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JEE-ADVANCED PAPER-II
Time: 2.00 PM to 5.00 PM IMPORTANT INSTRUCTIONS Max Marks: 180
PHYSICS: Section Question Type +Ve
Marks - Ve
Marks No.of
Qs Total marks
Sec – I(Q.N : 1 – 10) Questions with Single Correct Choice 3 -1 10 30
Sec – II(Q.N : 11 – 16) Questions with Comprehension Type
(3 Comprehensions – 2 +2+2 = 6Q) 3 -1 6 18
Sec – III(Q.N : 17 – 20) Matrix Matching Type 3 -1 4 12
Total 20 60
CHEMISTRY:
Section Question Type +Ve Marks
- Ve Marks
No.of Qs
Total marks
Sec – I(Q.N : 21 – 30) Questions with Single Correct Choice 3 -1 10 30
Sec – II(Q.N : 31 – 36) Questions with Comprehension Type (3 Comprehensions – 2 +2+2 = 6Q) 3 -1 6 18
Sec – III(Q.N : 37 – 40) Matrix Matching Type 3 -1 4 12
Total 20 60
MATHEMATICS:
Section Question Type +Ve
Marks
- Ve
Marks
No.of
Qs
Total
marks
Sec – I(Q.N : 41 – 50) Questions with Single Correct Choice 3 -1 10 30
Sec – II(Q.N : 51 – 56) Questions with Comprehension Type
(3 Comprehensions – 2 +2+2 = 6Q) 3 -1 6 18
Sec – III(Q.N : 57 – 60) Matrix Matching Type 3 -1 4 12
Total 20 60
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PART-I_PHYSICS Max Marks : 60 Section-1
(Only one Option correct Type) This section contains 10 Multiple Choice questions. Each Question has Four choices (A), (B), (C) and (D). Out of Which Only One is correct
1. The length of a cylinder is measured with a metre rod having least count 0.1cm. Its
diameter is measured with vernier calipers having least count 0.01cm. Given that
length is 5.0 cm and radius is 2.0cm. The percentage error in the calculated value of
the volume will be
A) 1% B) 2% C) 3% D) 4%
2. A car is fitted with a device which transmits sound 60 times per minute. There is no wind
and speed of sound in still air is 345 m/s. If you hear the sound 68 times per minute,
when you are moving towards the car with a speed of 12m/s , the speed of the car must
be
A) 20.0 m/s towards you B) 30.0 m/s towards you
C)10.0 m/s away from you D) 10.0 m/s towards you
3. In a regular polygon with11 sides each cornet is at a distance ‘a’ from centre. Identical
charges are placed at 10 corners. At the centre the intensity is E and the potential is V.
The ratio of VE
has magnitude
A) 11a B) 10a
C) 1011
a D) 10a
4. A micrometer screw gauge with pitch of 0.5cm and 50 divisions on circular scale is used
to measure the diameter of a thin wire. Initially when the gap is closed the line of fourth
division coincides with the reference line. Three reading shows 46th, 48th and 44th
division coinciding with the reference line which is beyond 0.5 mm of the main scale.
The (best) measured value is
A) 0.46 mm B) 0.94 mm C) 0.92 mm D) 1.00 mm
5. How much heat must be supplied to convert 1 kg ice at 010 C to steam at 0100 C ( Take
specific heat of ice 00.5 /iS cal gm C )
A) 725 kcal B) 720 kcal C) 730 kcal D) 735 kcal
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6. The diagram shows a small bead carrying charge q. The bead can freely move on smooth
fixed ring placed on a smooth horizontal plane. Potential due to Q at P is V. If bead is
given a very small velocity tangential from Q. Velocity of bead when it reaches at P .
A) 6qVm
B) qVm
C) 3qVm
D) Zero
7. An electron (mass m, charge e) orbiting around a nucleus has angular momentum L.
the magnetic field produced by the electron at the centre of the orbit can be expressed
as
A) 30 / 8B e mr L B) 3
0 / 4B e mr L
C) 30 /B e mr L D) 3
0/ 4B e mr L
8. A bowl of water, initially at 010 C is brought to boiling after being 9 minutes at the
stove top. If it remains on the stove top, how long will it further take for all the water
to evaporate? Neglect heat losses and the heat capacity of the bowl.
A) 18 min B) 36 min C) 54 min D) 15 min
9. A skier plans to ski a hemisphere of radius R . He starts from rest a curve surface of
height (R/4) . The angle at which he leaves the hemisphere is
A) 1 2cos3
B) 1 5cos3
C) 1 5cos6
D) 1 1cos3
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10. A cylinder of mass 2kg is rolling up the place without slipping instantaneous velocity
of centre of gravity at point A is 110ms . The distance traveled by the cylinder before
coming to rest in metre is
A) 15 m B) 304
m C) 306
m D) 156
m
Section-2 (Paragraph Type)
This section contains 3 paragraphs each describing theory, experiment, data etc. Six questions relate
to three paragraphs with two questions on each paragraph. Each question pertaining to a particular
paragraph should have only one correct answer among the four choices A, B, C and D. Paragraph- I For Question No.s 11 to 12 :
Standing transverse waves can be set up in a string clamped at both ends and under
tension. For Example an arrangement such as one shown in the figure can set up such
standing waves. The weight W provides the necessary tension. In one such arrangement a
wire of length L , is in resonance in fundamental mode with a tuning fork.
11. If the weight is immersed in water and the length L is altered to L1 , there is again
resonance with the same tuning fork in fundamental mode. What can you say about L
and 1L ?
A) 1L L B) 1L L C) 1L L D) Data Insufficient
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12. Now the weight is immersed in a liquid and for length L , the wire in resonance with
the same tuning fork but in the first overtone. What is the ratio of densities of block
and liquid?
A) 4/3 B) 2/3 C) 5/3 D) 3/4
Paragraph- II For Question No.s 13 to 14 : A small disc and a thin uniform rod of length L , whose mass is times greater than
the mass of the disc, lie on a smooth horizontal plane. The disc is set in motion , in horizontal direction and perpendicular to the rod with velocity V , after which it elastically collides with the end of the rod.
L
m V
13. The velocity of the disc after collision is
A) 44
V
B) V C) 44
V
D) 2
V
14. Angular velocity of the rod after the collision is
A) 2VL
B) VL C) 4
4V
D)
12
4V
L
Paragraph -III For Question No.s 15 to 16:
A non-conducting disc of radius r and uniform positive surface charge density is placed on the ground, with its axis vertical. A Particle of mass m and charge q is dropped along the axis of the disc from a height h with zero initial velocity. The ratio of charge to
mass of the particle is given by 04 gqm
15. What is the value of h if the particle just reaches the disc?
A) 43r B) 2r C) 3
2r D) 2
5r
16. At what position z (from the ground) will the particle attain equilibrium position?
A) 3rz B)
3rz C)
2rz D)
2rz
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Section-3 (Matching List Type)
This section contains four questions, each having two matching lists (List-1 & List-II). The options for the correct match are provided as (A), (B),(C) and (D) out of which ONLY ONE is correct. 17. In the first column 1 2,m m and M and situation is indicated. Match the description in
column-II
List-I List-II
P) M=3 kg, 1 6m kg , 2 4m kg .
System is released from rest 1) Friction 1m is static
Q) M=3 kg, 1 2m kg , 2 6m kg .
System is released from rest 2) Friction 2m is static
R) M=3 kg, 1 7m kg , 2 3m kg .
System is released from rest 3) Friction 1m is kinetic
S) M=3 kg, 1 1m kg , 2 3m kg .
System is released from rest 4) Friction 2m is kinetic
P Q R S
A) 2,3 1,2 1,4 1,4
B) 1,2 2,3 1,4 2,3
C) 2,3 1,2 2,3 1,4
D) 1,2 2,3 2,4 1,2
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18. Match List(I) with List (II) and select the correct answer using given below the Lists .
List I List II
P)
1) 1 2
1 2
2m k k
Tk k
Q)
2) 1 2
2 mTk k
R)
3) 2 mTk
S)
4) 22mTk
Codes: P Q R S A) 3 2 1 4 B) 4 3 2 1 C) 2 1 4 3 D) 1 2 3 4
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19. Column-I shows certain situations and Column-II shows information about forces List-I List-II
P) Situation
Front view of a car rounding a curve with constant speed
1) 1 2 0F F
Q)
Passengers in a rotor not sliding relative to rotor wall cylindrical rotor is rotating with constant angular velocity about its symmetry axis
2) 1 2 3F F F
is centripetal force
R)
Particle kept on rough surface of a bowl , no relative motion of particle in bowl , bowl has constant angular velocity
3) 1F
is static friction
S)
Car parked on a banker road with no sideways skidding
4) 1 2 3 0F F F
Codes: P Q R S P Q R S A) 2,3 1,2,3 2,3 3,4 B) 1,2,3 2,3 2,3 3,4 C) 1,2 1,2 1,2,3 4 D) 1,2,3 1,2 2,3 2,3
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20. Match List (1) with List(II) and select the correct answer using codes given below the
lists. A proton and an -particle have their kinetic energies in ratio 1:8
List I List II
P) Ratio of their masses 1) 1/ 2
Q) Ratio of their velocities 2) (1/4)
R) Ratio of their charges 3) 1/2
S) Ratio of their De-Broglie
wavelength 4) 4 2
Codes :
P Q R S P Q R S
A) 2 4 3 1 B) 3 4 2 1
C) 3 1 2 4 D) 2 1 3 4
PART-II_CHEMISTRY Max Marks : 60
Section-1 (One or more options correct type)
This section contains 10 Multiple Choice questions. Each Question has Four choices (A), (B), (C) and (D). Out of Which Only One is correct
21. Phosphine gas is not prepared by
A) 3 2 .Ca P dil HCl B) 4 solnPH I KOH
C) Red phosphorus + NaOH soln D) 4 solnP NaOH
22. Given : 2 4 22N O g NO g
Degree of dissociation of 2 4N O
d = Vapour density of equilibrium mixture. Which is correct graph?
A)
1/ d B)
1/ d C)
1/ d D)
1/ d
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23. Potential difference of electrical double layer formed in a colloidal solution is called.
A) Zeta potential B) Brownian potential C) Dorn potential D) Nernst potential
24.
OH
||
3 32 2Oxidation
O
HNO CH C ClHNO HNi
products (x) is A) Aspirin B) Paracetamol C) Phenophthaline D) Phenylalanine
25. Which of the following co-ordination compound has three stereoisomers
A) 2 3Cd gly H O NH
B) 2 2 2Pt Br H O
C) 3
3Cr en
D) 2 2
Co Br NO en
26. What is the approximate average number of glucose units in an aqueous solution of
10 g/L of starch has an osmotic pressure 35 10 atm at 25 C ?
A) 300 units B) 100 units C) 450 units D) 1000 units
27. For the reaction A B following graph is given:
B
time The correct graph for the given reaction is
A)
0.5t
0A B)
rate
A C) 0A
0.5t
D) t
A
28. 5PCl g Ag x y
Where product x is water insoluble but y reacts with water, then product x is insoluble
in solution of :
A) KCN B) 2 2 3Na S O C) 3.dil HNO D) 3NH
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29. Which of the following co-ordination ion/compound does not exhibit structural isomerism.
A) 2 44PtBrCl H O SO B) 3 45
CoBr NH Cd CN
C) 2 4Co ox H O Br D) 23 3
Ir ONO H O
30. The energy of separation of an electron moving in He is 13.6 eV. Which is correct
statement?
A) kinetic energy associated with electron is 13.6 eV
B) Velocity associated with electron is 6 11.09 10 secm
C) orbit angular momentum of electron is 2h
D) none of these
Section-2 (Paragraph Type)
This section contains 3 paragraphs each describing theory, experiment, data etc. Six questions relate
to three paragraphs with two questions on each paragraph. Each question pertaining to a particular
paragraph should have only one correct answer among the four choices A, B, C and D.
Paragraph For Questions 31 & 32
XWatersoluble
salt
Excess KI Y Z Coloured(solution)
2 2 3 Colourless productsNa S O
whiteY
31. Salt ‘X’ is
A) 2 4 3Fe SO B) 4 2.5CuSO H O C) 2KNO D) 3 2
Hg NO
32. Salt ‘X’ does not produce precipitate with solution of
A) 4 6K Fe CN B) 2BaCl C)NaOH D) Excess 4NH OH
Paragraph For Questions 33 & 34
500 ml 0.2M XOH 710bK and 500 ml 60.16 10bM YOH K are mixed together.
Given: log 3 = 0.48 33. pH of final solution is A) 3.52 B) 6.52 C) 10.48 D) 7.48 34. The degree of dissociation of XOH in final solution is
A) 310
3
B) 410
3
C)
4102
D) 71.8 10
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Paragraph For Questions 35 & 36
The neutralization Equivalent is Eq.wt geq
of an acid as determined by titration with
standard NaOH . The number of ionisable H of an acid is the number of equivalents
per mole and is equal to mwNE
.
(Gemdicarboxyllic acids on heating loses 2CO 35. Which carboxylic acid (A) , NE=52g/eq , loses 2CO when heated to given an acid
, 60 /B NE g eq . Where mass
molecularNENumber of ionisable H
)
A) 2 32;A CH COOH B CH COOH
B) A 2CH COOH
2CH COOH3;B CH COOH
C) A
HOOC COOH
; B
OO
COOH
D) 3A CH CH COOH
COOH3 2; B CH CH COOH
36. Which of the following acid have higher pKa ?
A)
COOH
2NO
3CH B)
COOH
2NO
3CH C)
COOH
2NO
3CH D)
COOH
2NO
3CH
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Section-3
(Matching List Type) This section contains four questions, each having two matching lists (List-1 & List-II). The options for
the correct match are provided as (A), (B),(C) and (D) out of which ONLY ONE is correct.
37.
List-I (Conc.cell)
List-II (Condition for working of cell)
P) 2 2, | || | ,Pt H g H pH x H pH y H g Pt 1bar 1bar
1) y x
Q) 2 2, | | ,Pt H g HCl aq H g Pt
1P2P
2) 1 2P P
R) 1bar 1bar
2 2, | || | ,Pt Cl g Cl y Cl x Cl g Pt
3) x y
S) 1P
2P 2 2, | || ,Pt Cl g KCl aq Cl g Pt
4) 2 1P P
Codes :
P Q R S A) 2 3 1 4 B) 3 2 4 1 C) 3 2 1 4 D) 2 3 4 1
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38.
List--I List-II
P)
CHO
2CH OH
H OH
HOHH
HOD Xylose
1) On oxidation give meso
Q) D-Ribose
CHO
2CH OH
H OHH
OHHOH
2) Give the same osazone as D-arabinose
R) HO
CHO
2CH OH
HH OHD-Threose
3) Smallest aldose able to form cyclic hemiacetal
S) D-galactose
CHO
2CH OH
H OH
H
OHH
HOHHO
4) C-4 epimer of D-glucose
Codes : P Q R S A) 3 2 1 4 B) 4 3 2 1 C) 2 1 4 3 D) 1 2 3 4
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39.
List—I (Reactions )
List-II (One of the product)
P) ....3 2 32Co NO Al O 1) 3NH
Q) ....2coolNO g NO g 2) 2NO g
R) ....4 2 72NH Cr O s 3) 2N g
S) 4 4 4Na NH HPO CuSO 4) Coloured substance
Codes :
P Q R S A) 4 2 3 1 B) 4 1 3 2 C) 2 3 1 4 D) 2 4 3 1
40.
List--I List-II P) Pyruvic acid 1) 2,4 DNP Test
Q) Aspirine 2) Decolourises 2 4/Br CCl
R) Acrylic acid 3) Evolve 2H g with Na metal
S) Benzyl alcohol 4) Give 2CO g with 3NaHCO
Codes :
P Q R S A) 3 2 1 4 B) 4 3 2 1 C) 1 4 2 3 D) 1 2 3 4
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PART-III_MATHEMATICS Max Marks : 60 Section-1
(Only one Option correct Type) This section contains 10 Multiple Choice questions. Each Question has Four choices (A), (B), (C) and
(D). Out of Which Only One is correct
41. Let 1 1 32 3 2
x y z and 1
1 5 1x k y z
be two lines intersect at , , then
k equals
A) 1 B)4 C)6 D)9
42. Let 1, 2,3, 4,5,6,7,8A be a set Let :f A A be a function such that
, ,f X X X A f X is even when ever X is even and f X is odd when ever X is
odd. Then total number of on-to functions satisfying these conditions will be
A)36 B) 49 C) 64 D) 81
43. Let A be square matrix of order n and nI be an identity matrix of order . 0n A and
3 0A . Let 212 nM A A I and 21
2 nN A A I be two matrices . Then which of the
following must be correct ?
A) 1M N B) det 0M C) TM N D) det 1MN
44.
1
1
3 23 3 3 sin 1lim
30 sin .sin 2
x
x
t t t t dt
x x x x
equals :
A) 110
B) 15
C) 25
D) None of these
45. Let ,Z x iy x y R be a complex number such that 2 3 2Z i and 5 3Z i
then Z is equal to
A) 31 B) 615
C) 315
D) 5
46. Let
24 42 33 31 1 1 1
n kSn k k k k
then 2 / 3
SnLimn n
equals
A) 0 B) 14
C) 12
D) 1
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47. 2
21
11
xln dxx x
equals
A) 0 B)1 C) 2 D) None of these
48. The line 1y mx cuts the parabola 2 4y ax at two points P and Q if equation of circle
with one diameter PQ is 2 2 18 4 5 0x y x y then a m equals
A) 0 B) 3 C) 5 D) None of these
49. Let A,B,C and D be four points in space satisfying 4 4 4 1 4x y z xyz then the volume
of tetrahedron A BCD is
A) 16 B) 163
C) 83
D) None of these
50. Let 0,0 be the focus of a parabola which is passing through the point 1,1 . If the line
2 3x y is tangent to the parabola at 1,1 then the length of latus-rectum of the
parabola is
A) 36 25
B) 18 25
C) 9 25
D) 9 2
Section-2 (Paragraph Type)
This section contains 3 paragraphs each describing theory, experiment, data etc. Six questions relate
to three paragraphs with two questions on each paragraph. Each question pertaining to a particular
paragraph should have only one correct answer among the four choices A, B, C and D.
Paragraph for Questions 51 & 52
Let ,a b and c be three non-negative numbers such that
3 2
3 2
3 2
a a a bb b b cc c c a
51. Number of possible triplets of type , ,a b c is /are A) 0 B)1 C)2 D) More than 2
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52. If at least one among ,a b and c is different from other two then number of possible
triples of type , ,a b c is /are
A)0 B)1 C)2 D) More than 2
Paragraph For Questions 53 & 54
In ,ABC AB AC . Points D and E lie on BC such that BD DC and BE CE .
tan EAC , tan EAD and tan EAB are in G.P.
53. EAD is equal to
A) 6 B)
4 C)
3 D) 1 3tan
4
54. If 10AE then AD equals
A) 5 2 B) 5 3 C) 5 D) 6
Paragraph For Questions 55 & 56
Let y f x be a polynomial such that 5
2
, 0x
x
f x dx ax b x R a
and ,a b R
0 3f and 1 5f
55. The function y f x is
A) one-one and on-to B) on-to but not one-one
C) one-one but on-to D) Neither one-one nor on-to
56. Area bounded by the curve y f x , between the ordinates 0x and 2x and the x-
axis is
A) 3 B) 7 C) 9 D) 10
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Section-3 (Matching List Type)
This section contains four questions, each having two matching lists (List-1 & List-II). The options for the correct match are provided as (A), (B),(C) and (D) out of which ONLY ONE is correct. 57.
List--I List-II P) Number of real roots of
2013 2014 2015x x x 1) 1
Q) If 4 3 210 26 10 1 0x x x x has n
distinct real roots than n 2) 2
R) Let a,b,c and d be four positive real
numbers such that 1abcd . If n is
the least value of
1 1 1 1a b c d then
positive integral factors of n which
are not a perfect square are
3) 3
S) 2
20
sin cos sinx
xLim
x
equals
. GIF
4) 4
Codes :
P Q R S
A) 3 2 1 4
B) 4 3 2 1
C) 2 1 4 3
D) 1 4 2 3
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58. Let 2 10y x be a parabola, From 15 ,02
three normals are drawn to the parabola . ,A B
and C are co-normal points .
List--I List-II
P) Area of ABC is 1) 252
Q) Radius of circumcircle of ABC 2) 254
R) Centroid of ABC 3) 5 ,03
S) Circumcentre of ABC 4) 25 ,04
Codes: P Q R S A) 3 2 1 4 B) 4 3 2 1 C) 2 1 4 3 D) 1 2 3 4
59. Let ,a b and c be three distinct real numbers such that 3 3 32 2 2 3a b c
a b c
List--I List-II P) a b c 1) 6 Q) 3 3 3a b c 2) 12 R) ab bc ca 3) 0 S) 2 2 22 a b c 4) -3
Codes: P Q R S A) 3 1 4 2 B) 4 3 2 1 C) 2 1 4 3 D) 1 2 3 4
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60.
List--I List-II
P) 0
2
1 1 2 3x x x x x dx
is equal to 1) 1
Q) If 5 4 3 2 0x ax bx cx dx e has exactly 3 distinct
real root, then minimum number of points where
5 4 3 2f x x ax bx cx dx e is not
differentiable is , , , ,a b c d e R
2) 0
R) 8 41
8 41 1x
Limx x
equals 3) 3
S) If the roots of the equation 4 3 2 60 0x ax bx cx are natural numbers other
than 1. If 61 2na b c then n equals
, ,a b c R
4) 2
Codes:
P Q R S
A) 3 2 1 4
B) 4 3 2 1
C) 2 1 4 3
D) 1 2 3 4
VARSITY EDUCATION MANAGEMENT LIMITED
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Page 2
Solutions
PHYSICS
Single correct choice Type 1. (C) Sol: 5 0.1l cm 2 0.01r cm 2V r l
% error in volume= 2 2 0.01 0.1100 100 3%2 5
r lr l
2. (B)
Sol: 00
0
,appV Vf fV V
assuming car moving towards us .
345 1268 60 30 /345 C
c
V m sV
3. (D) Sol: 2
10,kq kqE Va a
10V aE
4. (C) Sol: 0.5. 0.01
. . 50PitchL C mmC S D
Zero error is positive Reading . . . . . .X M S R C S R Zero Error L C
1 0.5 46 4 0.01 0.92X mm 2 0.5 48 4 0.01 0.94X mm 3 0.5 44 4 0.01 0.90X mm
Best reading= 0.92meanX mm 5. (A) Sol: 10 100total i f w vQ mS mL mS mL Putting 11 , 0.5, 1, 540, 80w V fm kg S S L L 6. (A) Sol: 21. . 0
4 4 2i i f fkQq kQqU K E U K E mv
a a
Given 64kQ qVV v
a m
7. (B) Sol: 0 .... 1
2iB
r
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Page 3
Where 2
e eiT
.
Also 2L I mr 2
Lmr
Putting values in (1) , 034
eB Lmr
8. (C) Sol: Let rate of heat supply = P Heat to boil 1Q P (9 min) = 100 10 90wmS m Heat to evaporate 2 540vQ Pt mL m
540 54min9 90t t
9. (C) Sol: At point of leaving contact
2 2 2 1 cos4Rv gh g R
And 2
cos 0mvMg NR
2 5cos cos
6vRg
10. (A) Sol:
/v r
V
Rest
hl
2 21 1
2 2MV I Mgh
2 2
22
1 sin2 2 2
MR vMV MglR
Putting 030 and 10 /v m s 15l m Section-II
Comprehension Type Paragraph for Questions No.s 11 to 12 11. (B) 12. (A) Sol: 3;
2 4 4new New bV T TV T F plVg
0T Vg
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Page 4
0
0
3 44 3
ll
Paragraph for Questions No.s 13 to 14 13. (C) 14. (D )
CM
2V
V1V
CM
Sol: i fL L about CM of rod
2
1 ...... 12 2 12L L MLmV mV
1 2 ...... 2i f mV mV mV
2
2 2 2 21 2
1 1 1 1 ...... 32 2 2 2 12i f
mLE E mV mV mV
Solving the equations
144
V V
and
124
VL
15. (A) 16. (B) Sol: 2 2 2 2
0 0 0
; 0 ;2 2 2c hV R X X X V R V R h h
2 2
0 0 0 0
0; 4 22 2 2q q q qmgh R h h R mg mg
2 2 2 22 2 ; 2 2mgh mg R h h mgR h R h h R
2 2 2 2 2 2 2 2 2 42 2 ;4 4 4 ;4 4 ;3 43RR h R h R h R h Rh h h Rh h Rh h
For equilibrium 0NetF 2 2 2 2
0
1 ; 2 12q x xmg mg mg
R X R X
2 2
1 12
xR X
2 2 2 2 2
2 2
1 4 ;32 3
x RX R X X R XR X
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Section-III
17. (B)
1m
2m
Sol :
1maxsf 1kf
2maxsf 2kf
1 6m kg 18 12 16 12 2 4m 1 2m kg 6 4 24 18 2 6m 1 7m kg 21 14 12 9 2 3m 1 1m kg 3 2
If all three stationary T=15N
2T
30
For Case –I : In
1 2max max& 15s sP F f Both static : 1,2P In 1R f static 2f kinetic : 1,4R In 2Q f static , 1f kinetic : 2,3Q (Check option) 18. (C) 19. A
(P) speed constant & moving in circle 2
1 2 3 3 2& 0cmvF F F f F FR
(for equilibrium in vertical) & 1F
must be static friction. (Q) 1 2&F F will cancel each other.
1F friction (static) & 1 2 3 cF F F F
(as circular motion)
(R) 1 2 3 cF F F F
1F static friction (S) Car at rest 1 2 3 0F F F 20. D
18
p
K
2P
2 2 2
22 21 1 1 1 1; ;8 4 8 82 2
2
p p p p
p
V V V PmPPm V V V mm
1/22 1 1 1 1; ; ; 4 2
8 4 8 4 2p p p p p
p
P m P PP m P P
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CHEMISTRY 21. C
3 2 2 36 3 2Ca P HCl CaCl PH
4 3 2PH I KOH PH KI H O
4 2 3 2 23 3 3P NaOH H O PH NaH PO
Red phosphorus + NaOH soln. no reaction
22. D
1 2 1Dd
46 1d
23. A
Potential difference of electrical double layer formed in a colloidal solution is called
Zeta potential.
24. B
25. D
Complexes Hyd. Of central
Metal cation
No. of
stereoisomers
(A) 2 3Cd gly H O NH
3sp 2
(B) 2 2 2Pt Br H O 2dsp 2
(C) 3
3Cr en
2 3d sp 2
(D) 2 2Co Br NO en
2 3d sp 3
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26. A
mRT (m = molarity, R = 0.082 L atm/mol. K, 25 298T C K )
3
45 10 2 100.082 298
M mRT
wMm V
wmM V
44
10 5 102 10
m
Each glucose unit (mw = 180)
Bonded to the starch chain with bss of 21 18H O mm giving a effective molecular
mass 180 18 162
So approximate average number of glucose 45 10 309 300
162
27. D
t
AReaction is zero order
28. C
5 3PCl Ag AgCl PCl
3PCl is water soluble while AgCl is insoluble in dil 3HNO .
29. C
A) Ionization isomerism B) Co-ordination isomerism
C) No isomerism D) Linkage isomerism
30. A
2
2
13.6 13.6sepzE
n 2 2n z
2
213.6 2 13.6
2nKE E eV
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8 622.18 10 2.18 10 /2
V m s
22 2h h hJ n
31. B
2Cu give ppt with excess of KI
23excess brownCu KI CuI KI
32. D
2Cu gives deep blue colour solution in excess of 3NH .
33. C
7 60.1 10 0.08 10OH
7 70.1 10 0.08 10
89 10
43 10
4 log3pOH
34. A
7 3
4
10 0.1 100.1 3 10 3XOH
35. A
+mol.massNE=
H
Assume B is monocarboxylic aid and NE = MW the –COOH accounts for 45 g/ml of
molecular wt, leav 60 45 15 /g mol for the remainder 3due to CH so “b” is
3CH COOH
“A” has a second COOH replacing an H of 3CH COOH , it is malonic acid
2CHCOOH
COOH104 52 /
2g mol
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36. A
Due to H-bonding it is weak acid & have higher pKa.
37. C
P: 0.05911cell anode cathodeE pH pH
0.059cellE x y
;cellE ve x y
Q: 1
2
0.0591 log2cell
PEP
cellE ve 1 2P P
R: 0.0591 log1cell
yEx
,cellE ve y x
S: 2
1
0.0591 log2cell
PEP
2 1cellE ve P P
38. D
(P) D-xylose
OH
OHHO H
H
HCHO
2CH OH
OxidationOH
OHHO H
H
H
COOH
P.O.S
COOH MESO
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(Q) D-Ribose
OH
OHH
HCHO
2CH OH
OHH 2 epimer of D-Arabinose, give same osazone as D-arabinoseC
(R) D-threose
OH
OHH
HCHO
2CH OH
OH
OHH
H
H C OH
2CH
: :O
Smallest aldose (4C) able to form cyclic hemiacetal.
(S) D-galactose = it is C-4 epimer of D-glucose
OHH
CHO
2CH OH
OHH
OHH
OHH
5
6
1
234
4EpimerC
OH H
CHO
2CH OH
OH H
OHH
OHH
5
1
234
(D-glucose) (D-galactose) 39. (D) 3 2 3 2 22
Co NO Al O CoO NO g O g
Cool2 2 3NO g NO g N O s
4 2 7 2 2 3 22NH Cr O s N g Cr O s H O g
4 4 4 3 3 2Na NH HPO CuSO NaPO NH g H O g
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40. C
(P) Pyrcuric acid ||
3
O
CH C COOH
have carbonyl group i.e. show 2, 4 DNP
test.
(Q) Aspirine is
COOH3OCOCH
& give 2CO gas with 3NaHCO
(R) Acrylic acid 3CH CH CH COOH
Due to bond , it declourise 2 4/Br CCl (Unsaturation test).
(S) Benzyl alcohol is
OH
& react with Na metal evolve 2H gas.
MATHEMATICS Single correct choice Type
41. (B)
Sol: Let 1 2 ,1 3 , 3 2p p p be a point on the first line and , 1 5 ,k q q q be a point on
the line. If they are co-ordinates of point of intersection then
3 2 p q and 1 3 1 5p q
1 2 p k q
1p q and 2k
Point of intersection will be 3, 4, 1
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42. (D)
Sol: From given condition odd elements of the domain can associate with unequal odd
elements of the co-domain and even elements of the domain can associate with
unequal even number of the co-domain
Number of ways if X is odd = 1 1 1 14! 1 91! 2! 3! 4!
Number of ways if X is even = 1 1 1 14! 1 91! 2! 3! 4!
43. (A)
Sol: 212 nM A A I ; 21
2 nN A A I
4 31 1.4 4n nM N A I A A I
nI 3 0A
1M N
44. (B)
Sol: 1 1
33 2 3 3
1 1 0
3 3 3 sin 1 1 4 sin 1 4 sin 2 sinx x x
x x x
t t t t dt t t dt t tdt t tdt
13 2
130
3 3 3 sin 1lim
sin sin 2
x
xx
t t t t dt
x x x
33
040 0
2 sinsin 2 1lim . . lim . .
sin sin 2 5 sin sin 2 5
x
x x
t tdtx x x x x x
x x x x x x
45. (B)
Sol: 2 3 2z i is a circle and 5 3z i is another circle
The distance between their centres is equal to sum of their radii that’s why ‘Z’ will be
their point of contact .
16 7 615 5 5
Z i Z
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46. (C)
Sol:
4 2 2 43 3 3 31 1 . 1 1
kkT
k k k k
2 23 3
2 23 3
3 32 23 3
1 11 1 14
1 1
k k kk k
k k
2 22 23 33 3
1 11 1 0 1 14 4nS n n n n
23
22/3 2/33
1 1 1 11 14 2
n n
x
S SLimn n nn
47. (C)
Sol: 21
1Ix
ln 2
1x dx
x
Put 1xt
2
dtdxt
0 1 1 1 1
1 0 0 0 0
1 1 1 2 21
I ln dt lnt t dt lntdt ln t dt lntdtt t
48. (A)
Sol: Let 1 1,P x y & 2 2,Q x y then the roots of the equation 21 4 0mx ax
22 2
2 4 1 0m ax xm m
are 1x and 2x
And the roots of the equation 2 21 4 44 0y a ay a y ym m m
and 1y and 2y
Required circle is
2 22 2
2 4 4 1 4 0m a a ax y X ym m m m
………(1)
2 2 18 4 5 0x y x y ……………………………………………..(2)
From (1) and (2)
2
4 1 44, 5a am m m
and 2
2 4 10m am
13
m and 13
a
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49. (C)
Sol: 4 4 4 1 4 0x y z xyz
4 4 2 2 4 2 2 2 22 1 2 2 2 4 0x y x y z z x y z xyz
2 2 22 2 2 1 2 0x y z xy z
2 1z xy z and 2 2x y
1z 1x 1y
1x 1y
1 1 1z x y
1 1x y
1,1,1 1, 1,1 1,1, 1 1, 1, 1A B C and D
2 2AB i j 2 2AC i k
2 2AD j k
2 2 0
1 1 82 0 2 8 86 6 3
0 2 2Volume
50. (B)
Sol:
0,0S
1,1P
Q
R
From properties of parabola
RS PS and RQ PR
: 2 3PR x y
0 3, 3RS x y R
Now: : 2 9
9, 9RQ x yPQ x y Q
1 2PS l
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2 9 2QS l
Length of latus-rectum= 1 2
1 2
4 4 9 2 2 36 2 18 210 59 2 2
l ll l
Section-II
Comprehension Type
Paragraph for question Nos : 51-52
51. (C)
52. (A)
Sol: Consider the function 3 2f x x x x
f x is an increasing function such that
0 0,1f x x x
And 0 1f x x x
Now , if , , 0,1a b c
,b a c b and a c (not possible)
If , , 1,a b c
,b a c b and a c (not possible)
1a b c ir 0a b c
Paragraph for question Nos : 53-54
53. (B)
54. (A)
A
B D C E Sol: EAD and CAD
tan , tan and tan are in GP ,
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2 22
2 2
sin sin sin sintancos cos cos sin
2 2 2 2 2 2 2 2sin cos sin sin cos sin cos sin
2sin 0 or 2tan 1
04
cos 5 24
AD AE
Paragraph for question Nos : 55-56
55. (A)
56. (D)
Sol: 5
2
x
x
f x dx ax b x R
5 2f x f x a x R
' '5 2f x f x a x R
'f x is a periodic function but f x is polynomial 'f x is a polynomial
'f x k (a constant)
'f x kx c
Now 0 3f and 1 5f
2 3f x x
Section-III
Matching List Type
57. (D)
58. (D)
Sol: The co-normal points will be 0,0 5 ,52
and 5 , 52
centroid 5 ,03
Circumcenter 25 ,0 ;4
Radius = 254
; Area of 252
ABC
59. (A)
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Sol: 3 3 32 2 2 3a b c
a b c
Let 32 3x
x
, ,x a b c
3 3 2 0x x
0, 3a b c ab bc ca and 2abc 3 3 3 3 3 33 0 6a b c abc a b c
2 2 2 2 6a b c ab bc ca
60. (C)
Sol: (A) 0 1
2 1
1 1 2 3 2 1 1 2 0x x x x x dx x x x x x dx
(B) If 0f x has two pairs of equal roots than y f x has 1 point where it is not
differentiable .
(C) 8 41
8 4lim ....... 11 1x
Lx x
8 4
8 41
8 4lim ....... 21 1x
x xLx x
1 2
2 8 4 4 2L L
(D) 4 3 260 2.2.3.5 60 2 2 3 5x ax bx cx x x x x
31 60 8 2a b c
VARSITY EDUCATION MANAGEMENT LIMITED
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Page 1
JEE-ADVANCED : KEY : PAPER-II
PHYSICS KEY CHEMISTRY KEY MATHEMATICS KEY
1 C 21 C 41 B
2 B 22 D 42 D
3 D 23 A 43 A
4 C 24 B 44 B
5 A 25 D 45 B
6 A 26 A 46 C
7 B 27 D 47 C
8 C 28 C 48 A
9 C 29 C 49 C
10 A 30 A 50 B
11 B 31 B 51 C
12 A 32 D 52 A
13 C 33 C 53 B
14 D 34 A 54 A
15 A 35 A 55 A
16 B 36 A 56 D
17 B 37 C 57 D
18 C 38 D 58 D
19 A 39 D 59 A
20 D 40 C 60 C
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