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2015-2016/ JEE Advance/ P-2/Pg-1
BATCH
TARGET
ABC Classes
A BRILLIANT COMPANION
CODE
204
JEE ADVANCE 2015
Date : 22-04-2015
Duration : 3 Hours
Max. Marks : 225
PAPER -2
AWAIT INSTRUCTIONS FROM THE INVIGILATOR
INSTRUCTIONS :
A.
1.
2.
3.
4.
5.
6.
7.
8.
B.
9.
10.
11.
12.
13.
14.
C.
General :
This Question Paper contains 54 questions.
The question paper CODE is printed on the right hand top corner on this sheet of this booklet.
No additional sheets will be provided for rough work.
Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in
any form are not allowed.
The answer sheet, a machine-gradable Optical Marks Reader (OMR), provided separately.
Do not Tamper / multilate the OMR or this booklet.
Do not break the seats of the question-paper booklet before instructed to do so by the invigilators.
Write your Name, Roll No. and Sign in the space provide on the back page of this booklet.
Filling the bottom-half of the OMR :
Use only Black ball point pen only for filling the OMR. Do not use Gel / Ink / Felt pen as it might
smudge the OMR.
Write your Roll no. in the boxes given at the top left corner of your OMR with black ball point pen. Also,
darken the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your
OMR in the space provided (if the OMR is both side printed).
Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ball
point pen.
If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be
displayed and 5 marks will be deducted (paper wise) from the total.
Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful while
darken the bubble corresponding to your answer.
Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do not
scribble, smudge, cut, tear, or wrinkle the OMR. Do not put any stray marks or whitener anywhere on the OMR.
If there is any discrepancy between the written data and the bubbled data in your OMR, the bubble data will
be taken as final.
Filling the bottom-half of the OMR :
16. For each question in Section I, you will be awarded 3 marks if you darken only the bubble corrresponding
to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded for
incorrect answers in this section.
17. For each question in Section II, you will be awarded 4 marks if you darken only the bubble corresponding
to the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark
will be awarded.
18. For each question in Section III, you will be awarded 4 marks if you darken only the bubble corresponding to the correct answer. In all other cases, minus one (–1) mark will be awarded.
19. For each question in Section IV, you will be awarded 8 marks if you darken only the bubble corrresponding
to the correct answer and zero mark if no bubbles are darkened. No negative marks will be awarded for
incorrect answers in this section.
Address : 2 nd Floor Baldev Plaza Golghar, Gorakhpur. Phone No. : 05516450989
2015-2016/ JEE Advance/ P-2/Pg-2
PART-I : CHEMISTRY
SECTION-I
Single Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (a), (b), (c) and (d) out of
which ONLY ONE is correct.
1.
Copper metal on treatment with dilute HNO3 produces a gas (X). (X) when passed through acidic
solution of stannous chloride, a nitrogen containing compound (Y) is obtained. (Y) on reaction with
nitrous acid produces a gas (Z). Gas (Z) is
(a) NO
2.
(b) N2
(d) N2O
Correct order of rate of hydrolysis for following compounds is
(a)
3.
(c) NO2
(b)
For a reversible reaction, A
(c)
k1
k2
(d)
B the initial molar concentrations of A and B are ‘a’ M ‘b’ M,
respectively. If ‘x’ mol/L of A is reacted till the achievement of equilibrium, then x is (k1 and k2 are rate
constants)
k1a  k 2 b
(a) k  k
1
2
k1a  k 2 b
(b) k  k
1
2
(c)
k1a  k 2 b
k1 k 2
k1a  k 2 b
(d) k  k
1
2
4.
Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time
required to liberate 0.01 mol of H2 gas at the cathode is
(1 Faraday = 96500 C mol–1)
(a) 9.65 × 104 sec
(b) 19.3 × 104 sec
(c) 28.95 × 104 sec
(d) 38.6 × 104 sec
5.
A metal M which is not affected by strong acids and strong bases but dissolves in aqua-regia froms MCl3
which is used for toning in photography. The metal M is
(a) Ag
(b) Au
(c) Cu
(d) Hg
Space For Rough Work
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2015-2016/ JEE Advance/ P-2/Pg-3
SECTION-II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (a), (b), (c) and (d) out
of which ONE OR MORE is correct.
6.
as one of the product. A can be
(a)
7.
(b)
(c)
(d)
The species/molecule is having same shape but different hybridisation.
(a) XeF2, CO2
(b) I3 , HgCl2
(c) OCl–, CO
(d) SO2, OCl2
8.
In which of the following cases, the synergic bonding takes place at the * orbital of the ligand ?
(a) [PtCl3(C2H4)]–
(b) [Ni(PF3)4]
(c) [Cr(C6H6)2]
(d) [Fe( – C5H5)2]
9.
Choose the incorrect option(s).
10.
(a) Rate of SN2
(b)
(c)
(d) Mel(excess)  NH 3 
 Me3 N
Pb | PbSO4 | SO 24  (0.1 M) || Pb2+ (0.01 M)|Pb
2303 RT
[Given, Ksp (PbSO4) = 10–16 M2 EoPb2 /Pb = – 0.12 V]. Use,
 0.06
F
Select the correct option(s)
(a) E oPb/PbSO
2
4 /SO 4
(c) E ocell is zero
is 0.36 V
(b) Ecell is 0.39 V
(d) E oPb/PbSO
2
4 /SO 4
is 0.60 V
Space For Rough Work
Address : 2 nd Floor Baldev Plaza Golghar, Gorakhpur. Phone No. : 05516450989
2015-2016/ JEE Advance/ P-2/Pg-4
SECTION-III
(Single integer type)
This section contains 6 questions. This answer to each question is single-digit integer, ranging from 0 to 9.
The correct digit below the question number in the ORS is to be bubbled.
11.
Mass of one atom of an element X is 2.32481 × 10–23 g. Express this mass in terms of (10 + y) amu. Find
the value of y.
12.
The mono nitration will mainly take place at which position ?
13.
Number of alkene produced
14.
Calculate number of molecules of Grignard reagent consumed by 1 molecule of following compound.
15.
Na2SO3, NaCl, Na2C2O4, Na2HPO4, Na2CrO4, NaNO2, CH3CO2Na are separately treated with
AgNO3 solution. In how many cases white ppt is/are obtained ?
16.
Find the number of unpaired electrons in t2g set of d-orbitals in [CO(H2O)3F3] complex.
Space For Rough Work
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2015-2016/ JEE Advance/ P-2/Pg-5
SECTION – IV
Maticx-Match Type
This section contains 2 questions. Each question contains statements given in two column,
which have to be matched. The statements in Column-1 are labelled (A), (B), (C), (D)
while the statements in Column-II are labelled p, q. r, s and t. Any given Statement in
Column -1 can have correct matching with ONE OR MORE statement(s) in Column-II.
The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example. If the correct matches are A-p, s and t ; B-q and r; C-p and q; and Ds and t; then the correct darkening of bubbles will look like the following :
17.
(a)
Column-I
Tendency of metals to show ionic bonding
p.
Column-II
decreases along the period
(b)
Electron affinity
q.
increases along the period
(c)
Oxidising power
r.
decreases down the group
(d)
Metallic character
s.
increases down the group
18.
(a)
Column-I
Column-II
(CH3)3C+
p.
(b)
Aromatic
q.
Hyperconjugation
r.
Diamagnetic
s.
All carbon atoms are sp3 hybridised
+
(c)
-
(d)
Space For Rough Work
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2015-2016/ JEE Advance/ P-2/Pg-6
PART-II : MATHEMATICS
SECTION-I
Single Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (a), (b), (c) and (d) out of
which ONLY ONE is correct.
19.
PQ is chord of contact of tangents from point T to a parabola y2 = 4ax. If PQ is normal at P, then
directrix divides PT in the ratio
(a) 1 : 2
(b) 2 : 1
(c) 3 : 1
(d) 1 : 1
20.
Find out the probability when we throw 4 distinct dice the minimum number appears on the dice is 2
and maximum is 5
(a)
21.
45
628
(b)
(c)
35
618
(d)
55
648
How many quadrilaterals are there in the following diagram?
(a) 66
22.
65
638
(b) 55
Let g(x) = ef(x)
(c) 44
(d) 33
1

g ' N  
2  g '(1/ 2)


and f(x + 1) = x + f(x) then the value of
equal to (where
1  g (1 / 2)

gN  
2

N  Natural number)
1 
 1 1
(b) 2  1    ..... 

2N 1 
 3 5
(d) 0
(a) 2  1  1  1  .....  1 
N
 2 3
(c) N
3
23.
The value of
(a)
1 4
ln  
2 3
ln 4
x 2 cos x 3
 cos x3  cos(ln12  x3 ) dx
3
ln3
(b)
1 4
ln  
6 3
(c)
1 4
ln  
4 3
(d)
1 4
ln  
3 3
Space For Rough Work
Address : 2 nd Floor Baldev Plaza Golghar, Gorakhpur. Phone No. : 05516450989
2015-2016/ JEE Advance/ P-2/Pg-7
SECTION-II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (a), (b), (c) and (d) out
of which ONE OR MORE is correct.
24.
If f(x) is a differentiable function satisfying f "( x)  3 f '( x)  3x  0 and f ´(0) = –1 then
(a) f(x) + x is increasing function  x > 0
(b) f(x) + x is decreasing function  x > 0
(c)   f ( x)  0 x  0
(d) 0  f ( x)   x  0
25.
A circle passing through  and
1
(|  | 1) are orthogonal to circle S then equation of circle S be

(b) |z – 1| = 2
(c) |z – 2| = 3
(d) |z| = 2
(a) |z| = 1
26.
If f(x) be such that f(x) = max (|2 – x|, 2 – x3) then
(a) f(x) is continuous x  R
(b) f(x) is differentiable x  R
(b) f(x) is non differentiable at three points only(d) f(x) is non differentiable at four point only
27.
The values of  for which system of equations (sin 3)x – y + z = 0, (cos 2)x + 4y + 3z = 0,
2x + 7y + 7z = 0 has a non trivial solutions in (0, 3)
(a) 
28.
Let
(b)
A,
B,
C,
D

6
(c)
be
(not
5
6
necessarily
(d)
square)
17
6
real
matrices
that AT  BCD, BT  CDA, C T  DAB and DT  ABC for the matrix S  ABCD then
(a) S 3  S
(b) S 4  S 2
(c) S T  S
(d) S 3  S T
Space For Rough Work
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such
2015-2016/ JEE Advance/ P-2/Pg-8
SECTION-III
(Single integer type)
This section contains 6 questions. This answer to each question is single-digit integer, ranging from 0 to 9.
The correct digit below the question number in the ORS is to be bubbled.
29.
  
The number o f values o f  in t he int erval   ,  sat isfying t he eq uat io n
 2 2
sec 2 
 3
 tan 4   2 tan 2  is
30.
1
If z  ( 3  i) , then the least possible integral values of m such that (z101 + i109)106 = zm + 1
2
31.
Let a  iˆ  ˆj  kˆ, c is a vector such that a .c | c |, | a  c | 27 then a .c is equal to
32.
A bag contain n identical red balls, 2n identical black balls, and 3n identical blue balls. If n balls are
drawn from bag the probability that all balls are same colour cannot exceed 1/6 then minimum
number of red balls in the bag is equal to
33.
34.
x2 y2

 1 then the value of maximum area of PQR is
Let P, Q, R be any three point of ellipse
16 3
Let f : [0, 1]  [0, 1/2] be a function such tht f(x) is a polynomial of 2nd degree satisfy conditions.
(i) f(0) = 0
(ii) f(x) has maximum value of 1/2 at x = 1.
If A be the area bounded by y = f(x), y = f– 1(x) and the line 2x + 2y – 3 = 0 in 1st quadrant then value
of 24 A is equal to
Space For Rough Work
Address : 2 nd Floor Baldev Plaza Golghar, Gorakhpur. Phone No. : 05516450989
2015-2016/ JEE Advance/ P-2/Pg-9
SECTION – IV
Maticx-Match Type
This section contains 2 questions. Each question contains statements given in two column,
which have to be matched. The statements in Column-1 are labelled (A), (B), (C), (D)
while the statements in Column-II are labelled p, q. r, s and t. Any given Statement in
Column -1 can have correct matching with ONE OR MORE statement(s) in Column-II.
The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example. If the correct matches are A-p, s and t ; B-q and r; C-p and q; and Ds and t; then the correct darkening of bubbles will look like the following :
35.
Column I
(A) If


0
Column II
( f ( x )  f "( x )) sin xdx  6 and f(0) = 2 then the value of f() is
 3, if  4  x  0
(B) If f ( x)  
then number of points of non
 x  3, if 0  x  4
differentiability of the function f(|x|) + |f(x)| in [– 4, 4] is
x
(p) 0
(q) 1
(C) If f ( x)  x 3   e t f ( x  t )dt then f(0) + f ´(0) is
(r) 2
(D) If f(x) = tan x and A, B, C are the angles of a ABC, then
(s) 3
0
 f ( A)
M   f ( / 4)
 f ( / 4)
f ( / 4)
f ( B)
f ( / 4)
f ( / 4) 
f ( / 4) 
the det M is
f (C ) 
(t) 4
Space For Rough Work
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2015-2016/ JEE Advance/ P-2/Pg-10
36.
Column I
Column II
 
(A) If 2sin x  tan x  k xx   0,  largest value of k is
 2
(B) Total number of local maxima and local minima of the function
(2  x)3 if  3  x  1
f ( x)   2/3
if  1  x  2
 x
(C) Let A, B, C be three sets of complex number as defined below
A = {z : Im z  1}
B = {z : |z – 2 – i| = 3}
C = {z : Re((1 – i)z) = 2 }
then number of elements in the set A  B  C is
(D) If the x-axis divide the area of region bounded by curves y = 4x – x2
and y = x2 – x in the ratio
(p) 0
(q) 1
(r) 2
(s) 3
121
then the value of k
k
(t) 4
Space For Rough Work
Address : 2 nd Floor Baldev Plaza Golghar, Gorakhpur. Phone No. : 05516450989
2015-2016/ JEE Advance/ P-2/Pg-11
PART-III : PHYSICS
SECTION-I
Single Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (a), (b), (c) and (d) out of
which ONLY ONE is correct.
37.
38.
39.
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2015-2016/ JEE Advance/ P-2/Pg-12
40.
41.
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2015-2016/ JEE Advance/ P-2/Pg-13
SECTION-II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has four choices (a), (b), (c) and (d) out
of which ONE OR MORE is correct.
42.
43.
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2015-2016/ JEE Advance/ P-2/Pg-14
44.
45.
46.
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2015-2016/ JEE Advance/ P-2/Pg-15
SECTION-III
(Single integer type)
This section contains 6 questions. This answer to each question is single-digit integer, ranging from 0 to 9.
The correct digit below the question number in the ORS is to be bubbled.
47.
48.
49.
Space For Rough Work
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2015-2016/ JEE Advance/ P-2/Pg-16
50.
51.
52.
Space For Rough Work
Address : 2 nd Floor Baldev Plaza Golghar, Gorakhpur. Phone No. : 05516450989
2015-2016/ JEE Advance/ P-2/Pg-17
SECTION – IV
Maticx-Match Type
This section contains 2 questions. Each question contains statements given in two column,
which have to be matched. The statements in Column-1 are labelled (A), (B), (C), (D)
while the statements in Column-II are labelled p, q. r, s and t. Any given Statement in
Column -1 can have correct matching with ONE OR MORE statement(s) in Column-II.
The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example. If the correct matches are A-p, s and t ; B-q and r; C-p and q; and Ds and t; then the correct darkening of bubbles will look like the following :
53.
(A)
(B)
(C)
(D)
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2015-2016/ JEE Advance/ P-2/Pg-18
54.
(A)
(B)
(C)
(D)
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2015-2016/ JEE Advance/ P-2/Pg-19
ABC Classes
CODE
204
A BRILLIANT COMPANION
JEE ADVANCE 2015
TARGET BATCH
TEST PAPER-2
ANSWERS
Date : 22-04-2015
CHEMISTRY
MATHEMATICS
PHYSICS
37.
A
38.
39.
A
C
40.
A
B
A
41.
D
42.
ACD
25.
26.
A
AD
43.
ABCD
44.
D
ABCD
BD
27.
28.
ABCD
45.
D
46.
BC
11.
12.
4
4
29.
30.
4
9
47.
5
48.
5
13.
14.
5
5
31.
32.
4
5
49.
9
15.
16.
5
2
33.
34.
9
5
50.
51.
8
4
17.
A  P,S
B  Q,R
35.
A t
B r
52.
53.
8
A- P
1.
2.
D
A
19.
20.
D
D
3.
4.
A
B
21.
22.
B
C
5.
6.
B
ABCD
23.
24.
7.
8.
ABCD
ACD
9.
10.
C  Q,R
D  P,S
18.
A  Q,R
B  P,R,S
C  P,R,S
D  P,R
B- Q
C- Q
C p
D r
36.
A s
B r
C q
D t
54.
D- S
A- P
B- Q
C- P
D- S
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