SECTION – 1: (Only one option correct Type)
This section contains 10 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which ONLY ONE is correct.
Q. 1  10 carry 2 marks each.
Q.
One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another
horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces
at two ends, the ratio of the elongation in the thin wire to that in the thick wire is
The work done on a particle of mass m by a force (K being a constant of appropriate dimensions, when the particle is taken from the point (a, 0) to the point (0, a) along a circular
path of radius a about the origin in the xy plane is
Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity k and the other 2k . The temperature difference between the ends along the xaxis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is
A ray of light travelling in the direction is incident on a plane mirror. After reflection, it travels
along the direction The angle of incidence is
Let angle between the directions of incident ray and reflected ray be θ
The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero
of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions
equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale
divisions. The diameter of the cylinder is
Two nonreactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their
partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their
densities is
Here ρ1 and ρ2 are the densities of gases in the vessel containing the mixture
In the Young’s double slit experiment using a monochromatic light of wavelength λ, the path difference (in
terms of an integer n) corresponding to any point having half the peak intensity is
The image of an object, formed by a planoconvex lens at a distance of 8 m behind the lens, is real and is
onethird the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free
space. The radius of the curved surface of the lens is
A particle of mass m is projected from the ground with an initial speed u_{0} at an angle α with the horizontal.
At the highest point of its trajectory, it makes a completely inelastic collision with another identical
particle, which was thrown vertically upward from the ground with the same initial speed u_{0}. The angle that
the composite system makes with the horizontal immediately after the collision is
Velocity of particle performing projectile motion at highest point
= v_{1} = v_{0}cos α
Velocity of particle thrown vertically upwards at the position of collision
A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the
pulse is 30 mW and the speed of light is 3 x 10^{8} m/s. The final momentum of the object is
SECTION – 2 : (One or more options correct Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
Q. No. 11 15 carry 4 marks each and 1 mark is deducted for incorrect answer
Q.
In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch
S_{1} is pressed first to fully charge the capacitor C_{1} and then released. The switch S_{2} is then pressed to charge
the capacitor C_{2}. After some time, S_{2} is released and then S_{3} is pressed. After some time,
After switch S_{1} is closed, C_{1} is charged by 2CV_{0}, when switch S_{2} is closed, C_{1} and C_{2} both have upper plate
charge CV_{0}.
When S_{3} is closed, then upper plate of C_{2} becomes charged by CV_{0} and lower plate by +CV_{0}
A particle of mass M and positive charge Q, moving with a constant velocity enters a region
of uniform static magnetic field normal to the xy plane. The region of the magnetic field extends from x =
0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after
10 milliseconds with a velocity The correct statement(s) is (are)
A horizontal stretched string fixed at two ends, is vibrating in its fifth harmonic according to the equation y(x, t) = 0.01m sin [(62.8m^{1})x] cos[(628s^{1})t]. Assuming π = 3.14, the correct statement(s) is (are)
A solid sphere of radius R and density ρ is attached to one end of a massless spring of force constant k.
The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete
arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct
statement(s) is (are)
For equilibrium of the complete system, net force of buoyancy must be equal to
the total weight of the sphere which holds true in the given problem. So both
the spheres are completely submerged
Two nonconducting solid spheres of radii R and 2R, having uniform volume charge densities ρ_{1} and ρ_{2}
respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere,
along the line joining the centre of the spheres is zero. The ratio ρ_{1}/ρ_{2} can be
SECTION – 3 : (Integer value correct Type)
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).
Q. No. 1620 carry 4 marks each and 1 mark is deducted for every incorrect answer
Q.
A bob of mass m , suspended by a string of length l_{1} is given a minimum velocity required to complete a
full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m
suspended by a string of length l_{2}, which is initially at rest. Both the strings are massless and inextensible.
If the second bob, after collision acquires the minimum speed required to complete a full circle in the
vertical plane, the ratio l_{1}/l_{2} is
A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to
the particle. If the initial speed (in m/s) of the particle is zero, the speed (in m/s) after 5 s is
The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the
stopping potential versus frequency plot for Silver to that of Sodium is
Slope of graph is h/e = constant
1
A freshly prepared sample of a radioisotope of halflife 1386 s has activity 10^{3} disintegrations per second.
Given that ln 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage)
that will decay in the first 80 s after preparation of the sample is
A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s^{1}
about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m,
are gently placed symmetrically on the disc in such a manner that they are touching each other along the
axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest
relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s^{1}) of
the system is
SECTION – 1
Q. No. 21 40 carry 2 marks each
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Q.
In the reaction,
P+Q →R+S
the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q
varies with reaction time as shown in the figure. The overall order of the reaction is
Overall order of reaction can be decided by the data given t_{75%} = 2t_{50%}
It is a first order reaction with respect to P.
From graph [Q] is linearly decreasing with time, i.e. order of reaction with respect to Q is zero and the rate
expression is r = k [P]1[Q]0.
Hence (D) is correct.
Consider the following complex ions, P, Q and R
The correct order of the complex ions, according to their spin–only magnetic moment values (in B.M.) is
P = Fe^{+3} (no. of unpaired e^{} = 5)
Q = V^{+2} (no. of unpaired e^{} = 3)
R = Fe^{+2} (no. of unpaired e^{} = 4)
As all ligands are weak field, hence the no. of unpaired electrons remains same in the complex ion.
Hence (B) is correct.
The arrangement of X^{–} ions around A^{+} ion in solid AX is given in the figure (not drawn to scale). If the
radius of X^{–} is 250 pm, the radius of A^{+} is
According to the given figure, A^{+} is present in the octahedral void of X^{}. The limiting radius in octahedral void is related to the radius of sphere as
Concentrated nitric acid, upon long standing, turns yellow–brown due to the formation of
NO_{2} remains dissolved in nitric acid colouring it yellow or even red at higher temperature
The compound that does NOT liberate CO_{2}, on treatment with aqueous sodium bicarbonate solution, is
pK_{a} of PhOH (carbolic acid) is 9.98 and that of carbonic acid (H_{2}CO_{3}) is 6.63 thus phenol does not give
effervescence with HCO_{3}^{} ion.
Sulfide ores are common for the metals
Sulfide ore of Ag → Argentite (Ag_{2}S), Pb → Galena (PbS), Cu → Copper glance (Cu_{2}S)
Hence (A) is correct.
Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 250C. For this process, the
correct statement is
Adsorption of methylene blue on activated charcoal is physical adsorption hence it is characterised by decrease in enthalpy. Hence (B) is correct
KI in acetone, undergoes S_{N}2 reaction with each of P, Q, R and S. The rates of the reaction vary as
Relative reactivity for S_{N}2 reaction in the given structures is
The standard enthalpies of formation of CO_{2}(g), H_{2}O(l) and glucose(s) at 25^{0}C are –40^{0} kJ/mol,
–300 kJ/mol and –1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at
25^{0}C is
Upon treatment with ammoniacal H_{2}S, the metal ion that precipitates as a sulfide is
Among Fe^{3+}, Al^{3+}, Mg^{2+}, Zn^{2+} only Zn^{2+} is precipitated with ammonical H_{2}S as ZnS.
SECTION – 2
Q.No 31  35 carry 4 marks each 1 mark is deducted for every incorrect answer.
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
Q.
The initial rate of hydrolysis of methyl acetate (1 M) by a weak acid (HA, 1M) is 1/100^{th} of that of a strong acid (HX, 1M), at 25^{o}C. The K_{a} of HA is
The hyperconjugative stabilities of tertbutyl cation and 2butene, respectively, are due to
The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)
(an octahedral complex) and (a square planar complex) will show geometrical isomerism.
will show ionization isomerism
Among P, Q, R and S, the aromatic compound(s) is/are
Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s)
is(are)
SECTION3 (Integer value correct Type)
Q. No 36 40 carry 4 marks each and 1 mark is deducted for every incorrect answer
This section contains 5 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. (both inclusive).
Q.
The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength
of He gas at – 73^{o}C is “M” times that of the de Broglie wavelength of Ne at 727^{o} C. M is
EDTA^{4} is ethylenediaminetetraacetate ion. The total number of N – Co – O bond angles in [Co(EDTA)]^{1}
complex ion is
The total number of carboxylic acid groups in the product P is
A tetrapeptide has – COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine
(Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences
(primary structures) with – NH_{2} group attached to a chiral center is
Because –COOH group of tetrapeptide is intact on alanine, its NH_{2} must be participating in condensation.
Alanine is at one terminus, – – – A.
To fill the 3 blanks, possible options are:
(i) When NH_{2} group attached to non chiral carbon
(ii) When NH2 group attached to chiral carbon
where, Glycine (G)
Valine (V)
Phenyl alanine (P)
Alanine (A)
So the number of possible sequence are 4.
The total number of lonepairs of electrons in melamine is
lone pairs
SECTION  1
Q. No. 4150 carry 2 marks each
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Q.
Perpendiculars are drawn from points on the line to the plane x + y + z = 3. The feet of perpendiculars lie on the line
The foot of the perpendicular from point (– 2, – 1, 0) on the plane is the point A (0, 1, 2)
For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and
bx + ay + c = 0 is less than 2√2 , then
The area enclosed by the curves y = sinx + cosx and y = cosx  sinx over the interval is
=
Four persons independently solve a certain problem correctly with probabilities then the
probability that the problem is solved correctly by at least one of them is
P(at least one of them solves correctly) = 1 – P(none of them solves correctly)
Let complex numbers lie on circles
respectively. If z_{0} = x_{0} + iy_{0} satisfies the equation 2z_{0}^{2} = r^{2} + 2, then α =
The number of points in (∞, ∞), for which x^{2}  xsinx  cosx = 0, is
Let (the set of all real numbers) be a positive, nonconstant and differentiable function such that f'(x) < 2f(x) and f(1/2) =1 Then the value of lies in the interval
Let determine diagonals of a parallelogram PQRS and
be another vector. Then the volume of the parallelepiped determined by the vectors
The value of
A curve passes through the point Let the slope of the curve at each point (x, y) be Then the equation of the curve is
SECTION  2
Q. No 51 55 carry 4 marks each and 1 mark is deducted for every incorrect answer
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
Q.
A line l passing through the origin is perpendicular to the lines
Then, the coordinate(s) of the point(s) on l_{2} at a distance of from the point of intersection of l and l_{1} is
(are)
The common perpendicular is along
Let f(x) = xsin πx, x > 0. Then for all natural numbers n, f'(x) vanishes at
Let Then S_{n} can take value(s)
For 3 x 3 matrices M and N, which of the following statement(s) is (are) NOT correct ?
(A) (N^{T}MN)^{T} = N^{T}M^{T}N = N^{T}MN if M is symmetric and is – N^{T}MN if M is skew symmetric
(B) (MN  NM)^{T} = N^{T}M^{T}  M^{T}N^{T} = NM  MN = –(MN – NM). So, (MN – NM) is skew symmetric
(C) (MN)^{T} = N^{T}M^{T} = NM MN if M and N are symmetric. So, MN is not symmetric
(D) (adj. M) (adj. N) = adj(NM) adj (MN).
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an
open rectangular box by folding after removing squares of equal area from all four corners. If the total area
of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the
rectangular sheet are
Let the sides of rectangle be 15k and 8k and side of square be x then (15k – 2x)(8k – 2x)x is volume
SECTION  3
Q. No 5660 carry 4 marks each and 1 mark is deducted for every incorrect answer
This section contains 5 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive).
Q.
Consider the set of eight vectors Three noncoplanar vectors can be
chosen from V in 2^{p }ways. Then p is ________
Let (1, 1, 1), (–1, 1, 1), (1, –1, 1), (–1, –1, 1) be vectors rest of the vectors are and let us find the number of ways of selecting co–planar vectors.
Observe that out of any 3 coplanar vectors two will be collinear (anti parallel)
Number of ways of selecting the anti parallel pair = 4
Number of ways of selecting the third vector = 6
Total = 24
Number of non co–planar selections =
Of the three independent events E_{1}, E_{2}, and E_{3}, the probability that only E_{1} occurs is α, only E_{2} occurs is β
and only E_{3} occurs is γ. Let the probability p that none of events E_{1}, E_{2} or E_{3} occurs satisfy the equations
(α  2β) p = αβ and (β  3γ) p = 2βγ. All the given probabilities are assumed to lie in the interval (0, 1).
The coefficients of three consecutive terms of (1 + x)^{n+5} are in the ratio 5 : 10 : 14. Then n = _______
A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the
pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the
removed cards is k, then k ? 20 = ________
A vertical line passing through the point (h, 0) intersects the ellipse at the points P and Q. Let
the tangents to the ellipse at P and Q meet at the point R. If Δ(h) = area of the triangle PQR, Δ_{1} =
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