Paper Code : 0000CT103115004
TARGET : JEE (MAIN) 2016
Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005
+91-744-5156100 [email protected] www.allen.ac.in
dlp.allen.ac.in, dsat.allen.ac.in
LEADER TEST SERIES / JOINT PACKAGE COURSE
Your Target is to secure Good Rank in JEE (Main) 2016
Form Number :
DISTANCE LEARNING PROGRAMME(Academic Session : 2015 - 2016)
Important Instructions
Do not open this Test Booklet until you are asked to do so.
1. Immediately fill in the form number on this page of the Test Booklet
with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited.
2. The candidates should not write their Form Number anywhere else
(except in the specified space) on the Test Booklet/Answer Sheet.
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 total score will be made
if no response is indicated for an item in the Answer Sheet.
7. Use Blue/Black Ball Point Pen only for writting particulars/
marking responses on Side–1 and Side–2 of the Answer Sheet.
Use of pencil is strictly prohibited.
8. No candidate is allowed to carry any textual material, printed or
written, bits of papers, mobile phone any electronic device etc,
except the Identity Card inside the examination hall/room.
9. Rough work is to be done on the space provided for this purpose
in the Test Booklet only.
10. On completion of the test, the candidate must hand over the Answer
Sheet to the invigilator on duty in the Room/Hall. However, the
candidate are allowed to take away this Test Booklet with them.
11. Do not fold or make any stray marks on the Answer Sheet.
1.
2.
3. 3 4. 90360
5. A, B, C 30 4
6.
7.
8.
9.
10.
11.
Note : In case of any correction in the test paper, please mail to [email protected] within 2 days along with Paper Code & YourForm No. (Correction Paper Code Form No. Test Details [email protected] mail)
Test Type : ALL INDIA OPEN TEST (MAJOR) Test Pattern : JEE-Main
TEST # 06 TEST DATE : 20 - 03 - 2016
1/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
BEWARE OF NEGATIVE MARKING
HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS
PART A - PHYSICS
1. An ideal gas heat engine operates in a Carnot's
cycle between 227°C and 127°C. It absorbs
6 × 104 J at high temperature. The amount of
heat converted into work is :
(1) 4.8 × 104 J (2) 3.5 × 104 J
(3) 1.6 × 104 J (4) 1.2 × 104 J
2. Which one of the following graphs represents the
behaviour of an ideal gas for isothermel process.
(1)
PV
V
(2)
PV
V
(3)
PV
V
(4)
PV
V
1. 227°C
127°C
6 × 104 J
(1) 4.8 × 104 J (2) 3.5 × 104 J
(3) 1.6 × 104 J (4) 1.2 × 104 J
2.
(1)
PV
V
(2)
PV
V
(3)
PV
V
(4)
PV
V
0000CT1031150042/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
3. A parallel plate air capacitor has a capacitance
C (figure-1). When it is half filled with a
dielectric of dielectric constant 5 (figure-2),
the percentage increase in the capacitance will
be:-
Cfigure-1 figure-2
(1) 400% (2) 33.3%
(3) 66.6% (4) 200%
4. Identify the logic operation performed by the
circuit given below.
A
B
A
B
y
(1) NOT (2) AND
(3) OR (4) NAND
5. A thin prism P1 with angle 4° and made from
a glass of refractive index 1.54 is combinedwith another thin prism P2 made from glass
o f refract ive index 1.72 to producedispersion without deviation. The angle of
the prism P2 is :-
(1) 5.33° (2) 4° (3) 3° (4) 2.6°
3. C
-1 -2 5
Cfigure-1 figure-2
(1) 400% (2) 33.3%
(3) 66.6% (4) 200%
4.
A
B
A
B
y
(1) NOT (2) AND
(3) OR (4) NAND
5. P1 4° 1.54
1.72
P2
P2 (1) 5.33° (2) 4° (3) 3° (4) 2.6°
3/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
6. The following four wires of length L and radius
r are made of the same material. Which of these
will have the largest extension, when the same
tension is applied?
(1) L = 100 cm, r = 0.2 mm
(2) L = 200 cm, r = 0.4 mm
(3) L = 300 cm, r = 0.6 mm
(4) L = 400 cm, r = 0.8 mm
7. Eight equal drops of water are falling through
air with a steady velocity of 10 cm s–1. If the
drops combine to form a single drop big in size,
then the terminal velocity of this big drop is :-
(1) 40 cms–1 (2) 10 cms–1
(3) 30 cms–1 (4) 80 cm s–1
8. Three identical rods A, B and C are placed end
to end. A temperature difference is maintained
between the free ends of A and C. The thermal
conductivity of B is THRICE that of C and
HALF of that of A. The effective thermal
conductivity of the system will be :- (KA is the
thermal conductivity of rod A).
(1) 1/3 KA (2) 3 KA
(3) 2 KA (4) 2/3 KA
6. L r
(1) L = 100 cm, r = 0.2 mm
(2) L = 200 cm, r = 0.4 mm
(3) L = 300 cm, r = 0.6 mm
(4) L = 400 cm, r = 0.8 mm
7. 10 cm s–1
(1) 40 cms–1 (2) 10 cms–1
(3) 30 cms–1 (4) 80 cm s–1
8. A, B C
A C
B C
A
(KA, A
)
(1) 1/3 KA (2) 3 KA
(3) 2 KA (4) 2/3 KA
0000CT1031150044/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
9. Which one of the following is m – T graph for
perfectly black body? m is the frequency of
radiation with maximum intensity. T is the
absolute temperature.
A B
CD
T(K)
v(H
z)m
(1) A (2) B
(3) C (4) D
10. Two tuning forks, A and B, produce notes of
frequencies 258 Hz and 262 Hz. An unknown
note sounded with A produces certain beats.
When the same note is sounded with B, the
beat frequency gets doubled. The unknown
frequency is :-
(1) 250 Hz (2) 252 Hz
(3) 254 Hz (4) 256 Hz
9. m – T
m T
A B
CD
T(K)
v(H
z)m
(1) A (2) B
(3) C (4) D
10. A B, 258 Hz 262 Hz
A
B
(1) 250 Hz (2) 252 Hz
(3) 254 Hz (4) 256 Hz
5/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
11. A wire under tension vibrates with a
fundamental frequency of 600 Hz. If the
length of the wire is doubled, the radius is
halved and the wire is made to vibrate under
one-ninth the tension. Then the fundamental
frequency will become :-
(1) 200 Hz (2) 300 Hz
(3) 600 Hz (4) 400 Hz
12. The critical angle of a certain medium is
1 3sin
5
. The polarizing angle of the medium
is :-
(1) 1 4
sin5
(2) 1 5
tan3
(3)1 3
tan4
(4) 1 4
tan3
13. A conductor wire having 1029 free electrons/m3
carries a current of 20A. If the cross-section
of the wire is 1mm2, then the drift velocity of
electrons will be :- (e = 1.6 × 10–19C).
(1) 1.25 × 10–4ms–1 (2) 1.25 × 10–3 ms–1
(3) 1.25 × 10–5 ms–1 (4) 6.25 × 10–3 ms–1
11. 600 Hz
1
9
(1) 200 Hz (2) 300 Hz
(3) 600 Hz (4) 400 Hz
12. 1 3sin
5
(1) 1 4
sin5
(2) 1 5
tan3
(3)1 3
tan4
(4) 1 4
tan3
13. 1029 m3
20A
1mm2
(e = 1.6 × 10–19C).
(1) 1.25 × 10–4ms–1 (2) 1.25 × 10–3 ms–1
(3) 1.25 × 10–5 ms–1 (4) 6.25 × 10–3 ms–1
0000CT1031150046/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
14. If n-p-n transistor is to be considered to be
equivalent to two diodes connected (according
to biasing only). Which of the following figures
is the correct one:-
(1) B
E C
(2) B
E C
(3) B
E C
(4) B
E C
15. The viscosity of a fluid µ, can be determinedby measuring the terminal velocity VT of asphere when it descends in the fluid. The fluidhas a density f while the sphere has a densitys and a diameter of d. The viscosity can thenbe calculated by the formula
2s f
T
5( )d
9V
The values measured areVT = (1.60 ± 0.04) ms–1
s = (2700 ± 20) kg m–3
f =(900 ± 10) kg m–3
d = (20.0 ± 0.4) mmWhat is the percentage uncertainty in the valueof µ?
(1) 6.2% (2) 7.1% (3) 8.2% (4) 8.4%
14. n-p-n
(1) B
E C
(2) B
E C
(3) B
E C
(4) B
E C
15. µ, VT f s d
2s f
T
5( )d
9V
VT = (1.60 ± 0.04) ms–1
s = (2700 ± 20) kg m–3
f =(900 ± 10) kg m–3
d = (20.0 ± 0.4) mm
µ (1) 6.2% (2) 7.1% (3) 8.2% (4) 8.4%
7/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
16. A person of weight 500 N does a bungee jump
using an elastic rope of unstretched length
40 m and having a spring constant k equal to
50 N/m. During the initial fall there is a
transfer of energy from gravitational potential
energy to kinetic energy and elastic potential
energy. The person falls through a distance of
80 m before beginning to move upwards.
Which set of graphs correctly represent the
variation of the three energies?
GravitationalPotential Energy
ElasticPotential Energy
Kinetic Energy
(1)
0 10 20 30 40 50 60 70 80 90 10005
101520253035404550
(2)
0 10 20 30 40 50 60 70 80 90 10005
101520253035404550
(3)
0 10 20 30 40 50 60 70 80 90 10005
101520253035404550
(4)
0 10 20 30 40 50 60 70 80 90 10005
101520253035404550
16. 500 N
40 m 50 N/m
80m
GravitationalPotential Energy
ElasticPotential Energy
Kinetic Energy
(1)
0 10 20 30 40 50 60 70 80 90 10005
101520253035404550
(2)
0 10 20 30 40 50 60 70 80 90 10005
101520253035404550
(3)
0 10 20 30 40 50 60 70 80 90 10005
101520253035404550
(4)
0 10 20 30 40 50 60 70 80 90 10005
101520253035404550
0000CT1031150048/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
17. The graphs in figure show how the
displacement x, velocity v and the accelerationa of a body vary with time t when it is oscillating
with simple harmonic motion. What is the valueof T?
x/m
t/s20
–2 T
v/m s–1
t/s
6
0
–6T
a/m s–2
t/s
18
0
–18T
(1) s9
(2)
2s
9
(3) s
3
(4)
2s
3
18. A current balance is used to measure themagnetic flux density B of a electromagnet. Theside PQ of a current balance is inserted insidea large electromagnet. The direction ofmagnetic field is as shown in figure. Length ofPQ is L. Perpendicular distances of PQ and RSare d1 and d2 respectively from the pivot. A loadof mass m is placed along side RS. Takeacceleration due to gravity to be g. The directionand magnitude of the current along PQ are
P
Q R
SB
17. x, v a t T
x/m
t/s20
–2 T
v/m s–1
t/s
6
0
–6T
a/m s–2
t/s
18
0
–18T
(1) s9
(2)
2s
9
(3) s
3
(4)
2s
3
18. B PQ PQ L PQ RS d1 d2 m RS g PQ
P
Q R
SB
9/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
Direction Magnitude
(1) from P to Q2
1
md
BLd
(2) from P to Q2
1
mgd
BLd
(3) from Q to P2
1
md
BLd
(4) from Q to P2
1
mgd
BLd
19. The graph represents the decay of a newly
prepared sample of radioactive nuclide X to a
stable nuclide Y. The half-life of X is . The
growth curve for Y intersects the decay curve
for X after time T. What is the time T?
number ofatoms
x Y
0 T time
(1) 2
(2) In
2
(3) (4) 2
(1) P Q 2
1
md
BLd
(2) P Q 2
1
mgd
BLd
(3) Q P 2
1
md
BLd
(4) Q P 2
1
mgd
BLd
19. X
Y X
Y T X
T
number ofatoms
x Y
0 T time
(1) 2
(2) In
2
(3) (4) 2
0000CT10311500410/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
20. Ball 1 is launched up an inclined plane from
point A with an initial speed that is the minimum
speed for it to just reach point B at the top of
the plane. At the same moment that ball 1 is
launched up the plane, ball 2 is released from
rest from point B. The two balls make their first
contact at a point C somewhere on the inclined
plane between A and B. What is the ratio of the
distance AC to the distance BC?
Ball 1
Ball 2
A
B
(1) 1 (2) 2 (3) 3 (4) 4
21. A block and a sphere of equal mass m are placed
on an inclined plane. If the maximum frictional
force that can exist between the block and the
plane is equal to the weight of the block, and
there is no frictional force between the sphere
and the plane, what is the maximum angle at
which the plane can be inclined before the block
starts to slip?
(1) 30° (2) 45° (3) 60° (4) 90°
20. 1 A B 1 2B C A B AC BC
Ball 1
Ball 2
A
B
(1) 1 (2) 2 (3) 3 (4) 4
21. m
(1) 30° (2) 45° (3) 60° (4) 90°
11/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
22. A hollow metal cylinder floats upright in a bodyof water with the bottom of the cylinder at adepth of D below the water surface as shownin the figure below. The cylinder is pressedfurther down into the water and upon release,performs simple harmonic motion. Which ofthe following graphs (all drawn to scale) showshow the upthrust U and net force F acting onthe cylinder vary with d, the depth the bottomof the cylinder below the water surface?
D
(1)
U,F
0d
F
U
D
(2)
U,F
0d
F
UD
(3)
U,F
0d
F
U
D
(4)
U,F
0d
F
U
D
22. D U F d
D
(1)
U,F
0d
F
U
D
(2)
U,F
0d
FU
D
(3)U,F
0d
F
U
D
(4)
U,F
0d
F
U
D
0000CT10311500412/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
23. A progressive wave travelling to the right hits
a hard surface and gets reflected after suffering
a phase change of 180°. The diagram below
shows the incident wave at a particular instant
of time. Which of the following shows the
corresponding reflected wave?
(1)
(2)
(3)
(4)
23.
180°
(1)
(2)
(3)
(4)
13/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
24. A guitar string of length L is stretched between
two fixed points P and Q and made to vibrate
transversely as shown in the figure. Two
particles A and B on the string are separated by
a distance s. The maximum kinetic energies of
A and B are KA and KB respectively. Which of
the following gives the correct phase difference
and maximum kinetic energies of the particles?
A
Bs
P Q
L
Phase difference Maximum kinetic
energy
(1)3s
3602L
KA < KB
(2)3s
3602L
same
(3) 180° KA < KB
(4) 180° same
24. L P
Q
A B
s A B
KA KB
A
Bs
P Q
L
(1)3s
3602L
KA < KB
(2)3s
3602L
(3) 180° KA < KB
(4) 180°
0000CT10311500414/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
25. An atom X is excited to an energy level E2 from its
ground state E0 by collision with another atom Y.
Atom X is initially at rest. Which of the following
gives possible energy values of X and Y?
Kinetic energy of atom Kinetic energy of atom
Y before collision X after the collision
(1) less than (E2– E0) zero
(2) (E2 – E0) non-zero
(3) (E2 – E0) zero
(4) greater than (E2–E0) non-zero
26. In the figure shown, pan C is massless.
All strings and pulleys are ideal. Block B is
dropped from a height on pan C. Collision
between block B and pan C is perfectly
inelastic. Just after collision tension in string A
differ from tension in string A before collision
by a magnitude of :-
M
ABM
C
(1) Mg (2) Mg
2(3)
Mg
4(4) 2Mg
25. X Y E0 E2 X X Y
Y X (1) (E2– E0) (2) (E2 – E0) (3) (E2 – E0) (4) (E2–E0)
26. C B CB C A A
M
ABM
C
(1) Mg (2) Mg
2(3)
Mg
4(4) 2Mg
15/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
27. In a screw gauge, there are 100 divisions oncircular scale and each main scale division isof 1 mm. When there is no gap between thejaws, 97th divisions coincides with the mainscale zero and zero of main scale is not visible.While measuring the diameter of a ball, thecircular scale is between 3 mm mark and 4 mmmark such that the 76th division of circular scalecoincides with the reference line. Select thecorrect alternative :-(1) the least count of the micrometer is 0.01 cm
(2) the zero error is – 0.04 mm
(3) the diameter of the ball is 3.79 cm
(4) the main scale reading is 4 mm
28. A uniform solid square plate ABCD of mass m
and side a is moving in x – y horizontal smooth
plane. The velocity of centre of mass is
0ˆ ˆv 2i 4 j m / s . The end A of square plate
is suddenly fixed by a pin, find the new velocity
of centre of mass of square :-
(1) 0ˆ ˆv 2i 4 j
(2) 0 03v 3vˆ ˆi j4 4
x
y
B C
A D
v = v i jcm 0(2 + 4 )^ ^
(3) 0 03v 3vˆ ˆi j
2 2
(4) 0 0ˆ ˆ3v i 3v j
27. 100 1 mm 97 3 mm 4 mm 76 (1) 0.01 cm (2) – 0.04 mm (3) 3.79 cm (4) 4 mm
28. m a
ABCD x – y
0ˆ ˆv 2i 4 j m / s
A
(1) 0ˆ ˆv 2i 4 j
(2) 0 03v 3vˆ ˆi j4 4
x
y
B C
A D
v = v i jcm 0(2 + 4 )^ ^
(3) 0 03v 3vˆ ˆi j
2 2
(4) 0 0ˆ ˆ3v i 3v j
0000CT10311500416/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
29. In Young's double slit experiment with light of
wavelength = 600 nm, intensity of central
fringe is I0. Now one of the slit is covered by
glass plate of refraction index 1.4 and thickness
t = 5 µ m, the new intensity at the same point
on screen will be :-
(1) 0I
4(2)
03I
4
(3) I0
(4) 0I
2
30. Heat is supplied to a diatomic gas at constant
pressure, with the usual notation the ratio
Q : U : W is
(1) 5:2:2
(2) 5:2:3
(3) 7:5:2
(4) 7:2:5
29. = 600 nm
I0
1.4 t = 5 µm
(1) 0I
4(2)
03I
4
(3) I0
(4) 0I
2
30.
Q : U : W
(1) 5:2:2
(2) 5:2:3
(3) 7:5:2
(4) 7:2:5
17/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
PART B - CHEMISTRY
31. In a constant pressure calorimeter, 224 ml of
0.1M KOH (aq.) solution at TK is mixed with
50 ml of 0.1M H2SO
4 (aq.) solution at TK then
increase in temperature of solution will be
(assume heat capacity of calorimeter is
negligible) -
Given : neut
H for strong acid base
is = 13.7 kcal / eq.
Specific heat of solution = 1 cal/gm–K
Density of solution = 1 gm/ml
(1) 0.5 K (2) 1K
(3) 2K (4) 0.25
32. Small amount of HCl(aq) is added in freshly
precipitated Al(OH)3 to form a colloidal sol.
The only correct statement regarding the
characteristic of this sol is
(1) Coagulation will occur near anode in
electrophoresis.
(2) The level of water will increase in cathode
compartment during electro- osmosis.
(3) The coagulation power of electrolytes for
this sol is in the order :
3 4 3 4A C MgSO K PO
(4) Basic dye like methylene blue will result
mutual coagulation.
31. TK 224 ml 0.1M KOH
(aq.) 50 ml 0.1M H2SO
4 (aq.)
neut
H = 13.7 kcal / eq.
= 1 cal/gm–K
= 1 gm/ml
(1) 0.5 K (2) 1K
(3) 2K (4) 0.25
32. Al(OH)3 HCl(aq)
(1)
(2)
(3)
3 4 3 4A C MgSO K PO
(4)
0000CT10311500418/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
33. Calculate the mass of anhydrous oxalic
acid, which can be oxidised to CO2 (g) by
100 ml of a MnO-4 solution, 10 ml of which
is capable of oxidising 50 ml of 1N I– to I2.
(Consider acidic medium for both reaciton)
(1) 45 gm (2) 22.5 gm
(3) 30 gm (4) 12.25 gm
34. Sulphuric acid leaching is involved in
hydrometallurgy of
(1) low grade gold ore
(2) high grade copper ore
(3) low grade copper ore
(4) low grade aluminum ore
35. Which oxy acid/salt can convert AgNO3 aq.
to Ag.
(1) H3PO
4(2) H
3PO
2
(3) CuSO4 solution (4) conc. HNO
3
36. When finely powdered iron react with HCl
solution it produce
(1) ferric chloride + H2
(2) ferrous chloride + H2
(3) ferrous chloride + ferric chloride + H2
(4) Fe does not react with HCl solution
33.
100 ml MnO-4 CO2 (g)
MnO-4
10 ml, 50 ml 1N I– I2
(1) 45 gm (2) 22.5 gm
(3) 30 gm (4) 12.25 gm
34.
(1)
(2)
(3)
(4)
35. AgNO3 aq.
Ag
(1) H
3PO
4(2) H
3PO
2
(3) CuSO4 (4) HNO
3
36. HCl
(1) + H2
(2) + H2
(3) + + H2
(4) Fe, HCl
19/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
37. CH3 CH CH2
CH3
CH2 CH3
Number of monochlorinated product when
following compound undergo reaction with
Cl2/hv is -
(1) 10 (2) 15
(3) 8 (4) 20
38. Which of the following is a pair of Enantiomer
(1)HCH3
Me
CH3H
Me
HCH3
Me
Me
CH3 H
(2) OHH
Me
COOH
HHO
COOH
Me
(3)OH
HO H
COOH
COOH
H
OH
HO H
COOH
COOH
H
(4) OHH
COOH
COOH
H
HO
H
COOH
COOH
H
OHOH
37. CH3 CH CH2
CH3
CH2 CH3
Cl2/hv
(1) 10 (2) 15
(3) 8 (4) 20
38.
(1)HCH3
Me
CH3H
Me
HCH3
Me
Me
CH3 H
(2) OHH
Me
COOH
HHO
COOH
Me
(3)OH
HO H
COOH
COOH
H
OH
HO H
COOH
COOH
H
(4) OHH
COOH
COOH
H
HO
H
COOH
COOH
H
OHOH
0000CT10311500420/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
39. The compound which is least stable among
following -
(1) (2)
(3)
O
(4)
40. Which of the following is more soluble in water
(1) MnS (Ksp = 8 × 10-37 M2)
(2) ZnS (Ksp = 7 × 10–16 M2)
(3) Bi2S3 (Ksp = 1×10-72 M5)
(4) Ag3 (PO4) (Ksp = 1.8 × 10-18 M4)
41. At 273 K temp and 9 atm pressure, the
compressibility for a gas is 0.9. The volume of
1 millimoles of gas at this temperature &
pressure is
(1) 2.24 litre (2) 0.020 ml
(3) 2.24 ml (4) 2.48 ml
42. An atomic orbital having equal number of radial
and angular nodes is
(1) 2s (2) 2p
(3) 3p (4) 3d
39. -
(1) (2)
(3)
O
(4)
40.
(1) MnS (Ksp = 8 × 10-37 M2)
(2) ZnS (Ksp = 7 × 10–16 M2)
(3) Bi2S3 (Ksp = 1×10-72 M5)
(4) Ag3 (PO4) (Ksp = 1.8 × 10-18 M4)
41. 273 K 9 atm
0.9 1
(1) 2.24 litre (2) 0.020 ml
(3) 2.24 ml (4) 2.48 ml
42.
(1) 2s (2) 2p
(3) 3p (4) 3d
21/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
43. X (Halogen atom)
[other then F]
= ns np nd
Above excited state electronic configuration
(before hybridisation) is NOT responsible for
(1) +3 oxidation state of X in interhalogen
compound of X
(2) bent 'T' shape geometery in interhalogen
compound to X
(3) bent shape geometry of XO2– anion of X
(4) lowest possible oxidiation number of X in
their compounds
44. Which of the following specie does NOT haved10 or d0 configuration of metal ion
(1) [Cu(NCCH3)
4]BF
4
(2) (NH4)
2[TiCl
6]
(3) MnO42–
(4) CrO42–
45. Which acid of boron is monobasic proton donoracid
(1) Ortho-boric acid (2)Tetrafluroboric acid
(3) Boron trifluoride (4) All of the above46. Compound which can consume more than one
mole of Ph–NHNH2 per mol is-
(1) O
(2) HO O
(3)
OH
O
(4)
OH
O
43. X (F )
[ ]
= ns np nd
(1) X X +3
(2) X (bent)'T'
(3) X XO2
–
(4) X
44.
d10 dº
(1) [Cu(NCCH3)
4]BF
4(2) (NH
4)
2[TiCl
6]
(3) MnO42– (4) CrO
42–
45.
(1) - (2)
(3) (4)
46. Ph–NHNH2
(1) O
(2) HO O
(3)
OH
O
(4)
OH
O
0000CT10311500422/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
47. Which of the following are incorrect statement
(1) Benzil benzylic acid rearrangement is not
an oxidation reduction reaction
(2) Michael addition follows 1,4-addition an
unsaturated carbonyl compound
(3) Zn is used as a reactant in Reformtasky
reaction
(4) Attacking nucleophile is generated from
aliphatic acid anhydride in perkin's reaction
48. Which one of the following represent correct
major product for the given reaction.
CH –CH –CH=CH3 2 2
CH3
HBrPeroxide
(1) Br
(2)
Br
(3) Br
(4) Br
49. In the parallel radioactive decay,1A B
2A C
the time when number of radioactive nuclei of
A, B & C becomes equal is
[Given 1 = n3 hr–1,
2 = n3 hr–1]
(1) 0.5 min (2) 30 min
(3) 60 min (4) 90 min
47. -(1)
(2) (Michael) 1,4-
(3) Zn,
(4)
48.
CH –CH –CH=CH3 2 2
CH3
HBrPeroxide
(1) Br
(2)
Br
(3) Br
(4) Br
49. 1A B
2A C
A, B C
[ 1 = n3 hr–1,
2 = n3 hr–1]
(1) 0.5 min (2) 30 min
(3) 60 min (4) 90 min
23/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
50. In between A and B layers in ABABAB.....
type packing of a metal, there is
(1) Only tetrahedral voids
(2) cubic void, tetrahedral void & octahedral
voids
(3) Only cubic voids
(4) Tetrahedral & octahedral voids.
51. The freezing point of a 0.1M formic acidaqueous solution is –0.2046ºC. Find
equilibrium constant of the reaction -
HCOO–(aq.)+H2O (l)
HCOOH(aq.)+OH–(aq.)
Given : Kf(H
2O) = 1.86 K-kg mole–1
Assume solution to be very dilute
(1) 1.1 × 10–3 M (2) 9 × 10–12 M
(3) 9 × 10–13 M (4) 1.1 × 10–11 M
52. If some (CH3)
3 SiCl is mixed with (CH
3)
2 SiCl
2
and hydrolysed followed by condensationpolymerisation then(1) It will increase the length of straight chain
polymer
(2) It will increase the branches of straight chainpolymer
(3) It does not affect the formation of chainpolymer
(4) It will block the end of straight chainpolymer
50. ABABAB..... A B
.................................
(1)
(2)
(3)
(4)
51. 0.1M –0.2046ºC
HCOO–(aq.)+H2O (l) HCOOH(aq.)+OH–(aq.)
Kf(H
2O) = 1.86 K-kg mole–1
(1) 1.1 × 10–3 M (2) 9 × 10–12 M
(3) 9 × 10–13 M (4) 1.1 × 10–11 M
52. (CH3)
3 SiCl (CH
3)
2 SiCl
2
(1)
(2)
(3)
(4)
(block)
0000CT10311500424/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
53. Which of the following have same bond order
& magnetic nature like dioxygen
(1) S2
(2) C2
(3) B2
(4) O3
54. Which ions of lanthanides have completelyfilled 'N' shell
(1) La3+, Ce+4 (2) Lu3+, Yb2+
(3) Gd3+, Tb3+ (4) La3+, Lu3+
55. Product P3
in following reaction sequence :
NBS P1Mg
P2D.E.
CH –CH3 P3
O
H /+
(Majorproduct)
(1)
(2)
(3)
OH
(4)
56. Major product in following reaction sequence :
1. O3
2. H O2
Product
(1) HO OH
O O
(2) H OH
O O
(3) H H
O O
(4) HO OH
O O
53. (1) S
2(2) C
2(3) B
2(4) O
3
54. 'N'
(1) La3+, Ce+4 (2) Lu3+, Yb2+
(3) Gd3+, Tb3+ (4) La3+, Lu3+
55. P3
NBS P1Mg
P2D.E.
CH –CH3 P3
O
H /+
(Majorproduct)
(1) (2)
(3)
OH
(4)
56.
1. O3
2. H O2
(1) HO OH
O O
(2) H OH
O O
(3) H H
O O
(4) HO OH
O O
25/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
57. Which of the following is the correct oxidation
product of CH3–CH=CH–CH
3 by H/KMnO
4
(1) CH3–CH
3(2) CH
3–CH
2–OH
(3) CH3–CHO (4) CH
3–COOH
58. 0.1M HNO3(aq) solution is being titrated with
0.05M NH4OH(aq.) The correct plot for the
titration is
(1)
Vol of NH OH(ml)4
cond
ucta
nce
ofso
luti
on
(2)
Vol of NH OH(ml)4
cond
ucta
nce
ofso
luti
on
(3)
Vol of NH OH(ml)4
cond
ucta
nce
ofso
luti
on
(4)
Vol of NH OH(ml)4
cond
ucta
nce
ofso
luti
on
57. CH3–CH=CH–CH
3 H/KMnO
4
(1) CH3–CH
3(2) CH
3–CH
2–OH
(3) CH3–CHO (4) CH
3–COOH
58. 0.1M HNO3(aq) 0.05M NH
4OH(aq.)
(1)
Vol of NH OH(ml)4
cond
ucta
nce
ofso
luti
on
(2)
Vol of NH OH(ml)4
cond
ucta
nce
ofso
luti
on
(3)
Vol of NH OH(ml)4
cond
ucta
nce
ofso
luti
on
(4)
Vol of NH OH(ml)4
cond
ucta
nce
ofso
luti
on
0000CT10311500426/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
59. Copper is in metallic form in
(1) Schweizer's salt
(2) Bordeaux mixture
(3) German silver
(4) Chalcopyrites
60.
OH
+ CHCl3 + NaOH
O Na+–
CHO
The electrophile involved in the above reaction is
(1) Dichlorocarbene ( :CCl2)
(2) Trichloromethyl anion 3(C Cl )
(3) Formyl cation (CHO)
(4) Dichloromethyl cation 2(CHCl )
59.
(1) (Schweizer's)
(2)
(3)
(4)
60.
OH
+ CHCl3 + NaOH
O Na+–
CHO
(1) (:CCl2)
(2) 3(C Cl )
(3) (CHO)
(4) 2(CHCl )
27/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
PART C - MATHEMATICS
61. The image of line x 2 y 1 z
1 2 3
in the plane
2x + y + z = 5 is the line-
(1) x 2 y 1 z
11 1 2
(2) x 2 1 y z
11 1 2
(3) x 2 y 1 z
11 1 2
(4) x 2 1 y z
11 1 2
62. If a b 2c b c a 2c a b c
, then
is equal to-
(1) –1 (2) 1 (3) 2 (4) 3
63. The integral 2 1
x2 x
11 2x e dx
x
is equal
to-
(1) 2 1
xx2x 1 e C
(2) 2 1
xx2x 1 e C
(3) 2 1
xxxe C
(4) 2 1
xxx e C
(where C is integeration constant)
61. 2x + y + z = 5 x 2 y 1 z
1 2 3
-
(1) x 2 y 1 z
11 1 2
(2) x 2 1 y z
11 1 2
(3) x 2 y 1 z
11 1 2
(4) x 2 1 y z
11 1 2
62. a b 2c b c a 2c a b c
,
-
(1) –1 (2) 1 (3) 2 (4) 3
63. 2 1
x2 x
11 2x e dx
x
-
(1) 2 1
xx2x 1 e C
(2) 2 1
xx2x 1 e C
(3) 2 1
xxxe C
(4) 2 1
xxx e C
(C )
0000CT10311500428/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
64. The common tangent of Parabola y2 = 4x and
Hyperbola 2 2x y
14 3 touches them at P and
Q respectively, then Q can be-
(1) (4,3) (2) (3,4)
(3) (–4,–3) (4) (4,–3)
65. Three positive numbers form an increasing GP.
If the first term is doubled and second term is
trebled, the new numbers are in AP. Then the
common ratio of the G.P. is-
(1) 3 7 (2) 3 7
(3) 2 (4) 7
66. A line L passing through (1, 1) intersect lines
L1 : 12x + 5y = 13 and L
2 : 12x + 5y = 65 at A
and B respectively. If AB = 5, then line L can
be -
(1) 16x – 33y + 17 = 0
(2) 8x + 9y – 17 = 0
(3) 16x + 63y – 79 = 0
(4) 56x – 33y – 33 = 0
64. y2 = 4x 2 2x y
14 3
P Q
Q -
(1) (4,3) (2) (3,4)
(3) (–4,–3) (4) (4,–3)
65.
-
(1) 3 7 (2) 3 7
(3) 2 (4) 7
66. (1, 1) L,
L1 : 12x + 5y = 13 L
2 : 12x + 5y = 65
A B AB = 5
L -
(1) 16x – 33y + 17 = 0
(2) 8x + 9y – 17 = 0
(3) 16x + 63y – 79 = 0
(4) 56x – 33y – 33 = 0
29/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
67. Let
3 0 5 6 2
2 5 0 1 y
A 5 2 x 8 0
0 3 2 3 5
4 7 2 1 9
is a 5 × 5
square matrix.
Each row and column of matrix A has a value
assigned to it. Every element is the sum of its
row and column values. For example –9 is the
sum of the value assigned to 5th
row and 5th
column. Then the value of x + y is-
(1) –7 (2) 0 (3) 7 (4) 14
68. Let matrix 4 1
B9 2
, then which of the
following will not be an element of matrix B100 -
(1) 300 (2) 301 (3) –299 (4) 100
69. 20 soldiers are standing in a row and theircaptain want to send 7 out of them for a mission.In how many ways can captain select them suchthat at least one soldier find the soldier next tohim is also selected.
(1) 20C7
(2) 14C7
(3) 20C7 – 13C
7(4) 20C
7 – 14C
7
67.
3 0 5 6 2
2 5 0 1 y
A 5 2 x 8 0
0 3 2 3 5
4 7 2 1 9
, 5 × 5
A
–9, 5
5x + y
-
(1) –7 (2) 0 (3) 7 (4) 14
68. 4 1
B9 2
B100-
(1) 300 (2) 301 (3) –299 (4) 100
69. 20 7 (1) 20C
7(2) 14C
7
(3) 20C7
– 13C7
(4) 20C7
– 14C7
0000CT10311500430/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
70.3 2
x 2
60 x 4lim
sin(x 2)
(1) 1
4(2) 0
(3) 1
12(4) Does not exist
71./ 2
0
sin 4x cot xdx
is equal to-
(1) 2
(2) 0 (3)
2
(4)
72. If ƒ(x) = –x3 – 3x
2 – 2x + a, a R, then the real
values of x satisfying ƒ(x2 + 1) > ƒ(2x2 + 2x + 3)
will be-
(1) (–) (2) (0,)
(3) (–,0) (4)
73. If is a solution of [cot–1x] < [tan–1x], then
[cot–1] + [tan–1] is (where [.] greatest integer
function)
(1) 0 (2) 1
(3) 2 (4) greater than 2
74. The value of
2x4
2x 00
n 1 4tlim cosec x dt
t 1
is
(1) 1 (2) 2 (3) 3 (4) 4
70.3 2
x 2
60 x 4lim
sin(x 2)
-
(1) 1
4(2) 0
(3) 1
12(4)
71./ 2
0
sin 4x cot xdx
-
(1) 2
(2) 0 (3)
2
(4)
72. ƒ(x) = –x3 – 3x2 – 2x + a, a R
ƒ(x2 + 1) > ƒ(2x2 + 2x + 3) x
-(1) (–) (2) (0,)
(3) (–,0) (4)
73. [cot–1x] < [tan–1x] [cot–1] + [tan–1]
([.] )
(1) 0 (2) 1
(3) 2 (4) 2
74.
2x4
2x 00
n 1 4tlim cosec x dt
t 1
-
(1) 1 (2) 2 (3) 3 (4) 4
31/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
75. A box contains 20 identical balls of which 5
are white and 15 black. The balls are drawn at
random from the box one at a time with
replacement. The probability that a white ball
is drawn for the 3rd time on the 6th draw is-
(1) 1
2(2)
135
2048
(3) 135
1024(4)
27
4096
76. Let a = 8 and b = 39 and we define a sequence
{un} as follows
u1 = b,
n nn 1
n
1u ; if u ismultiple of 3
u 3
u a ; otherwise
then u500 – u300 – u400 is equal to
(1) 1 (2) 3 (3) 5 (4) 7
77. Let a,b,c R0 and each of the quadratic
equations in x, x2 + 2(a2 + b2)x + (b2 + c2)2 = 0
and x2 + 2(b
2 +c
2)x + (c
2 + a
2)2 = 0 has two
distinct real roots. Then equation
x2 + 2(c2 + a2)x + (a2 + b2)2 = 0 has-
(1) Two distinct positive real roots
(2) Two equal real roots
(3) Two distinct negative real roots
(4) No real roots
75. 20 5
15
-
(1) 1
2(2)
135
2048
(3) 135
1024(4)
27
4096
76. a = 8 b = 39 {un} :
u1 = b,
n nn 1
n
1u ; u ,3
u 3
u a ;
u500 – u300 – u400
(1) 1 (2) 3 (3) 5 (4) 7
77. a,b,c R0 x
x2 + 2(a2 + b2)x + (b2 + c2)2 = 0
x2 + 2(b2 + c2)x + (c2 + a2)2 = 0
x2+ 2(c2+ a2)x + (a2 + b2)2 = 0
-
(1)
(2)
(3)
(4)
0000CT10311500432/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
78. The ellipse with equation 2 2x y
19 4
is rotated
couterclockwise about origin by 45°.
Then resulting equation can be written as
ax2 + bxy + cy
2 = 72, then (a + b + c) is
(1) 6 (2) 16 (3) 26 (4) 36
79. Consider a set 'A' of vectors ˆ ˆ ˆxi yj zk where
x,y,z {1,2,3}. Three vectors are selected atrandom from set A. If the probability that theyare mutually perpendicular is p, then-
(1) 1
p27
(2) 1 1
p ,27 9
(3) 1 1
p ,9 3
(4) 1
p ,13
80. The statement ~p (r p) is -
(1) equivalent to negation of p r
(2) equivalent to ~ p r
(3) a tautology
(4) a fallacy
81. Let S = {(x, y)|siny = sinx, x, y R}, then S is
(1) not transitive
(2) equivalence
(3) transitive but not reflexive
(4) partial order relation
78. 2 2x y
19 4
,
45°
ax2 + bxy + cy2 = 72 (a + b + c)
(1) 6 (2) 16 (3) 26 (4) 36
79. ˆ ˆ ˆxi yj zk 'A',
x,y,z {1,2,3} A
p -
(1) 1
p27
(2) 1 1
p ,27 9
(3) 1 1
p ,9 3
(4) 1
p ,13
80. ~p (r p) -
(1) p r
(2) ~ p r
(3)
(4)
81. S = {(x,y)|siny = sinx, x,y R} S
(1)
(2)
(3)
(4)
33/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
82. Let 2 is variance of following frequency
distribution
i
i
x 1 2 3 4 5 6 7 8 9
ƒ 1 0 1 7 9 4 1 1 1
then 2 is equal to-
(1) 2.4 (2) 2.5 (3) 2.6 (4) 2.7
83. Let 1 be a complex cube root of unity.
If 2 22 n 2 2 n 2(4 5 6 ) (6 5 4 )
22 n 2(5 6 4 ) 0 , then n can be -
(1) 133 (2) 113 (3) 111 (4) 331
84. The coefficient of x3 in the expansion of
(1 + 2x – 3x2)10 is -
(1) less than 200
(2) less than 400 but greater than 200
(3) 400
(4) 420
85. A curve y = ƒ(x) which passes through (4,0)
sat isfy the differential equation
xdy + 2ydx = x(x – 3)dx.
The area bounded by y = ƒ(x)
and line y = x (in square unit) is-
(1) 32 (2) 64
3(3)
128
3(4) 64
82.
i
i
x 1 2 3 4 5 6 7 8 9
ƒ 1 0 1 7 9 4 1 1 1
2 2 -
(1) 2.4 (2) 2.5 (3) 2.6 (4) 2.7
83. 1
2 22 n 2 2 n 2(4 5 6 ) (6 5 4 )
22 n 2(5 6 4 ) 0 n -
(1) 133 (2) 113 (3) 111 (4) 331
84. (1 + 2x – 3x2)10 x3-
(1) 200
(2) 400 200
(3) 400
(4) 420
85. (4,0) y = ƒ(x),
xdy + 2ydx = x(x – 3)dx
y = ƒ(x) y = x
() -
(1) 32 (2) 64
3(3)
128
3(4) 64
0000CT10311500434/35
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
86. Let x x 1 2
2 3
sin x(2 2 ) tan (x x 1)ƒ(x)
(7x 3x 1)
,
then ƒ'(0) is equal to -
(1) 0 (2)
(3) (4) does not exist
87. If ƒ(x) is a different iable function and
ƒ(1) = sin1, ƒ(2) = sin4, ƒ(3) = sin9, then the
minimum number of distinct solutions of
equation ƒ'(x) = 2xcosx2 in (1, 3) is -
(1) 1 (2) 2 (3) 3 (4) 4
88. Let z1, z
2, z
3 are three complex number
satisfying |z| = 1 and 4z3 = 3(z
1 + z
2),
then |z1 – z
2| is equal to -
(1) 2
3(2)
5
3
(3) 3
2(4)
2 5
3
89. Radius of largest circle with center (0, 1) which
can be inscribed in the ellipse 4x2 + y2 = 4 is -
(1) 2
3(2)
2
3(3)
2
3(4)
1
3
90. Let ƒ(x) is a cubic polynomial with real
coefficients, x R such that ƒ"(3) = 0, ƒ'(5) = 0.
If ƒ(3) = 1 and ƒ(5) = –3, then ƒ(1) is equal to-
(1) 2 (2) 3 (3) 5 (4) 6
86. x x 1 2
2 3
sin x(2 2 ) tan (x x 1)ƒ(x)
(7x 3x 1)
ƒ'(0) -
(1) 0 (2)
(3) (4)
87. ƒ(x) ƒ(1) = sin1,
ƒ(2) = sin4, ƒ(3) = sin9 (1, 3)
ƒ'(x) = 2xcosx2
-
(1) 1 (2) 2 (3) 3 (4) 4
88. z1, z
2, z
3 |z| = 1
4z3 = 3(z
1 + z
2) |z
1 – z
2|
-
(1) 2
3(2)
5
3
(3) 3
2(4)
2 5
3
89. 4x2 + y2 = 4 (0, 1)
-
(1) 2
3(2)
2
3(3)
2
3(4)
1
3
90. ƒ(x) x R ƒ"(3) = 0, ƒ'(5) = 0 ƒ(3) = 1 ƒ(5) = –3 ƒ(1) -(1) 2 (2) 3 (3) 5 (4) 6
35/350000CT103115004
SPACE FOR ROUGH WORK /
ALL INDIA OPEN TEST/JEE (Main)/20-03-2016
SPACE FOR ROUGH WORK /