Br Br
X Y

1) CH3CHBr CH2 CH2

2) CH2OH  CH2OH CH2 CH2

3) CH2 CHBr CH  CH
4) CH  CBr CH  CH

NUMERICAL VALUE QUESTIONS:

46. The standard reduction potential for Cu2 / Cu is 0.34 V . What will be the reduction potential at
pH  14 ? (Given : K sp of Cu(OH)2 is 1.0  1019 ]
1) 2.2 V 2) 3.4 V 3) –0.22 V 4) –2.2 V
47. An element crystallizing in body centred cubic lattice has an edge length of 500 pm. If its density
is 4 g cm3 , the atomic mass of the element (in g mol–1) is (consider N A  6  1023 )
1) 100 2) 250 3) 125 4) 150
48. 250 mL of sodium carbonate solution contains 2.65 g of Na 2CO3 . If 10 mL of this solution is diluted
to 500 mL, the concentration of the diluted acid will be
1) 0.01 M 2) 0.001 M 3) 0.05 M 4) 0.002 M
49. 3.6 gram of oxygen is adsorbed on 1.2 g of metal powder. What volume of oxygen adsorbed per gram
of the adsorbent at STP ?
1) 0.19 Lg 1 2) 1 Lg 1 3) 2.1 Lg 1 4) None of these
50. The pH of a solution prepared by mixing 2 M, 100 mL, HC and 1 M, 200 mL NaOH at 25°C is
1) 8 2) 7 3) 4 4) 5
MATHEMATICS
25 X 4 = 100M
51. If the mode of a data is 18 and the mean is 24, then the median is
1) 18 2) 21 3) 22 4) 24
52. The inverse of the proposition (p   q)  r is
1)  r   p  q 2)  p  q   r 3) r  p   q 4)  p  (p  r)
53. A market research group conducted a survey of 1000 consumers and reported that 720 consumers
like product A and 450 consumers like product B. The least number that must have likes both
products is
1) 170 2) 180 3) 450 4) 1000
54. 12  (12  22 )  (12  22  32 )  ..... up to ‘n’ brackets =

n(n  1)2 (n  2)2 n 1 n(n  1)2 (n  2) n2 (n  1)(n  2)

1) 2) 3) 4)
12 2 12 12

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55. If the equation 2x  3y  1  0 , 3x  y  2  0 and ax  2y  b  0 are consistent, then

1) a  b  2 2) a  b  1  0 3) a  b  3 4) a  b  8  0
56. The complete solution set of sin1 (sin5)  x 2  4x , is

1) x  2  9  2 2) x  2  9  2  3) x  9  2 4) x  9  2

 y2 y2 
57. If f  2x 2  , 2x 2    xy , then the value of f(60, 48)  f(80, 48)  f(13, 5) must be
 8 8 
1) 211 2)121 3) 112 4) 21
A B
58. In a ABC , tan and tan satisfy 6x 2  5x  1  0 . Then
2 2
1) a 2  b2  c2 2) a 2  b2  c2 3) a 2  b2  c2 4) none of these
59. The general value of  satisfying the equation 2sin2   3sin   2  0 is

n 7 n  n 5 n 
1) n  ( 1) 2) n  ( 1) 3) n  ( 1) 4) n  ( 1)
6 2 6 6
60. Consider the triangle OAB where O  (0, 0) , B  (3, 4) . If orthocentre of the triangle is H  (1, 4) ,
then co-ordinate of A is

 15   7   21   19 
1)  0,  2)  0,  3)  0,  4)  0, 
 4  4  4  4

d2 y
61. If (x  y )  ( y  x )  a , then equals
dx 2
1) 2/a 2) 2 / a 2 3) 2 / a 2 4) none of these

62. The trigonometric form of z  (1  icot8)3 (where i  1 ) is

3 i(24  3  /2 )
1) cosec 8  e 2) cosec 3 8  e  i( 24  3  /2 ) 3) cosec3 8  e i( 36/2) 4) cosec3 8  e 24i  /2
63. Consecutive odd integers whose sum is 252  112 are
1) 23, 25, 27, ..., 49 2) 25, 27, 29, ..., 51 3) 21, 23, 25, ..., 49 4) 19, 21, 23, ..., 47
10
40 40  j
64. The value of C31   C10 j is equal to
j 0

1) 15
C20 2) 2  50C20 3) 2  45C15 4) none of these
65. The equation of a plane passing through (1, 2, –3), (0, 0, 0) and perpendicular to the plane
3x  5y  2z  11 , is

5 z
1) 3x  y  z  0 2) 4x  y  2z  0 3) 3x  y  0 4) x  y  z  0
3 3
66. Two numbers are selected simultaneously from the set {6, 7, 8, 9,...,39} . If the sum of selected
numbers is even, then the probability that both the selected numbers are odd, is equal to
11 40 51 40
1) 2) 3) 4)
51 51 91 91

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 2
67.  (ln x) dx is equal to

1) x[(ln x )2  2 lnx  2]  C 2) x[(ln x )2  2 lnx  2]  C

3) x[(ln x )2  2 ln x  2]  C 4) x[(ln x )2  2 ln x  2]  C

68. The general solution of the differential equation (2y  6xy 2 )dx  (3x  8x 2 y)dy  0 , is equal to

1) x 3 y 2  2x 4 y 3  c 2) x 3 y 2  2x 3 y 4  c 3) x 2 y 3  2x 4 y 3  c 4) x 2 y 3  2x 3 y 4  c

69. The triangles PQR is inscribed in the circle x 2  y 2  25 . If Q and R have co-ordinates (3, 4) and
(–4, 3) respectively, then QPR is equal to

   
1) 2) 3) 4)
2 3 4 6
70. Minimum distance between the curve y 2  4x and x 2  y 2  12x  31  0 , is equal to

1) 21 2) 26  5 3) 21  5 4) 28  5

NUMERICAL VALUE QUESTIONS:


 sin1 x
71. lim 2 
x 1 0
1  x2
1) 0 2) 1 3) 2 4) 3
72. Least value of f(x )  x  1  x  2  x  3 is
1) 0 2) 1 3) 2 4) 3
73. If the sum of the roots of the equation ax 2  bx  c  0 is equal to the sum of the squares of their
b 2 bc
reciprocals, then  is equal to
ac a 2
1) 1 2) 2 3) 3 4) 4
74. The number of terms free from radical sign in the expansion of (1  31/3  71/7 )10 is
1) 3 2) 4 3) 5 4) 6
75. Area enclosed by the curve x  2  y  1  1 is equal to
1) 2 2) 4 3) 6 4) 8

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