Question Paper (Section wise)

1) A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds , is close to:

3.16

0.32

0.45

2.24


2) A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to:

1.0 × 10^{7 }T

1.5 × 10^{7 }T

1.5 × 10^{5 }T

1.0 × 10^{5 }T


3) Three charges +Q, q, +Q are placed respectively, at distance 0, d/2 and d from the origin, on the xaxis. If the net force experienced by +Q, placed at x = 0, is zero, then value of q is

Q/4

+Q/2

+Q/4

Q/2


4) An unknown metal of mass 192 g heated to a temperature of 100Â°C was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4Â°C. Calculated the specific heat of the unknown metal if water temperature stabilized at 21.5Â°C. (Specific heat of brass is 394 J kg^{1}k^{1}).

458 J kg^{1}K^{1}

919 J/Kg K^{1}

T_{h} = 1.5T_{c}

T_{h} = 0.5_{c}


5) The selfproduce emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1 s, the change in the energy of the inductance is:

740 J

437.5 J

540 J

637.5 J


6) A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is:

692 pJ

508 pJ

560 pJ

600 pJ


7) A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980 Ã…. The radius of the atom in the excited state, in terms of Bohr radius a_{0}, will be (hc = 12500 eVÃ…)

25a_{0}

9a_{0}

16a_{0}

4a_{0}


8) A particle undergoing simple harmonic motion has time dependent displacement given by . The ratio of kinetic to potential energy of the particle at t = 210s will be

1/9

1

2

1/3


9) The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following, graph is the correct one, if D_{m} is the angle of minimum deviation?


10) A planoconvex lens (focal length f_{2}, refractive index Âµ_{2}, radius of curvature R) fits exactly into a plano concave lens (focal length f_{1}, refractive index Âµ_{1}, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

f_{1} â€“ f_{2}



f_{1} + f_{2}


11) A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is l_{1}, and that below the piston is l_{2}, such that l_{1 }> l_{2}. Each part of the cylinder contains n moles of an ideal gas at equal temperature. T.
(R is universal gas constant and g is the acceleration due to gravity)


12) In a Frankhertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to:

1700 nm

2020 nm

220 nm

250 nm


13) A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at same position even if the concave mirror, by itself would produce a virtual image would be:

20 cm

10 cm

30 cm

20 cm


14) A particle starts from origin O from rest and moves with a uniform acceleration along the positive x â€“ axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)
Â
a.
b.
c.
d.

a, b, c

A

b, c

a, b, d


15) The given diagram shows four processes i.e., isochoric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by:

a d c d

a d b c

d a c b

d a b c


16) An NPN transistor is used in common emitter configuration as an amplifier with 1 kÎ© load resistance. Signal voltage of 10 mV is applied across the baseemitter. This produces a 3 mA change in the collector current and 15 Î¼A change in the base current of the amplifier. The input resistance and voltage gain are:

0.67 kÎ©, 300

0.67 kÎ©, 200

0.33 kÎ©, 1.5

0.33 kÎ©, 300


17) Following figure shows two processes A and B for a gas. If âˆ†Q_{A} and âˆ†Q_{B} are the amount of heat absorbed by the system in two cases, and âˆ†U_{A} and âˆ†U_{B} are changes in internal energies, respectively, then:

âˆ†Q_{A} = âˆ†Q_{B}; âˆ†U_{A} = âˆ†U_{B}

âˆ†Q_{A} > âˆ†Q_{B}; âˆ†U_{A} = âˆ†U_{B}

âˆ†Q_{A} < âˆ†Q_{B}; âˆ†U_{A} < âˆ†U_{B}

âˆ†Q_{A} > âˆ†Q_{B}; âˆ†U_{A} > âˆ†U_{B}


18) A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of Î¸, where Î¸ is the angle by which it has rotated, is given as kÎ¸^{2}. If its moment of inertia is I then the angular acceleration of the disc is:


19) A bullet of mass 20 g has an initial speed of 1 ms^{1} just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers mean resistance of 2.5 Ã— 10^{2} N, the speed of the bullet after emerging from the other side of the wall is close to

0.7 ms^{1}

0.3 ms^{1}

0.1 ms^{1}

0.4 ms^{1}


20) In free space, a particle A of charge 1 Âµ C is held fixed at a point P. Another particle B of the same charge and mass 4 Âµg is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is

1.5 Ã— 10^{2} m/s

2.0 Ã— 10^{3} m/s

1.0 m/s

None


21) A source of sound S is moving with the velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the sound as 1000Hz. The apparent frequency of the source when it is moving away from the observer after crossing him is ______.
(Take velocity of sound in air is 350 m/s)

22) What will be value of x in the given equation below which is used to express dimension of resistance?
(Here, R is electrical resistance, âˆˆ_{0} is the permittivity of vacuum and Î¼_{0} is the permeability of vacuum)

23) Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be. The angle between polarizer A and C is ________Â°.

24) A spaceship orbits around a planet at a height of 20 km from surface. Assuming that only gravitational field of the plant acts on the spaceship. The approximate number of revolution made by the spaceship in 24 hours around the plane is ______.
[Given: Mass of plane = 8 Ã— 10^{22 }kg, Radius of planet = 2 Ã— 10^{6} m, Gravitational constant G = 6.67 Ã— 1011 Nm^{2}/kg^{2}]

25) A plane is inclined at an angle α = 30° with respect to the horizontal. A particle is projected with a speed u = 2 ms1, from the base of the plant, making an angle θ = 15° with respect to the plane as shown in the figure. The distance from the base at which the particle hits the plane is close to ______ cm.
(Take, g = 10 m/s^{2})

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1) 0.5 moles of gas A and X moles of gas B exert a pressure of 200 Pa in a container of volume 10m^{3 }at 1000 K. Given R is the gas constant in JK^{1 }moI^{1},x is


2) A solution of sodium sulphate contains 92 g of Na^{+ }ions per kilogram of water. The Molality of Na^{+} ions in that solution in mol kg^{1} is

12

4

8

16


3) According to molecular orbital theory, which of the following is true with respect to Â and

Â is unstable and Â is stable

Â is stable and Â is unstable

Both are stable

Both are unstable


4) Among the following reactions of hydrogen with halogens, the one that requires a catalyst is:

H_{2 }+ l_{2 }â†’ 2HI

H_{2} + CI_{2} â†’ 2HCI

H_{2 }+ Br_{2Â }â†’ 2HBr

H_{2 }+ F_{2 }â†’ 2HF


5) The process with negative entropy change is:

Dissociation of CaSo_{4}(s) to CaO(s) and SO_{3}(g)

Sublimation of dry ice

Dissolution of iodine in water

Synthesis of ammonia from N_{2} and H_{2}


6) The major product obtained in the following reaction is:


7) A 10 g effervescent tablet containing sodium bicarbonate and oxalic acid releases 0.25 ml of CO_{2} at T = 298.15 K and p = 1 bar. If molar volume of CO_{2 }is 25.0 L under such condition, what is the percentage of sodium bicarbonate in each tablet? [Molar mass of NaHCO_{3}= 84 g mol^{1}]

0.84

33.6

16.8

8.4


8) An organic compound is estimated through Dumas method and was found to evolve 6 mole of CO_{2}, 4 moles of H_{2}O and 1 mole of nitrogen gas. The formula of the compound is:

C_{12}H_{8}N

C_{12}H_{8}N_{2}

C_{6}H_{8}N_{2}

C_{6}H_{8}N


9) The major product of the following reaction is


10) The major product of the following reaction is:


11) An open vessel at 27Â°C is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is:

500Â°C

500 K

750Â°C

750 K


12) The upper stratosphere consisting of the ozone layer protects us from the sunâ€™s radiation that falls in the wavelength region of:

200 â€“ 315 nm

400 â€“ 550 nm

0.8 â€“ 1.5 nm

600 â€“ 750 nm


13) Calculate the standard cell potential (in V) of the cell in which following reaction takes place:
Fe^{2} + (aq) + Ag^{+} (aq) â†’Fe^{3+}(aq)+ Ag (s)
Given that:

x â€“ z

x + y â€“z

x â€“ y

x + 2y â€“ 3z


14) The covalent alkaline earth metal halide
(X = Cl, Br, l)is:

BeX_{2}

CaX_{2}

SrX_{2}

MgX_{2}


15) Which one of the following alkenes when treated with HCl yields majorly an anti Markovnikov product?

H_{2}N â€“CH = CH_{2}

F_{3}C â€“CH = CH_{2}

CH_{3}O â€“ CH = CH_{2}

Cl â€“ CH = CH_{2}


16) Consider the van der Waals constants, a and b, for the following gases.
Which gas is expected to have the highest critical temperature?

Ar

Xe

Kr

Ne


17) Among the following the set of parameters that represents path functions, is:
a.Â Â Â Â Â Â q + w
b.Â Â Â Â Â Â q
c.Â Â Â Â Â Â w
d.Â Â Â Â Â Â H â€“ TS

(b) and (c)

(b), (c) and (d)

(a), (b) and (c)

(a) and (d)


18) The degenerate orbitals of [Cr(H_{2}O)_{6}]^{3+Â Â }are:

d_{xz} and d_{yz}

d_{x}^{2}_{y}^{2} and d_{xy}

d_{yz} and d_{z}^{2}

d_{z}^{2} and d_{xz}


19) The difference between Î”H and Î”U (Î”H  Î”U), when the combustion of one mole of heptane (I) is carried out a temperature T is equal to

4 RT

3 RT

3 RT

4 RT


20) The correct order of the first ionization enthalpies is

Mn < Ti < Zn < Ni

Zn < Ni < Mn < Ti

Ti < Mn < Zn < Ni

Ti < Mn < Ni < Zn


21) How many statement/s is/are INCORRECT for R_{f} in chromatography?
 R_{f }value depends on the type of chromatography
 The value of R_{f}cannot be more than one.
 Higher R_{f}value means higher adsorption.
 R_{f}value is dependent on the mobile phase.

22) How many products will formed in the following reaction?

23) Among the following how many number of species are responsible for photochemical smog?
CO_{2}, NO, NO_{2}, O_{3}, SO_{2}, N_{2 }and hydrocarbons

24) The atomic number of a metal with ‘Zn’ symbol gives hydrogen gas upon treatment with both acid as well as base is:

25) Consider the following reaction and statements:
 Two isomers are produced if the reactant complex ion is a cisisomer
 Two isomers are produced if the reactant complex ion is a transisomer
 Only one isomer is produced if the reactant complex ion is a transisomer
 Only one isomer is produced if the reactant complex ion is a cisisomer
The correct statements are

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1) If y = y(x) is a solution of the differential equation Â satisfying y(1) = 1, then y Â is equal to:


2) For x Ïµ R â€“ {0, 1}, let f_{1}(x) = , f_{2}(x) = 1 â€“ x and f_{3}(x) = Â be three given functions. If a function, J(x) satisfies (f_{2}oJof_{1}) (x) = f_{3}(x) then J(x) is equal to:

f_{3}(x)


f_{2}(x)

f_{1}(x)


3) Let Â be a vector such that Â is equal to:


9

8



4) The value of Î» such that sum of the squares of the roots of a quadratic equationÂ x^{2 }+ (3 â€“ Î») x + 2 = Î», has the least value is:


1


2


5) Let f: (1, 1) â†’ R be a function defined by f(x) = max. If K be the set of all points at which f is not differentiable, then K has exactly:

five elements

one elements

three elements

two elements


6) The number of values of Î¸ Ïµ (0, Ï€) for which the system of linear equations, x + 3y + 7z = 0, x + 4y + 7z = 0 and (sin3Î¸) x + (cos2Î¸) y+ 2z = 0 has a nontrivial solution, is:

Three

Two

Four

One


7) Â for k = 1, 2, 3,â€¦ Then for all x Ïµ R, the value of f_{4}(x) â€“ f_{6}(x) is equal to:


8) The area (in sq. units) of the region bounded by the curve x^{2} = 4y and the straight line x = 4y â€“ 2 is:

5/4

9/8

7/8

3/4


9) The value of r for which ^{20}C_{r }^{20}C_{0 }+ ^{20}C_{r1 }^{20}C_{1 }+ ^{20}C_{r2 }^{20}C_{2 }+ â€¦ + ^{20}C_{0 }^{20}C_{r }is maximum is:

15

20

11

10


10) In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is:

Â

0

Â



11) If a straight line passing through the point P(3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is:

3x â€“ 4y + 25 = 0

4x â€“ 3y + 24 = 0

x â€“ y + 7 = 0

4x + 3y = 0


12) Let z_{1} and z_{2 }be two complex numbers satisfying Then the minimum value of Â is:

0

âˆš2

1

2


13) Which one of the following statements is not a tautology?

(p Ë… q) â†’ (p Ë… (âˆ¼q))

(p Ë… q) â†’ p

p â†’ (p Ë… q)

(p Ë„ q) â†’ (âˆ¼p) Ë… q


14) If a point R(4, y, z) lies on the line segment joining the points P(2, â€“3, 4) and Q(8, 0, 10), then the distance of R from the origin is:

âˆš53

6

2âˆš14

2âˆš21


15) If the fourth term in the binomial expansion of Â is equal to 200, and x > 1, then the value of x is:

10^{4}

100

10^{3}

10


16) If the standard deviation of the numbers 1, 0, 1, k is âˆš5 where k > 0, then k is equal to:


17) If f(x) is a nonzero polynomial of degree four, having local extreme points at x = 1, 0, 1; then the set S = {x Ïµ R; f(x) = f(0)} contains exactly:

four irrational numbers

four rational numbers

two irrational and one rational number

two irrational and two rational numbers


18) Let the sum of the first n terms of a nonconstant A.P., a_{1}, a_{2}, a_{3}, â€¦â€¦â€¦ be , where A is a constant. If d is the common difference of this A.P., then the ordered pair (d, a_{50}) is equal to:

(A, 50 + 46A)

(A, 50 + 45A)

(50, 50 + 45A)

(50, 50 + 46A)


19) If the line ax + y = c, touches both the curves x^{2} + y^{2} = 1 and y^{2} = 4√2x then c is equal to:


√2


2


20) If the plane 2x â€“ y + 2z + 3 = 0 has the distances Â and Â units from the planes 4x â€“ 2y + 4z + Î» = 0 and 2x â€“ y + 2z + Âµ = 0, respectively, then the maximum value ofÂ Î» + Âµ is equal to:Â

15

13

5

9


21) If where c is a constant of integration, then g(–2) is equal to _________.

22) If e^{y} + xy = e such that the ordered pair at x = 0 is equal to , then the value of n is _____.

23) If the equation y = sin x sin(x + 2) – sin^{2}(x + 1) represents a straight line, then the number of quadrants it lies in is ___________.

24) For x âˆŠ R, let [x] denote the greatest integer ≥ x, then the sum of the series is equal to ________.

25) If the value of p is _______.

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