Oxidation states of the metal in the minerals haematite and magnetite, respectively, are
Among the following complexes (K-P),.
Kj[Fe(CN)](K), [Co(NH₃);]C13 (L), Na[Co(0xa|ate);](M), [Ni(H,O),]Cl, (N),
K,[Pt(CN)4] (O) and [Zn(H,O);](NO3)2(P)
the diamagnetic complexes are
Consider the following cell reaction:
E = 1.67 V
) > 2Fe2+
(aq) + 2H,O(l1)
(aq)
At [Fe*] = 10- M, P(O₂) = 0.1 atm and pH = 3, the cell potential at 25 C is
Amongst the compounds given, the one that would form a brilliant colored dye on
treatment with NaNO2 in dil. HCl followed by addition to an alkaline solution of
-naphthol is
N(CH₃)2
NHCH3
The major product of the following reaction is
RCH,OH
H
(anhydrous)
The following carbohydrate is
H
OH
HO
HO
HO
OH
H
HO
H
H
Reduction of the metal centre in aqueous permanganate ion involves.
The equilibrium
2 Cu'=Cu + Cu"
in aqueous medium at 25 oC shifts towards the left in the presence of.
For the first order reaction
2N,Os(g) -> 4NO,(g) + O,(g)
The correct functional group X and the reagent/reaction conditions Y in the following
scheme are
(i) Y
X(CH)4-X
condensation polymer
0
(ii)
HO
OH
heat
Among the following, the nurnber of compounds than can react with PCl, to give POCl, is
O₂, CO, SO₂, H,O, H,SO4, P₄O₁₀
ANSWER : 4
The volume (in mL) of 0.1 M AgNO, required for complete precipitation of chloride ions
present in 30 mL of 0.01 M solution of [Cr(H,O),Cl]C1, as silver chloride is close to
ANSWER : 6
In 1 L saturated solution of AgCl [Ks(AgCl) = 1.6 x 10'], 0.1 mol of CuCl
1.6 10^. The value of "x" is.
ANSWER : 7
The number of hexagonal faces that are present in a truncated octahedron is
ANSWER : 8
The maximum number of isomers (including stereoisomers) that are possible on mono-
chlorination of the following compound, is
CH₃
CH3CH2 J`CH2CH₃
H
ANSWER : 8
The total number of contributing structures showing hyperconjugation (involving
C-H bonds) for the following carbocation is
HgCCH2CH₃
ANSWER : 6
CHEMISTRY
SECTION - IV (Total Marks : 16)
(Matrix-Match Type)
This section contains 2 questions. Each question has four statements (A, B, C and D)
given in Column I and five statements (p, q, r, s and t) in Column il. Any given.
statement in Column I can have correct matching with ONE or MORE statement(s) given
in Column II. For example, if for a given question, statement B matches with the
statements given in q and r, then for the particular question, against statement B, darken
the bubbles corresponding to q and r in the ORS..
Match the transformations in column I with appropriate options in column II
Column!
Column II
Match the reactions in column I with appropriate types of steps/reactive intermediate
involved in these reactions as given in column II.
Column !
Column II
A satellite is moving with a constant speed 'v' in a circular orbit about the earth. An object
of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull
of the earth. At the time of its ejection, the kinetic energy of the object is.
A long insulated copper wire is closely wound as a spiral of 'N' turns. The spiral has inner
radius 'a' and outer radius 'b. The spiral lies in the X-Y plane and a steady current 'I'
flows through the wire. The Z-component of the magnetic field at the center of the spiral
is
A point mass is subjected to two simultaneous sinusoidal displacements in x-direction,
2t
x(t)=Asinwt and x(t)=Asin|wt+
Adding a third sinusoidal displacement
3
x,(t) = B sin(wt +) brings the mass to a complete rest. The values of B and are
Which of the field patterns given below is valid for electric field as well as for magnetic
field?
A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg,
traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the.
collision, the ball and bullet travel independently. The ball hits the ground at a distance of.
20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V
of the bullet is
V m/s
1
1
0
20
100
The density of a solid ball is to be determined in an experiment. The diameter of the ball
is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the.
20 divisions. If the measured mass of the ball has a relative error of 2%, the relative
percentage error in the density is
A wooden block performs SHM on a frictionless surface with frequency, vo. The block
carries a charge +Q on its surface. If now a uniform electric field E is switched-on as
shown, then the SHM of the block will be
Two solid spheres A and B of equal volumes but of different densities dA and dg are
connected by a string. They are fully immersed in a fluid of density dr. They get arranged
into an equilibrium state as shown in the figure with a tension in the string. The
arrangement is possible only if
A
A series R-C circuit is connected to AC voltage source. Consider two cases;
Which of the following statement(s) is/are correct?.
A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane
with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the
opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity
10 m/s. Immediately after the collision.
10m/s
20m/s
0.75
1 m/s
m
A train is moving along a straight line with a constant acceleration 'a'. A boy standing in
the train throws a ball forward with a speed of 10 m/s, at an angle of 60 to the horizontal.
The boy has to move forward by 1.15 m inside the train to catch the ball back at the initial
height. The acceleration of the train, in m/s? , is
ANSWER : 5
A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of
friction between the block and the floor is 0.1. Initially the block is at rest and the spring is
un-stretched.An impulse is given to the block as shown in the figure. The block slides a
distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in
m/s is V = N/10. Then N is
ANSWER : 4
Two batteries of different emfs and different internal resistances are connected as shown.
The voltage across AB in volts is
6V
1 Q
A
B
0
0
2 Q
3V
ANSWER : 5
PHYSICS
Water (with refractive index =
) in a tank is 18 cm deep. Oil of refractive index
7
lies on
4
water making a convex surface of radius of curvature 'R = 6 cm' as shown. Consider oil
to act as a thin lens. An object 'S' is placed 24 cm above water surface. The location of
its image is at 'x' cm above the bottom of the tank. Then 'x' is
S
: =1.0
R = 6 cm -
:=7/4
=4/3
ANSWER : 2
A series R-C combination is connected to an AC voltage of angular frequency
w = 500 radian/s. If the impedance of the R-C circuit is R1.25, the time constant
(in millisecond) of the circuit is.
ANSWER : 4
A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an
insulating thread in free-space. It is under continuous illumination of 200 nm wavelength
light. As photoelectrons are emitted, the sphere gets charged and acquires a
potential. The maximum number of photoelectrons emitted from the sphere is A 10
(where 1 < A < 10). The value of Z' is
ANSWER : 7
PHYSICS
SECTION - IV (Total Marks : 16)
(Matrix-Match Type)
This section contains 2 questions. Each question has four statements (A, B, C and D).
given in Column I and five statements (p, q, r, s and t) in Column II. Any given
statement in Column I can have correct matching with ONE or MORE statement(s) given
in Column II. For example, if for a given question, statement B matches with the.
statements given in q and r, then for the particular question, against statement B, darken
the bubbles corresponding to q and r in the ORS..
One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the.
P-V diagram. Column II gives the characteristics involved in the cycle. Match them with.
each of the processes given in Column I..
IB
3P
1P
|c
0
1V
3V
9V
Column I
Column II
Column I shows four systems, each of the same length L, for producing standing waves.
The lowest possible natural frequency of a system is called its fundamenta! frequency,
Column II describing the nature and wavelength of the standing waves.
Column I
Column II
(d)
Longitudinal waves.
Let P(6,3) be a point on the hyperbola
r2
y2
=1. If the normal at the point P intersects
a"
b2
the x- axis at (9, 0), then the eccentricity of the hyperbola is
5!
3
A value of b for which the equations
x2+bx-1=0
x?+x+b=0,
have one root in common is
Let w =1 be a cube root of unity and S be the set of all non-singular matrices of the form
a
b7
@
1
C
w?
where each of a, b, and c is either w or w?. Then the number of distinct matrices in the
set S is
The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also
passes through the point
If
lim [1+xIn(I+b2)]==2bsin0, b>0 and 0(x, m],
then the value of 0 is.
Let f :[-1,2]->[0,) be a continuous function such that f(x)= f(1--x) for all xe[-1,2].
Let R, = x f(x)dx, and R, be the area of the region bounded by y = f(x), x = -1, x= 2,
and the x-axis. Then.
Let f(x)=x2 and g(x)=sinx for all xeR. Then the set of all x satisfying.
(fog gof)(x)=(g gof)(x), where (f og)(x)= f(g(x)), is
Let (x,y) be any point on the parabola y2 =4x. Let P be the point that divides the line
segment from (0, 0) to (x, y) in the ratio 1:3. Then the locus of P is.
If
x
2'
2
Tt
f(x)={-cosx,
05x>
2
x-1,
15x>0
In x,
x>1,
then
Let E and F be two independent events. The probability that exactly one of them occurs
is
11
and the probability of none of them occurring is
2
If P(T) denotes the probability
25
25
of occurrence of the event T, then
4
3|n
2
Let L be a normal to the parabola y' = 4x. If L passes through the point (9, 6), then L
is given by
Let f : (0,1) -> R be defined by
b-x
f(x)=
1-bx
where b is a constant such that 0<b<1. Then
The number of distinct real roots of x4 -4x' +12x' + x-1=0 is.
ANSWER : 2
d f(x)
and g(x) is
Lety(x)+y(x)g'(x)=g(x)g'tx), y(0)=0, xE R, where f'(x)denotes
dx
a given non-constant differentiable function on R with g(0)= g(2)=0. Then the value of
y(2) is
ANSWER : 0
MATHEMATICS
Let M be a 3x3 matrix satisfying
[0]
-17
m
1
2
and M1
0
0
0
12
Then the sum of the diagonal entries of M is
ANSWER : 9
Let a=-i-k, b=-i+j and c=i+2j+3k be three given vectors. If 7 is a vector such
that 7 x b =c b and r. a =0, then the value of r.b is
ANSWER : 9
The straight line 2x-3y =1 divides the circular region x? + y? 6 into two parts. If
{19)(-)()(}-s
then the number of point(s) in S lying inside the smaller part is
ANSWER : 2
MATHEMATICS
SECTION IV (Total Marks : 16)
(Matrix-Match Type)
This section contains 2 questions. Each question has four statements (A, B, C and D).
given in Column I and five statements (p, q, r, s and t) in Column II. Any given
statement in Column I can have correct matching with ONE or MORE statement(s) given
in Column Ii. For example, if for a given question, statement B matches with the
statements given in q and r, then for the particular question, against statement B, darken.
the bubbles corresponding to q and r in the ORS..
Match the statements given in Column I with the values given in Column II.
Column !
Column II-
Match the statements given in Column I with the intervals/union of intervals given in
Column II
Column1
Column II
