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2d
GRAND TEST Time: 9.00 AM to 12.00 Noon
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Sec: Sr.IPLCO
Total Syllabus
Chemistry :
Total Syllabus
Maths
Total Syllabus
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:
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:
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Physics
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Syllabus
Max Marks:180
JEE-Adv_GT_P1_Q’Paper
Paper-I JEE-ADVANCE-2013-P1-Model IMPORTANT INSTRUCTIONS
Time: 3:00
Max Marks: 180
PHYSICS: Section
Question Type
Sec – I(Q.N : 1 – 10)
Questions with Single Correct Choice Questions with Multiple Correct Choice Questions with Integer Answer Type
Sec – II(Q.N : 11 – 15) Sec – III(Q.N : 16 – 20)
+Ve Marks 2
- Ve Marks 0
No.of Qs 10
Total marks 20
4
-1
5
20
4
-1
5
20
20
60
Total
CHEMISTRY: Question Type
Sec – I(Q.N : 21 – 30)
Questions with Single Correct Choice Questions with Multiple Correct Choice Questions with Integer Answer Type
Sec – III(Q.N : 36 – 40)
Total
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MATHEMATICS:
Question Type
Sec – I(Q.N : 41 – 50)
Questions with Single Correct Choice Questions with Multiple Correct Choice Questions with Integer Answer Type
Sr.IPLCO
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Section
Sec – III(Q.N : 56 – 60)
- Ve Marks 0
No.of Qs 10
Total marks 20
4
-1
5
20
4
-1
5
20
20
60
2d
Sec – II(Q.N : 31 – 35)
Sec – II(Q.N : 51 – 55)
+Ve Marks 2
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Section
Total space for rough workPage
+Ve Marks 2
- Ve Marks 0
No.of Qs 10
Total marks 20
4
-1
5
20
4
-1
5
20
20
60 Page 2
JEE-Adv_GT_P1_Q’Paper
PHYSICS
Max Marks: 60
Section-I (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.
A time varying magnetic field
B B 0 tkˆ is
confined in a cylindrical region. cutting the XY
plane on a circle of radius x2 + y2 = 4. We have placed a wire frame as shown. Segment A1A2 and A3A4 are identical quarter circles. The net emf induced in the wire
b)
2 B0
c)
4 B0
d)
B0
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a) zero
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frame is equal to
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JEE-Adv_GT_P1_Q’Paper
2.
Two particles A and B start moving from the same point on the X-axis. The velocity versus time graph for the particle is as shown in figure. The maximum relative separation between the two particles will be equal to VA
VB
2 m/s
2 m/s 1 m/s 1s
a) 3.
1
2s
b)
m
2
1s
time 3
c)
m
4
5
2s
time
d) None
m
4
A ray of light is incident at the origin at an angle 60º with Y-axis as shown in figure. The refractive index is a function of y according to the relation Y
2d
H
1
2
b)
3
. What is the
X
c)
3 1
d) None
a)
E
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LC B
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Dimensionally power of lens is equivalent to : E
b)
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4.
2
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3
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2
a)
1 y
The path of the light followed after successive refraction is as shown
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60º
2
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value of H, shown in figure?
B
c)
LC
B
LC E
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B
d) E
LC
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JEE-Adv_GT_P1_Q’Paper
The potential in certain region is given as V = 2x2, then the charge density of that region is a)
6.
0
b)
4
c)
0
4 0
d)
2 0
A disc of mass m1 radius r is released from rest in the fig shown. If the cylinder is on the verge of slipping as well as toppling then coefficient of friction between cylinder and table surface is :
a) 1
1
b)
c) 3
2
d)
1
3
At time t = 0, some radioactive gas is injected into a sealed vessel. At time T, some more of the same gas is injected into the same vessel. The graph representing the variation of the logarithm of the activity A of the gas with time t is
b)
c)
d)
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a)
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7.
4x
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5.
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JEE-Adv_GT_P1_Q’Paper
8.
a)
I
c)
I
V 0 cos t R V 0 cos t R
b)
I
d)
I
V 0 cos t / 2 R 3V 0 cos t R
A resistor is formed in the shape of a hollow, quarter cylinder from a material of resistivity . The length of cylinder is L, inner and outer radii are R1 and R2 respectively. The resistance of this resistor between the shown terminals P and Q is
R
Sr.IPLCO
2 2
R1
2
b)
2
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2 L
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a)
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9.
The diagram shows an AC circuit with two voltage sources of same frequency. Find out the value of current I shown in the fig.
R L ln 2 R1
c)
R 2 L ln 2 R1
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d)
R1 L R 2 R1
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JEE-Adv_GT_P1_Q’Paper
10. Standing waves are set up in a string of length 240 cm clamped horizontally at both ends. The separation between any two consecutive points where displacement amplitude is 3
2 cm
is 20 cm. The standing waves were set by two traveling waves of
equal amplitude of 3 cm. The overtone in which the string is vibrating will be a) 2nd
b) 3rd
c) 4th
d) 5th
Section-II (One or More options correct Type) This section contains 5 multiple choice question. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
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11. In the diagram shown, both the capacitors have the same capacitance C. One capacitor has charge +q and other is uncharged. The switch is closed at time t =0. The graph shows the variation of the charge on C1 as a function of time. Then charge
-q
q1
C2 = C
C1 = C
V
q
time
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R
S
2d
+q
V
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a) Initial value of current in the circuit is
q
C
R
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b) Charge present in second capacitor in steady state is
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c) Value of q1 in steady state is
CV q 2
CV q 2
d) Heat energy will be generated in the circuit on closing the switch Sr.IPLCO
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JEE-Adv_GT_P1_Q’Paper
12. A uniform magnetic field B 0 kˆ exists to the right of the plane y x tan as shown. At t = 0 a particle of mass m and positive charge q with velocity v 0 iˆ enters in magnetic field at origin. Then y
(q, m)
x
Magnetic
m
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a) particle will come out from magnetic field after
t
qB 0
t
2 m qB 0
2d
b) particle will come out from magnetic field after time
c) Co-ordinate of point from which particle will come out is
bs
m v0 m v0 sin 2 , 1 cos 2 , 0 qB 0 qB 0
m v0 m v0 sin , 1 cos , 0 qB 0 qB 0
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d) Co-ordinate of point from which particle will come is
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JEE-Adv_GT_P1_Q’Paper
13. In the shown circuit reading of voltmeter V1 and V3 are 300 volt each then choose
b) V2 = 400 V
c)
R 10
d)
R 20
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a) V2 = 300 V
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correct option/options if reading of ammeter is 10A :
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JEE-Adv_GT_P1_Q’Paper
14. Two large on conducting plates having surface charge densities
and
,
respectively, are fixed ‘d’ distance apart. A small test charge q of mass m is attached to two non – conducting identical springs of spring constant k as shown in the adjacent fig. The charge q is now released from rest with springs in natural length. Then q will
q
m
bs
b) perform SHM with amplitude
2k
2d
a) perform SHM with angular frequency
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[neglect gravity]
2 k 0
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d) remain stationary
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c) not perform SHM, but will have a periodic motion if charges are removed on plates as well as on m
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JEE-Adv_GT_P1_Q’Paper
15. A satellite close to the earth is in orbit above the equator with a period of rotation 1.5hours. If it is above a point P on the equator at some time, it will be above P again after time a) 1.5 hours b) 1.6 hours if it is rotating from west to east c) 24/17 hours if it is rotating from east to west d) 24/17 hours if it is rotating from west to east
2d
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Section-III (Integer value correct Type) This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive) 16. A metal rod AB of length L rotates with a constant angular velocity about an axis
bs
passing through O and normal to its length. The magnitude of emf induced between mL 2
ke
2
. Hence m is mass of
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ends A and B in the absence of external magnetic field is
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electron and e is charge on electron. Find the value of k.
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JEE-Adv_GT_P1_Q’Paper
17.
8
The centre of mass of a disc of radius
m
is moving with a velocity of 4 m/s on a
5
horizontal plane. The angular velocity of the disc about it's centre is
5 rad / s
. Find the
radius of curvature of the point 'P shown in the figure in meter? 5 rad / s
P
18.
4 m/s
A uniform vertical cylinder is released from rest when its lower end just touches the liquid surface of a deep lake. Calculate maximum displacement of cylinder (in meter). 4 m and
1 2
A sample of radioactive nuclide A150 is having half life 2 hours and it produce B146
particle. Initially in sample only A was present having mass 50 gm.
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after emitting
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19.
2d
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Take
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After four hours difference in mass of sample (A + B) is x gm then value of x is.
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JEE-Adv_GT_P1_Q’Paper
20.
0.01 moles of an ideal diatomic gas is enclosed in an adiabatic cylinder of cross– sectional area A = 10–4m2. In the arrangement shown, a block of mass M = 0.8 kg is placed on a horizontal support, and another block of mass m = 1kg is suspended from a spring of stiffness constant k = 16 N/m. Initially, the spring is relaxed and the volume of the gas is V = 1.4 10–4 m3. What is the angular frequency (in rad.s–1) of the (P0 = 105 N/m2, g = 10 m/s2)
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suspended system ?
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JEE-Adv_GT_P1_Q’Paper
CHEMISTRY
Max Marks: 60
Section-I (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. 21. Standard enthalpy and standard entropy of vaporization of water are + 40 kJ mol -1 and + 120 J mol-1 K-1 respectively. Vapour pressure of water at 27°C expressed as ln PH
2O
will be (consider Standard temp. to be 300K)
(A) – 1.6 22.
(C) – 6.1
(B)1.6
(D) – 3.2
Copper I chloride (CuCl) used in fireworks emits blue light of wave length 450 nm when heated to high temperature. What is the increment of energy that is emitted at
(A) 23.
44 10
23
J
(B)
44 10
23
kJ
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this wave length?
(C) 4 .4 1 0 2 3 J
(D)
4 .4 1 0
23
kJ
In an alloy of Mn – Si, atoms of Mn are at 50% of corners and that of Si are at
2d
remaining 50% corners of a primitive cubic crystal lattice. If Mn also occupies cubical
(B) 50%
(C) 75%
(D) 33.33%
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(A) 25%
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void, atomic % of Mn in the alloy will be
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24.
For the cell representation A g ( s ) | A g B r( s ) | K B r( aq ) C
1
|| K C l ( aq ) C | A g C l ( s ) | A g ( s ) ; 2
which of the
following facts are TRUE? P:
It is an example of concentration cell, if the concentration of metal ion used in both the half cells is identical This cell can also be represented as A g | A g K
Q:
K sp A gC l Cl
| Ag
S:
The cell reaction would be spontaneous if K sp A gB r C l K sp A gC l B r (B) R
(C) QS
(D) PQRS
b)
PC l3
c)
N C l3
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Aqueous solution of which of the following halide is oxidising d)
PC l5
AsC l3
Which of the following pair of salts forms precipitate with excess of C uSO 4 , C dSO 4
I:
C o H O 2 6
b)
C u N O3 2 , Z nSO 4
3
;
II :
C u H O 2 6
2
c)
d) all the above
FeC l3 , AlC l3
2d
a)
; III :
P t F 6
N H 4 OH
2
IV :
C o H O F 2 3 3
The correct
bs
27.
Br
|| A g
It is an example of electrolytic concentration cell
a) 26.
A gB r
R:
A) P 25.
sp
statement about the hybridisation of underlined atom of above complexes :
2
2
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d sp
3
3
b) I, II, III, IV d 2 sp 3 d) I & IV
sp d 3
2
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c) I & III
sp d
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a) I, II, III, IV
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JEE-Adv_GT_P1_Q’Paper
28.
Consider the following sequence of reactions. The products (X) and (Y), respectively, are:
C 2 H 5 C l D X 3 Y M SO , heat prolonged heat H O
KCN
29.
a)
C 2 H 5C N
and
C 2 H 5C H 2 N H 2
b)
C 2 H 5C N
and
C 2 H 5 CONH 2
c)
C2H 5 NC
and
C 2 H 5 NHCH 3
d)
C 2 H 5C N
and
C 2 H 5C O O H
Consider the following reactions. Their final product C is: CH 3
C O B C A C 2 H 5O N a B :,
a)
Ph3 PCH 2CH 3 Br
b)
Ph3 P C H C H 3
CH 3
CH 3 C CH CH 3
CH CH CH 2
CH 3
CH 3
2d
d)
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c)
CH 3
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P h3 P C H 3 C H 2 B r A :,
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JEE-Adv_GT_P1_Q’Paper O
OMe
'X'.
30.
What should be
' X '?
O O
OMe
OMe
b)
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a)
:O: OMe
d) The reaction will not proceed.
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2d
c)
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Section-II (One or More options correct Type) This section contains 5 multiple choice question. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 31. Which of the following is/are CORRECT? (A) One mole of a liquid mixture containing one mole each of liquid A and liquid B is PT
vaporized. Total vapour pressure is found to be
o
o
PA PB
(B) A solution of HCl in water forms higher boiling azeotrope which can be distilled with same composition. (C) A 0.1 M solution of does not ionise in water
H gCl 2 in
water freezes at – 0.186°C.It concludes that H gCl 2
( K f ) H O 1.86 Kkgm ol 1 2
Which of the following is/are TRUE?
B)
In
basic
SnO 2
forms a positively charged colloidal sol containing S n O 2 S n 4
medium
SnO 2
containing SnO 2 SnO 32
(D)
is amphoteric in nature
SnO 2
negatively
charged
colloidal
sol
neither reacts with acid nor with base
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b) HCl
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a) HF
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Which of the Hydrohalic acid cannot form acidic salt
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33.
SnO 2
a
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C)
forms
2d
A) In acid medium
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(D) Ideal solutions can be distilled to separate the pure components.
c) HBr
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d) HI
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JEE-Adv_GT_P1_Q’Paper
In which of the following reaction t-butylbenzene is formed? a) Benzene + iso-butyl chloride,
A lC l 3
b) Benzene + C H 3 2 C
BF .HF
C H 2 3
c) Benzene + t-butyl alcohol d) Benzene + C H 3 2 C 35.
2 4
H SO
C H 2 3 A lC l
Which of the following compound will give positive Tollens test?
a)
O
b)
C H 3 C HO
OH
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34.
OCH 3
CH 3CH 2CH 2CH 2CH OCH 3
2d
OH
OCH 3
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d)
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c)
CH 3 CH
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Section-III (Integer value correct Type) This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive) 36.
For the reaction
2 NO H 2 N 2 O H 2 O ,
value of
dp changes dt
from 1.5 torr s-1 to
0.25 torr s-1 when pressure is changed from 360 torr to 150 torr with respect to NO
keeping pressure of hydrogen to be constant. If pressure of
is observed that value of
dp dt
NO
is kept constant, it
changes from 1.6 torr s-1 to 0.8 torr s-1 with respect to
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pressure of hydrogen from 300 torr to 150 torr. Order of the reaction will be log 2 0.301; log 3 0.477; log 5 0.699; log 7 0.845
38.
Among N F3 , C C l4 , SF6 , PC l5 , SiF4 ,
BC l3 .
is _____
The no. of halides which can’t under go
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The no. of stereo isomers of
2d
P t gly 3
37.
Sr.IPLCO
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hydrolysis at ordinary conditions ___
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39.
How many of the following would produce a tertiary alcohol on treatment with C H 3 C H 2 M gBr ?
O
(i) O
O
ii) Ph
Cl
iii)
O
O
iv)
O
O
O
v)
H C H
vi)
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O
O
CH 3 C N
viii)
ix)
C O2
How many enentiomeric forms are possible for glucose molecule?
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40.
bs
2d
vii)
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MATHEMATICS
Max Marks: 60
Section-I (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.
1
f ( x)
Range of the function
3
x
9
x
is (where . represents fractional part
1
function) b) 1, 2
a) 1, 2 42.
c) 1, 2
A circle touches two of the smaller sides of
ABC
d) none of these and has its centre on the greatest
side where a > b > c. If r is the radius of the incircle and
is the radius of the given
r1
43.
0
If
r1
1
b) 1
r f : 0,1 0,
r1
2
c)
r
r
3
d)
r1
3
4
r
then the number of mappings f such that
1
bs
0
b) 1
c) 0
1
f ( x ) dx 1,
0
xf ( x ) dx 0
d) Infinite
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44.
r1
1
and x 2 f ( x ) dx 2 is a) 2
2
2d
a)
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circle, then
Five numbers out of 1, 2, 3,.......,9 are written randomly at four vertices and centroid of
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b) 4/9
w
a) 5/9
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a regular tetrahedron. The probability that 6 is written at centroid of tetrahedron is c) 8/9
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d) 1/9
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JEE-Adv_GT_P1_Q’Paper
45.
Let A, B, C, D be distinct points on a circle with centre at O. If there exists non zero real numbers x and y such that
46.
xO A yO B xO B yO C xO C yO D xO D yO A
a) ABCD is a rectangle
b) ABCD is a square
c) ABCD is a rhombus
d) nothing can be said
then
The number of values of k for which x 2 k 2 x 2 k x 2 kx 2 k 4 is a perfect square is a) 1
47.
b) 2
c) 0
d) none of these
2 sin 2 x cos x
The values of a and b which satisfy dx a log 2 4 cos x 4 sin x
sin x 1 b log sin x 3 c ,
are respectively
48.
3 11 , 2 2
b)
3 11 , 2 2
c)
3
,
2
2
Let O be an interior point of to area of
a) 2 Let
AOC
b) 3/2 p( x) x x 1 5
2
has zeroes
3 2
,
11 2
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such that
d) 4
O A 2 O B 3O C 0
c) 3
. Then the ratio of area
d) 5/3
x1 , x 2 , x3 , x 4 , x 5
and
g ( x ) x 2. 2
Then the product
is equal to
w
g ( x1 ) g ( x 2 ) g ( x 3 ) g ( x 4 ) g ( x 5 )
a) 1/23
is
c) 1005
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ABC
ABC
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of
2d
b) 1006
bs
a) 1004
50.
d)
The number of natural numbers less than or equal to 2012, which are relatively prime to 2012 is
49.
11
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a)
b) 23
c) -23
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JEE-Adv_GT_P1_Q’Paper
Section-II (One or More options correct Type) This section contains 5 multiple choice question. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 51. Let f x x 1 x x 1 . Then which of the following is/are true? a)
f
1
b) f is continuous at
3
c) f is not differentiable at x = 0 52.
Let
a1
a2
a3
a4
a5
d)
Rf
1
x
1
5
a6
p a1 a 2 a 3 ........ a 6 q a1 a 3 a 3 a 5 a 5 a1 a 2 a 4 a 4 a 6 a 6 a 2 r a1 a 3 a 5 a 2 a 4 a 6 .
3
2
has
b) two roots between a1 , a 3
c) two roots between a1 , a 4
d) two roots between a 3 , a 5
If
f : N 2 , 2 such th a t f ( x ) sin x cos x ,
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a) one root between a1 , a 2
a) one-one
then f(x) is
b) onto
c) many-one
d) into
A hyperbola has center C and one focus at P(6,8). If it’s two directrices are
bs
54.
2 x px qx r 0
2d
53.
Then the equation
CP = 10
5
d) eccentricity =
5
b) eccentricity =
w
a)
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3x+4y+10 = 0 and 3x+4y-10 = 0, then
/2
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c) CP = 8
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55.
If n different objects are distributed at random among n +2 persons so that each person can get any number of things (i.e., 0, 1, 2, ……., n things) then the probability that a) exactly 2 persons will get none of the objects is
n 1 ! n 1 2. n 2 C 3 n 1 C 2 n 2 !
n2
n
b) exactly 3 persons will get none of the objects is
n 2
n
n. n 1 . n 1 2
c) exactly 3 persons will get none of the objects is
12 n 2 n . n 1 2
d) exactly 2 persons will get none of the objects is
n 2
n 1
2
n 1
The least positive integral value of real
Let
z1 , z 2 , ......., z n
. Then
b c d e
equi-modular n n zj Re j 1 k 1 z k
non-zero
has distinct real roots is______ complex
numbers
such
that
is equal to____________
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z1 z 2 ....... z n 0
be
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57.
so that the equation
bs
x a x c x e x b x d 0, a
2d
56.
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Section-III (Integer value correct Type) This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive)
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58.
The number of distinct terms in the expansion of
in the expansion of 3 3
1 1 1 x y z x y z
1 1 1 x yz xy yz xz
2
is m and that
2
is n, then
matrix with real entries. If AA T
I,
m n _________
then the value of
det( A I 3 ) _____
59.
Let A be a
60.
Number of divisors of a natural number n is 105 and n is divisible by exactly 3 distinct
2
prime numbers and is having the least value. The number of divisors of 4k +1 form kN
) of the number n is ____
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2d
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