Sample Paper JEE Adv-1

Transcription

JEE (Advanced) PATTERN
(JEE AdvAncE_sAmplE pApEr)
PAPER - 1
Time : 3 Hours
Name :
Maximum Marks : 180
Enroll. No.:
INSTRUCTIONS
A.
General :
1.
This booklet is your Question Paper. Do not break the seal of the booklet before being instructed to do so by the invigilators.
2.
The question paper CODE is printed on the left hand top corner of this sheet and on the back cover page of this booklet.
3.
Blank spaces and blank pages are provided in the question paper for your rough work. No additional sheets will be provided for rough
work.
4.
Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers and electronic gadget of any kind are
NOT allowed inside the examination hall.
5.
Write your Name and Roll number in the space provided on the back cover of this booklet.
6.
Answers to the questions and personal details are to be filled on an Optical Response Sheet, which is privided separately. The ORS is
a doublet of two sheets - upper and lower, having identical layout. The upper sheet is a machine-gradable Objective Response Sheet
(ORS) which will be collected by the invigilator at the end of the examination. The upper sheet is designed in such a way that darkening
the bubble with a ball point pen will leave an identical impression at the corresponding place on the lower sheet. You will be allowed to
take away the lower sheet at the end of the examination. (On the back cover page for the correct way of darkening the bubbles for valid
answer.)
7.
Use a Ball point pen only to darken the bubbles on the upper original sheet. Apply sufficient pressure so that the impression is
created on the lower sheet. On the back cover page for appropriate way of darkening the bubbles for valid answers.
8.
DO NOT TAMPER WITH/MULTIPLE THE ORS OR THIS BOOKLET.
9.
On breaking the seal of the booklet check that it contains all the 60 questions and corresponding answer choices are legible. Rad
carefully the instruction printed at the beginning of each section.
B.
Filling the right part of the ORS
10.
The ORS also has a CODE printed on its left and right parts.
11.
Verify that the CODE printed on the ORS (on both the left and right parts) is the same as that on this booklet and put your signature in
the Box designated as R4.
12.
IF THE CODES DO NOT MATCH, ASK FOR A CHANGE OF THE BOOKLET/ORS AS APPLICABLE.
13.
Write your Name, Roll No. and the name of centre and sign with pen in the boxes provided on the upper sheet of ORS. Do not write any
of the anywhere else. Darken the appropriate bubble UNDER each digit of your Roll No. in such way that the impression is created on
the bottom sheet. (see example in Figure 2 on the back cover)
C.
Question Paper Format
The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of two sections.
14.
Section 1 contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE
THAN ONE are correct.
15.
Section 2 contains 10 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9 (both inclusive).
D.
Marking Scheme
16.
For each question in Section 1, you will be awarded 3 marks. If you darken all the bubble(s) corresponding to the correct answer(s) and
zero mark. If no bubbles are darkened. No negative marks will be answered for incorrect answer in this section.
17.
For each question in Section 2, you will be awarded 3 marks if you darken only the bubble corresponding to the correct answer and
zero mark if no bubble is darkened. No negative marks will be awarded for incorrect answer in this section.
CORPORATE OFFICE : 2nd Floor, Kumar Tower, Boring Road Chauraha,
Patna-800 001 • Tel: 0612-6440009, 93047252/57/58/59
Sample Paper
PART - I : (PHYSICS)
SECTION-1 : (One or More than one options correct Type)
This section contains 10 multipole choice questions. Each questions has four choices (A), (B), (C) and (D) out of which ONE or
MORE THAN ONE are correct
1.
Charges are so arranged on the surface of an infinitely long hollow cylinder that
the right-hand half of the cylinder surface from section 00| is charged positively,,
and the left hand half negatively. The surface charge density of the charges
increases in the both directions and directly proportional to the distance from
section 00| then,
(A) electric field intensity is directed along the axis of the cylinder at all points inside the cylinder.
(B) electric field intensity is directed along the axis of the cylinder only on the points lying on the axis
of the cylinder.
(C) the magnitude of electric field intensity is same at all the points inside the cylinder.
(D) the magnitude of electric field intensity is same only on the points lying on the axis of the cylinder.
2.
A horizontal beam supported at each end sags under its own weight.
Then the beam will experience
(A) tensile stress
(B) compressive stress
(C) shear stress
(D) bulk stress
3.
An insulating sheet is slowly slid between the plates of a parallel plate capacitor, completely filling the
space between the plates. If the voltage of the capacitor is kept constant. during the process, then
(A) The electric field between the plates of the capacitor pulls the sheet into the capacitor
(B) work done by the field and increase in the energy of the capacitor are equal
(C) The stored energy of the battery decreases by twice the amount of increase in the energy of the
capacitor
(D) The electric filed between the plates of the capacitor pushes the sheet out of the capacitor.
4.
In the diagram shown, an irregular loop of the wire carrying a current
lies in the plane of the paper here. Now, the loop is distorted into
some other shape while remaining in the same plane. Point P is still
within the loop. Which of the following is/are true ?
(A) The magnetic field at point P may be zero
(B) The magnetic field at point P will not change in magnitude when
the loop is distorted.
(C) The magnetic filed at ‘P’ will not change in direction when the loop is distorted.
(D) None of the above is true.
2
CORPORATE OFFICE : 2nd floor, Kumar Tower, Boring Road Chauraha, Patna - 1 • Tel: 0612-6440009, 9304725257-58-59
Sample Paper
5.
A man stretches a horizontal spring attached to the front wall of a railway carriage over a distance ‘ l ’
in a train moving with uniform velocity. During this time, the train covers a distance ‘L’. The man
stretches the spring opposite to the direction of motion of the train. The co-ordinate system attached
to earth is s1 and the co-ordinate system attaches to train is s2 . Then the work preformed by man in
stretching the spring is
6.
(A)
1 2
kl in s1
2
(B)
1 2
k l in s2
2
(C)
1
kl (L  1) in s1
2
(D)
1
k (L  1)2 in s1
2
Find the true statements
(A) it is easier to launch a satellite into an eastward orbit than into a westward one.
(B) effect of friction on an orbiting satellite (assuming the height of the orbit is small so that atmosphere
is present) would finally result in increasing its speed.
(C) An astronaut feels weightlessness as the astronaut’s acceleration is zero.
(D) The earth is in free fall under the action of the net gravitational force of the sun and the planets
(neglect the effect of other astronomical objects)
7.
Charge Q is uniformly distributed on a thin insulating ring of mass m; Which is initially at rest. A
magnetic field perpendicular to the plane of the ring which can attain its maximum value B is switched
on. Let the final angular velocity attained by ring be  . then (neglect magnetic field produced by the
rotating ring)
(A) Magnitude of ‘  ’ does not depend on the radius of the ring
(B) direction of ‘  ’ is opposite to the direction of magnetic field, if Q is negative
(C) Magnitude of ‘  ’ depends on the radius of the ring
(D) Direction of ‘  ’ is opposite to the direction of magnetic field, if Q is positive.
8.
For piston-cylinder arrangement and different types of ideal gases, a
plot of work done (W) verses heat supplied (Q) is plotted. It is
y  3 sin100t . known that one of the straight lines in the fig. is an
isotherm and the other two are isobars of two gases. The initial states of
the two gases are same. It is known that one gas is helium and the other
is CO 2 .
(A) straight line 3 corresponds to isothermal process
(B) straight line 1 corresponds to isothermal process
(C) straight line 2 corresponds to He (helium)
(D) straight line 2 corresponds to CO 2
9.
A particle is subjected to two simple harmonic motion along x and y-directions according to the equations
x  4 sin100 t and y  3 sin100t . Choose the correct statementss
(A) Motion of particle will be on a ellipse
(B) motion of the particle will be on a straight line
(C) particle will execute SHM of amplitude 5.
(D) particle will not execute SHM.
3
Sample Paper
10.
Two identical dimension resistors having resistance R1, R 2 at 0o C and temperature co-efficient of
resistance a1 , a 2 respectively are connected in series. If their resistivities are respectively 1 and 2
then
(A) Their effective temperature co-efficient of resistance is
(B) Their effective combined resistivity is
(C) Their effective combined resistance is
a1R1  a2R2
R1  R 2
1  2
2
R1R2
R1  R 2
(D) Resistance of combination doesn’t change with temperature if a1R1  a 2R 2  0
SECTION – 2 : (One Integer Value Correct Type)
This section contains 10 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).
11.
In the figure a 19 Kg cart is connected by means of a
coiled spring to a 38 Kg cart. The two carts are moving to
the right at a speed of 25 m/s when the spring suddenly
becomes uncoiled and propels the 19 Kg cart forward
with a speed of 27 m/s. find the speed of the second cart
(in m/s) in centre of mass frame.
12.
There is an infinite grid of resistors shown in the diagram. The
resistance of each resistance is R. The equivalent resistance of
2R
n
when the resistor joining them is removed. Then find the value of
n.
the grid between two neighboring grid points is given by
13.
A reinforced-concrete column is subjected to compression by a certain load. Assume that modulus of
elasticity of concrete is one-tenth of that of iron and the cross sectional area of the iron is one-twentieth
of that of concrete. If
FC
 n . Where FC is the part of the load acting on concrete and F is the part of
F
the load acting on iron, then find the value of 'n'
14.
Water is being poured in a vessel at a constant volume rate of "  " . There is a small hole of area " a "
at the bottom of the tank. If the maximum level in the vessel is proportion to
n
, then find the product
am
mn.
15.
A radioactive material consists of nuclides of 3 isotopes which decay by   emission,   emission
and deuteron emission respectively. Their half lives are T1  400sec,T2  800 sec and T3  1600sec
respectively. At t  0 , probability of getting ,  and deuteron from radio nuclide are equal. If the
probability of  emission at t  1600 seconds is n / 13 , then find the value of ‘n’.
4
Sample Paper
16.
A small positively charged ball of mass ‘m’ suspended by an insulated thread of
negligible mass. Another positively charged small ball is moved very slowly from a
large distance until it is in the original position of the first ball. As a result, the first
ball rises by ‘h’. If the work done by external agent is Kmgh, then find the value of
‘K’.
17.
Two soap bubble with radii of curvature R1 and R2 ,
where R2  R1 are brought into contact as shown in
figure . R is the radius of curvature of film between
them. If the contact angle of the films is  
n
radian,
12
then find the value of ‘n’.
18.
A parallel plate capacitor consists of two square plates of side length
a  6 cms . There is dielectric slab in the shape of a cylinder of parabolic
cross-section between the plates, as shown in figure. The dielectric
constant of the material is K  2 . The length of latus rectum of the
parabola is equal to the side length of the plate. Then the capacitance is
given by 4 0 N  10 2 farad , then fin d the value of ‘N’.
19.
In a potentiometer circuit, to measure the internal resistance(r) of a cell, when the cell is connected
across an external resistor R1  10  , then balancing length is obtained at 60 cm from one side of
potentiometer wire. Instead of R1 if another resistance R2  5  is taken, then balancing length is
obtained over 50 cm of potentiometer wire. Then R1 / r  ?
20.
An infinite ladder is constructed with 1 and 2  resistors as shown in diagram find the current
through the cell (in A)
A 1

1
2
6V
1
2
1
2

B
5
Sample Paper
PART - II : (CHEMISTRY)
21.
For the spinel structure (MgAl2 O 4 ) , the correct statement is/are
(A)
50% OVs are occupied by ions.
(B)
22.
Al 3 is equally distributed in TVs and OVs.
(C) Oxide ions occupy ccp lattice.
(D) 12.5% TVs are occupied by ions.
Which out of the following are nonresolvable?
(A)
23.
(B)
(C)
(D)
Which of the following statement(s) is/are correct ?
(A) The halides of Be are electron deficient and are polymeric with halogen bridges.
(B)
BeF2 is very soluble in water owing to high solvation energy of Be2  but fluorides of other alkaline
earth metals are almost in soluble.
(C) CaO, SrO and BaO react exothermically with water forming soluble hydroxides.
24.
(D) The bicarbonates of alkaline earth metals are only stable in solutions.
Which of the following cannot be used as dehydrating agents for ammonia?
(A)
Con. H2SO 4
(B)
anhydrous CaCl2
(C)
P4 O10
(D) CaO
25.
[Fe(en)2 (H2O)2 ]2  en  complex(x). the correct statement about the complex(x) is
26.
(A) it is a low spin complex
(C) it shows geometrical isomerism
Which of the following statements are true?
(B)
(D)
it is diamagnetic
it is outer orbital complex
(A)
CH 3  CH 2  CH 2  I will react more readily than  CH 3  2 CHI for SN 2 reactions
(B)
CH 3  CH 2  CH 2  Cl will react more readily than CH 3  CH 2  CH 2  Br for SN 2 reactions
(C) CH 3  CH 2  CH 2  CH 2  OH will react more readily than  CH3 3 C  CH 2  OH for SN i reactions
in the presence of pyridine
(D) CH 3  O  C6 H 5 Br will react more readily than NO 2  C6 H 5  CH 2 Br for SN 2 reactions
27.
o
o


MCO3( s) 
 MO(s)  CO2(g) the equilibrium pressure of CO 2 at 127 C and 147 C are 0.14 and 0.35
bar respectively.
(A) The enthalpy of the reaction is nearly +64 kj / mole
(B) increase in temperature decreases the yield of CO 2 gas at equilibrium
(C) it is endothermic reaction
(D) on addition of MCO3 at equilibrium, the equilibrium shifts towards right
6
Sample Paper
28.
29.
2
Which of the following statements are correct with respect to  NiCl4 
2
and  Ni  PPh 3  2 Cl2  ?
(A)
 NiCl4 
is tetrahedral
(B)
 Ni  PPh 3  2 Cl2  is tetrahedral
(C)
 Ni  PPh 3  2 Cl2  is square planar
(D)
 NiCl4 
2
is square planar
Select the correct option against mentioned property
(A)
(B)
(Rate of reaction with CH 3 I )
>
O
(Basic nature)
(D)
I  F (Nucleofugacity)
(A) six P-P single bonds
(B)
covalency of phosphorus, 5
(C) four lone pairs of electrons
(D)
PPP angle of 60o
(C)
Rate of reaction with H2SO 4
30.
White phosphorous (P4 ) has
31.
1, 2-Dibromopropane on treatment with X moles of NaNH2 followed by treatment with C2H5Br gives
a pentyne. the value of X is :
32.



z x 


in the above nuclear disintegration the number of nuclides having same
isotopic number
33.
The hydrolysis constant of the aqueous solution of the salt ZnCl2 is calculated from the expression
A
Kh 
(Kw)x
. The sum of the values of x and y is _______
(Kb)y
(Kw=ionic product of water, Kb = dissociation constant of Zn(OH)2 ).
N
N
molecules are moving at Zms1 ,
at y ms 1 and the
10
30
remaining ones are moving at X ms-1 . If rms velocity of the gas is 4.89 ms-1 under same conditions.
What is X?
34.
A flask has ‘N’ gas molecules out of which
35.
heat
3B 2H6  6NH3  3X 
 2Y  12H2 . In the anionic part of the intermediate X the covalency of the
central atom is __.
7
Sample Paper
6.
o
high
300 C
 L  M  N . If oxidation state of the central atom in
Green vitriol 
anhydrous salt 
temp
L,M,N are X,Y,Z respectively (X  Y  Z) . The value of Y  Z  X is _____
37.
When a system is taken from state A to B along path ACB, as shown in the
figure, 8J of heat flows into system and system does 3J of work. How much
heat flows into the system along the path ADB , if the work done by the
system is 4J?
B
C
38.
A
D
When copper sulphate dissolves in the ammonium hydroxide one deep blue complex is formed. What
is the co-ordination no of copper in this complex?
39.
The mono nitration will mainly take place at which position?
40.
If 80% of a radioactive element undergoing decay is left over after a certain period of time t from the
start, how many such periods should elapse from the start for just over 50 % of the element to be leftt
over ?
PART - III : (MATHEMATICS)
41.
If m1 and m2 are the slopes of the tangents to the hyperbola
x2 y2

 1 which pass through the point
25 16
(6, 2) then
(A)
42.
m1  m2 
24
11
(B)
m1m2 
20
11
(C)
m1  m2 
48
11
(D) m1m2 
11
20
If each of a, b, c is orthogonal to the sum of the other two vectors and a  3, b  4, c  5 then
which of the following statement(s) is/are true

(A) if a makes angles of equal measures with x,y,z axes, then tangent of this angle is  2
(B) range of | a  b | is [1, 7]
(C) range of | b  c | is [1, 9]
(D) | a  b  c |  2 5
43.
8
Let [x] denote the greatest integer less than or equal to x. If f(x)  [x sin  x] ,then f(x) is
(A) Continuous at x  0
(B)
Continuous in ( 1, 0)
(C) Differentiable at x  1
(D)
Differentiable in ( 1, 1)
Sample Paper
44.
If b2  4ac for the equation ax 4  bx 2  c  0 , then all roots of the equation will be non zero real if
b  0, a  0, c  0
(B)
b  0, a  0, c  0
(C) b  0, a  0, c  0
(D)
b  0, a  0, c  0
(A)

4
45.
Let n   tann x dx, n N , Then the true statements among the following are
0
(A)
n  1   n
(C) n   n  2 
46.
47.
If z 
n  1  n
(D)
1
1
 2 n 
for n  2
n1
n1
1
 2 then the true statements among the following are
z
(A) Maximum value of | z | is
2 1
(B)
Minimum value of | z | is
2 1
(C) Maximum value of | z | is
5 2
(D)
Minimum value of | z | is
5 2
If the first and (2n  1)th terms of an A.P; a G.P. and H.P. are equal and their nth terms are p,q and s
respectively, then which of the following options is/are correct?
(A)
48.
1
for n  2
n 1
(B)
pqs
(B)
psq
(C)
ps  q2
(D) p  q  s
C1, C2 are two circles of radii a, b(a  b) touching both the coordinate axes and have their centres in
the first quadrant. Then the true statements among the following are
(A) If C1,C2 touch each other then
(B) If C1,C2 are orthogonal then
b
32 2
a
b
2 3
a
(C) If C1, C2 intersect in such a way that their common chord has maximum length then
(D) If C2 passes through centre of C1 then
7
49.
The value of

k0
  7
 
  k
 14
 
 k 
14

rk
b
2 2.
a


 r  14 
 k  r   , where  n denotes n , is
Cr
 r 


(B) greater than 76
67
The solution set of | sin x |  | cos 2x | contains
(A)
50.
(A)


(C)
 
  n  6 , n  6  

n I


 
   n  8 , n  8  
n I
b
3
a

(C)
87
(B)
 n  2 
(D) greater than 78




n I
(D)
 
  n  4 , n  4  
n I

9
Sample Paper
51.
If the number of solutions of the equation cos x  x 2  x  1 in the interval [ 4, 8] is  , the value of
 2    1 is equal to ..........
52.
If the point where the line joining the points (2,  3, 1) , (3,  4,  5) cuts the plane 2x  y  z  7 lies on
2x  4y  2z  P  0 , then P  2 equals..........
35
, then value of 10x  3 is.......
16
53.
If the sum to infinity of the series 1  4x  7x 2  10x 3  ..... is
54.
Let n be total number of onto functions from E to F, where E  {1, 2, 3, 4} and F  {1, 2} . then
n6
is
2
equal to......
55.
If y  mi x 
1
( i  1, 2, 3) represent three straight lines whose slope are roots of the equation
mi
2 m3  3m2  3m  2  0 and sum of the intercepts made by the lines on x-axis is K then value of | [k ] | is
([] represents greatest integer function)......
56.
Three normals are drawn to the parabola y 2  4x from the point (C,0) . If these normals are real and
distinct then minimum integral value of C is
57.
r is the remainder abtained when 7103 is divided by 25, then value of
is
2
58.
The natural number number n( 5) for which n  0 e x (x  1)n dx  16  6e is
59.
Fifteen persons, among whom are A and B, sit down at random at a round table. If P is the probability
that there are exactly 4 persons between A and B, then value of 7P  1 is
60.
If cot  equals the integral solution of the inequality 4x 2  16x  15  0 and sin equals to the slope of
r
1
line equally inclined to co-ordinate axes, and S  sin(  ) sin(  ) , then | 3  5 S | is
10

Sample Paper JEE Adv-1

Transcription

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