Post on 14-Apr-2020
Test Type : FULL SYLLABUS Test Pattern : JEE-Main
TEST DATE : 07 - 02 - 2016
SCORE-I
JEE (Main + Advanced) : ENTHUSIAST COURSE
Paper Code : 1001CT102115077Form Number :
CLASSROOM CONTACT PROGRAMME(Academic Session : 2015 - 2016)E
NG
LIS
H
PAPER – 2
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3. The test is of 3 hours duration.
4. The Test Booklet consists of 90 questions. The maximum marks are 360.
5. There are three parts in the question paper A,B,C consisting of Physics, Chemistry and Mathematics having
30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.
6. One Fourth mark will be deducted for indicated incorrect response of each question. No deduction from the
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Your Target is to secure Good Rank in JEE (Main) 2016
Enthusiast Course/Score-I/07-02-2016/Paper-2
E-1/181001CT102115077
SPACE FOR ROUGH WORK
PART A - PHYSICS
BEWARE OF NEGATIVE MARKING
HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS
1. A particle is thrown with velocity v0 at an angle
0 with the horizontal. For which of the
following combinations of v0 and
0, the radius
of curvature at the highest point of motion will
be maximum?
(1) v0 = 10 m/s,
0 = 30o
(2) v0 = 10 m/s,
0 = 45o
(3) v0 = 20 m/s,
0 = 45o
(4) v0 = 20 m/s,
0 = 60o
2. A carbon resistor is marked with the rings
coloured brown, black, green and gold. The
resistance (in ohm) is :-
(1) 1 × 105 ± 5 % (2) 1 × 106 ± 10%
(3) 1 × 107 ± 5 % (4) 1 × 106 ± 5 %
3. A man watches a steamboat starting from a
point directly in front of him on the opposite
bank of river flowing at a speed of 5 km/hr.
The boat has a velocity v0 with respect to river
flow at an angle 0 with the bank. If the
steamboat blows a whistle of frequency f0, then
for which of the following combinations of v0
and 0 the frequency registered by the man will
be highest?
(1) v0 = 10 m/s,
0 = 30o
(2) v0 = 10 m/s,
0 = 45o
(3) v0 = 10 m/s,
0 = 60o
(4) same for all the above
4. The equivalent resistance between the points
A and B is (R is the resistance of each side of
smaller square)
A
B
R
R
(1) R (2) 2
3R
(3) R2 (4) 2
R
1001CT102115077E-2/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
SPACE FOR ROUGH WORK
5. N particles of masses of m, 2m, 4m, 8m, ………
2N-1m respectively are kept along a frictionless
horizontal surface at non-uniform distances
between them, but in increasing order of masses
as shown. The plane is curved on its right end
as shown upto a height H. A particle of mass m
is released from the top of the plane and collides
perfectly inelastically with the mass m on the
horizontal surface. All the subsequent collisions
are inelastic. The value of H so that the velocity
of the system after last collision becomes 1 m/s
is:-
H
m
m 2m 4m 2N-1m
(1) g
N 12
(2) g
N2
(3) g
N 122
(4)
g
N 122
6. A radioactive nuclei is being produced in a
reactor at constant rate Q = 2No (where is
the decay constant and initial number of
radioactive nuclei is No). Which of the
following curves represents the number of
nuclei as a function of time t ?
(1)
No
t
N
(2)
2No
t
N
No
(3)
2No
t
N
No
(4)
2No
t
N
No
Enthusiast Course/Score-I/07-02-2016/Paper-2
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SPACE FOR ROUGH WORK
7. If the frequency of the incident radiation is
doubled in a photoelectric effect experiment,
the kinetic energy of the fastest photoelectron
becomes
(1) double (2) more than double
(3) less than double (4) none of these
8. In YDSE distance between slits S1 and S
2 is d.
P1 and P
2 are two points equidistant from O at
an angular position as shown. A parallel beam
of monochromatic light is incident at an angle
on the slits. Then the ratio of path difference
at P1 and P
2 is :-
D (>>d) O
P1
P2
d
S1
S2
(1) 2
cot2
tan
(2) 2
cot2
tan
(3) 2
cos2
sin
(4) 2
sin2
cos
9. The primary winding of the transformer to
power the radio receiver has 1200 turns with
input voltage of 120 V. What should be the
number of turns of the transformer in secondary
winding to power the lamp filament, if it
requires 3.6 V voltage and current of 1A?
Secondary has a resistance of 0.4 ohms. The
loss in the primary winding may be neglected :
(1) 40 (2) 36
(3) 4800 (4) 4320
10. A thin plano-convex glass lens ( = 1.5) has
its plane surface silvered and R is the radius of
curvature of curved part, then which of the following
ray diagram is true for an object placed at O?
(1)
2R
R
O
(2)
2R
R
O
(3)
3R
R
O
(4)
2R
R
O
1001CT102115077E-4/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
SPACE FOR ROUGH WORK
11. A conducting rod is moving with a constant
velocity v over the parallel conducting rails
which are connected at the ends through a
resistor R and capacitor C as shown in the
figure. Magnetic field B is into the plane.
Consider the following statements.
A
L
B
C R
E H
G
v
F
(i) Current in loop AEFBA is anticlockwise
(ii) Current in loop AEFBA is clockwise
(iii) Current through the capacitor branch is zero
(iv) Energy stored in the capacitor is 222
2
1vLCB
Which of the following options is correct?
(1) statements (i) and (iii) only are correct.
(2) statements (ii) and (iv) only are correct.
(3) statements (i), (iii) and (iv) only are correct.
(4) all the above
12. An electromagnetic wave travels in vacuum
along z direction : 0ˆE E i
cos(kz – t). AA
rectangular area is to be kept such that at t = 0
displacement current may flow through the
area. Which of the following is correct
orientation :-
(1)
y
x
z
(2)
y
x
z
(3)
y
x
z
(4) None of these
13. In the given figure, block executes SHM with
total energy of oscillation E. The ratio of
K1 and K
2 is 2 : 1. The energy associated with
spring of spring constant K1 when block is at
A/2 distance away from mean position
(A is amplitude) is :-
K1 K2
(1) E/4 (2) E/3 (3) E/12 (4) E/6
Enthusiast Course/Score-I/07-02-2016/Paper-2
E-5/181001CT102115077
SPACE FOR ROUGH WORK
14. A sphere of radius 0.625 m is rotating about a
horizontal axis with angular velocity 2 rad/s
and is released from rest in vertical plane under
gravity as shown in the figure. The ratio of
displacement of point P to that of point C after
0.5 s from the start will be (g = 10 m/s2) :-
P
C
(1) 1 : 1 (2) 2 : 1
(3) 3 : 1 (4) 4 : 1
15. A tunnel is dug inside the earth across one of
its diameters. A particle is projected inside the
tunnel with velocity R
GM from one of its
ends. Then maximum velocity attained by the
particle in the subsequent motion is (assuming
tunnel to be frictionless)
(1) R
GM(2)
R
GM2
(3)R
GM
2
3(4)
R
GM2
16. Consider an open-circuited p-n junction in
thermal equilibrium. Let Jp, drift
and Jp, diff
be the
hole drift and diffusion current densities,
respectively, and let Jn, drift
and Jn, diff
be the
corresponding electron current densities. Of the
following equalities, mark true, at all points in
the p-n junction structure :
(1) Jp, drift
+ Jn, drift
= Jp, diff
+ Jn, diff
= 0
(2) Jn, drift
+ Jn, diff
= 0
(3) Jp, drift
+ Jp, diff
= 0
(4) Jp, drift
+ Jn, drift
+ Jp, diff
+ Jn, diff
= 0
17. An experiment is performed to obtain the value
of acceleration due to gravity g by using a
simple pendulum of length L. In this
experiment time for 100 oscillations is
measured by using a watch of 1 second least
count and the value is 90.0 seconds. The length
L is measured by using a meter scale of least
count 1 mm and the value of 20.0 cm. The
error in the determination of g would be :-
(1) 2.7 % (2) 2.27 %
(3) 1.7 % (4) 4.4 %
1001CT102115077E-6/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
SPACE FOR ROUGH WORK
18. A body at rest breaks into two fragments ofmasses m
1 and m
2 respectively. The ratio of
their de-Broglie wavelengths is :-
(1) 2
1
m
m(2)
1
2
m
m(3) 1 : 1 (4)
2
1
m
m
19. Statement-1 : When a P-N Junction is heavilydoped, width of depletion region becomes verysmall.
Statement-2 : When a semiconductor is doped,the molarity of charge carrier increases.
(1) Statement-1 is true, statement-2 is true andstatement-2 is correct explanation forstatement-1
(2) Statement-1 is true, statement-2 is true andstatement-2 is NOT the correct explanationfor statement-1.
(3) Statement-1 is true, statement-2 is false.
(4) Statement-1 is false, statement-2 is true.20. A bar magnet is suspended from the ceiling by
a string as shown. If a uniform magnetic fielddirected parallel to the ceiling and to the left isthen established, the resulting orientation of themagnet and the string in equilibrium will becorrectly shown by :-
S
N
(1)
S
N
(2)
S
N
(3)
S
N
(4)
S
N
21. A water barrel stands on a table of height h. If
a small hole is punched in the side of the barrel
at its base, it is found that the resultant stream
of water strikes the ground at a horizonatl
distance R from the barrel. The depth of water
in the barrel is :-
(1) 2
R(2)
h4
R2
(3) h
R 2
(4) 2
h
Enthusiast Course/Score-I/07-02-2016/Paper-2
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SPACE FOR ROUGH WORK
22. Consider the following statements about aconducting rod of length l hung from fixedpoints at a distance a from a infinitely longcurrent carrying wire by means of two flexibleconducting wires connected with an emf sourceas shown in the figure. All are in the same plane.
l a
I
A. Body will gain rotational tendency.B. Body will not gain any rotational tendencyC. Centre of magnetic force will be shifted
towards left of the centre of mass of therod.
D. Centre of magnetic force will be shiftedtowards right of the center of mass of therod.
E. Centre of magnetic force will coincide withthe center of mass of the rod.
Choose the correct option(1) A and C are correct (2) B and C are correct(3) A and D are correct (4) A and E are correct
23. In a common-base configuration of transistor, = 0.98, I
B = 0.02 mA, R
L = 5 k. Output
voltage across load is :
(1) 3.2 V
(2) 4.9 VIB
RL
VBCVBE
(3) 5.2 V
(4) 6.2 V
24. The energy band diagrams for threesemiconductor samples of silicon are as shown.We can then assert that :-
X Y Z
(1) Sample X is undoped while samples Y andZ have been doped with a trivalent and apentavalent impurity respectively
(2) Sample X is undoped while both samples Yand Z have been doped with a pentavalentimpurity
(3) Sample X has been doped with equalamounts of trivalent and pentavalentimpurities while samples Y and Z areundoped
(4) Sample X is undoped while samples Y andZ have been doped with a pentavalent anda trivalent impurity respectively
25. Which one of the following is INCORRECTstatement in the t ransmission ofelectromagnetic waves?(1) Ground wave propagation is for high
frequency transmission(2) Sky wave propagation is facilitated by
ionospheric layers(3) Space wave is used for satellite
communication(4) Very high frequency waves cannot be
reflected by the ionospheric layers
1001CT102115077E-8/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
SPACE FOR ROUGH WORK
26. A solid sphere of mass M and radius R is givenvelocity as shown. Then the value of angularmomentum of the sphere with respect to originis given by :-
(1) kRMvoˆ
5
3
(2) kRMvoˆ
5
3
x
y
vo
vo/R
R
z
O
(3) kRMvoˆ
5
7
(4) 5
7 kRMvoˆ
27. A sound wave propagates through nitrogenunder NTP. At what frequency will thewavelength be equal to the mean free path ofthe gas molecules? Diameter of N
2 molecules is
0.4 nm.(1) 6.5 GHz (2) 2.9 MHz(3) 8.4 GHz (4) 7.3 MHz
28. One mole of an ideal monatomic gas is takenfrom temperature T
o to 2T
o by the process
CPT 4 . Considering the following
statements choose the correct alternative.
I. Molar heat capacity of the gas is 2
3R
II. Molar heat capacity of the gas is 2
3R
III. Work done by the gas is oRT3
IV. Work done by the gas is oRT3
(1) Statements I and IV are correct.
(2) Statements I and III are correct.
(3) Statements II and IV are correct
(4) Statements II and III are correct.
29. Consider a system of n particles of masses m1,
m2, …., m
n moving with velocities 1v
, 2v
, …..,
nv
. Assuming no external forces are acting on
the system, consider the following statements.
I. K. E. of system of particles is minimum in
the center of mass frame.
II. K. E. of system of particle is maximum in
the center of mass frame.
III. Centre of mass will either be at rest or
moving along straight line.
(1) Only statement I is correct.
(2) Only statement III is correct.
(3) Statements I and III are correct.
(4) Statements II and III are correct.
30. A longitudinal sound wave given by P = 2.5
sin 2
(x – 660t) (P is in N/m2 and x is in m
and t is in s) is sent down an closed organ
pipe. If the pipe vibrates in its second overtone,
the length of the pipe is :-
(1) 6 m (2) 8 m
(3) 5 m (4) 10 m
Enthusiast Course/Score-I/07-02-2016/Paper-2
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SPACE FOR ROUGH WORK
PART B - CHEMISTRY
31. [Co(H2N – CH
2 – CH
2 – NH
2)
3]
2S
3oxidation
Co+4 + CO3–2 + NO
3– + SO
4–2
What is the equivalent weight of the reactant
in the above reaction ?
(1) 3M
182(2)
M
182(3)
11M
182(4)
7M
182
32. Standard entropy of X2, Y
2 and X
2Y
3 are 60,
40 and 150 in J/K mol
X2 +
3
2Y
2 X
2Y
3H = +30 kJ
The temperature at which reaction will attain
equilibrium is :
(1) 250 K (2) 1000 K
(3) 750 K (4) 200 K
33.
r
4 r 2 r
This radial probability distribution graph can
represent the orbital.
(1) 5s (2) 5d
(3) 4p (4) 6d
34. A graph showing variation of osmotic pressure
() versus molar concentration 'C' of an
aqueous solution at temperature T is given
below :
C
The slope of the line is equal to :
(1) Solution constant R
(2) Absolute temperature T
(3) RT
(4) Degree of ionization of solute
35. We can represent the decomposition of N2O
5(g)
at a fixed temperature by the following two
chemical equations :
(a) 2N2O
5(g) 4NO
2(g) + O
2(g) ;
Activation energy Ea
(b) N2O
5(g) 2NO
2(g) +
1
2O
2(g) ;
Activation energy Ea' then
(1) Ea = Ea' (2) Ea > Ea'
(3) Ea < Ea' (4) Ea = 2Ea'
1001CT102115077E-10/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
SPACE FOR ROUGH WORK
36. Latimer diagram for Cu in an acidic solution is
Cu+2 +0.15 V Cu+
Cu+0.50 V
Find 2Cu / CuE
(1) +0.65 volt (2) +0.325 volt
(3) –0.0325 volt (4) –0.325 volt
37.
I-Cube II-Cylinder III-Sphere
5cm5cm
5cm 5cm
There are three closed containers in which
equal moles of gas is filled if the containers
are placed at the same temperature, then which
of the following is correct
(1) Pressure in I is the maximum.
(2) Pressure in II is the maximum.
(3) Pressure in III is the maximum.
(4) All the vessel have equal pressure.
38. A crystalline solid is made of X, Y and Z
elements. Atoms of X form f.c.c. packing Y
occupy octahedral voids, while atoms of Z
occupy tetrahedral voids. What will be the
simplest formula of the solid if atoms along
any one body diagonal are removed.
(1) X5Y
4Z
8(2) XYZ
(3) X8Y
4Z
5(4) X
2YZ
39. Relationship between volume strength of H2O
2
aqueous solution and molarity depends on
pressure and temperature of O2(g) collected
Example :
At 1 atm, 273K , volume strength = 11.2 × M
At STP , volume strength = 11.35 × M
[Note : By default STP is taken for volume
strength calculation].
Find the relationship between volume strength
& molarity at 300K & 1 atm
(1) 12.315 × M (2) 24.63 × M
(3) 11.35 × M (4) 22.7 × M
40. Hydrogen peroxide ionises as H2O
2H+
+ HO2– . If pH of H
2O
2 is 5.7 at 25°C, the ionic
product of H2O
2 is
(1) 2 × 10–12 (2) 4 × 10–12
(3) 1 × 10–14 (4) 1.4 × 10–12
41. Planar geometry around the central atom is
shown by :
(1) N(SiH3)
3(2) ICl
2–
(3) XeF2
(4) All of these
Enthusiast Course/Score-I/07-02-2016/Paper-2
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SPACE FOR ROUGH WORK
42. Match the following
(a) Smithsonite (p) Iron
(b) Carnallite (q) Copper
(c) Azurite (r) Magnesium
(d) Limonite (s) Zinc
(1) a - p, b - q, c - r, d - s
(2) a - s, b - r, c - p, d - q
(3) a - s, b - r, c - q, d - p
(4) a - q, b - p, c - s, d - r
43. When copper reacts with hot conc. H2SO
4 gives ?
(1) H2
(2) SO2
(3) O2
(4) None of these
44. Which of the following is not arranged in
correct sequence ?
(1) MO, M2O
3, MO
2, M
2O
5 - decreasing order
of basic nature (M = d block metal)
(2) Sc, Ti, V, Cr, Mn - increasing order of
highest possible oxidation state
(3) d5, d3, d1, d4 - increasing magnetic moment
(4) Mn+2, Fe+2, Cr+2, Co+2 - decreasing stability
45. NHCl + A4
Microcosmic salt
B Heat+DO
(C)
Violet colour
(oxide of D)
A, B, C & D are respectively
(1) Na3PO
4, NaPO
3, MnNaPO
4, MnO
(2) Na2HPO
4, NaPO
3, MnNaPO
4, MnO
(3) Na3PO
4, NaPO
3, CuNaPO
4, CuO
(4) Na2HPO
4, NaPO
3, CuNaPO
4, CuO
46. Match the following.
Column I Column II
(A) Borax (i) SiO2
(B) B2H
6 + H
2O (ii) H
2SiO
3
(C) B2H
6 + Excess of (iii) BN
NH3
(D) SiCl4
2(i) H O
(ii) 1000 C (iv) NaBO
2 + B
2O
3
(v) H3BO
3
A B C D
(1) i iii iv v
(2) ii iii iv v
(3) iv v iii ii
(4) iv v iii i
1001CT102115077E-12/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
SPACE FOR ROUGH WORK
47. Xenon hexafluoride reacts with silica to form
oxygen and xenon compound (X). The
hybridisation and oxidation state of xenon in the
compound
(1) sp3d2, +6 (2) d2sp3, +6
(3) sp3, +8 (4) sp3d, +6
48. In octahedral complex Ma2b
2cd, total number
of steroisomers is
(1) 2 (2) 4 (3) 5 (4) 8
49. The compound which is not associated with
Solvay ammonia process for the production
of Na2CO
3
(1) NH4HCO
3(2) NaHCO
3
(3) NaCl (4) Na2C
2O
4
50. Which of the following molecule or molecular
ion has highest number of total electrons in
antibonding molecular orbitals
(1) O2
(2) N2
(3) N2+ (4) O
22–
51. Acidic hydrolysis of an ester CH3CH
2COOCH
3
produces A & B, which can be distinguished
by :
(1) Na metal (2) NaHCO3
(3) Fehling solution (4) Tollen's Reagent
52. Which of the following is a biodegradable
polymer ?
(1) Cellulose (2) Polyethene
(3) Poly vinyl chloride (4) Dacron
53. Among following the most reactive towards
alcoholic KOH is :
(1) CH2 = CHBr
(2) Ph–CH2–CH
2–Br
(3) CH3CH
2Br
(4) CH3CH
2CH
2Br
54. Consider the following reaction :
3 4
3 2 4
CH Cl KMnOZn
dust Anhy. AlCl dil.H SOPhenol X Y Z
the product Z is -
(1) Benzaldehyde (2) Benzoic acid
(3) Benzene (4) Toluene
Enthusiast Course/Score-I/07-02-2016/Paper-2
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SPACE FOR ROUGH WORK
55. Which is the most basic among the following :
(1) C6H
5NH
2
(2) (C6H
5)
2NH
(3) C2H
5NH
2
(4) (C2H
5)
2NH
56. The final product of the reaction given below
is
3 2 2
O||
CH – CH C NH 2
2
HNONaOH
BrA B
(1) Ethanol (2) Methanol
(3) Methyl amine (4) Ethyl amine
57. Pyrimidine bases present in RNA are -
(1) cytosine + adanine
(2) thymine + cytosine
(3) cytosine + uracil
(4) thymine + uracil
58. Aromatic nitriles (ArCN) is not obtained as a
major product in reaction :
(1) ArCONH2 + P
2O
5
(2) ArN2
+ CuCN
(3) ArX + KCN
(4) ArCONH2 + SOCl
2
59. How many stereoisomers are possible for
a compound of the molecular formula
CH3 – CH = CH – CH
2 – CH(Br) – CH
3
(1) 2 (2) 4
(3) 6 (4) 8
60. Which of the following compound yields
acetone on ozonolysis ?
(1) 2-Methyl-1-butene
(2) 2-Methyl-2-butene
(3) 3-Methyl-1-butene
(4) 2,3-Dimethyl-1-butene
1001CT102115077E-14/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
SPACE FOR ROUGH WORK
PART C - MATHEMATIC
61. If k
1r
r 1
ksin (B )
2
and
k
rr 1
1A B
k
, then
the value of x A
xlim(1 x) tan
2
is
(1) 2
(2)
2
(3) 0 (4)
62. The distance of the point (–9, 0) from the
director circle of the parabola y2 = 16(x + 3) is
(1) 1 (2) 2 (3) 3 (4) 0
63. Let
1 x x 0
f(x) 1 [x] sin x 0 x2
x32
If f(x) is discontinuous at x = then is
(where [.] is greatest integer function)
(1) 0 (2) 1
(3) 2
(4) none of these
64. The tens digit of 1! + 2! + 3! + .... + 73! is :-
(1) 1 (2) 2 (3) 3 (4) 4
65. Let a differentiable function 'f' satisfying
f(x + y) = f(x) f(y) for all x, y R and
ƒ'(0) = 4. If f(x0) = 200 then f'(x
0) =
(1) 800 (2) 240
(3) 0 (4) none of these
66. For real valued functions fr(x) = cos2p
rx
r = 1, 2, 3; pr N such that period of
f1(x) + 2f
2(x) + 3f
3(x) is , period of
2f1(x) + 3f
2(x) is
2
and period of
3f1(x) + 2f
3(x) is ,
3
then minimum value of
(p1 + p
2 + p
3) is
(1) 6 (2) 10 (3) 11 (4) 17
67. If the function f(x) = x3 + x
5e and g(x) = f–1(x),
then the value of g'(1) + log5(g'(1)) is
(1) 6 (2) 2 (3) 3 (4) 1
268. The plane x + y + z = 5 is rotated by 90° along
the line of intersection with the plane x – y – z = 2.If the equation of plane in new position isax + by + cz + d = 0 where a, b, c, d I, then
least value of |a + b + c + d| is
(1) 10 (2) 9 (3) 4 (4) 11
Enthusiast Course/Score-I/07-02-2016/Paper-2
E-15/181001CT102115077
SPACE FOR ROUGH WORK
69. If and are the roots of quadratic equation
12x2 – 5x – 1 = 0, then the value of r r
r 1
( )
is
(1) 3
8(2)
5
8
(3) 7
6(4) none of these
70. If u = f(tan x), v = g(sec x) and f'(x) = tan–1x;
g'(x) = cosec–1x then du
dv at x
4
is
(1) 2 2 (2) 2 (3) 1
2(4) 3 2
71. The position vector of point of intersection of
the planes 2 3ˆ ˆr (n n ) 1,
3 1ˆ ˆr (n n ) 2 and
1 2ˆ ˆr (n n ) 3,
1 2 3
ˆ ˆ ˆ([n n n ] 0) is
(1) 1 2 3
1 2 3
ˆ ˆ ˆn 2n 3n
ˆ ˆ ˆ[n n n ]
(2) 1 2 3
21 2 3
ˆ ˆ ˆn 2n 3n
ˆ ˆ ˆ[n n n ]
(3) 2 3 3 1 1 2
1 2 3
ˆ ˆ ˆ ˆ ˆ ˆn n 2n n 3n n
ˆ ˆ ˆ[n n n ]
(4) 2 3 3 1 1 2
21 2 3
ˆ ˆ ˆ ˆ ˆ ˆn n 2n n 3n n
ˆ ˆ ˆ[n n n ]
72. If x,y
R, satisfying equation
2 2(x 4) y1
4 9,
then the maximum value of 2 2x y
8 18 is
(1) 9 (2) 7
2(3)
9
2(4) 10
73. The general solution of the equation
sin106x – cos106x = 1 is
(1) 2n + 2
(2) n +
2
(3) 2n – 2
(4) n
(where n I)
74. The area of the region bounded by the curves
y = x2 + 7, y = x, x = 3 and x = 0 is
(1) 61
2(2)
51
2(3)
31
2(4)
21
2
75. xe 2
9e log (3x 2) dx
(3x 2)
is -
(1) xe
3e log (3x 2) C
3x 2
(2) xee log (3x 2) C
(3) xe
1e log (3x 2) C
3x 2
(4) none of these
(where 'C' is the constant of integration)
1001CT102115077E-16/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
SPACE FOR ROUGH WORK
76. The number of real roots of the equation
x5 + e8x = 0 is
(1) 0 (2) 1 (3) 2 (4) 3
77. If
2 5 7 9
0 1 9 7A
0 0 1 8
0 0 0 1
then the value of
|adj (adjA)| is
(1) 1024 (2) 512
(3) –512 (4) –1024
78. If roots of the equation
(m – 1)x2 + (1 + 3m)x – (8 – 3m) = 0 are
opposite in sign, then the number of integral
value(s) of m is
(1) 0 (2) 1 (3) 2 (4) 3
79.
4
18 11
0
sin x cos x dx is equal to -
(1) 11
32(2)
11
64(3) 0 (4)
3
8
80. The number of complex numbers which satisfy
both the equations |z – 3 – 4i| = 2 and |z| = 1 is
(1) 2 (2) 1 (3) 0 (4) 4
81. The coefficient of x7 in
1 + (1 + x) + (1 + x)2 + ..... + (1 + x)100 is
(1) 101C93
(2) 100C93
(3) 100C7
(4) 0
82. If the matrix A is given by 3 2
A4 3
then
determinant value of (A27 – 2A26) is
(1) –5 (2) –7 (3) –10 (4) 0
83. In a multiple choice examination with 7
possible answers (out of which only one is
correct) for each of the four questions, what is
the probability that a candidate would get three
or more correct answers just by guessing is
(1) 4
1
7(2) 4
24
7(3) 4
25
7(4) 4
16
7
84. Given p and q are respectively the maximum and
minimum value of f(x) = 5sinx + 12cosx + 1. If
(p, q) are the centre of the circle touching the
x-axis, then radius of the circle is
(1) 14 (2) 12 (3) 13 (4) 11
85. A tangent of slope 2 of the ellipse 2 2
2
x y1
a 1
is normal to the circle x2 + y2 + 4x + 1 = 0, then
the value of log4(4a2 + 1) is
(1) 1 (2) 2 (3) 0 (4) 16
Enthusiast Course/Score-I/07-02-2016/Paper-2
E-17/181001CT102115077
SPACE FOR ROUGH WORK
86. If is the angle between the line
x 1 y 1 z 2
3 2 4
and the plane
2x + y – 3z + 4 = 0, then 64 cosec2 is equal to
(1) 1264 (2) 1624
(3) 1628 (4) 1648
87. All the 7 digit numbers containing each of the
digits 1, 2, 3, 4, 5, 6, 7 exactly once and not
divisible by 5 are arranged in increasing order.
Then 1201th number is
(1) 3124567 (2) 3765421
(3) 3124675 (4) 3124657
88. If a,b,c
are non-coplanar vectors,
[3a b c a b c 7a] is equal to [a b c] ,
then =
(1) 1 (2) 8
(3) 9 (4) 6
89. If the variance of 1, 2, 2, 3 is , then the value
of log2 is
(1) 8 (2) 1 (3) –1 (4) –2
90. If the length of subnormal at any point on the
parabola y2 = kx is 2 units, then |k| is equal to
(1) 1 (2) 2 (3) 4 (4) 8
1001CT102115077E-18/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
SPACE FOR ROUGH WORK
SPACE FOR ROUGH WORK
1.
2.
3. 3
4. 90360
5. A, B, C 30
4
6.
7.
8.
9.
10.
11.
Paper Code : 1001CT102115077Form Number :
CLASSROOM CONTACT PROGRAMME(Academic Session : 2015 - 2016)
HIN
DI
Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005
+91-744-5156100 info@allen.ac.in www.allen.ac.in
Your Target is to secure Good Rank in JEE (Main) 2016
Test Type : FULL SYLLABUS Test Pattern : JEE-Main
TEST DATE : 07 - 02 - 2016
SCORE-I
JEE (Main + Advanced) : ENTHUSIAST COURSE
PAPER – 2
H-1/181001CT102115077
Enthusiast Course/Score-I/07-02-2016/Paper-2
PART A - PHYSICS
BEWARE OF NEGATIVE MARKING
HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS
1. v0
0
v0
0
(1) v0 = 10 m/s,
0 = 30o
(2) v0 = 10 m/s,
0 = 45o
(3) v0 = 20 m/s,
0 = 45o
(4) v0 = 20 m/s,
0 = 60o
2.
(1) 1 × 105 ± 5 % (2) 1 × 106 ± 10%
(3) 1 × 107 ± 5 % (4) 1 × 106 ± 5 %
3. 5 km/hr
v0
0 f
0
v0
0
(1) v0 = 10 m/s,
0 = 30o
(2) v0 = 10 m/s,
0 = 45o
(3) v0 = 10 m/s,
0 = 60o
(4)
4. A B
(R )
A
B
R
R
(1) R (2) 2
3R
(3) R2 (4) 2
R
1001CT102115077H-2/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
5. m, 2m, 4m, 8m, ……… 2N-1m N Hm m H 1 m/s
H
m
m 2m 4m 2N-1m
(1) g
N 12
(2) g
N2
(3) g
N 122
(4)
g
N 122
6. Q = 2N
o (
N0
) t ?
(1)
No
t
N
(2)
2No
t
N
No
(3)
2No
t
N
No
(4)
2No
t
N
No
H-3/181001CT102115077
Enthusiast Course/Score-I/07-02-2016/Paper-2
7.
(1) (2)
(3) (4)
8. YDSE S1 S
2 d
P1 P
2, O
P1 P
2
D (>>d) O
P1
P2
d
S1
S2
(1) 2
cot2
tan
(2) 2
cot2
tan
(3) 2
cos2
sin
(4) 2
sin2
cos
9.
1200
120 V
3.6 V 1A
0.4 ohms
(1) 40 (2) 36 (3) 4800 (4) 4320
10. ( = 1.5)
R
O
?
(1)
2R
R
O
(2)
2R
R
O
(3)
3R
R
O
(4)
2R
R
O
1001CT102115077H-4/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
11. v
R C
B
A
L
B
C R
E H
G
v
F
(i) AEFBA
(ii) AEFBA
(iii)
(iv) 222
2
1vLCB
(1) (i) (iii)
(2) (ii) (iv)
(3) (i), (iii) (iv)
(4)
12. : 0ˆE E i
cos(kz – t)
z t = 0
(1)
y
x
z
(2)
y
x
z
(3)
y
x
z
(4)
13. E K
1 K
2 2 : 1
A A/2
K1
K1 K2
(1) E/4 (2) E/3
(3) E/12 (4) E/6
H-5/181001CT102115077
Enthusiast Course/Score-I/07-02-2016/Paper-2
14. 0.625 m
2 rad/s
d s 0.5 s P C
(g = 10 m/s2)
P
C
(1) 1 : 1 (2) 2 : 1
(3) 3 : 1 (4) 4 : 1
15.
R
GM
(1) R
GM(2)
R
GM2
(3) R
GM
2
3(4)
R
GM2
16. p-n
Jp, drift
Jp, diff
Jn, drift
Jn, diff
p-n
(1) Jp, drift
+ Jn, drift
= Jp, diff
+ Jn, diff
= 0
(2) Jn, drift
+ Jn, diff
= 0
(3) Jp, drift
+ Jp, diff
= 0
(4) Jp, drift
+ Jn, drift
+ Jp, diff
+ Jn, diff
= 0
17. L
g
1
100
90.0 L 1 mm
20.0 cm g
(1) 2.7 % (2) 2.27 %
(3) 1.7 % (4) 4.4 %
1001CT102115077H-6/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
18. m1 m
2
(1) 2
1
m
m(2)
1
2
m
m(3) 1 : 1 (4)
2
1
m
m
19. -1 : P-N -2 : (1) -1 , -2 -2
-1 (2) -1 , -2 -2
-1 (3) -1 , -2 (4) -1 , -2
20.
S
N
(1)
S
N
(2)
S
N
(3)
S
N
(4)
S
N
21. h
R
(1) 2
R(2)
h4
R2
(3) h
R2
(4) 2
h
H-7/181001CT102115077
Enthusiast Course/Score-I/07-02-2016/Paper-2
22. l a
l a
I
A. B. C.
D.
E.
(1) A C (2) B C (3) A D (4) A E
23. = 0.98,
IB = 0.02 mA, R
L = 5 k
(1) 3.2 V
(2) 4.9 V IB
RL
VBCVBE
(3) 5.2 V
(4) 6.2 V
24.
:-
X Y Z
(1) X Y Z
(2) X Y Z
(3) X
Y Z
(4) X Y Z
25.
(1)
(2)
(3)
(4)
1001CT102115077H-8/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
26. M R
(1) kRMvoˆ
5
3
(2) kRMvoˆ
5
3
x
y
vo
vo/R
R
z
O
(3) kRMvoˆ
5
7
(4) 5
7 kRMvoˆ
27. N
2
0.4 nm (1) 6.5 GHz (2) 2.9 MHz
(3) 8.4 GHz (4) 7.3 MHz
28. T
o 2T
o PT–4 = C
I. 2
3R
II. 2
3R
III. –3RT0
IV. 3RT0
(1) I IV (2) I III (3) II IV (4) II III
29. m1, m
2, …., m
n n
1v
, 2v
, ….., nv
I.
II.
III.
(1) I
(2) III
(3) I III
(4) II III
30. P = 2.5 sin 2
(x – 660t)
(P, N/m2 x, m t, s )
(1) 6 m (2) 8 m
(3) 5 m (4) 10 m
H-9/181001CT102115077
Enthusiast Course/Score-I/07-02-2016/Paper-2
PART B - CHEMISTRY
31. [Co(H2N – CH
2 – CH
2 – NH
2)
3]
2S
3oxidation
Co+4 + CO3–2 + NO
3– + SO
4–2
?
(1) 3M
182(2)
M
182
(3) 11M
182(4)
7M
182
32. X2, Y
2 X
2Y
3 J/K mol
60, 40 150
X2 +
3
2Y
2 X
2Y
3H = +30 kJ
(1) 250 K (2) 1000 K
(3) 750 K (4) 200 K
33.
r
4 r 2 r
(1) 5s (2) 5d
(3) 4p (4) 6d
34. T ()
'C'
C
:
(1) R
(2) T
(3) RT
(4)
35. N
2O
5(g) :
(a) 2N2O
5(g) 4NO
2(g) + O
2(g);
Ea
(b) N2O
5(g) 2NO
2(g) +
1
2O
2(g);
Ea'
(1) Ea = Ea' (2) Ea > Ea'
(3) Ea < Ea' (4) Ea = 2Ea'
1001CT102115077H-10/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
36. Cu
Cu+2 +0.15 V Cu+
Cu+0.50 V
2Cu / CuE
(1) +0.65 volt (2) +0.325 volt
(3) –0.0325 volt (4) –0.325 volt
37.
I-Cube II-Cylinder III-Sphere
5cm5cm
5cm 5cm
(1) I (2) II
(3) III
(4)
38. X, Y Z X fcc Y Z
(1) X5Y
4Z
8(2) XYZ
(3) X8Y
4Z
5(4) X
2YZ
39. H2O
2
O2(g)
:
1 atm, 273K , = 11.2 × M
STP , = 11.35 × M
[:
STP ]
300K 1 atm
(1) 12.315 × M (2) 24.63 × M
(3) 11.35 × M (4) 22.7 × M
40.
H2O
2H+ + HO
2– . 25°C H
2O
2
pH, 5.7 H2O
2
(1) 2 × 10–12 (2) 4 × 10–12
(3) 1 × 10–14 (4) 1.4 × 10–12
41.
(1) N(SiH3)
3 (2) ICl
2–
(3) XeF2 (4)
H-11/181001CT102115077
Enthusiast Course/Score-I/07-02-2016/Paper-2
42. -
(a) (p)
(b) (q)
(c) (r)
(d) (s)
(1) a - p, b - q, c - r, d - s
(2) a - s, b - r, c - p, d - q
(3) a - s, b - r, c - q, d - p
(4) a - q, b - p, c - s, d - r
43. H2SO
4
(1) H2
(2) SO2
(3) O2
(4)
44.
(1) MO, M2O
3, MO
2, M
2O
5 -
(M = d )
(2) Sc, Ti, V, Cr, Mn -
(3) d5, d3, d1, d4 -
(4) Mn+2, Fe+2, Cr+2, Co+2 -
45. NHCl + A4
B +DO
(C)
(D )
A, B, C D
(1) Na3PO
4, NaPO
3, MnNaPO
4, MnO
(2) Na2HPO
4, NaPO
3, MnNaPO
4, MnO
(3) Na3PO
4, NaPO
3, CuNaPO
4, CuO
(4) Na2HPO
4, NaPO
3, CuNaPO
4, CuO
46.
I II
(A) (i) SiO2
(B) B2H
6 + H
2O (ii) H
2SiO
3
(C) B2H
6 + NH
3(iii) BN
(D) SiCl4
2(i) H O
(ii) 1000 C (iv) NaBO
2 + B
2O
3
(v) H3BO
3
A B C D
(1) i iii iv v
(2) ii iii iv v
(3) iv v iii ii
(4) iv v iii i
1001CT102115077H-12/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
47.
(X)
(1) sp3d2, +6 (2) d2sp3, +6
(3) sp3, +8 (4) sp3d, +6
48. Ma2b
2cd
(1) 2 (2) 4 (3) 5 (4) 8
49. Na2CO
3
(1) NH4HCO
3(2) NaHCO
3
(3) NaCl (4) Na2C
2O
4
50.
(1) O2
(2) N2
(3) N2+ (4) O
22–
51. CH3CH
2COOCH
3
A B
(1) Na (2) NaHCO3
(3) (4)
52.
(1) (2)
(3) (4)
53. KOH
(1) CH2 = CHBr
(2) Ph–CH2–CH
2–Br
(3) CH3CH
2Br
(4) CH3CH
2CH
2Br
54.
3 4
3 2 4
CH Cl KMnOZn
dust Anhy. AlCl dil.H SOX Y Z
Z
(1) (2)
(3) (4)
H-13/181001CT102115077
Enthusiast Course/Score-I/07-02-2016/Paper-2
55.
(1) C6H
5NH
2(2) (C
6H
5)
2NH
(3) C2H
5NH
2(4) (C
2H
5)
2NH
56.
3 2 2
O||
CH – CH C NH 2
2
HNONaOH
BrA B
(1) (2)
(3) (4)
57. RNA
(1) +
(2) +
(3) +
(4) +
58.
(ArCN)
(1) ArCONH2 + P
2O
5
(2) ArN2
+ CuCN
(3) ArX + KCN
(4) ArCONH2 + SOCl
2
59. CH3–CH=CH–CH
2–CH(Br)–CH
3
(1) 2 (2) 4 (3) 6 (4) 8
60.
(1) 2--1-
(2) 2--2-
(3) 3--1-
(4) 2,3--1-
1001CT102115077H-14/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
PART C - MATHEMATICS
61. k
1r
r 1
ksin (B )
2
k
r
r 1
1A B
k
x A
xlim(1 x) tan
2
(1) 2
(2)
2
(3) 0 (4)
62. y2 = 16(x + 3) (–9, 0) -
(1) 1 (2) 2 (3) 3 (4) 0
63.
1 x x 0
f(x) 1 [x] sin x 0 x2
x32
f(x), x =
([.])
(1) 0 (2) 1
(3) 2
(4)
64. 1! + 2! + 3! + .... + 73! :-
(1) 1 (2) 2
(3) 3 (4) 4
65. 'f', x, y R f(x + y) = f(x)f(y) ƒ'(0) = 4 f(x
0) =
200 f'(x
0)
-
(1) 800 (2) 240
(3) 0 (4)
66. fr(x) = cos2p
rx
r = 1, 2, 3; pr N f
1(x) + 2f
2(x) + 3f
3(x)
2f1(x) + 3f
2(x)
2
3f1(x) + 2f
3(x)
3
(p1 + p
2 + p
3)
(1) 6 (2) 10 (3) 11 (4) 17
67. f(x) = x3 + x
5e g(x) = f–1(x)
g'(1) + log5(g'(1))
(1) 6 (2) 2 (3) 3 (4) 1
2
68. x + y + z = 5 x – y – z = 2 90° ax + by + cz + d
= 0, a, b, c, d I |a + b + c + d|
(1) 10 (2) 9 (3) 4 (4) 11
H-15/181001CT102115077
Enthusiast Course/Score-I/07-02-2016/Paper-2
69. 12x2 – 5x – 1 = 0
r r
r 1
( )
(1) 3
8(2)
5
8
(3) 7
6(4)
70. u = f(tan x), v = g(sec x) f'(x) = tan–1x;
g'(x) = cosec–1x x4
du
dv
(1) 2 2 (2) 2 (3) 1
2(4) 3 2
71. 2 3ˆ ˆr (n n ) 1,
3 1ˆ ˆr (n n ) 2
1 2ˆ ˆr (n n ) 3,
1 2 3
ˆ ˆ ˆ([n n n ] 0)
(1) 1 2 3
1 2 3
ˆ ˆ ˆn 2n 3n
ˆ ˆ ˆ[n n n ]
(2) 1 2 32
1 2 3
ˆ ˆ ˆn 2n 3n
ˆ ˆ ˆ[n n n ]
(3) 2 3 3 1 1 2
1 2 3
ˆ ˆ ˆ ˆ ˆ ˆn n 2n n 3n n
ˆ ˆ ˆ[n n n ]
(4) 2 3 3 1 1 22
1 2 3
ˆ ˆ ˆ ˆ ˆ ˆn n 2n n 3n n
ˆ ˆ ˆ[n n n ]
72. x, y R,
2 2(x 4) y
14 9
2 2x y
8 18
(1) 9 (2) 7
2(3)
9
2(4) 10
73. sin106x – cos106x = 1 -
(1) 2n + 2
(2) n +
2
(3) 2n – 2
(4) n
( n I)
74. y = x2 + 7, y = x, x = 3 x = 0 -
(1) 61
2(2)
51
2(3)
31
2(4)
21
2
75.x
e 2
9e log (3x 2) dx
(3x 2)
-
(1) xe
3e log (3x 2) C
3x 2
(2) xee log (3x 2) C
(3) xe
1e log (3x 2) C
3x 2
(4) ( 'C' )
1001CT102115077H-16/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2
76. x5 + e8x = 0 -(1) 0 (2) 1 (3) 2 (4) 3
77.
2 5 7 9
0 1 9 7A
0 0 1 8
0 0 0 1
|adj (adjA)|
-
(1) 1024 (2) 512
(3) –512 (4) –1024
78. (m – 1)x2 + (1 + 3m)x – (8 – 3m) = 0
m
-
(1) 0 (2) 1 (3) 2 (4) 3
79.
4
18 11
0
sin x cos x dx -
(1) 11
32(2)
11
64
(3) 0 (4) 3
8
80. |z – 3 – 4i| = 2 |z| = 1 -
(1) 2 (2) 1 (3) 0 (4) 4
81. 1 + (1 + x) + (1 + x)2 + ..... + (1 + x)100 x7 -
(1) 101C93
(2) 100C93
(3) 100C7
(4) 0
82. A, 3 2
A4 3
(A27 – 2A26) -
(1) –5 (2) –7 (3) –10 (4) 0
83. () 7 -
(1) 4
1
7(2) 4
24
7
(3) 4
25
7(4) 4
16
7
84. p q, f(x) = 5sinx + 12cosx + 1
(p, q)
x-
-(1) 14 (2) 12 (3) 13 (4) 11
85. 2 2
2
x y1
a 1 2
x2 + y2 + 4x + 1 = 0 log
4(4a2 + 1) -
(1) 1 (2) 2 (3) 0 (4) 16
H-17/181001CT102115077
Enthusiast Course/Score-I/07-02-2016/Paper-2
86. x 1 y 1 z 2
3 2 4
2x+y–3z+4=0 64 cosec2
-(1) 1264 (2) 1624
(3) 1628 (4) 1648
87. 7 1, 2, 3, 4,
5, 6, 7 5 1201 -(1) 3124567 (2) 3765421
(3) 3124675 (4) 3124657
88. a,b,c
[3a b c a b c 7a] =
[a b c]
-
(1) 1 (2) 8 (3) 9 (4) 6
89. 1, 2, 2, 3 log2
-
(1) 8 (2) 1 (3) –1 (4) –2
90. y2 = kx
2 |k| -
(1) 1 (2) 2 (3) 4 (4) 8
1001CT102115077H-18/18
Target : JEE (Main + Advanced) 2016/07-02-2016/Paper-2