Sec: Sr.IPLCO Time: 2.00 PM to 5.00 PM
Max Marks: 198
Syllabus :
Total Syllabus
Chemistry
:
Total Syllabus
Maths
:
Total Syllabus
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Physics
JEE-Adv_GT_P2
PAPER-II JEE-ADVANCE-2012-P2-Model
IMPORTANT INSTRUCTIONS
Time: 3:00
Max Marks: 198
PHYSICS: Section
Question Type
Sec – I(Q.N : 1 – 8)
Questions with Single Correct Choice Questions with Comprehension Type (3 Comprehensions : 2+2+2 = 6Q) Questions with Multiple Correct Choice Total
Sec – II(Q.N : 9 – 15) Sec – III(Q.N : 16 – 20)
+Ve Marks
- Ve Marks
No.of Qs
Total marks
3
-1
8
24
3
-1
6
18
4
0
6
24
20
66
CHEMISTRY: Question Type
Sec – I(Q.N : 21 – 28)
Questions with Single Correct Choice Questions with Comprehension Type (3 Comprehensions : 2+2+2 = 6Q) Questions with Multiple Correct Choice Total
Sec – III(Q.N : 35 – 40)
2d
Sec – II(Q.N : 29 – 34)
+Ve Marks
- Ve Marks
No.of Qs
Total marks
3
-1
8
24
3
-1
6
18
4
0
6
24
20
66
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Section
MATHEMATICS:
Question Type
+Ve Marks
- Ve Marks
No.of Qs
Total marks
Sec – I(Q.N : (41 – 48)
Questions with Single Correct Choice
3
-1
8
24
Sec – II(Q.N : (49 – 54)
Questions with Comprehension Type (3 Comprehensions : 2+2+2 = 6Q)
3
-1
6
18
Sec – III(Q.N : 55 – 60)
Questions with Multiple Correct Choice
4
0
6
24
20
66
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Section
Sr.IPLCO_PAPER-2
Total
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JEE-Adv_GT_P2
PHYSICS:
Max.Marks : 66
SECTION I Single Correct Answer Type This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1.
Power of the only force acting on a particle of mass 1kg moving in straight line depends on its velocity as P = J 2 where J is in msis 1ms-
1
and P is in Watt. If initial velocity of the particle
, then the displacement of the particle in 'ln 2' seconds will be
(A) 1m 2.
1
2
(C) (ln 2) m
(B) 2m
(D) (ln 2 - 1)m
A wheel has eight equally space, very thin spokes of length 30 cm . It is rotating about axis
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OO1 which is perpendicular to its plane and passing through centre, with 2.5 rps . We want
to pass a 20 cm long arrow parallel to the axis and without hitting any spoke. What should
2d
be the minimum velocity of the arrow? [Assumed as initially the arrow is just ready to poss]
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>>>
O1
1
(B) 5 ms-
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(A) 6 ms-
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Sr.IPLCO_PAPER-2
1
(C) 4 ms-
1
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(D) 3ms-
1
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JEE-Adv_GT_P2
3.
The bob of a simple pendulum, which is in the shape of a hollow cylinder of mass ' M ' , radius ' r ' and length ' h ' is suspended by a long string (the mass of the base and lid of the cylinder are negligible). The cylinder is filled with a liquid of density ' r ' upto a height of
' x ' . Then the value of ' x ' for which the time period of the pendulum is maximum is given by which of the following equations (use l = p r 2r ) \\\\\\\\\\\\\\\\\\\\\\\\\\\\\
h
(A) x =
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x
H 2
(B) l x 2 + 2Mx - Mh = 0
(D) l x 2 - 2Mx + Mh = 0
A variable resistance is connected across a non ideal cell of constant emf and constant
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4.
2d
(C) l x 2 + 2Mx + Mh = 0
internal resistance. Initial value of variable resistance is R. Now the magnitude of variable
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resistance has been made ' n ' times, then its new value is nR . Surprisingly the new value of
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power dissipated in variable resistance is still same as its initial value. The value of internal
æ1 + n ö÷ (B) ççç ÷R è 2 ø÷
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(A) R n
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resistance of cell is :
Sr.IPLCO_PAPER-2
(C) R + nR
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(D )
n2 + 1 R 2 Page 4
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5.
An inductor L =
1 1 H , a capacitor , C = F and a resistance , R = 3W is connected 100p 500p
in series with an AC voltage source as shown in the figure. The voltage of the AC source is given as V = 10cos (100p t ) volt. What will be the potential difference between A and B ? B
A
^^^^
~
(
)
(B) 8cos 100 p t + 530 Volt
(
)
(D) 8cos 100 p t - 370 Volt
(A) 8cos 100 p t + 370 Volt
6.
)
(
)
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(C) 8cos 100 p t - 1270 Volt
(
AB and CD are two plates each of area ' a ' such that the plate CD is just submerged into a
liquid whose dielectric constant is K . If the plates are charged using a battery to charge
2d
density ' s ' the height to which the level of liquid in the capacitor rises is (density of liquid is 'r ')
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A
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C
B
D
d
)
2Î
0
r gK 2
(B )
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(A)
Sr.IPLCO_PAPER-2
(
)
s 2 K2 - 1
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(
s 2 K2 + 1
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dielectric
2Î
0
r gK 2
s2 (C ) 2 Î 0 r gK
space for rough work
s 2 (K - 1) (D ) 2 Î 0 r gK Page 5
JEE-Adv_GT_P2
7.
1 mole of an ideal gas undergoes an isothermal expansion as energy is added to it as heat Q . Graph shows the value V versus Q . The gas temperature is nearly equal to :
V(m3) 0.4 0.2 0 (A) 353.8K
(B) 312.6K
(C) 268.2K
(D) 208.4K
A uniform thin hemispherical shell is kept static on an inclined plane of angle q = 300 as
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8.
600 1200 1800 Q(J)
shown. If the surface of the inclined plane is sufficiently rough to prevent sliding then the
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2d
angle ' a ' made by the plane of hemisphere with inclined plane is
(C) 450
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(A) value of ' m' is needed to calculate (B) 300 Sr.IPLCO_PAPER-2
(D) 600 space for rough work
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SECTION II Paragraph Type This section contains 6 multiple choice questions relating to three paragraphs with two questions on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
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PARAGRAH – I : A tank of height ' H ' and base area ' A ' is half filled with water and there is a very small A orifice at the bottom and there is a heavy solid cylinder having base area and height of the 3 cylinder is same as that of the tank. The water is flowing out of the orifice. Here cylinder is put into the tank to increase the speed of water flowing out. 09. The speed of water flowing out of orifice after the cylinder is kept inside it 3 gH gH (A) (B ) (C) 2gH (D) 3gH 2 2 H 10. After long time, when the height of water inside the tank again becomes equal to , the 2 solid cylinder is taken out. Then the velocity of liquid flowing out of orifice (just after removing the cylinder) will be æH ö æH ö 3 gH gH ÷ (A) (B ) (C) 2 g ççç ÷ ( D) 2 g ç ÷ ÷ ççè ø ÷ è ø 3 2÷ 2 3 PARAGRAH – II : Three identical uniform blocks of mass ' m ' each and length ' L ' are placed on a smooth fixed
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horizontal surface as shown. There is friction between A and B while there is no friction between A and C . At the instant shown i.e at t = 0 , the block A has horizontal velocity of
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magnitude ' u ' towards right where as speed of B and C is zero. At the instant block A has
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covered a distance ' L ' relative to block B , velocity of all blocks are same.
Sr.IPLCO_PAPER-2
L A B
L C
smooth horizontal surface space for rough work
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11.
12.
The speed of block A when it just looses contact with B is u u u 2u (A) (B ) (C ) (D ) 2 3 4 3 The magnitude of total work done by friction on system of three block is (A)
1 2 mu 3
(B )
1 mu 2 4
(C )
2 2 mu 3
(D )
3 2 mu 4
PARAGRAH – III : Figure shows a plane convex lens of refractive index
3 placed in air. The maximum
thickness of the lens is 3mm and its aperture diameter is 8mm . Point A lies on the curved surface on the principal axis. A light ray is incident at the point A as shown in the figure
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making 600 with the normal.
A
(B) 3mm
(D) 3 3mm
(C) 3mm
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(A) zero
(A)
5 mm 12
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The focal length of the lens if treated as a thin lens is (B )
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14.
2d
The lateral displacement of the light ray in passing through the lens is
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13.
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60
0
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5 mm 24
(C )
25 12
(
)
3 + 1 mm
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(D )
5 24
(
)
3 + 1 mm Page 8
JEE-Adv_GT_P2 SECTION III Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 15. A smooth hemisphere of mass m and radius R is at rest. A smooth solid sphere of mass 2m
and radius R moving with velocity V0 between two horizontal smooth surfaces separated by a distance slightly greater than 2R as shown in figure. Solid sphere collides with the 1 hemisphere. If coefficient of restitution is , then 2 /////////////////////////////////////////
V0 //////////////////////////////////////////
0
mV02 4 1 (D) The final kinetic energy of hemisphere is th the initial kinetic energy of the sphere 4 A car moves towards a hill with speed Vc . It blows a horn of frequency ' f ' which is heard by an observer following the car with speed V0 . The speed of sound in air is 'V ' . V (A) The wavelength of sound reaching the hill is f V - Vc (B) The wavelength of sound reaching the hill is f 2V (V + V0 ) f (C) The beat frequency observed by the observer is c 2 V - Vc 2 V + Vc (D) The wavelength of sound of horn directly reaching the observer is f
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2d
(C) The loss in kinetic energy of the system is
16.
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(A) The speed of hemisphere after collision is V0 V (B) The speed of solid sphere after collision is 0 2
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17.
In a decay process A decays to B , A ® B . Two graphs of number of nuclei of A and B versus time is given then NB
NA NO
NO 9 NO 10
NO/5 NO/8 O
t1
(A) t2 - t1 = 4sec
(B) t2 - t1 = 2sec
O
t2
(C) t1 2log 2 5sec
t(sec)
(D) t 2 log 2 100sec
x x x x x x x x x x x x x
x x x x B x x x x x x x x
x x x x x x x x x x x x x
x x x x x x x
bs
x x x x x x x
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A circular conducting loop of Radius ' ro ' and having resistance per unit length 'l ' as shown in the figure is placed in a magnetic field B which is constant in space and time. The ends of the loop are crossed and pulled in opposite directions with a velocity ' J ' such that the loop always remains circular and the radius of the loop goes on decreasing then
2d
18.
t(sec)
6
Jt p
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(A) Radius of the loop changes with r = r0 -
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æ Jtö ÷ (B) EMF induced in the loop as a function of time is 2 BJ çççr0 ÷ è ø p÷ BJ (C) Current induced in the loop is 2pl BJ (D) Current induced in the loop is pl Sr.IPLCO_PAPER-2
space for rough work
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19.
Two long conducting wires carrying equal currents are placed to the Z-axis. A charged particle is made to move in a circular path of radius ' a ' with centre of the path at point (0,2a) in clockwise direction. During the course of motion, it passes through four points P, Q, R and S having coordinates (0, a),(- a,2a),(0,3a) and
(a,2a) respectively. The
magnitude of force exerted on the particle by the magnetic field created by the wires is maximum when it passes through points.
y
(0,2a) x
(A) P (B ) Q (C ) R (D ) S When a hydrogen atom is excited from ground state to first excited state then, (A) its kinetic energy increases by 10.2ev
bs
(B) its kinetic energy decreases by 10.2ev
2d
20.
x O (a,0)
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x (-a,0)
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(C) its potential energy increases by 20.4ev
34
J- S
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(D) its angular momentum increases by 1.05´ 10-
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CHEMISTRY:
Max.Marks : 66
SECTION I Single Correct Answer Type This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
21.
The terpene ocimene has the IUPAC name (3Z) – 3, 7 – dimethyl – 1, 3, 6 – octatriene, what is the structural formula of this compound?
(A)
(C )
(D )
The major product formed upon addition of 1 mole of HBr is
HBr (1 mole)
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22.
(B )
Major Product?
Br
Br Br
(C )
(D )
Which of the following interstetial sites is formed when the three closed packed spheres of one layer
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23.
(B )
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(A)
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2d
Br
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is put on three close packed spheres of the second layers, their positions being inverted with
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respective to each other? (A) Tetrahedral Sr.IPLCO_PAPER-2
(B) Rhombohedral
(C) Octahedral
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(D) Cubic Page 12
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24.
Consider the following consecutive reactions: k
k
1 B ( slow) , B 2 C ( fast ) A
25.
The activation energy of reaction is given as (A) Ea (B) Ea (C) Ea Ea (D) Ea Ea 2 1 2 1 1 1 Compare bond strength between B and N in given two compounds :
CH3 3 Si NBH 2
CH 3 3 C NBH 2
Si CH 3
26.
C CH 3
3 3 (I) (II) (A) There is no -bond character between B and N (B) Same in I and II (C) I II (D) II I What is the order of spin only magnetic moment of the following system? (I) Mn 2 in presence of weak field ligand in octahedral field
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(II) Ni 2 in presence of strong field ligand in octahedral field
2d
(I) CO is the main reducing agent
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27.
(III) Cr 3 in presence of CN ligand in octahedral field (IV) Sc3 in presence of weak field ligand in octahedral field (A) I II III IV (B) I III II IV (C) I III IV II (D) I IV III II Consider the following statements in the extraction of iron from haematite :
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(II) Limestone is used to remove SiO 2 as slag , CaSiO3 (III) Smelting process is carried out in blast furnance.
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(IV) When air is used to oxidise the impurities, iron nitride is formed.
(B) I, IV
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(A) I, II
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Pick the correct set of statement(s):
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(C) I, II, III space for rough work
(D) All of these Page 13
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28.
The incorrect statement amongst the following is : (A) LiAlH 4 and NaBH 4 act as reducing agent due to the presence of hydride ion (B) Al H bond is more ionic than B H bond and hence LiAlH 4 can produce larger concentration of hydride ion than that of NaBH 4 (C) Copper Cu 2 / Cu has least standard reduction potential value. (D) Silver nitrate on strong heating liberates two gases with paramagnetic nature. SECTION II
Paragraph Type This section contains 6 multiple choice questions relating to three paragraphs with two questions on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
PASSAGE-1
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In monosubstituted benzene derivatives, if the substituent group provides electron density to the ring by its resonance effect, it is always ortho-para directing. The arenes stabilize the
2d
arenium ion by +I and hyperconjugative effect so are also activating and ortho-para directing.
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If the substituted group withdraws electron density by resonance effect then it is meta
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directing. In case of disubstituted benzenes, the strongly activating group dominates over
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weakly activating or deactivating groups in deciding the orientation of major product. There
repulsion
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is often little substitution between two groups that are meta to each other due to steric
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29.
Major product of the following reaction is Cl Con.HNO3 Con.H2SO4
Cl
(A)
O2N
O2N Cl
NO2
O2N
(B)
NO2
NO2
NO2
Cl
NO2
(C)
(D) NO2
NO2
O2N
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NO2
30.
Cl
Which of the following compound forms a six membered ring most readily when treated with
2d
anhydrous AlCl3
(A)
O
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O2N
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Cl
NO2
Cl
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(C)
CH3 Cl
(B)
O CH3 Cl
(D)
O
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O2N
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O2N
O
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PASSAGE II The Arrhenius relationship of two different reactions is shown below:
log K
B
A
1/T
32.
Which reaction is faster at a lower temperature? (A) A
(B ) B
(C) equal
(D) nothing can be predicted
Which is more sensitive to changes of temperature? (A) A
(B)B
(C) equal
(D) nothing can be predicted
PASSAGE III
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31.
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(i) Produce smell of chlorine in moist air
2d
An inorganic compound (X) gives brick red flame test and also gives following observing :
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(ii) Produce brown coloration with CH3COOH and KI (iii) Produce an anaesthetic compound with ethanol What is the oxidation state of chlorine in compound ( X ) ?
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33.
(C) both +1 and -1
(D) Zero
What is the formula of compound which is formed by the reaction of (X) and C2 H5OH ?
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(B) -1
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(A) +1
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(A) CHCl3
(B) CH 3Cl
(C) CCl4
(D) C2 H5Cl
SECTION III Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
35.
The compound shown below is a synthetic estrogen It is marketed as an oral contraceptive under the name Enovid. OH
O
(C) It can decolorise bromine solution (D) It is , - Unsaturated carbonyl compound H O heat
H / Ni heat
3 CH CHNC 2 A B 3
CH3
2d
36.
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Which of the following statements are correct regarding Enovid. (A) It liberate hydrogen gas on addition of sodium metal (B) It reacts with ammonical AgNO3
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Products ‘A’ and ‘B’ can be distinguished by (A and B are Nitrogen containing products) (A) the treatment of CHCl3 , OH gives a foul smelling compound (B) the action of HNO2 ; A liberates N 2 gas whilst B does not
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(C) the actions of CS2 , HgCl2 . B gives odour of mustard oil whilst A doesn’t (D) the treatment of p-toluene sulphonyl chloiride; ‘A’ gives alkali soluble product Which of the following statements are true
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(A) All crystalline solids are isotropic Sr.IPLCO_PAPER-2
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(B) SF6 molecule has no net dipole moment. (C) Amorphous solids are super cooled liquids with high viscosity. (D) In crystals, short range order exists 38.
In which reactions(s) blood red coloration is observed in product ? H O
KSCN
2 2 ..... Product (A) FeSO4
Fe3
KCN
Product (B) Na2 S2O3 ..... Ferric alum
Product (C) NH 4 SCN Fe3
..... Product (D) NO2 Thiourea
Select compound which is / are isoelectronic CH 3
CH3
O
Si
P
O
(A)
O
CH 3
O
O
O O
S
S
P
O
O O
Cl
C
O
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O
O
P
O
(D)
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O
O
Cl
N
N
C
C N
Cl
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The Variation of solubility (S) of a salt A Bs in water with temperature (T) is given by the
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40.
bs
S
O O
2d
CH 3
(C)
O
Si
Si
O
(B)
CH3
CH3
O
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39.
following graph then the correct statements is/are Sr.IPLCO_PAPER-2
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S
T
(A) The solubility process is endothermic (B) The lattice energy of salt is less than the hydration energy of ions. (C ) Solubility decreases with increase of temperature.
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MATHEMATICS:
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(D) The salt may be NH4Cls
Sr.IPLCO_PAPER-2
Max.Marks : 66
SECTION I Single Correct Answer Type space for rough work
Page 19
JEE-Adv_GT_P2 This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
41.
Let f (x)= x3 + 3x2 - 33x - 33: x > 0 and g be its inverse of f, then the value of ' K ' such that Kg1 (2)= 1 is (A) -36 (B) 51
(C) 72 (D) 42 2 x y F is one of the foci of the ellipse 2 + 2 = 1 where AB is the major axis and CD is the a b minor axis and O is the centre of the ellipse. If OF = 6 and the in-radius of D OCF is 1, then the product of the lengths of AB and CD is (A) 60 (B) 65 (C) 70 (D) 75 p a2 a3 p 2 1 - cos 2nx dx then the value of a4 a5 a6 Let an = ò 2 0 1 - cos 2 x a7 a8 a9 2
43.
p (D) none 2 Radius of circle that passes through origin and touches the parabola y 2 = 4ax at the point
(A) 1 44.
(B ) 2
(C )
(B) 2 2a
(C )
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42.
(A)
(D )
3 a 2
The number of divisors of the form 2n-1 n 2 of the number 2 p.3q.4r.5s
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where p, q, r, s N (A) qs q s 1
(B) p 1 q 1 r 1 s 1 1
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(C) qs q s (D) qs A batsman can score 0, 1, 2, 3, 4 or 6 runs from a ball. The number of different sequences in which he can score exactly 30 runs in an over of six balls is (A) 4 (B) 72 (C) 56 (D) 71
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46.
5 a 2
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45.
5 a 2
2d
(a,2a) is
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47.
The four common tangents to the ellipses
2
2
x y x y 1 and 1 forms a square of area 9 4 4 9
(A) 13 Sq. units 48.
2
(B) 26 Sq. units (C) 25 Sq. units x x If f : R R such that f x then f 1 x 2 1 1 2 (A) (B) (C) x x x
(D) none
(D) does not exist
SECTION II Paragraph Type This section contains 6 multiple choice questions relating to three paragraphs with two questions on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
PARAGRAPH – I : The director circle of a circle is the locus of points from which tangents to the circle are at
Cr let equation of C1 be x 2 y 2 4 The length of a chord of C11 which touches C10 is (A) 64 2
(D) 32
2d
50.
(C) 32 2
(B) 64
The distance of the chord of contact of tangents of a point on C11 with respect to C10 from the center of C10 is (B) 32 2
(C) 64
(D) 32
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(A) 64 2
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49.
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right angles C1 , C2 , C3 , is a sequence of circles such that Cr 1 is the director circle of
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PARAGRAPH – II If f (x)= ax2 + 2 x + 3 touches y + x = 2 at A and a line through A parallel to x-axis is Normal at A to f (x) makes a triangle with coordinate axis whose area is
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51.
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drawn to intersect y = x - 1 in B and C then ,
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10 20 (B ) 9 3 Area of triangle OBC is ( O is origin). 580 290 (A) (B ) 81 81
(A) 52.
(C )
50 9
(D )
40 3
(C )
290 9
(D )
88 9
PARAGRAPH – III : Let
S = O be the equation of reflection of
(x - 4)2 16
+
( y - 3)2 9
= 1 about the line
x - y - 2 = 0 . P is any point of S , A and B are foci of S , then
Equation of minor axis of S is (A) y – 2 = 0
54.
(B ) x – 5 = 0
(C ) x – 4 = 0
(D ) y – 3 = 0
Locus of point of intersection of perpendicular tangents of S is (A) x 2 + y 2 + 10 x - y - 4 = 0
(B) x2 + y 2 = 25
(C) x 2 + y 2 - 10 x - 4 y + 4 = 0
(D) x 2 y 2 10 x 4 y 0
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53.
Let a, b, c be three vectors such that a ¹ 0 and a ´ b = 2a ´ c , a = c = 1, b = 4 and b´ c =
15 . If b - 2c = l a then value of l =
t® ¥
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f (x) = lim
(a + sin p x)t - 1
(a + sin p x)t + 1
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56.
(B ) 3
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(A) 4
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55.
bs
2d
SECTION III Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
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(C ) 2
(D ) 1
, x Î (0,6) then
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(A) if a = 1 then f (x)has five point of discontinuity (B) if a = 3 then f (x)has no point of discontinuity (C) if a = 0.5 then f (x)has six point of discontinuity (D) if a = 0 then f (x)has four point of discontinuity 57.
If Ai is the area bounded by x - ai + y = bi , where ai + 1 = ai + bi , a1 = 0 ; b1 = 32 then 2 (A) A3 = 128
3 bi and 2
bi + 1 =
(B) A3 = 256
n
n
8 2 (C) lim å Ai = (32) 3 n® ¥ i = 1
ac bc is divisible by c 2 (D) none
If I n
(B ) P + q + r > 0 Sin nx
1 . Sin x
10
(A) I n I n2
(C ) P + q + r < 0
(D ) r 0
dx , n = 0, 1, 2, --- then
x
2d
If px 2 qx r 0 has no real roots for real values p, q, r and 4p +2q + r >0 then (A) r > 0
60.
(C) 48
ab b 2 bc
4 (16)2 3
bs
59.
(B) 144
Ai =
ay .in
a 2 If a, b, c are three consecutive integers then ab ac (A) 36
å
n® ¥ i = 1
(B )
.jo
58.
(D) lim
I 2m1 10
I m 1
2m
0
(D) I n I n1
w
w
w
m 1
10
(C )
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