Section 1
Q. No. 1  8 Carry 4 marks each
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.
Q.
An electron in an excited state of Li^{2+} ion has angular momentum 3h/2π. The de Broglie wavelength of the
electron in this state is pπa_{0} (where a_{0} is the Bohr radius). The value of p is
A large spherical mass M is fixed at one position and two identical point masses m are kept on a line
passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of
length and this assembly is free to move along the line connecting them. All three masses interact only
through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3 from
M, the tension in the rod is zero for m = k(M/288). The value of k is
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The energy of a system as a function of time t is given as E(t) = A_{2}exp(αt), where α = 0.2 s^{1}. The
measurement of A has an error of 1.25 %. If the error in the measurement of time is 1.50 %, the percentage
error in the value of E(t) at t = 5 s is
The densities of two solid spheres A and B of the same radii R vary with radial distance r as ρ_{A}(r) =
, respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are I_{A} and I_{B}, respectively. If
the value of n is
Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, π/3, 2π/3 and π.
When they are superposed, the intensity of the resulting wave is nI_{0}. The value of n is
For a radioactive material, its activity A and rate of change of its activity R are defined as and , where N(t) is the number of nuclei at time t. Two radioactive sources P (mean life ) and
Q(mean life 2) have the same activity at t = 0. Their rates of change of activities at t = 2 are RP and RQ,
respectively. If , then the value of n is
A monochromatic beam of light is incident at 60^{0} on one face of an equilateral prism of refractive index n and
emerges from the opposite face making an angle θ(n) with the normal (see the figure). For n = √3 the value of θ is 60^{0} and . The value of m is
In the following circuit, the current through the resistor R (=2) is I Amperes. The value of I is
Section 2
Q. No. 9 18 carry 4 marks each and 2 marks is deducted for every wrong answer.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four
option(s) is(are) correct.
Q.
A fission reaction is given by where x and y are two particles. Considering to be at rest, the kinetic energies of the products are denoted by K_{Xe}, K_{Sr}, K_{x}(2MeV) and K_{y}(2MeV),
respectively. Let the binding energies per nucleon of be 7.5 MeV, 8.5 MeV and 8.5 MeV respectively. Considering different conservation laws, the correct option(s) is(are)
Two spheres P and Q of equal radii have densities ρ_{1} and ρ_{2}, respectively. The spheres are connected by a massless string and placed in liquids L_{1} and L_{2} of densities σ_{1} and σ_{2} and viscosities η_{1} and
η_{2}, respectively. They float in equilibrium with the sphere P in L_{1} and sphere Q in L_{2} and the string being taut (see figure). If sphere P alone in L_{2} has terminal velocity and Q alone in L_{1} has terminal velocity ,
ρ then
In terms of potential difference V, electric current I, permittivity ε_{0}, permeability μ_{0} and speed of light c,
the dimensionally correct equation(s) is(are)
Consider a uniform spherical charge distribution of radius R1 centred at the origin O. In this distribution, a spherical cavity of radius R_{2}, centred at P with distance OP = a = R_{1} – R_{2} (see figure) is made. If the electric field inside the cavity at position then the correct statement(s) is(are)
In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the yaxis and stress on the xaxis as shown in the figure. Then the correct statement(s) is(are)
A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own
gravity. If P(r) is the pressure at r(r < R), then the correct option(s) is(are)
parallel plate capacitor having plates of area S and plate separation d, has capacitance C_{1} in air. When
two dielectrics of different relative permittivities (ε_{1} = 2 and ε_{2} = 4) are introduced between the two plates
as shown in the figure, the capacitance becomes C_{2}. The ratio C_{2}/C_{1 }is
An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the
figure). Initially the gas is at temperature T_{1}, pressure P_{1} and volume V_{1} and the spring is in its relaxed state.
The gas is then heated very slowly to temperature T_{2}, pressure P_{2} and volume V_{2}. During this process the
piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct
statement(s) is(are)
SECTION 3
Q. No. 1720 carry 4 marks each and 2 marks is deducted for every wrong answer.
This section contains TWO paragraphs
Based on each paragraph, there will be TWO questions
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four
option(s) is(are) correct
PARAGRAPH 1
Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n_{1} surrounded by a medium of lower refractive index n_{2}. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n_{1} and n_{2} as shown in the figure. All rays with the angle of incidence i less than a particular value i_{m} are confined in the medium of refractive index n_{1}. The numerical aperture (NA) of the structure is defined as sin i_{m}.
Q.
For two structures namely S_{1} with n_{1} = and n_{2=} 3 / 2, and S_{2} with n_{1} = 8/5 and n_{2} = 7/5 and
taking the refractive index of water to be 4/3 and that of air to be 1, the correct option(s) is(are)
PARAGRAPH 1
Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n_{1} surrounded by a medium of lower refractive index n_{2}. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n_{1} and n_{2} as shown in the figure. All rays with the angle of incidence i less than a particular value i_{m} are confined in the medium of refractive index n_{1}. The numerical aperture (NA) of the structure is defined as sin i_{m}.
Q.
If two structures of same crosssectional area, but different numerical apertures NA_{1} and
NA_{2} (NA_{2} < NA_{1} ) are joined longitudinally, the numerical aperture of the combined structure is
PARAGRAPH 2
In a thin rectangular metallic strip a constant current I flows along the positive xdirection, as shown in the figure. The length, width and thickness of the strip are , w and d, respectively. A uniform magnetic field is applied on the strip along the positive ydirection. Due to this, the charge carriers experience a net deflection along the zdirection. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the zdirection is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.
Q.
Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are
w_{1} and w_{2} and thicknesses are d_{1} and d_{2}, respectively. Two points K and M are symmetrically located on
the opposite faces parallel to the xy plane (see figure). V_{1} and V_{2} are the potential differences between K
and M in strips 1 and 2, respectively. Then, for a given current I flowing through them in a given magnetic
field strength B, the correct statement(s) is(are)
PARAGRAPH 2
In a thin rectangular metallic strip a constant current I flows along the positive xdirection, as shown in the figure. The length, width and thickness of the strip are , w and d, respectively. A uniform magnetic field is applied on the strip along the positive ydirection. Due to this, the charge carriers experience a net deflection along the zdirection. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the zdirection is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.
Q.
Consider two different metallic strips (1 and 2) of same dimensions (lengths , width w and thickness d)
with carrier densities n_{1} and n_{2}, respectively. Strip 1 is placed in magnetic field B_{1} and strip 2 is placed in
magnetic field B_{2}, both along positive ydirections. Then V_{1} and V_{2} are the potential differences developed
between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips,
the correct option(s) is(are)
SECTION 1
Q. No. 21 28 carry 4 marks each.
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive
Q.
In dilute aqueous H_{2}SO_{4}, the complex diaquodioxalatoferrate(II) is oxidized by . For this reaction, the ratio of the rate of change of [H^{+}] to the rate of change of is
The number of hydroxyl group(s) in Q is
Among the following, the number of reaction(s) that produce(s) benzaldehyde is
In the complex acetylbromidodicarbonylbis(triethylphosphine)iron(II), the number of Fe–C bond(s) is
Among the complex ions,
number of complex
ion(s) that show(s) cistrans isomerism is
Three moles of B_{2}H_{6} are completely reacted with methanol. The number of moles of boron containing
product formed is
The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar
conductivity of a solution of a weak acid HY (0.10 M). If the difference in their pK_{a} values,
pK_{a} (HX)  pK_{a} (HY), is (consider degree of ionization of both acids to be << 1)
closed vessel with rigid walls contains 1 mol of and 1 mol of air at 298 K. Considering complete
decay of , the ratio of the final pressure to the initial pressure of the system at 298 K is
SECTION 2
Q. No. 2936 carry 4 marks each and 2 marks is deducted for every wrong answer.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four
option(s) is(are) correct
Q.
One mole of a monoatomic real gas satisfies the equation p(V – b) = RT where b is a constant. The
relationship of interatomic potential V(r) and interatomic distance r for the gas is given by
In the following reactions, the product S is
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