In the experiment to determine the speed of sound using a resonance column,
A) prongs of the tuning fork are kept in a vertical plane
B) prongs of the tuning fork are kept in a horizontal plane
C) in one of the two resonances observed, the length of the resonating air column is
close to the wavelength of sound in air
D) in one of the two resonances observed, the length of the resonating air column is
close to half of the wavelength of sound in air
A student performs an experiment to determine the Young's modulus of a wire,
exactly 2 m long, by Searle's method. In a particular reading, the student measures
the extension in the length of the wire to be O.8 mm with an uncertainty of
0.05 mm at a load of exactly 1.0 kg.The student also measures the diameter of the
wire to be 0.4 mm with an uncertainty of 0.01 mm.Take g =9.8 m/sexact.The
Young's modulus obtained from the reading is
- 2.00.3101N/m
- 2.00.210N/m
- 2.00.1101N/m²
- 2.00.05101N/m²
A particle moves in the X-Y plane under the influence of a force such that its linear
momentum is pt=Aicos(kt-jsinkt,where A and k are constants. The
angle between the force and the momentum is
- 0
- 30
- 45
- 90
A small object of uniform density rolls up a curved surface with an initial
with respect to the initial
4g
position.The object is
A)ring
Bsolid sphereC hollow sphere D disc
Water is filled up to a height h in a beaker of radius R as
2R
shown in the figure.The density of water is p,the surface
B
tension of water is T and the atmospheric pressure is Po
Consider a vertical section ABCD of the water column
h
through a diameter of the beaker.The force on water on one
side of this section by water on the other side of this section
D
has magnitude
- 2PRh+nRpgh-2RT
- 2PRh+Rpgh-2RT
- PnR+Rpgh-2RT
- PoR+Rpgh+2RT
A spherical portion has been removed from a solid sphere having a charge distributed
uniformly in its volume as shown in the figure. The electric field inside the emptied
space is
- zero everywhere
- non-zero and uniform
- non-uniform
- zero only at its center
A magnetic field B=Boj exists in the region Bo
a<x<2a and B=-Bjin the region
2a<x<3awhere Bo is a positive constant.
0
a
2a
Ba
A positive point charge moving with a velocity
-B
=voiwhere vo is a positive constant,
enters the magnetic field at x=a.The
trajectory of the charge in this region can be
like,
A
Z
Electrons with de-Broglie wavelength fall on the target in an X-ray tube. The
cut-off wavelength of the emitted X-rays is
2h
The electrophile in this reaction is
ACHC1
STATEMENT-1
A cloth covers a table.Some dishes are kept on it. The cloth can be pulled out without
dislodging the dishes from the table.
because
STATEMENT-2
For every action there is an equal and opposite reaction.
(A Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation
for Statement-1
B
Statement-1 is TrueStatement-2 is True; Statement-2 is NOT a correct
explanation for Statement-1
C
Statement-1 is True,Statement-2 is False
STATEMENT-1
A vertical iron rod has a coil of wire wound over it at the
bottom end. An alternating current flows in the coil.The rod
goes through a conducting ring as shown in the figure. The
ring can float at a certain height above the coil.
because
STATEMENT-2
In the above situation, a current is induced in the ring which
interacts with the horizontal component of the magnetic field
to produce an average force in the upward direction.
STATEMENT-1
The total translational kinetic energy of all the molecules of a given mass of an ideal
gas is 1.5 times the product of its pressure and its volume.
because
STATEMENT-2
The molecules of a gas collide with each other and the velocities of the molecules
change due to the collision.
The speed of sound of the whistle is
The distribution of the sound intensity of the whistle as observed by the passengers
in train A is best represented by
The spread of frequency as observed by the passengers in train B is
- 310Hz
- 330Hz
- 350Hz
- 290Hz
Light travels as a
The phases of the light wave at c,de and f are a and respectively.
It is given that f
- cannot be equal to
- a can be equal to
- a-isequalto-e
- - is not equal tof-
Speed of light is.
Column I describes some situations in which a small object moves. Column II
describes some characteristics of these motions.Match the situations in Column I
with the characteristics in Column II and indicate your answer by darkening
appropriate bubbles in the 4 4 matrix given in the ORS.
Column I
Column II
A) The object moves on the x-axis under a (p) The object executes a
conservative force in such a way that its
simple harmonic motion.
"speed" and "position satisfy v =cc-x2,
where c and c are positive constants.
B
The object moves on the x-axis in such a way
q The object does not
that its velocity and its displacement from
change its direction.
the origin satisfy v=-kxwhere k is a
positive constant.
C) The object is attached to one end of a
r) The kinetic energy of the
mass-less spring of a given spring constant
object keeps on decreasing.
The other end of the spring is attached to the
ceiling of an elevator. Initially everything is
at rest. The elevator starts going upwards
with a constant acceleration a.The motion
of the object is observed from the elevator
during the period it maintains this
acceleration.
D The object is projected from the earth's
s) The object can change its
surface vertically upwards with a speed
direction only once.
2GM/Rewhere,Mis the mass of the
earth and R is the radius of the earth.
Neglect forces from objects other than the
earth.
Answer
p
b
S
A
B
C
D
OR
P
b
r
S
A
B
C
D
Two wires each carrying a steady current I are shown in four configurations in
Column I. Some of the resulting effects are described in Column II. Match the
statements in Column I with the statements in Column II and indicate your
answer by darkening appropriate bubbles in the 4 4 matrix given in the ORS.
ColumnI
Column II
A)Point P is situated
(p)
The magnetic fields (B
P
midway between the
at P due to the currents
wires.
in the wires are in the
same direction.
Column I gives some devices and Column II gives some processes on which the
functioning of these devices depend. Match the devices in Column I with the
processes in Column II and indicate your answer by darkening appropriate bubbles
in the 4 4 matrix given in the ORS.
Column I
Column II
Consider a titration of potassium dichromate solution with acidified Mohr's salt
solution using diphenylamine as indicator. The number of moles of Mohr's salt
required per mole of dichromate is
- 3
- 4
- 5
- 6
Among the following metal carbonyls, the C-O bond order is lowest in
A[MnCO]BFeCO]
C[CrCO]
D[VCO]
A solution of a metal ion when treated with KI gives a red precipitate which dissolves
in excess KI to give a colourless solution.Moreover, the solution of metal ion on
treatment with a solution of cobalt(Il) thiocyanate gives rise to a deep blue
crystalline precipitate.The metal ion is
APb2+
Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives
compound E. Compound E on further treatment with aqueous KOH yields
compound F.Compound F is
The number of stereoisomers obtained by bromination of trans-2-butene is
- 1
- 2
- 3
Among the following,the least stable resonance structure is
For the process HOl1 bar,373 KHOg1 bar,373 Kthe correct set of
thermodynamic parameters is
- AG=0S=+ve
- G=0S=-ve
- AG=+veS=0
- G=-veS=+ve
Consider a reaction aG + bH- Products.When concentration of both the reactants
G and H is doubled,the rate increases by eight times.However, when concentration
of G is doubled keeping the concentration of H fixed, the rate is doubled.The overall
order of the reaction is
STATEMENT-1: Alkali metals dissolve in liquid ammonia to give blue solutions.
because
STATEMENT-2: Alkali metals in liquid ammonia give solvated species of the type
[M(NH3n](M=alkali metals.
A) Statement-1 is True, Statement-2 is TrueStatement-2 is a correct explanation
for Statement-1
BStatement-1 is True Statement-2 is True; Statement-2 is NOT a correct
explanation for Statement-1
STATEMENT-1: Glucose gives a reddish-brown precipitate with Fehling's solution
because
STATEMENT-2:Reaction of glucose with Fehling's solution gives CuO and
gluconic acid.
STATEMENT-1: Molecules that are not superimposable on their mirror images.are
chiral.
because
STATEMENT-2:All chiral molecules have chiral centres.
STATEMENT-1:Band gap in germanium is small.
because
STATEMENT-2:The energy spread of each germanium atomic energy level is
infinitesimally small.
Among the following, identify the correct statement.
A) Chloride ion is oxidised by O
BFe2+ is oxidised by iodine
While Fe3+ is stable, Mn3+ is not stable in acid solution because
Sodium fusion extract, obtained from aniline, on treatment with iron(Il sulphate
and HSO in presence of air gives a Prussian blue precipitate.The blue colour is
due to the formation of
- Fe[FeCN3
- Fe[FeCN
- Fe4[FeCN2
- Fe[FeCN3
Which one of the following reagents is used in the above reaction?
A
aq.NaOH+CHCl
B) aq.NaOH+CHCl
The structure of the intermediate Iis
Match the reactions in Column I with nature of the reactions/type of the products in
Column II. Indicate your answer by darkening the appropriate bubbles of the
44 matrix given in the ORS.
ColumnI
Column II
A0O+O
p)redox reaction
BCrO+H-
q) one of the products has trigonal
planar structure
CMnO+NO+H
dimeric bridged tetrahedral metal ion
DNO+HSO+Fe+-
s
disproportionation
Answer
p
b
A
B
C
D
Match the compounds/ions in Column I with their properties/reactions in Column II.
Indicate your answer by darkening the appropriate bubbles of the
44 matrix given in the ORS.
Column I
Column II
ACgHCHO
(p) gives precipitate with
2,4-dinitrophenylhydrazine
Match the crystal system/unit cells mentioned in Column I with their characteristic
features mentioned in Column II. Indicate your answer by darkening the
appropriate bubbles of the 4 x 4 matrix given in the ORS.
Column I
Column II
Let O0,0)P3,4),Q6,0) be the vertices of the triangle OPQ.The point R inside
the triangle OPQ is such that the triangles OPR,PQR,OQR are of equal area. The
coordinates of R are
(4- )
23
(V)
If|z=1 and z1, then all the values of
lie on
Let E denote the complement of an event E. Let E,F,G be pairwise independent
events with PG>0 and PEFnG=0.Then PEF|Gequals
APE+PFc
BPE-P(F
CPE-P(F
d-xd
The differential equation
determines a family of circles with
dx
y
A variable radii and a fixed centre at 0,1
B
variable radii and a fixed centre at 0,-1
C
fixed radius 1 and variable centres along the x-axis
D
fixed radius 1 and variable centres along the y-axis
Let abc be unit vectors such that a+b+c =0.Which one of the following is
correct?
Aaxb=bxc=cxa=0
B)
axb=bxc=cxa+0
Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and
AB =2 CD.Let AD be perpendicular to AB and CD.If a circle is drawn inside the
quadrilateral ABCD touching all the sides, then its radius is
A3
STATEMENT-1: The parametric equations of the line of intersection of the given
planes are x=3+14t,y=1+2tz=15t.
because
STATEMENT-2:The vector 14i +2j+15k is parallel to the line of intersection of
given planes.
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:The curve y=
+x+1 is symmetric with respect to the line
2
x=1.
because
STATEMENT-2:A parabola is symmetric about its axis.
(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 TrueStatement-2 is NOT a correct
explanation for Statement-1
CStatement-1is True,Statement-2 is False
DStatement-1 is False,Statement-2 is True
Let fx=2+ cosx for all real x.
STATEMENT-1:For each real t, there exists a point c in [t,t+] such that
fc=0.
because
STATEMENT-2ft=ft+2nfor each real t.
Which one of the following statements is correct?
AG>G>G>.
.> y>y>p (8)
CG=G=G=
DG<G<GandG>G>G>
Which one of the following statements is correct?
- A>A>A>
- A<A<A<
- A>A>A>andA<A4<A<
Which one of the following statements is correct?
AH>H>H>
B
HHH
C
H>H>H>andHHH6
DHH<HandH>H>H>
M61-63:Paragraph for Question Nos.61 to 63
If a continuous function f defined on the real line R, assumes positive and negative
values in R then the equation fx=0 has a root in R.For example,if it is known
that a continuous function f on R is positive at some point and its minimum value is
negative then the equation f(x)=0 has a root in R.
Consider f(x=ke-x for all real x where k is a real constant.
The line y=x meets y=ke*for k0 at
A)no point
Bone point
The positive value of k for which ke*-x =0 has only one root is
For k>0, the set of all values of k for which ke-x=0 has two distinct roots is
Match the statements in Column I with the properties 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
