SECTION – 1
This section contains 8 multiple choice quesions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
Q. No. 1 8 carry 3 marks each and 1 marks is deducted for every wrong answer.
Q.
Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from
the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The
correct statement(s) is (are)
Note: The energy of mass ‘m’ means its kinetic energy (KE) only and not the potential energy of interaction between m and the two bodies (of mass M each) – which is the potential energy of the system.
A particle of mass m is attached to one end of a massless spring of force constant k, lying on a frictionless
horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its
equilibrium position at time t = 0 with an initial velocity u_{0}. When the speed of the particle is 0.5 u_{0}. It
collides elastically with a rigid wall. After this collision,
v = u0 sinωt (suppose t_{1} is the time of collision)
Now the particle returns to equilibrium position at time with the same mechanical energy i.e. its speed will u_{0.}
Let t_{3} is the time at which the particle passes through the equilibrium position for the second time.
Energy of particle and spring remains conserved.
A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is
placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and
carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s)
is (are)
Due to field of solenoid is non zero in region 0 < r < R and non zero in region r>2R due to conductor.
Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other.
Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f_{1} . An
observer in the other vehicle hears the frequency of the whistle to be f_{2} . The speed of sound in still air is
V. The correct statement(s) is (are)
Using the expression 2d sinθ = λ, one calculates the values of d by measuring the corresponding angles θ in
the range θ to 90°. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As
θ increases from 0°,
As θ increases cotθ decreases and cosθ/sin^{2}θ also decrease
Two nonconducting spheres of radii R1 and R2 and carrying uniform volume charge densities + ρ and –ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,
The figure shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The
temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the
following statement(s) is (are) correct to a reasonable approximation.
Option (A) is correct because the graph between (0 – 100 K) appears to be a straight line upto a reasonable
approximation.
Option (B) is correct because area under the curve in the temperature range (0  100 K) is less than in
range (400  500 K.)
Option (C) is correct because the graph of C versus T is constant in the temperature range (400  500 K)
Option (D) is correct because in the temperature range (200 – 300 K) specific heat capacity increases with
temperature.
The radius of the orbit of an electron in a Hydrogenlike atom is 4.5 a_{0} where a_{0} is the Bohr radius. Its
orbital angular momentum is . It is given that h is Planck’s constant and R is Rydberg constant. The
possible wavelength(s), when the atom deexcites, is (are)
SECTION – 2 : (Paragraph Type)
This section contains 4 paragraphs each describing theory, experiment, date etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of paragraph has only one correct answer along the four choice (A), (B), (C) and (D).
Q. No. 916 carry 3 marks each and 1 mark is deducted for every wrong answer.
Paragraph for Questions 9 to 10
A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s^{2}).
Q.
The speed of the block when it reaches the point Q is
Using work energy theorem
A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s^{2}).
Q.
The magnitude of the normal reaction that acts on the block at the point Q is
Paragraph for Questions 11 to 12
A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers’ usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of stepup and stepdown transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a stepup transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers’ end, a stepdown transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with the power factor unity. All the currents and voltage mentioned are rms values.
Q.
If the direct transmission method with a cable of resistance 0.4 km^{1} is used, the power dissipation (in %) during transmission is
Paragraph
A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers’ usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of stepup and stepdown transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a stepup transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers’ end, a stepdown transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with the power factor unity. All the currents and voltage mentioned are rms values.
Q.
In the method using the transformers, assume that the ratio of the number of turns in the primary to that in
the secondary in the stepup transformer is 1 : 10. If the power to the consumers has to be supplied at
200 V, the ratio of the number of turns in the primary to that in the secondary in the stepdown transformer
is
40000/200=200
Paragraph for Questions 13 to 14
A point Q is moving in a circular orbit of radius R in the xy plane with an angular velocity ω. This can be considered as equivalent to a loop carrying a steady current Qω/2π. A uniform magnetic field along the positive zaxis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant γ.
Q.
The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change, is
Paragraph
A point Q is moving in a circular orbit of radius R in the xy plane with an angular velocity ω. This can be considered as equivalent to a loop carrying a steady current Qω/2π. A uniform magnetic field along the positive zaxis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant γ.
Q.
The change in the magnetic dipole moment associated with the orbit, at the end of time interval of the
magnetic field change, is
Paragraph for Questions 15 to 16
The mass of nucleus is less than the sum of the masses of (AZ) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of mass m_{1} and m_{2} only if (m_{1} + m_{2}) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M' only if (m_{3} + m_{4}) > M'. The masses of some neutral atoms are given in the table below:
Q.
The correct statement is
The kinetic energy (in keV) of the alpha particle, when the nucleus at rest undergoes alpha decay, is
SECTION – 3 (Matching List Type)
This section contains 4 multiple choice questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Q. No. 1720 carry 3 marks each and 1 mark is deducted for every wrong answer.
Q.
A right angled prism of refractive index μ_{1} is placed in a rectangular block of refractive index μ_{2}, which is surrounded by a medium of refractive index μ_{3}, as shown in the figure. A ray of light ‘e’ enters the rectangular block at normal incidence. Depending upon the relationships between μ_{1}, μ_{2} and μ_{3}, it takes one of the four possible paths ‘ef’, ‘eg’, ‘eh’, or ‘ei’.
Match the paths in List I with conditions of refractive indices in List II and select the correct answer using
the codes given below the lists:
Match List I with List II and select the correct answer using the codes given below the lists
One mole of monoatomic ideal gas is taken along two cyclic processes E→F→G→E and E→F→H→E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.
Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using
the codes given below the lists.
Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of
each process and then select the correct answer using the codes given below the lists:
SECTION –1
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
Q.No. 18 carry 3 marks each and 1 marks is deducted for every worng answer.
Q.
The K_{sp} of Ag_{2}CrO_{4} is 1.1 x 10^{–12} at 298K. The solubility (in mol/L) of Ag_{2}CrO_{4} in a 0.1M AgNO_{3} solution
is
In the following reaction, the product(s) formed is(are)
The major product(s) of the following reaction is (are)
After completion of the reactions (I and II), the organic compound(s) in the reaction mixtures is(are)
The correct statement(s) about O_{3} is(are)
In the nuclear transmutation
(X, Y) is (are)
The carbon–based reduction method is NOT used for the extraction of
Fe_{2}O_{3} and SnO_{2} undergoes C reduction. Hence (C) and (D) are correct
The thermal dissociation equilibrium of CaCO_{3}(s) is studied under different conditions
For this equilibrium, the correct statement(s) is(are)
For the equilibrium
The equilibrium constant (K) is independent of
initial amount of CaCO_{3} where as at a given temperature is independent of pressure of CO_{2}. ΔH is independent of catalyst and it depends on temperature. Hence (A), (B) and (D) are correct.
SECTION2 (Paragraph Type)
This section contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D).
Q.No. 2936 carry 3 marks each and 1 mark is deducted for every wrong answer.
Paragraph for Question Nos. 29 and 30
An aqueous solution of a mixture of two inorganic salts, when treated with dilute HCl, gave a precipitate (P) and a filtrate (Q). The precipitate P was found to dissolve in hot water. The filtrate (Q) remained unchanged, when treated with H_{2}S in a dilute mineral acid medium. However, it gave a precipitate (R) with H_{2}S in an ammoniacal medium. The precipitate R gave a coloured solution (S), when treated with H_{2}O_{2} in an aqueous NaOH medium
Q.
The precipitate P contains
Paragraph
An aqueous solution of a mixture of two inorganic salts, when treated with dilute HCl, gave a precipitate (P) and a filtrate (Q). The precipitate P was found to dissolve in hot water. The filtrate (Q) remained unchanged, when treated with H_{2}S in a dilute mineral acid medium. However, it gave a precipitate (R) with H_{2}S in an ammoniacal medium. The precipitate R gave a coloured solution (S), when treated with H_{2}O_{2} in an aqueous NaOH medium
Q.
The coloured solution S contains
Paragraph for Question Nos. 31 to 32
P and Q are isomers of dicarboxylic acid C_{4}H_{4}O_{4}. Both decolorize Br_{2}/H_{2}O. On heating, P forms the cyclic anhydride. Upon treatment with dilute alkaline KMnO_{4}, P as well as Q could produce one or more than one from S, T and U.
Q.
Compounds formed from P and Q are, respectively
P and Q are isomers of dicarboxylic acid C_{4}H_{4}O_{4}. Both decolorize Br_{2}/H_{2}O. On heating, P forms the cyclic anhydride. Upon treatment with dilute alkaline KMnO_{4}, P as well as Q could produce one or more than one from S, T and U.
Q.
In the following reaction sequences V and W are, respectively
Paragraph for Question Nos. 33 to 34
A fixed mass ‘m’ of a gas is subjected to transformation of states from K to L to M to N and back to K as shown in the figure
Q.
The succeeding operations that enable this transformation of states are
K – L heating, isobaric
L – M cooling, isochoric
M – N cooling, isobaric
N – K heating, isochoric
A fixed mass ‘m’ of a gas is subjected to transformation of states from K to L to M to N and back to K as shown in the figure
Q.
The pair of isochoric processes among the transformation of states is
K – L heating, isobaric
L – M cooling, isochoric
M – N cooling, isobaric
N – K heating, isochoric
Paragraph for Question Nos. 35 to 36
The reactions of Cl_{2} gas with colddilute and hotconcentrated NaOH in water give sodium salts of two (different) oxoacids of chlorine, P and Q, respectively. The Cl_{2} gas reacts with SO_{2} gas, in presence of charcoal, to give a product R. R reacts with white phosphorus to give a compound S. On hydrolysis, S gives an oxoacid of phosphorus, T
Q.
P and Q, respectively, are the sodium salts of
The reactions of Cl_{2} gas with colddilute and hotconcentrated NaOH in water give sodium salts of two (different) oxoacids of chlorine, P and Q, respectively. The Cl_{2} gas reacts with SO_{2} gas, in presence of charcoal, to give a product R. R reacts with white phosphorus to give a compound S. On hydrolysis, S gives an oxoacid of phosphorus, T
Q.
R, S and T, respectively, are
SECTION – 3: (Matching List Type)
This section contains 4 multiple choice questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Q.No. 37  40 carry 3 marks each and 1 mark is deducted for every wrong answer
Q.
The unbalanced chemical reactions given in List – I show missing reagent or condition (?) which are
provided in List – II. Match List – I with List – II and select the correct answer using the code given below
the lists:
Match the chemical conversions in List – I with appropriate reagents in List – II and select the correct
answer using the code given below the lists:
An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List – I. The variation in
conductivity of these reactions in List – II. Match List – I with List – II and select the correct answer using
the code given below the lists:
Initially conductivity increases due to ion formation after that it becomes practically constant because X alone can not form ions. Hence (3) is the correct match.
Number of ions in the solution remains constant until all the AgNO_{3} precipitated as AgI. Thereafter conductance increases due to increases in number of ions. Hence (4) is the correct match.
R. Initially conductance decreases due to the decrease in the number of ions thereafter it slowly increases due to the increases in number of H+ ions. Hence (2) is the correct match.
S. Initially it decreases due to decrease in H^{+} ions and then increases due to the increases in Hence (1) is the correct match.
The standard reduction potential data at 25^{o}C is given below :
Match E^{0} of the redox pair in List – I with the values given in List – II and select the correct answer using
the code given below the lists:
SECTION  1 : (One or more option correct Type)
Q. No. 1 8 carry 3 marks each and 1 mark is deducted for every wrong answer
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
Q.
For a R (the set of all real numbers)
Then a =
Circle(s) touching xaxis at a distance 3 from the origin and having an intercept of length 2√7 on yaxis is
(are)
Two lines are coplanar. Then α can take value(s)
Alternate Solution:
As x = 5 and x = α are parallel planes so the remaining two planes must be coplanar.
In a triangle PQR, P is the largest angle and cos P=1/3 . Further the incircle of the triangle touches the sides
PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even
integers. Then possible length(s) of the side(s) of the triangle is (are)
Let and H_{2} = where C is the set of all complex numbers. and O represents the origin, then z_{1 }Oz_{2} =
Possible position of z_{1} are A_{1}, A_{2}, A_{3} whereas of z_{2} are B_{1}, B_{2}, B_{3} (as shown in the figure)
So, possible value of z_{1}Oz_{2} according to the given options is
If 3^{x} = 4^{x1}, then x =
Let ω be a complex cube root of unity with ω 1 and P = [p_{ij}] be a n x n matrix with p_{ij} = ω^{i+j}. Then P^{2} 0,
when n =
P^{2} = Null matrix if n is a multiple of 3
The function has a local minimum or a local maximum at x =
According to the figure shown, points of local minima/maxima are x=2, 2/3, 0
SECTION  2 : (Paragraph Type)
Q. No. 49  54 carry 3 marks each and 1 mark is deducted for every wrong answer.
This section contains 6 multiple choice questions relating to three paragraphs with two questions on each paragraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
Paragraph for Questions 49 and 50
Let f : [0, 1] → R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) = 0 and satisfies
Q.
Which of the following is true for 0 < x < 1 ?
Since g is concave up so it will always lie below the chord joining the extremities which is y = x/2
Let f : [0, 1] → R (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0) = f(1) = 0 and satisfies
Q.
If the function e^{x} f(x) assumes its minimum in the interval [0, 1] at x = 1/4 which of the following is true ?
Paragraph for Questions 51 and 52
Let PQ be a focal chord of the parabola y^{2} = 4ax. The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0.
Q.
Length of chord PQ is
Let PQ be a focal chord of the parabola y^{2} = 4ax. The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0.
Q.
If chord PQ subtends an angle θ at the vertex of y^{2} = 4ax, then tanθ =
Paragraph for Questions 53 and 54
Let where
Q.
Area of S =
Area of region
Let where
Q.
Paragraph for Questions 55 and 56
A box B_{1} contains 1 white ball, 3 red balls and 2 black balls. Another box B_{2} contains 2 white balls, 3 red balls and 4 black balls. A third box B_{3} contains 3 white balls, 4 red balls and 5 black balls.
Q.
If 1 ball is drawn from each of the boxes B_{1}, B_{2} and B_{3}, the probability that all 3 drawn balls are of the
same colour is
P (required) = P (all are white) + P (all are red) + P (all are black)
A box B_{1} contains 1 white ball, 3 red balls and 2 black balls. Another box B_{2} contains 2 white balls, 3 red balls and 4 black balls. A third box B_{3} contains 3 white balls, 4 red balls and 5 black balls
Q.
If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B_{2} is
Let A : one ball is white and other is red
E_{1} : both balls are from box B_{1}
E_{2} : both balls are from box B_{2}
E_{3} : both balls are from box B_{3}
SECTION  3 : (Matching list Type)
Q. No. 57  60 carry 3 marks each and 1 mark is deducted for every wrong answer
This section contains 4 multiple choice questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Q.
Match List I with List II and select the correct answer using the code given below the lists :
A line L : y = mx + 3 meets yaxis at E(0, 3) and the arc of the parabola y2 = 16x, 0 y 6 at the point
F(x_{0}, y_{0}). The tangent to the parabola at F(x_{0}, y_{0}) intersects the yaxis at G(0, y_{1}). The slope m of the line L
is chosen such that the area of the triangle EFG has a local maximum.
Match List I with List II and select the correct answer using the code given below the lists
Match List I with List II and select the correct answer using the code given below the lists :
Consider the lines and the planes P_{1} : 7x + y + 2z = 3, P2: 3x + 5y  6z = 4. Let ax + by + cz = d be the equation of the plane passing through the point of
intersection of lines L_{1} and L_{2}, and perpendicular to planes P_{1} and P_{2}.
Match List I with List II and select the correct answer using the code given below the lists :
Plane perpendicular to P_{1} and P_{2} has Direction Ratios of normal
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