A particle P starts from the point zo=1+2iwhere i=-1.It moves first
horizontally away from origin by 5 units and then vertically away from origin by
3 units to reach a point z.From z the particle moves 2 units in the direction of
the vector i+j and then it moves through an angle
in anticlockwise direction on a
2
circle with centre at origin, to reach a point z.The point z is given by
Let the function g-
be given by gu=2tane-.Then
2'2
2
gis
A)
even and is strictly increasing in 0,)
B
odd and is strictly decreasing in-o,
C odd and is strictly increasing in-,
D neither even nor odd,but is strictly increasing in-
Consider a branch of the hyperbola
x2-2y2-22x-42y-6=0
with vertex at the point A.Let B be one of the end points of its latus rectum.If C is
the focus of the hyperbola nearest to the point A, then the area of the triangle
ABC is
2
3
2
The area of the region between the curves y =
and y=
cosx
cosx
by the lines x=0 and x=
4
2-1
2-1
ConsiderthreepointsP=-sin-a)-cosQ=cos-asinand
4
A)P lies on the line segment RQ
B Q lies on the line segment PR
C
R lies on the line segment QP
An experiment has 10 equally likely outcomes.Let A and B be two non-empty
events of the experiment. If A consists of 4 outcomes,the number of outcomes that
B must have so that A and B are independent, is
A2,40r8
B3,60r9
C4or8
D5or10
Let two non-collinear unit vectors a and 6 form an acute angle.A point P moves so
that at any time t the position vector OP where O is the origin) is given by
a cost+bsint.When P is farthest from origin O,let M be the length of OP and
be the unit vector along OP.Then,
a+6
a-6
Au=
andM=1+a62
Let
dx,
J
dx
e
Then,for an arbitrary constant C,the value of J-I equals
e4x-e2x+1
2x+e+1
Let gx=logf(x where f(x) is a twice differentiable positive function on 0
such that fx+1=x fx.Then,for N=1,23,...,
e{N+1)-1)
Suppose four distinct positive numbers a, aa3a are in G.P.Let b=a
b=b+ab3=b+a3andb4=b3+a4.
STATEMENT-1:The numbers bbb3b4 are neither in A.P.nor in G.P.
and
STATEMENT-2:The numbers bbb3b4 are in H.P.
A
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct
explanation for STATEMENT-1
Consider
L2x+3y+p-3=0
L2x+3y+p+3=0,
where p is a real number,andC:x+y2+6x-10y+30=0.
STATEMENT-1If line L is a chord of circle C, then line L is not always a
diameter of circle C.
and
STATEMENT-2: If line Lis a diameter of circle C,then line L is not a chord of
circle C.
A
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is a correct
explanation for STATEMENT-1
Let a solution y=y(x) of the differential equation
xx2-1dy-yy-1dx=0
2
satisfy y2=
3
STATEMENT-1yx=secsecx-
6
and
STATEMENT-2:yx) is given by
1_23
1
y
x
A
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is a correct
explanation for STATEMENT-1
Which of the following is true?
A2+af1+2-af-1=0B2-af1-2+af-1=0
Cf1f'-1=2-a2
Df'1f-1=-2+a2
Which of the following is true?
A
fx is decreasing on-1,1 and has a local minimum at x=1
B
fx is increasing on -1,1 and has a local maximum at x=1
C fx) is increasing on -1,1 but has neither a local maximum nor a local
minimumat x=1
D fx is decreasing on -1,1 but has neither a local maximum nor a local
minimum at x=1
Let
f'(t)
gx=
dt.
1+t2
Which of the following is true?
Agx is positive on-0 and negative on0,
B
gxis negative on-,0 and positive on0,
(C
g'x changes sign on both-,0and0,
The unit vector perpendicular to both L and L is
-i+7j+7k
-i-7j+5k
The shortest distance between L and L is
17
41
17
The distance of the point (1,1,1) from the plane passing through the point
-1,-2,-1 and whose normal is perpendicular to both the lines Land L is
2
7
13
23
Consider the lines given by
L:x+3y-5=0
L3x-ky-1=0
L3:5x+2y-12=0
Match the Statements/Expressions in Column I with the Statements/Expressions
in Column II and indicate your answer by darkening the appropriate bubbles in the
44 matrix given in the ORS.
ColumnI
Column II
ALL2L3 are concurrent,if
(d)
k=-9
BOne of LLL3 is parallel to at least one
(q)
k=
6
5
of the other two,if
5
CLLL form a triangle,if
(1
k=
6
D LLL3 do not form a triangle,if
(s)
k=5
p
b
r
S
A
Answer
B
C
D
Match the Statements/Expressions in Column I with the Statements/Expressions
in Column II and indicate your answer by darkening the appropriate bubbles in the
4 4 matrix given in the ORS.
ColumnI
Column II
is
(d)
0
x+2
B Let A and B be3x3 matrices of real numbers,
(q)
1
where A is symmetric, B is skew-symmetric,and
A+BA-B=A-BA+B.IfAB=-1AB
where (AB) is the transpose of the matrix AB
then the possible values of k are
CLet a=loglog32.An integer k satisfying
(1)
2
DIf sin=cos,then the possible values of
(s)
3
2
p
b
r
S
A
Answer
B
C
D
Consider all possible permutations of the letters of the word ENDEANOEL.
Match the Statements/Expressions in Column I with the Statements/Expressions
in Column II and indicate your answer by darkening the appropriate bubbles in the
4 4 matrix given in the ORS.
Column I
Column II
Consider a system of three charges
qq
and
placed at points A, B and C,
3'3
3
respectively, as shown in the figure.Take O to be the centre of the circle of
radius R and angle CAB=60
Figure:
A) The electric field at point O is
directed along the negative x-axis
8R
B) The potential energy of the system is zero
2
C) The magnitude of the force between the charges at C and B is
q
54nR
D) The potential at point O is
q
12R
A transverse sinusoidal wave moves along a string in the positive x-direction at a
speed of 10 cm/s.The wavelength of the wave is 0.5 m and its amplitude is 10 cm.At
a particular time t, the snap-shot of the wave is shown in figure. The velocity of
point Pwhen its displacement is 5 cm is
Figure:
y
3jm/s
A block
A bob of mass M is suspended by a massless string of length L. The horizontal
velocity V at position A is just sufficient to make it reach the point B. The angle O at
which the speed of the bob is half of that at A,satisfies
Figure:
B
V
A glass tube of uniform internal radius (r) has a valve separating the two identical
ends.Initially, the valve is in a tightly closed position.End 1 has a hemispherical
soap bubble of radius r.End 2 has sub-hemispherical soap bubble as shown in figure.
Just after opening the valve,
Figure:
A) air from end 1 flows towards end 2.No change in the volume of the soap bubbles
B) air from end 1 flows towards end 2.Volume of the soap bubble at end 1 decreases
C)no change occurs
D air from end 2 flows towards end 1. Volume of the soap bubble at end 1
increases
A vibrating string of certain length l under a tension T resonates with a mode
corresponding to the first overtone (third harmonic) of an air column of length 75 cm
inside a tube closed at one end. The string also generates 4 beats per second when
excited along with a tuning fork of frequency n. Now when the tension of the string is
slightly increased the number of beats reduces to 2 per second.Assuming the velocity
of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is
A344
B)
336
C117.3
A parallel plate capacitor C with plates of unit area and separation d is filled with a
liquid of dielectric constant K=2.The level of liquid is
p
initially.Suppose
3
the liquid level decreases at a constant speed V, the time constant as a function of
timetis
Figure:
3
68R
15d+9VtR
A light beam is traveling from Region I to Region IV (Refer Figure). The refractive
respectively.The angle of
8
incidence 0 for which the beam just misses entering Region IV is
Figure:
Region I
Region II
Region III
Region IV
no
26
no
no
e
2
8
0
0.2m
0.6m
13
(1)
(1)
STATEMENT-1
For an observer looking out through the window of a fast moving train, the nearby
objects appear to move in the opposite direction to the train, while the distant objects
appear to be stationary.
and
STATEMENT-2
If the observer and the object are moving at velocities V and V respectively with
reference to a laboratory frame, the velocity of the object with respect to the observer
isV-V.
A) STATEMENT-1 is True, STATEMENT-2 is TrueSTATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
STATEMENT-1
It is easier to pull a heavy object than to push it on a level ground.
and
STATEMENT-2
The magnitude of frictional force depends on the nature of the two surfaces in
contact.
STATEMENT-1
For practical purposes, the earth is used as a reference at zero potential in electrical
circuits.
and
STATEMENT-2
The electrical potential of a sphere of radius R with charge Q uniformly distributed
Q
on the surface is given by
4R
STATEMENT-1
The sensitivity of a moving coil galvanometer is increased by placing a suitable
magnetic material as a core inside the coil.
and
STATEMENT-2
Soft iron has a high magnetic permeability and cannot be easily magnetized or
demagnetized.
A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
The electric field at r = R is
A independent of
For a =0,the value of d (maximum value of p as shown in the figure is
3Ze
3Ze
4Ze
Ze
The electric field within the nucleus is generally observed to be linearly dependent
on r.This implies
R
2R
0=DV
The net external force acting on the disk when its centre of mass is at displacement x
with respect to its equilibrium position is
A-kx
The centre of mass of the disk undergoes simple harmonic motion with angular
frequency equal to
The maximum value of V, for which the disk will roll without slipping is
Column I gives a list of possible set of parameters measured in some experiments
The variations of the parameters in the form of graphs are shown in Column II.
Match the set of parameters given in Column I with the graphs given in Column II.
Indicate your answer by darkening the appropriate bubbles of the 44 matrix given
in the ORS.
Column I
Column II
A Potential energy of a simple
(d)
pendulum y axis) as a function of
displacement (x axis)
An optical component and an object S placed along its optic axis are given in
Column I. The distance between the object and the component can be varied. The
properties of images are given in Column II. Match all the properties of images from
Column II with the appropriate components given in Column I. Indicate your
answer by darkening the appropriate bubbles of the 4 4 matrix given in the ORS.
Column I
Column II
Column I contains a list of processes involving expansion of an ideal gas.Match this
with Column II describing the thermodynamic change during this process.Indicate
your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the
ORS.
Column I
Column II
A) An insulated container has two
(p The temperature of the gas
chambers separated by a valve.
decreases
Chamber I contains an ideal gas
and the Chamber II has vacuum.
The valve is opened.
II
ideal gas
vacuum
B) An ideal monoatomic gas expands
(q The temperature of the gas
to twice its original volume such
increases or remains constant
2whereV
is the volume of the gas
C An ideal monoatomic gas expands
rThe gas loses heat
to twice its original volume such
43where V
is its volume
The correct stability order for the following species is
(I)
(II)
(III)
(IV)
A
II>IV>I>III
BI>II>III>IV
C
II>I>IV>III)
DI>III>II>IV
Cellulose upon acetylation with excess acetic anhydride/HSO catalytic) gives
cellulose triacetate whose structure is
OAC
In the following reaction sequence, the correct structures of E,F and G are
O
I2
Ph
OHHeat[E]
F]+G]
NaOH
* implies 13C labelled carbon)
O
Among the following, the coloured compound is
Both [NiCO] and [Ni(CN]2~are diamagnetic. The hybridisations of nickel in
these complexes,respectively, are
Asp,sp3
Bspdsp
Cdsp,sp
Ddspdsp2
0
0
The IUPAC name of [NiNH)4][NiCl] is
A
Tetrachloronickel (II)-tetraamminenickel (II)
Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli
ampere current.The time required to liberate 0.01 mol of H gas at the cathode is
1 Faraday=96500C mol⁻¹
A9.6510sec
B19.310sec
Among the following, the surfactant that will form micelles in aqueous solution at
the lowest molar concentration at ambient conditions is
ACHCH15NCH3Br
BCHCHOSONa
Solubility product constants Kp of salts of types MX,MX and MX at
temperature T are 4.010-8,3.21014and 2.7 10-15respectively.Solubilities
(mol dm-) of the salts at temperature T are in the order
AMX>MX>MX
BMX>MX>MX
STATEMENT-1:Aniline on reaction with NaNO/HCl at 0 C followed by coupling
with -naphthol gives a dark blue coloured precipitate.
and
STATEMENT-2: The colour of the compound formed in the reaction of aniline with
NaNO/HCl at 0 C followed by coupling with -naphthol is due
to the extended conjugation.
A) STATEMENT-1 is True,STATEMENT-2 is True;STATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True,STATEMENT-2 is True;STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
STATEMENT-1:[Fe(HO)NO]SO is paramagnetic.
and
STATEMENT-2: The Fe in [Fe(HO)NO]SO has three unpaired electrons.
A STATEMENT-1 is True, STATEMENT-2 is TrueSTATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
C
STATEMENT-1 is True,STATEMENT-2 is False
D
STATEMENT-1 is False, STATEMENT-2 is True
O
C
Answer
A.BCD
STATEMENT-1The geometrical isomers of the complex [M(NH)Cl] are
optically inactive.
and
STATEMENT-2Both geometrical isomers of the complex [M(NH₃)Cl] possess
axis of symmetry.
STATEMENT-1: There is a natural asymmetry between converting work to heat
and converting heat to work.
and
STATEMENT-2: No process is possible in which the sole result is the absorption of
heat from a reservoir and its complete conversion into work.
Compound H is formed by the reaction of
O
The structure of compound I is
Ph
CH₃
The structures of compounds J, K and L,respectively, are
The number of atoms in this HCP unit cell is
A4
The volume of this HCP unit cell is
- 242r3
- 162r3
- 1223
The empty space in this HCP unit cell is
A
74%
B)47.6%
C32%
Match the compounds in Column I with their characteristic test(s)/reaction(s) given
in Column II.Indicate your answer by darkening the appropriate bubbles of the
44 matrix given in the ORS.
ColumnI
Column II
AHN-NHC1
(psodium fusion extract of the
compound gives Prussian blue
colour with FeSO
NHI
Match the conversions in Column I with the type(s) of reaction(s) given in
Column II. Indicate your answer by darkening the appropriate bubbles of the
4 4 matrix given in the ORS
Column I
Column II
APbSPbO
p)roasting
Match the entries in Column I with the correctly related quantum number(s) in
Column II. Indicate your answer by darkening the appropriate bubbles of the
4 4 matrix given in the ORS
Column I
Column II
(A Orbital angular momentum of the
(p)Principal quantum number
electron in a hydrogen-like atomic orbital
