24-04-2015 Paper-1

Transcription

24-04-2015 Paper-1

2015-2016/ JEE Advance/ P-1/Pg-1
BATCH
TARGET
ABC Classes
A BRILLIANT COMPANION
CODE
004
JEE ADVANCE 2015
Date : 24-04-2015
AWAIT INSTRUCTIONS FROM THE INVIGILATOR
INSTRUCTIONS :
A.
1.
2.
3.
4.
5.
6.
7.
8.
B.
9.
10.
11.
12.
13.
14.
C.
15.
16.
17.
18.
19.
Duration : 3 Hours
Max. Marks : 225
PAPER -1
General :
This Question Paper contains 60 questions.
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No additional sheets will be provided for rough work.
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any form are not allowed.
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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 :
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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.
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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 :
The question paper consists of 3 parts (Chemistry , Mathematics & Physics). Each part consists of
Three Sections.
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.
For each question in Section II, you will be awarded 5 marks if you darken only the bubble corresponding
to the correct answer and zero mark if no bubbles are darkened & minus one (–1) marks will be awarded
for incorrect answers in this section.
For each question in Section III, 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.
For each question in Section IV, you will be awarded 4 marks if you darken only the bubble corrresponding
to the correct answer and zero mark if no bubbles are darkened & minus one (–1) marks will be awarded
for incorrect answers in this section.
Address : 2 nd Floor Baldev Plaza Golghar, Gorakhpur. Phone No. : 0551-6450989
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.
In a reaction a A  products, the rate is doubled when the concentration of A is increased 4 times.
If 50% of the reaction occurs in 1414 s, how long would it takes for the completion of 75%
reaction ?
(A) 4242 s
(B) 2825 s
(C) 2414 s
(D) 2121 s
2.
Moderate electrical conductivity is shown by
(A) silica
3.
(B) graphite
(C) diamond
(D) carborundum
The end product of the following reaction is
(A)
(B)
(C)
(D)
Space For Rough Work
4.
The enthalpy of neutralisation of strong acid by strong base is –57.32 kJ mol–1. The enthalpy of formation
of water is –285.84 kJ mol–1. The enthalpy of formation of hydroxy ion is
(A) +228.52 kJ mol–1 (B) –114.26 kJ mol–1 (C) –228.52 kJ mol–1 (D) +114.26 kJ mol–1
5.
The Eo in the given diagram is
(A) 0.52 V
(B) 0.61 V
(C) 0.74 V
(D) 0.83 V
SECTION-II
Multiple Correct Choice Type
This section contains 4 multiple choice questions. Each question has four choices (a), (b), (c) and (d) out
of which ONE ORE MORE is correct.
6.
When one mole of monoatomic ideal gas at T K undergoes adiabatic change under a constant external
pressure of 1 atm changes volume from 1 litre to 2 litre, the final temperature in Kelvin would be
(A)
7.
T
2
(2/3)
2
(B) T   0.0821
3
(C) T
2
(D) T   0.0821
3
The correct order(s) among the following is/are
(A)
(B)
(C)
(D)
8.
9.
Which of the following compound form anhydride on heating ?
(A)
(B)
(C)
(D)
Pseudohalogenic acid(s) is are
(A) HN3
(B) HCNO
(C) HNCO
(D) N2H4
SECTION-III
(Paragraph type)
This section contains 2 paragraphs. Each paragraph has 2 multiple choice questions, each question has
four choices (a), (b), (c) and (d) out of which ONLY ONE is correct.
Paragraph for Q.no 10 & 11
10.
A volatile organic compound (X) on reaction with HI gives two products (Y) and (Z). (Z) gives red
colour in Victor Meyer test but when (Z) is heated with concentrated H2SO4 followed by hydrolysis gives
(P), which immediately reacts with anhydrous ZnCl2 + HCl. (Y) on treatment with C2H5OH + KOH
followed by O3/Me2S gives Q. (Q) can give haloform test. (Q) when heated with NaOH gives (R). (R)
also gives haloform test and can decolourise Br2 water.
Compound (X) is
(A)
11.
(B)
(C)
(D)
(C)
(D)
Compound (Y) is
(A)
(B)
Passage-2
Carbon monoxide is a very common ligand in organometallic chemistry. It is particularly good at stabilising
low oxidation states of central metal such as Fe(CO)5.
When CO approaches metal as ligand, a sigma bond is formed as a result of overlap of lone pair of
carbon atom and empty hybridised orbital of metal. Apart from it, empty CO antibonding orbital accepts
-electron density from the filled d-orbitals on the metal atom side by side, which is sometimes also
referred as -back bonding.
Carbon monoxide is not appreciably nucleophilic, i.e., -bond formed with metal is weak. But many
d-metal carbonyl compounds are very stable. Thus, we can infer that the strength of -back bonding
enhances the stability of carbonyl complexes by increasing the strength of -bond between metal and
carbonyl.
12.
13.
The longest CO bond length will be with
(A) [Mn(CO)6]+
(B) [V(CO)6]–
(C) Cr(CO)6
Which of the following has shortest metal carbon bond ?
(A) Cr(CO)6
(B) Cr(CO5) (PEt3)
(C) Cr(CO)5(PPh3)
(D) [Ti(CO)6]2–
(D) Ni(CO)4
SECTION-IV
(Single integer type)
This section contains 7 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.
14.
Find the number of R Mg X consumed per molecule with the following reactant.
O O
Cl – C – C – OEt
15.
Observed the following figure carefully, which is showing the initial conditions of the system when all
values are closed.
If at 0oC all valves are opened and system is allowed to come at equilibrium, then calculate the height
difference in the glycerine levels of the U tube manometer in (cm) and write the answer in the equivalent
atmosphere.
Assuming the complete reaction of
NH 3 (g)  HCl(g) 
 NH 4Cl(s) .
Neglect any volume of solid produced and connecting tube.
Assume that the manometer is sufficiently long and thin.
16.
Count the total number of X – O bonds, which are having equal length in HSO 4 .
17.
Calculate the minimum number of P – O linkages of identical length in P4O10.
18.
It required 0.70 g of hydrocarbon CnH2n(A) to react completely with 2g Br2. On treatment of (A) with
HBr, it yielded monobromoalkane (B). The same compound (B) was obtained when (A) was treated
with HBr in the presence of peroxide. What is the value of n in CnH2n
19.
3 A current was passed through an aqueous solution of an unknown salt of Pd for 1 h. 2.977 g of Pdn+
was deposited at cathode. Find n (At wt. of Pd = 106.4)
20.
A mixture contains AgCl, Al(OH)3, Zn(OH)2, Cu(OH)2. On adding excess of NH4OH how many of
them will transfer into filtrate ?
2015-2016/ JEE Advance/ P-1/Pg-10
PART-II : MATHEMATICS
SECTION-I
21.
A plane passes through (1, – 2, 2) and is perpendicular to two planes 2x – 3y + z = 0 and x – y + 2z = 4
the distance of the plane from the point (1, 2, 2) is
(a) 0
22.
12
35
(b)
(c)
17
35
(d)
11
35
If Z1 lies on |z| = 10 and Z2 on |Z + 3 – 4i| = 2 such that |Z1 – Z2| is minimum and  = arg(Z1 – Z2) then
cos  + sin 2 is equal
(a) 
4
25
(b) 
9
25
(c) 
39
25
(d) 
44
25
23.
Let C1 : x2 + y2 – 2x = 0 and C2 : x2 + y2 – 2x – 1 = 0. If P is a point on C2 and PA and PB are that tangents
to the circle C1, then angle between these two tangents is
(a) /6
(b) /4
(c) /3
(d) /2
24.
A box contains a normal coin and a doubly headed coin. A coin selected at random and tossed twice, fell
headwise on both the occasions. The probability. The probability that the drawn coin is a doubly headed
coin is
(a)
25.
2
3
(b)
5
8
(c)
3
4
(d)
4
5
tan x 
 1
T –1
If A  
 , then let us define a function f(x) = det (A A ), then which of the following

tan
x
1


f ( f ( f ( f ..... f ( x))))
cannot be the value of  ( n  2) ?
n times
n
(a) f (x)
(b) 1
(c) fn – 1(x)
(d) nf(x)
2015-2016/ JEE Advance/ P-1/Pg-11
SECTION-II
26.

1
1


 ...... upto n terms. If Tr denote rth term of given
2 1 1 2 3 2  2 3 4 3  3 4
sequence then
If S n 
99
(a) Tr > Tr + 1
(b) Tr < Tr + 1
(c)
T
r
r 1

9
10
(d) Sn < 1
27.
If 0 < a < b < c, and the roots of the equation ax2 + bx + c = 0 are non real complex roots, then
(a) || = ||
(b) || > 1
(c) || < 1
(d) None of these
28.
If (1 + 2x + 3x2)10 = a0 + a1x + a2x2 + ...... + a20x20 , then
(a) a1 = 20
(b) a2 = 210
(c) a4 = 8085
29.
(d) a20 = 22.37.7
0 0 1
If A   0 1 0  then


1 0 0 
(a) adj A is a zero matrix
 0 0 1


(b) adjA   0 1 0 
 1 0 0 
(c) A– 1 = A
(d) A2 = I
2015-2016/ JEE Advance/ P-1/Pg-12
SECTION-III
(Paragraph type)
Paragraph for (Q. No. 30 to 31)
 4a 2
 2
Given  4b
 4c 2

30.
31.
2
4a 1  f (1)  3a  3a 



4b 1  f (1)   3b 2  3b  and f(x) is a quadratic polynomial V is a point of maxima of
4c 1  f (2)  3c 2  3c 


f(x) and A is the point where f (x) cut the negative x-axis, B is point on f(x) such that AB subtends a right
angle at V
Equation of chord AB is
(a) 3x + 2y – 6 = 0
(b) 3x + 2y + 6 = 0
(c) 2x + 3y + 6 = 0 (d) 3x + y + 6 = 0
Area bounded between chord AB and y = f(x) be
(a)
5
sq. unit
3
(b)
25
sq. unit
3
(c)
125
sq. unit
3
(d) None of these
Paragraph for (Q. No. 32 to 33)
32.
33.
2 x,
if | x |  1

Let f(x) be a continuous function given by f ( x)   2
 x  ax  b, if | x |  1
The value fo f ´(2) + f(2) is equal to
(a) 0
(b) 13
(c) 6
(d) 3
Area of the region in the third quadrant bounded by the curves. x = – 2y2 and y = f(x) lying on the left of
the line 8x + 1 = 0 is
(a) 1 sq. unit
(b)
7
sq. unit
4
(c)
3
sq. unit
4
(d)
5
sq. unit
4
2015-2016/ JEE Advance/ P-1/Pg-13
SECTION-IV
34.
  t 5  24
sin
0  2  t dt 3k
If the value of integral.
Then k is equal to.

1
  t 3  11
5
0 cos  2  t dt
35.
The function f ( x )   t (et  1)(t  1)(t  2)3 (t  3)5 dt local maximum at x equal to
1
x
1
36.
If
k 2  4 ln x  k ln y  k 2  4 ln z  6k where k be a real, number such that k  2 then minimum
value of
1
(ln x) 2  (ln y ) 2  (ln z ) 2  be.
2
2
2
 i sin
and  then (1 + ) (1 + ) is equal to
7
7
37.
Let   cos
38.
If ab2c3, a2b3c4, a3b4c5 are in AP(a, b, c > 0), then the minimum value of a + b + c is
39.
There are ‘n + 1’ coins out of which one coin has heads on both faces, one has tail on both faces. A coin
is select at random and tossed 3 times and it is found that head occurs all of the three times if the
probability that the chosen coin is double headed is
40.
8
then value of n is_____________.
15
In a culture the bacteria count is 100000 the number increased by 10% in 2 hours. If the rate of growth
of bacteria is proportional to the number present and the count reaches 200000 in ‘t’ hours then the value
of (1 . 1)t is _____________.
2015-2016/ JEE Advance/ P-1/Pg-14
PART-III : PHYSICS
SECTION-I
41.
A planet of mass m and radius r is surrounded by an atmosphere of constant density. The atomoshere
consists of an ideal gas of molar mass M and its thickness (radial) is h(h<<r) from the surface. The
temperature of the atomosphere on the surface of the planet is
[R = universal gas constant]
(a)
42.
(b)
2mGMh
Rr 2
(c)
3mGMh
Rr 2
(d)
4mGMh
Rr 2
A certain amount of ideal monoatomic gas undergoes, process given by UV1/2 = C, where U is the
internal energy of the gas. The molar specific heat of the gas for the process will be (C = constant)
(a)
43.
mGMh
Rr 2
R
2
(b) 3R
(c)
5R
2
(d) 
R
2
The V-T diagram of an ideal gas for the process A  B  C (straight lines)
is as shown in the figure. In the process A  B  C
(a) pressure is always increasing
(b) for some interval pressure decreases but finally pressure is more than initial
pressure
(c) pressure first increases then remains constant
(d) graph AB is unpredictable about pressure
2015-2016/ JEE Advance/ P-1/Pg-15
44.
Wire AB and PQ lie in a same vertical plane and AB remains in
equilibrium due to magnetic repulsive force. Then the time period
of oscillation of the rod AB if it displaced by a small distance in
vertical plane(where PQ is fixed on a horizontal surface)
(a) 
45.
2 md 2
 0i1i2l
(b) 2
 md 2
 0i1i2l
(c) 2
2 md 2
 0i1i2 l
(d) None of these
Two coherent sources S1 and S2 are kept on the edges of a step as
shown in the figure. An infinetely long screen is placed on the right
side of sources and lies along y -z plane. Calculate total no. of
maximas observed on the screen. PS1 = 8  and PS2 = 6 . Where
 is wavelength of light used. (There is no reflection from steps).
(A) 18
(B) 16
(C) 14
(D) 12
2015-2016/ JEE Advance/ P-1/Pg-16
SECTION-II
46.
A luminous point object is placed at O, whose image is formed at I as shown
in the figure. AB is the optic axis. Which of the following statements are correct ?
(A) If a lens is used to obtain image, the lens must be converging
(B) If a mirror is used to obtain image, the mirror must be a convex mirror
having pole at the point of intersection of lines OI and AB.
(C) Position of principal focus of mirror cannot be found
(D) I is real image.
47.
A circular loop of radius r, having N turns of a wire, is placed in a uniform and constant magnetic field B.
The normal of the loop makes an angle  with the magnetic field. Its normal rotates with an angular
velocity  such that the angle  is constant. Choose the correct statement from the following.
NBr 2
cos 
2
(B) emf induced in the loop is zero.
(C) emf must be induced as the loop crosses magnetic lines
(D) emf must not be induced as flux does not change with time.
(A) emf in the loop is
2015-2016/ JEE Advance/ P-1/Pg-17
48.
A charged particle with velocity v  x i  y j moves in a magnetic field B  y i  x j . The magnitude of
magnetic force on particle is F. Which of the following statements are correct ?
(A) No force acts on particle if x = y
d
i
(B) F  x 2  y 2 if x  y
(C) Force acts along z -axis if x > y
(D) Force acts along y -axis if y > x
49.
Consider a source of sound S, and an observer P. The source emits sound of frequency N 0.
The frequency observed by P is found to be :
N1 if P approaches S at speed v and S is stationary,
N2 if S approaches P at speed v and P is stationary, and
N3 if each of P and S have speeds v/2 towards one another. Then,
(A) N1 = N2 = N3
(B) N1 < N2
(C) N3 > N0
(D) N3 lies between N1 and N2
2015-2016/ JEE Advance/ P-1/Pg-18
SECTION-III
(Paragraph type)
Uranium
238
92
U is an unstable nucleus. It decays to Thorium
which further decays to
234
91
234
90
Th , which is again an unstable nuclei
Pa . Such decay is called successive disintegration. Let
238
92
U is called as A of
decay constant  1 and 234
is called as B of decay constant  2 and stable nuclei 234
is named as
90 Th
91 Pa
C. Here A is called parent nucleus and B is called daughter nucleus of A. Any two adjacent nuclei may be
consider parent or daughter nuclei. Suppose N1, N2 and N3 are number of nuclei A, B and C respectively
at time t which undergoes decay. Then we can write


1 B 
2 C
A 

Rate of disintegration of A =
dN1
   1 N1
dt
Rate of disintegration of B =  2 N2 and net rate of formation of B =
dN2
  1 N1   2 N2
dt
dN3
  2 N2
dt
If at t = 0, there are N0 number of nuclei of A, where as nuclei B and C are absent in the sample answer
the following questions
Rate of formation of nuclei C is equal to
2015-2016/ JEE Advance/ P-1/Pg-19
50.
Number of nuclei of B at any time t is
F
GH
I
JK
N  F  t  t I
0 1
1 e 2
JK
(C)    G e
2 1H
F
I
GH
JK
N  F  t  t I
0 2
1 e 2
JK
(D)    G e
2 1H
N 
 t  t
0 1
1 e 2
(A)    e
2
1
51.
N 
 t  t
0 2
1 e 2
(B)    e
2 1
Number of nuclei of nuclei C at time t is
LM
N
L 
(C) N M    de
N
1
2
 2t

e   1t
(A) N 0 1     e
 2  1
2
1
1
0
2
  2t
 e   1t
1
OP
Q
LM
N
L 
(D) N M   
N
1
2
  2t

e   1t
(B) N0    e
 2  1
2
1
iOPQ
e   2t 
1
0
2
1
OP
Q
OP
Q
2
e   1t  1
 2  1
Many interesting wave phenomenon in nature cannot just be described by a single wave, instead one must
analyze complex waveforms in terms of a combination of many travelling waves. To analyze such wave
combinations, we make use of the principle of superposition which states that if two or more travelling
waves are moving through a medium and combine at a given point, the resultant displacement of the
medium at that point is sum of the displacement of individual waves. Two pulses travelling on the same
string are described by
y1 
5
b 3 x  4t g
2
2
and y2 
5
b3x  4t  6g  2
52.
The direction in which each pulse is travelling
(A) y1 is in positive x-axis, y2 is in positive x-axis.
(B) y1 is in negative x-axis, y2 is in negative x-axis.
(C) y1 is in positive x-axis, y2 is in negative x-axis.
(D) y1 is in negative x-axis, y2 is in positive x-axis.
53.
The time when the two waves cancel everywhere
(A) 1 sec
(B) 0.5 sec
(C) 0.25 sec
2
(D) 0.75 sec
2015-2016/ JEE Advance/ P-1/Pg-20
SECTION-IV
54.
An equilateral prism ABC is placed in air with its base side BC lying
horizontally along X-axis as shown in the figure. A ray given by
3 y  x  10 is incident at a point P on face AB of prism.
The value of  for which ray grazes the face AC is
55.
k
2 3
. Find k.
Light of wavelength   500 nm falls on two narrow slits placed
a distance d = 50 × 10–4 cm apart, at an angle   30 0 relative to
the slits shown in figure. On the lower slit a transparent slab of
thickness 0.1 mm and refractive index 3/2 is placed. The
interference pattern observed on screen at a distance D = 2 m
from the slits. Then 10 k fringes will pass over C, if we remove the
transparent slab from the lower slit. Find k.
56.
A man of mass 80 kg riding on a small cart of mass 40 kg which is rolling along a level floor at a speed
of 2 m/s. He is running on the cart so that his velocity relative to the cart is 3 m/s in the direction opposite
to the motion of cart. What is the speed (m/s) of the centre of mass of the system ?
2015-2016/ JEE Advance/ P-1/Pg-21
57.
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to
produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/s2 must be applied that
axis for a duration of (in second).
58.
An object of height 1 cm lying on the axis of a convex mirror of
focal length 20 cm at distance of 30 cm from its pole as shown in fig.
At this instant find the rate at which height of image is
changing. Express your answer in multiple of 103 cm / s.
59.
Two resistors R A  20 and a variable resistance RB are connected in parallel. The combination is
connected through a 5  resistor to 220 Volts source. The value of RB for which the power in RB is
maximum is_____  .
60.
One turn of insulated wire in the form of a planar square frame with side 0.2 m and resistance 1  is
placed in a uniform magnetic field perpendicular to the magnetic field lines. The current passing through
the turn when magnetic field starts to decrease at a constant rate of 0.1 T/s is ____ mA.
2015-2016/ JEE Advance/ P-1/Pg-22
ABC Classes
A BRILLIANT COMPANION
JEE ADVANCE 2015
TARGET BATCH
CODE
004
TEST PAPER-1
ANSWERS
Date : 24-04-2015
CHEMISTRY
MATHEMATICS
PHYSICS
1.
C
21.
B
41. A
2.
B
22.
C
42. D
3.
D
23.
D
43. C
4.
C
24.
D
44. C
5.
B
25.
D
45. A
6.
A
26.
AD
46. AD
7.
ABC
27.
AB
47. BD
8.
AC
28.
ABC
48. AD
9.
ABC
29.
BCD
49. BC
10.
D
30.
B
50. C
31.
C
11.
A
51. A
32.
B
12.
D
52. C
33.
D
53. D
13.
B
34.
2
54. 4
14.
4
35.
6
55. 5
15.
1
36.
2
56. 0
16.
3
37.
3
57. 2
17.
4
38.
1
58. 8
18.
4
39.
8
59. 4
19.
4
40.
4
60. 4
20.
3

24-04-2015 Paper-1

Transcription

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