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This section contains 4 multiple choice questions numbered 1 to 4. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct
A particle is kept at rest at the top of a sphere of diameter 42 m. When disturbed slightly, it slides down. At what height h from the bottom, the particle will leave the sphere
A source is moving on a circle of radius 3 m with constant angular velocity ω = 5 rad/s. If the observer is at a distance 5 m from the centre of circle, the time interval between maximum and minimum frequency received by the observer is
In the cyclic process 1234 shown in figure for a monoatomic gas, thevolume of the gas in process 1.
In a PV diagram clockwise cyclic process means positive work is done. Here, with non zero anti clockwise area negative work is being done.
W = P∆V
∆V is negative, since, P is positive.
So, the volume decreases.
A capacitor is charged to a potential of V_{0}. It is connected with an inductor through a switch S. The switch is closed at time t = 0. Which of the following statement is correct.
This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct
A disc of radius R rolls on a horizontal surface with linear velocity V and angular velocity ω. There is a point P on circumference of disc at angle θ with upward vertical diameter measured anticlockwise (see figure), which has a vertical velocity. Here θ is equal to
A source of sound moves along a circle of radius 2 m with constant angular velocity 40 rad/s. Frequency of the source is 300 Hz. A detector is kept at some distance from the circle in the same plane of the circle (as shown in figure). Which of the following is not the possible value of frequency registered by the detector? (Speed of sound = 320 m/s)
An electron in Hatom jumps from second excited state to first excited state and then from first excited to ground state. Let the ratio of wavelength, momentum and energy of photons emitted in these two cases be a, b and c respectively. Then
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
Paragraph for Question Nos. 10 and 11
Four satellites A, B, C and D are orbiting around a spherical planet of uniform density. The orbits of all the satellites are coplanar. Orbits of satellites A and B are circular where radius of orbit A is greater than diameter of orbit B. Orbit C is touching orbits A and B. While orbit D is touching orbit A but its nearest distance from the planet is least among all four orbits. All the satellites have same mass and these satellite can be considered as particles. There is no gravitational force between the satellite and also there is no chance of collision between the satellites. Consider gravitational potential energy to be zero under infinite separation.
In which orbit can the gravitational potential energy have least possible value?
Four satellites A, B, C and D are orbiting around a spherical planet of uniform density. The orbits of all the satellites are coplanar. Orbits of satellites A and B are circular where radius of orbit A is greater than diameter of orbit B. Orbit C is touching orbits A and B. While orbit D is touching orbit A but its nearest distance from the planet is least among all four orbits. All the satellites have same mass and these satellite can be considered as particles. There is no gravitational force between the satellite and also there is no chance of collision between the satellites. Consider gravitational potential energy to be zero under infinite separation.
In which orbit does the angular momentum have largest magnitude?
Paragraph for Question Nos. 12 and 14
A thin nonconducting ring of mass m, radius a carrying a charge q can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant t = 0 A uniform magnetic field is switched on which is vertically downward and increases with time according to the law B = B_{0}t. Neglecting magnetism induced due to rotational motion of ring.
The magnitude of induced emf will be
A thin nonconducting ring of mass m, radius a carrying a charge q can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant t = 0 A uniform magnetic field is switched on which is vertically downward and increases with time according to the law B = B_{0}t. Neglecting magnetism induced due to rotational motion of ring.
The magnitude of an electric field on the surface of the ring is
A thin nonconducting ring of mass m, radius a carrying a charge q can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant t = 0 A uniform magnetic field is switched on which is vertically downward and increases with time according to the law B = B_{0}t. Neglecting magnetism induced due to rotational motion of ring.
Find instantaneous power developed by electric force acting on the ring at t = 1 sec.
This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example:
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following:
Figure shows a setup to perform Young’s double slit experiment. A monochromatic source of light is placed at S. S_{1} and S_{2} act as coherent sources and interference pattern is obtained on the screen. Match ColumnI with ColumnII in regard to interference in Young’s double slit
experiment:
Referring to the given circuit, match ColumnI with ColumnII.
This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).
The lengths of sides of a cuboid are a, 2a and 3a. If the relative percentage error in the
measurement of a is 1%, then find the relative percentage error in the measurement of volume of cube (in percentage)….
For the arrangement shown in figure, the masses of the blocks are m_{A} = 2 kg, m_{B} = 1 kg, m_{C} = 1 kg. Find the frictional force between the blocks A and B (in Newton) (coefficient of friction between any two surfaces is 0.5)
Suppose potential energy between particle A and B at separation r is given by U = k ln r, where k is constant. For such hypothetical system, find the ratio of energy difference between energy
levels (n = 1 and n = 2) and (n = 2 and n = 4) (The energy of a particle in n^{th} level is –13.6/n^{2})
A uniform disc of radius R having charge Q distributed uniformly all over its surface is placed on a smooth horizontal surface. A magnetic field, B = kxt^{2}, where k is a constant, x is the distance (in metre) from the centre of the disc and t is the time (in second), is switched on perpendicular to the plane of the disc. Find the torque (in Nm) acting on the disc after 15 sec. (Take 4kQ = 1 S.I.unit and R = 1m) is
The hydrogen atom in its ground state are excited by means of monochromatic radiation of
wavelength 1023 Å. Find the number of lines which can be seen in the resulting spectrum…
Potash alum contains the metals like potassium and aluminium. What are the metal ions present in chrome alum?
For a gaseous reaction, the rate of reaction is expressed in terms of dp/dt instead of dc/dt or dn/dt where C is concentration and n is the number of moles. Hence, the relation between expression is:
An excited electron of Hatoms emits of photon of wavelength λ and returns in the ground state, the principal quantum number of excited state is given by:
One mole of a monatomic 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
Here attraction is zero , so potential energy can’t be less than 0
This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct
Identify the correct relationship:
Ni^{2+} complex becomes 3d^{8} with all e^{} paired.
Chiral molecules do not have plane of symmetry
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
Paragraph for Question Nos. 10 and 11
The cloud consist of charged particles of water dispersed in air. Some of them are +vely charged and other are vely charged. When +vely charged clouds come closer they have lightening and thundering whereas  ve and +ve charged colloids come closer they cause heavy rain due to the aggregation of minute particles. It is possible to cause artificial rain by throwing electrified sand or AgI from aeroplane and thus coagulation the mist hanging in air.
When excess of 3 AgNO is treated withKI solution, AgI forms.
+vely charged colloid and –vely charged solution
The cloud consist of charged particles of water dispersed in air. Some of them are +vely charged and other are vely charged. When +vely charged clouds come closer they have lightening and thundering whereas  ve and +ve charged colloids come closer they cause heavy rain due to the aggregation of minute particles. It is possible to cause artificial rain by throwing electrified sand or AgI from aeroplane and thus coagulation the mist hanging in air.
Electrical chimney are made on the principal of
Neutralisation of charge of colloidal particle.
Paragraph for Question Nos. 12 and 14
Compound (A) , which can be distilled in high vacuum, gives positive test with Br_{2} / H_{2}O , but does not react with Nametal in ethereal solution, but compound (B) and (C) gives H2 (g) with sodium metal. Compound (A) undergoes following sequence of reactions
Compound ' B' should be:
Compound (A) , which can be distilled in high vacuum, gives positive test with Br_{2} / H_{2}O , but does not react with Nametal in ethereal solution, but compound (B) and (C) gives H2 (g) with sodium metal. Compound (A) undergoes following sequence of reactions
Compound ' A' should be:
Compound (A) , which can be distilled in high vacuum, gives positive test with Br_{2} / H_{2}O , but does not react with Nametal in ethereal solution, but compound (B) and (C) gives H2 (g) with sodium metal. Compound (A) undergoes following sequence of reactions
Compound 'C '
This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as
illustrated in the following example:
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s
and t; then the correct darkening of bubbles will look like the following:
Match the following metal given in columnI with the appropriate metal exaction process listed
with column II
This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as
illustrated in the following example:
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s
and t; then the correct darkening of bubbles will look like the following:
Match the following metal given in columnI with the appropriate metal exaction process listed
with column II
This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).
A saturated solution of spraingly soluble salt MCl_{2} has a vapour pressure of 31.78 mm of Hg at 30^{0}C while pure water exerts a pressure of 31.82 mm of Hg at the same temperature. The
solubility product is . The value of x is
The number of unpaired e^{} in first excited state of O_{2} is
in excited state it is
The number of geometrical isomers of the octahedral complex of the type [Mabcdef] is n x 3. . The value of n is
Total 15 gemetrical isomers
How many double bond equivalents does amoxicillin (shown below) possesses?
Let where [.] denotes the greatest integer function. The value of S is
Usemaxima minima concept
Minimum value of function f (x) = x^{3} (x^{3} +1)(x^{3} + 2)(x^{3} + 3) : x ∈ R, is
The hands of a clock has lengths 3 & 4 units. The distance between their tips when the distanceis increasing most rapidly is
is rotated about O (origin) by 90° such that it crosses the positive y axis during the rotation. If A goes to B then
This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct
In ΔABC, if A = 45^{0}, B = 75^{0} then
Equation of plane through A(1, 0, 0), B(0,1, 0) and making an angle π/4with the plane x + y = 3 canbe
If the area bounded by the curve y = x  x^{2} and the line y = mx equals 9/2. Then the value of q m is
use graph
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
A box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.
Probability that head appears is
Use binomial triad for probability
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
A box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.
Probability that the coin is fair given that head has appeared is
ABC is a triangle. Complex numbers z_{1} , z_{2} , z_{3} are represented by A, B, C respectively. Which are in anticlock wise order. let z_{1}=z_{2}=z_{3} and arg
Use rotation of complex numbers
Use rotation of complex numbers.
If T(z) is any point such that HBTC is a parallelogram then  z  z_{1} =
Use rotation of complex numbers.
This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as
illustrated in the following example:
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s
and t; then the correct darkening of bubbles will look like the following:
This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as
illustrated in the following example:
If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s
and t; then the correct darkening of bubbles will look like the following:
This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).
In equilateral triangle ABC of side p, a square is inscribed in its incircle. If area of the square is p^{2}/k then value of k is
f is a function such that f (x) + 2 f (1 x) = x^{2} +1 . Value of f (3) is
Replace x by (1x) solve to get the result
Degree of differential equation of family of ellipses of same size having minor axis along a given line is
See minimum number of unknowns
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