Advance 3 Paper 1

7/25/2019 Advance 3 Paper 1

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9/9/2015 Question Revision

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Question 1.

Select the correct statement(s) :

[A] Heisenberg's principle is applicable to stationary

[B] Pauli's exc lusion principle is not applicable to photons

[C] For an electron in Bohr's orbit, the product of velocity and principal quantum number will be independent of principal quantum

number

[D] Quantum numbers and m determine the value of angular wave function

Question 2.

Following graph represents the Maxwell distribution curv e for an ideal gas at two temperatures and . Which of the following

option(s) are true ?

[A] Total area under the two curv es is constant

[B] If then

[C] and hence higher the temperature, sharper the curv e

[D] The fraction of molecules having speed = decreases as temperature increases

Question 3.Which of the following statements is(are) correct ?

If

[A] ions can be reduced by

[B] Cu can be oxidized by

[C] ions can be reduced by

[D] Sn can be oxidized by

Question 4.

If be the first, second and third ionization constant of H3PO4and , then which is(are)

correct statement(s) :

[A]

[B]

[C]

[D]


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Question 5.

In a AB unit cell (rock salt type), ass uming forming fcc :

[A] The nearest neighbour of is ion

[B] The nearest neighbour of is ion

[C] The second nearest neighbour of is

[D] The packing fraction of AB cry stal is

Question 6.

Select the correct statement(s) :

[A] The rate law of the elementary reaction must be

[B] The rate law for the complex reaction might not be

[C] If the experimentally observed orders differ from the corresponding coefficients in the balanced reaction, the reaction must be

complex

[D] If the experimentally observed orders differ from the corresponding coefficients in the balanced reaction, the reaction must be

elementary

Question 7.

Select the correct statement(s):

[A] When or then (where T = temperature, Ea = activation energy, k = rate constant, A= Arrhenius

parameter)

[B] A positive catalys t can change of the reaction

[C] A mixture of reactants may be thermodynamically unstable but kinetically stable[D] A negative catalyst increases the activation energy of the reaction

Question 8.

The total vapour pressure of a binary solutions given by :

Where, are the mole fractions of components A and B. This indicates that the:

[A] Vapour press ure of solution is less than the pure B component[B] Vapour pressure of solution is more than that of pure A component[C] Vapour pressure of pure A is 100 mm Hg and that of pure B is 260 mm Hg[D] The vapour pressure of pure A and B are 260 mm Hg and 100 mm Hg respectively

Question 9.

The gaseous product(s) expected at room temperature by reaction of sodium borohydride and boron trifluoride under anhydrousconditions is(are) :

[A]

[B]

[C]

[D]

Question 10.

Select corr ect statement(s) regarding and -bonds :

[A] - bond lies on the line joining the nuclei of bonded atoms

[B] - bond cloud lies on either side of the line joining the nuclei of bonded atoms


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[C] pi-bond is stronger than pi- bond.

[D] -bond has primary effect on the direction of covalent bond, while -bond has no primary effect on the direction of

covalent bond

Question 11.

It is observed that the voltage of a galvanic cell using the reaction varies linearly with the log

of the square root of the hydrogen pressure and the cube root of the M x+concentration. Find the value of x.

Question 12.

How many of the following have non-zero dipole moment ?

I. SO2 II. PH3 III. SO3 IV. XeO2F2

V. BrF5 VI. COCl2 VII. POCl3 VIII. SF6

IX. XeO3 X. BeCl2

Question 13.How many of the following are state function?

I. Internal energy II. Molar enthalpy

III. Irreversible expansion work IV. Heat supplied

V. Gibbs free energy VI. Entropy

VII. Reversible expansion work

Question 14.

Two buffers (X) and (Y) of pH 4.3 and 6.3 respectively are prepared from acid HA and salt NaA. Both buffers are 0.5 M in HA. What

would be the pH of the solution obtained by mixing equal volumes of the two buffers ? [Given :

]

Question 15.

Enough solid NH4HS and LiCl.3NH3are heated in a closed vessel at and the following equilibria are established.

If Kpfor the first equilibrium at is 9 atm2and the total pressure of the system is 6 atm, find the value of Kpfor second

equilibrium.

Question 16.

For zero order reaction , plot of concentration vs time is as follows.

Find half life period in minutes if the initial conc. of A be 1 M.


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Question 17.

Total number of isomers (including stereoisomers) obtained by monochlorination of 2, 2, 4-trimethylpentane is(are)__________.

Question 18.

When 2 mol of an alkaline earth metal nitrate is decomposed on heating, find the number of gaseous moles in the product ?

Question 19.

MATCH THE FOLLOWING :

Column 1 Column 2

A : Reversible cooling of an ideal gas at constant

volume 1 :

B : Reversible isothermal expansion of an ideal gas 2 :

C : Adiabatic expansion of ideal gas into vacuum 3 :

D : Reversible isothermal compression of an ideal gas 4 :

5 :

Question 20.

MATCH THE FOLLOWING :Column 1 Column 2(Ox yacids) (Ox idation state of individual S-atom)

Column 1 Column 2

A : 1 :+6

B : 2 :+5

C : 3 :0

D : 4 :

5 :+3

Question 21.

If a satellite orbits as close to the earth's surface as possible,

[A] Its speed is maximum[B] Time period of its rotation is minimum[C] The total energy of the 'earth plus satellite' sy stem is minimum[D] The total energy of the 'earth plus satellite' system is maximum

Question 22.

Two blocks A(5kg) and B(2kg) attached to the ends of a spring with spring constant 1120N/m are placed on a smooth horizontal planewith the spring in its natural length. Simultaneously velocities of 3m/s and 10m/s along the line of the spring in the same direction are


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imparted to A andBas shown in figure, then :

[A] When the extension of the spring is maximum, the velocities ofAandBare zero[B] The maximum extension of the spring is 25cm[C] Maximum extension and maximum compression occ ur alternately[D] The maximum extension of the spring is 50cm

Question 23.

A c ylinder block of density is partially immersed in a liquid of density 3 . The plane surface of the block remains parallel to the

surface of the liquid. The height of the block is 60cm. The block performs SHM when displaced from its mean position if the block does

not come out of the liquid. [Use g= 9.8m/s2]

[A] The maximum amplitude is 20cm[B] The maximum amplitude is 40cm

[C] The time period will be seconds

[D] None of the above

Question 24.

A s quare loop of s ide l is placed in the neighborhood of an infinitely long str aight wire carr ying a c urrent I1. The loop carries a current I2as

shown in figure. In this orientation:

[A] The magnetic moment of the loops is

[B] The magnetic moment of the loops is

[C] The potential energy of the loop is minimum[D] The torque experienced by the loop is maximum

Question 25.

A parallel plate c apacitor is to be designed with a voltage rating 1kV, using a material of di-electric constant 5 and di-electric strength is

107V/m. For safety, field should not exceed more than 10% of the di-electric strength. What area can be safely used to make acapacitance of 88.5 pF

[A] 0.01m2

[B] 0.001m2

[C] 0.1m

2

[D] 0.02m2

Question 26.

A particle is moving in xy-plane with y=x/2 and vx= 4 - 2t. Choose the correct options :

[A] Initial velocities inx and ydirections are negative[B] Initial velocities inx and ydirections are positive[C] Motion is first retarded, then accelerated[D] Motion is first accelerated, then retarded

Question 27.


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Two concentric shells have radii Rand 2Rcharges qA and qBand potential 2Vand (3/2)Vrespectively in this configuration. Now shell B

is earthed and charges on them become and . Then :

[A]

[B]

[C] Potential of A after earthing becomes (3/2)V[D] Potential difference betweenA andBafter earthing becomes V/2

Question 28.

A particle of mas s m and charge qis fastened to one end of a string fixed at point O. The whole system lies on a frictionless horizontalplane. Initially, the mass is at rest at A. A uniform electric field in the direction shown is then switched on. Then :

[A] The speed of the particle when it reaches Bis

[B] The speed of the particle when it reaches Bis

[C] The tension in the string when particle reaches atB is 2qE[D] The tension in the string when the particle reaches atB is qE

Question 29.

Potential difference across the terminals of a non ideal battery is :

[A] Zero when it is short circuited[B] Less than its emf when current flows from negative terminal to positive terminal inside the battery

[C] Zero when no curr ent is drawn from the battery[D] Greater than its emf when current flows from positive terminal to negative terminal inside the battery

Question 30.

A c apacitor C is connected to two equal resistances as shown in the figure. Then :


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[A] At the time of charging of capacitor time constant of the circuit is 2CR[B] At the time of disc harging of capacitor time constant of the circ uit is CR[C] At the time of discharging of the capacitor the time constant of the circuit is 2CR[D] At the time of charging of capacitor the time constant of the circuit isCR

Question 31.

A uniform cy linder rests on a cart as shown. The coefficient of static friction between the c ylinder and the c art is 0.5. If the c ylinder is 4cm

in diameter and 10cm in height, then what is the minimum acceleration (in m/s 2) of the cart needed to cause the cylinder to tip over?

Question 32.

2kg of ice at -20oC is mixed with 5kg of water at 20oC in an insulating vessel having a negligible heat capacity. Calculate the final mass of

water (in kg) remaining in the container. (Specific heat capacity of ice = 0.5cal/gm/oC. Latent heat of fusion of water = 80 cal/gm, specific

heat capacity of water = 1cal/gm/oC

Question 33.

A long container has air enc losed inside at r oom temperature and atmospheric press ure (105Pa). It has a volume of 20000cc. The areaof cross section is 100cm2and force constant of spring is kspring= 1000 N/m. We slowly push the left piston isothermally till it reaches

the original position of the right piston which is movable. Final length of air column is found to be 25 hcm. Assume that spring is initiallyrelaxed. Find h.

Question 34.

A uniform disc of mass mand radiusR is pivoted smoothly at its centre of mass. A light spring of stiffness k is attached with the disctangentially as shown in the figure. Find the angular frequency in rad/s for small oscillations of the disc. (Take m = 5 kg and k= 10 N/m).


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Question 35.

A c losed and an open organ pipe of s ame length ar e s et into vibrations simultaneously in their fundamental mode to produce 2 beats. Thelength of open organ pipe is now halved and of closed organ pipe is doubled. Now find the number of beats produced.

Question 36.

A c ircular curr ent loop of r adius ais placed in a hypothetical radial field B as shown in the figure. The net force acting on the loop

is_________.

Question 37.

A boy standing on a long railroad car throws a ball s traight upwards. T he c ar is moving on the horizontal road with an acc eleration of

1ms

2

and the projection velocity in the vertical direction is 9.8 ms

-1

. How far behind the boy will the ball fall on the car? (Specify theanswer in SI unit).

Question 38.

A wooden cube of s ide 10 cm and density 0.8 gm/cm3is floating in water (density = 1gm/cm3). A mass of (100x) gm is placed over thecube so that cube is completely immersed without wetting the mass. Find the value of x.

Question 39.

Column 1 contains a list of processes involving expansion of an ideal gas. Match this with column 2. Describing the thermodynamicchange during this process. Indicate your answer by darkening the appropriate bubbles of the matrix given in the OMR

Column 1 Column 2

A :

An i nsulated container has two chambers separatedby a valve. Chamber I contains an ideal gas and thechamber II has vacuum. The valve is opened.

1 : The temperature of the gas decreases

An i deal monatomic gas expands to twice its original


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B :volume such that its pressure

2 : The temperature of the gas increases or remainsconstant

C :

An i deal monatomic gas expands to twice its original

vo lu me such that its pressu re w he re Vi s

its volume.

3 : The gas loses heat

D :

An i deal monatomic gas expands such that itspressure Pand volumeVfollows the behavior

shown in the graph

4 : The gas gains heat

Question 40.

A block is projected with an initial velocity vBlockon a long conveyor belt moving with velocity vBelt (at this instant) having constant

acceleration aBelt. Mark the correct option regarding friction acting on the block after long time (friction coefficient between the block and

belt = ). If :

Column 1 Column 2

A : vBlock= 2vBeltand aBelt= 0 1 : Zero

B : vBlock= 2vBeltand aBelt> g 2 : fs: static friction (0 < fs< fL)

C : vBlock= 2vBeltand aBelt= g 3 : fL: limiting friction

D : vBlock= 2vBeltand aBelt< g 4 : fK: kinetic friction

Question 41.Let nbe the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in thequeue. Let mbe the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand

consec utively in the queue. Then, the value of is :

[A] Odd integer[B] Composite integer[C] Multiple of 3[D] Multiple of 5

Question 42.

Let the complex number (where ) satisfy then xcan be:

[A]

[B]

[C] 1[D] 2

Question 43.

If a function satisfies the relation and , then identify

which of the following statement(s) is(are) correct ?

[A] Equation f (x) = exhas two solutions


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[B] Equation f (x) = exhas exactly one solution

[C]

[D]

Question 44.

If such that and

and then :

[A]

[B]

[C]

[D]

Question 45.

If tangent drawn to the curv e at meets the curv e again at Q(x1, f (x1)). If mAdenotes the

slope of the tangent at A and mOBdenotes the slope of the line joining 'O' origin and a point B on the curve, then :

[A]

[B]

[C] , where

[D] , where

Question 46.

Let be sequences such that

I. II.

III. IV.

Then which of the following is(are) correct ?

[A]

[B]

[C]


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[D]

Question 47.

Suppose and . If C is an arbitrary constant of integration then which of

the following is(are) correct ?

[A]

[B]

[C]

[D]

Question 48.

Let and then :

[A]

[B]

[C]

[D]

Question 49.

Let f: be defined by . Which of the following statement(s) is(are) corr ect?

[A] f (x) has exactly one local maximum and two local minimum points

[B] f (x) is strictly increasing in

[C] Absolute minimum value of f (x) exists but absolute maximum value of f(x) does not exist

[D] In the interval has two distinct roots

Question 50.

The figure illustrates graph of the function defined in . Identify the corr ect statement(s) :


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[A] Range of is

[B] Domain of is

[C] Domain of is

[D] Range of is

Question 51.

Let f(x) satisfy and

If then is thenAis ________.

Question 52.

For each real number m, the quadratic polynomial, passes through (a, c), then a+c is

_________.

Question 53.

The value of is equal to __________. [Note : {y} denotes the fractional part of y]

Question 54.

If are the nthroots of unity and is a non-real complex cube root of unity, then the product

cannot be equal to Awhere , thenA+ 1 is _________.

Question 55.


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Consider a curv e, . If area enclosed by the curv e, tangent to it at x= 2 and thex-axis is

where pand qare relatively prime numbers, then the value of is __________.

Question 56.

The sum of first n terms of the sequence , is of the form

. The value of is _________.

Question 57.

If then the least value of is __________.

Question 58.

If a twice differentiable function y= f (x) satisfies the relation and then the

value of is____________.

Question 59.

Let be equation of a circle.

Column 1 Column 2

A : If circle lies in first quadrant, then 1 : g< 0

B : If circle lie above thex-axis, then 2 : g> 0

C : If circle lie on the left of the y-axis, then 3 :

D : If circle touches the positivex-axis and does not

intersect the y-axis, then 4 : c> 0

5 : c< 0

Question 60.

Let for all and for all . Match the entries in Column 1 with

Column 2.

Column 1 Column 2

A :Number of distinct real roots of equation

where can be 1 : 0

B :Number of distinct real roots of equation

2 : 1


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where can be

C :Number of distinct real roots of equation

where can be 3 : 2

D :Number of distinct real roots of equation

where can be4 : 3

5 : 4

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Advance 3 Paper 1