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Question 1.

If the pH of a solution is 11, c alculate the number of hydrogen ions pres ent per ml of the solution.

[A]

[B]

[C]

[D]

Question 2.

A weak, monoprotic ac id is dissoc iated to the ex tent of 3% in 0.02 M s olution. Calculate the ex tent of its dissoc iation in 0.05 M solution. T= 298 K.

[A] 1.39%[B] 2.19%[C] 2.32%[D] 1.93%

Question 3.

A mixture of CO 2(g), CO (g)and C(s)are maintained at equilibrium at in a one litre flask. If the mean molar mass of the

gaseous mixture is . What is the composition of the gas mixture.

[A] 1 : 1[B] 1 : 2[C] 2 : 1[D] 3 : 2

Question 4.

When increasing press ure is applied to the equilibrium sy stem, , which of the following will happen?

[A] More ice will evaporate[B] Water will evaporate

[C] More water will be formed[D] Any of the above depending on the temperature of the sys tem

Question 5.

A c ertain monoprotic weak acid shows enthalpy of neutralization = . Calculate its enthalpy of ionization as suming its

degree of ionization to be 0.25. For neutralization, enthalpy value = .

[A]

[B]

[C]

[D]

Question 6.

. The dissociation processes :

I. and

II. absorb 265 kcal/mol and respectively. Calculate the bond

energy of the bond.

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[A]

[B] + 93 k cal[C] + 73 k cal

[D]

Question 7.

The electrostatic force of attraction between is greater than that of because :

[A] Na has higher ionization energy[B] Na does not have filled d orbitals

[C] Na+has smaller size than Cs+

[D] Cs+ is more reactive than Na+

Question 8.

A molecule of the ty pe AX4with sp3d2hybridization will have:

[A]

[B]

[C] will depend on electronegativity of A and X

[D] will depend on direction of lone pair of electr ons

Question 9.

The struc ture and hybridization of is :

[A] Linear, sp3d2

[B] Angular, sp2

[C] Linear,sp3d

[D] Angular, sp3d

Question 10.

Statement 1 : NCl3has very small dipole moment while NH3has a large dipole moment.

Statement 2 : The electronegativity difference between N and Cl is very s mall and that between N and H is very large.

[A] Statement-1 is True, Statement-2 is True Statement-2 is a correct explanation for Statement-1[B] Statement-1 is True, Statement-2 is True Statement-2 is NOT a correct explanation for Statement-1[C] Statement-1 is True, Statement-2 is False[D] Statement-1 is False, Statement-2 is True

Question 11.

Statement 1 : For the heterogeneous equilibrium: , the reaction can be made to shift in

forward direction by increasing the volume of container.

Statement 2 : With an increase in volume of container, the concentration of CO 2decreases.

[A] Statement-1 is True, Statement-2 is True Statement-2 is a correct explanation for Statement-1[B] Statement-1 is True, Statement-2 is True Statement-2 is NOT a correct explanation for Statement-1[C] Statement-1 is True, Statement-2 is False[D] Statement-1 is False, Statement-2 is True

Question 12.

Statement 1 : LiCl is an ionic compound, with good covalent character.

Statement 2 : For cov alent character, cation size should be smaller anion size s hould be larger which results in greater polarization.

[A] Statement-1 is True, Statement-2 is True Statement-2 is a correct explanation for Statement-1[B] Statement-1 is True, Statement-2 is True Statement-2 is NOT a correct explanation for Statement-1[C] Statement-1 is True, Statement-2 is False

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[D] Statement-1 is False, Statement-2 is True

Question 13.

Statement 1 : The first member ofp block elements when compared to that of subsequent members in the same group showsdifferent chemical behaviour.

Statement 2 : The other members of a group have vacant d-orbitals.

[A] Statement-1 is True, Statement-2 is True Statement-2 is a correct explanation for Statement-1[B] Statement-1 is True, Statement-2 is True Statement-2 is NOT a correct explanation for Statement-1[C] Statement-1 is True, Statement-2 is False

[D] Statement-1 is False, Statement-2 is True

Question 14.

The formal charge on nitrogen bonded to oxygen in the molecule N2O is :

[A] +1

[B]

[C]

[D]

Question 15.

A gaseous hydroc arbon r equires 6 times its own v olume of O2for complete oxidation and produces 4 times its volume of CO2at same Pand T. The molecular formula of gas is :

[A] C4H10

[B] C4H8

[C] CH2

[D] C8H14

Question 16.

The given curv e shows the variation of as a function of T for a fixed mass and P of an ideal gas. It follows from the curv e that :

[A] P1= P2= P3

[B] P1> P2> P3[C] P1< P2< P3[D] Nothing can be predicted about the press ures

Question 17.

On a humid day in summer, the mole fraction of gaseous H2O (water vapour) in the air at can be as high as 0.02. Assuming a

total pressure of 0.95 atm, what is the partial pressure of dry air ?

[A] 0.95 atm[B] 0.93 atm[C] 0.02 atm[D] 0.97 atm

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Question 18.

X, Y and Z react in the 1 : 1 : 1 stoichiometric ratio.

The concentration of X, Y and Z where found to vary with time as shown in the figure below :

Which of the following equilibrium reaction represents the correct variation of concentration with time.

[A]

[B]

[C]

[D]

Question 19.

X, Y and Z react in the 1 : 1 : 1 stoichiometric ratio.

The concentration of X, Y and Z where found to vary with time as shown in the figure below :

The value of the equilibrium constant (Kc) for the equilibrium represented in above sketch will be :

[A]

[B]

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[C]

[D]

Question 20.

X, Y and Z react in the 1 : 1 : 1 stoichiometric ratio.

The concentration of X, Y and Z where found to vary with time as shown in the figure below :

If above equilibrium is established in a 2.0 L container by taking reactants in sufficient amount then how many moles of component Ymust have reacted to establish the equilibrium ?

[A] 0[B] 6[C] 12[D] 8

Question 21.

Two grams of gas A are introduced in a evacuated flask at . The press ure of the gas is 1 atm. Now 3g of another gas B is

introduced in the same flask the total pressure becomes 1.5 atm. The ratio of molecular mass of A and B is :

[A] 3/1[B] 1/3[C] 1/4[D] 2/3

Question 22.

The oxidation of SO2by O2to SO3 is an exothermic process. The yield of SO3is maximum if:

I. Temperature is increased II. Temperature is reduced

III. Pressure is increased IV. Temperature and pressure both are increased

The correct option is :

[A] I, II[B] I, III[C] II, III[D] II, III, IV

Question 23.

At a certain temperature T, a c ompound AB4(g) dissoc iates as with a degree of dissociationx,

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which is negligible compared with unity. The expression of K p in terms ofxand total pressure P is :

[A] 8P3x5

[B] 256 P333x5

[C] 4Px2

[D] None of these

Question 24.

Which of the following can act as Lewis acids ?

I. II. III. IV.

The correct option is :

[A] I, II[B] II, III[C] II, III, IV[D] III, IV

Question 25.

By observing adjacent graph what can be said about the relationship between vander waal's constant bof He and H2at thesame

temperature ?

[A]

[B]

[C]

[D] Nothing can be predicted between the values of and

Question 26.

If the bond dissoc iation energies of XY, and (all diatomic molecules) are in the ratio of 1 : 1 : 0.5 and for the

formation of XY is . The bond dissoc iation energy of will be :

[A]

[B]

[C]

[D] None of these

Question 27.

The value of enthalpy change for the reaction at 27oC is

. The value of internal energy change for the above reaction at this temperature will be :

[A]

[B]

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[C]

[D]

Question 28.

Which of the following is/not true for a thermo chemical reaction ?

[A] at constant pressure

[B] at constant volume

[C] when is zero

[D] when is zero

Question 29.

Which of the following is(are) Extensive properties :

I. Internal energy II. Specific heat

III. Enthalpy IV. Boiling point

The correct option is :

[A] I, II[B] I, III[C] I, II, III[D] II, IV

Question 30.

Which of the following can act as Bronsted Lowry acids ?

I. II. III.

IV. V.

The correct option is :[A] I, IV, V[B] I, III, IV, V[C] I, II, III, IV, V[D] I, IV

Question 31.

Two particles having mass ratio n : 1 are interconnected by a light inextensible string that pass es over a smooth pulley. If the system isreleased, then the acceleration of the centre of mass of the system is :

[A]

[B]

[C]

[D]

Question 32.

A block of mas s m is pushed towards a movable wedge of mass 2m and height hwith a velocity u.

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All surfaces are smooth. The minimum v alue of ufor which the block will reach the top of the wedge is:

[A]

[B]

[C]

[D]

Question 33.

A body dropped from a height 'H' reaches the ground with a speed of Calculate the work done by air fr iction.

[A] Zero[B] 0.28 mgH[C] 0.72 mgH[D] -0.28 mgH

Question 34.

A ball is projected fr om gr ound with a v elocity vat an angle to the vertical. On its path it makes an elastic collision with a vertical wall

and returns to ground. The total time of flight of the ball is :

[A]

[B]

[C]

[D]

Question 35.

Displacement of a particle of mass 2 kgmoving in a straight line varies with time as s= (2t3+ 2) m

Impulse of the force acting on the particle over a time interval between t = 0 and t= 1s is :

[A] 10 N-s[B] 12 N-s[C] 8 N-s[D] 6 N-s

Question 36.

A wire of length l and mass mis first bent in a circle, then in a square and then in an equilateral triangle. The moment of inertia in these

three cases about an axis perpendicular to their planes and passing through their centers of mass are respec tively.

Then maximum of them is :

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[A]

[B]

[C]

[D] Data insufficient

Question 37.

A uniform circular disc of r adius rplaced on a rough horizontal plane has initial velocity v0and an angular velocity as shown. The

disc comes to rest after moving some distance in the direction of motion. Then initially :

[A] The friction force acts in the forward direction[B] The point of contact of disc with ground has zero velocity

[C]

[D]

Question 38.

Two particles of equal mass m at A and B are connected by a rigid light rod AB, lying on a smooth horizontal table. An impulse J isapplied at A in the plane of the table and perpendicular to AB. Then the velocity of particle at A is :

[A]

[B]

[C]

[D] Zero

Question 39.

A disc of r adius rrolls without slipping on a rough horizontal floor.

If velocity of its centre of mass is v0, then velocity of point P, as shown in the figure (OP= r/2 and ), is :

[A]

[B]

[C]

[D]

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Question 40.

The acceleration aof the plank P required to keep the centre C of a solid cylinder in a fixed position during the motion is : ( No slippingtakes place between cylinder and plank)

[A]

[B]

[C]

[D]

Question 41.

A uniform rodABof mass m and length 2ais falling freely without rotation under gravity withABhorizontal. Suddenly the endA is fixedwhen the speed of the rod is v. The angular speed with which the rod begins to rotate is :

[A]

[B]

[C]

[D]

Question 42.

A rod of mas s m and length l is hinged at one of its endAas shown in figure.A forc e F is applied at a distancex fromA. The acceleration of centre of mass 'a' varies withxas :

[A]

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[B]

[C]

[D]

Question 43.An impulse J is applied on a disc of mas s m along a line passing through its centre O. The disc is placed on a rough horizontal surface.The linear velocity of centre of disc once it starts rolling without slipping is :

[A] J/2m[B] 2J/3m[C] J/4m[D] J/3m

Question 44.

A time vary ing forc e F= 2tis applied on a spool as shown in figure.The angular momentum of the spool at time tabout bottommost point is :

[A]

[B]

[C]

[D] Data is insufficient

Question 45.

A block weighing 10 N travels down a smooth curv ed track AB joined to a rough horizontal surface (figure). The rough surfac e has afriction coefficient of 0.20 with the block. If the block is released from rest on the track from a point 1.0 m above the horizontal surfac e,

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the distance it will move on the rough surface is :

[A] 5.0 m[B] 10.0 m[C] 15.0 m[D] 20.0 m

Question 46.

Figure shows a block sliding on a frictionless track which terminates in a straight horizontal section. If the block starts slipping from thepoint A, how far away from the track will the block hit the ground?

[A] At a horizontal distance of 1mfrom the end of the track[B] At a horizontal distance of 2mfro the end of the track[C] At a horizontal distance of 3mfrom the end of the track[D] Insufficient information

Question 47.

A block of mas s m is attached to two unstretched springs of spring constants k1and k2as shown in figure. The block is displaced

towards right through a distancexand is released. Find the speed of the block as it passes through the mean position :

[A]

[B]

[C]

[D] None of these

Question 48.

A body of mas s m dropped from a certain height strikes a light vertical fixed spring of stiffness k.

The height of its fall before touching the spring if the maximum compression of the spring is equal to is :

[A]

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[B]

[C]

[D]

Question 49.

A particle is moved from (0, 0) to ( a, a) under a force from two paths. Path 1 is OPand path 2 is OQP. Let W1 and W2

be the work done by this force in these two paths. Then,

[A] W1= W2[B] W1= 2W2

[C] W2= 2W1

[D] W2= 4W1

Question 50.

A block of mas s 50 kg is projected horizontally on a rough horizontal floor. The coefficient of friction between the block and the floor is0.1. The block strikes a light spring of stiffness k= 100 N/m with a velocity 2m/s, the maximum compression of the spring is :

[A] 1m[B] 2m[C] 3 m[D] 4 m

Question 51.

Two particles 1 and 2 are allowed to descend on two frictionless chords OP and OQ from O. The ratio of the speeds of the particles 1and 2 respectively when they reach on the circumference is :

[A]

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[B]

[C] 1

[D]

Question 52.

A body is moved from r est along a straight line by a mac hine delivering constant power. T he r atio of displacement and velocity (s/v)varies with time t as :

[A]

[B]

[C]

[D]

Question 53.

A uniform rod of length l is kept vertically on a rough horizontal surface atx= 0. It is rotated slightly and released. When the rod finallyfalls on the horizontal surface, the lower end will remain at :

[A] x= l/2[B] x> l/2[C] x< l/2[D] x= 0

Question 54.

Four particles of masses m1= 2m, m2= 4m, m3= m and m4are placed at four corners of a square. What should be the value of m4, s o

that the centre of mass of all the four particles are exactly at the centre of the square?

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[A] 2m

[B] 8m[C] 6m[D] None of these

Question 55.

What is the power output of a reactor if it takes 16 days to use up 864 gms of fuel and if each fission produces 235 MeV of

usable ener gy? ( Avogadr o number /mol)

[A] 10 MW[B] 60 MW[C] 600 MW[D] 100 MW

Question 56.

If a ball moving with velocity uovertakes another ball of twice its own mass moving with one - seventh of its velocity and if the coefficient

of restitution between them is , the velocity of the first ball after striking the second ball is :

[A] u/2[B] Zero[C] u/4[D] 3u/4

Question 57.

A ball falls vertically 2s and hits a plane inclined at 30oto the horizontal. If coefficient of restitution is 5/8, then find the time after which it

hits the plane again (g= 10 m/s2)

[A] 2s[B] 4s[C] 2.5s[D] 5s

Question 58.

A particle of mas s 0.5 kgmoves along a line y=x - 2 (x, y in metres) with a constant speed 6 m/s. Angular momentum of the particleabout the origin, in magnitude, is:

[A] kgm2/s

[B] 4 kgm2/s[C] kgm2/s

[D] kgm2/s

Question 59.

A uniform solid c ylinder of radius rstarts rolling without slipping down from the top of a fixed sphere of radius R. The angular velocity ofthe cylinder at the moment it breaks off the sphere will be :

[A]

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[B]

[C]

[D]

Question 60.

A s olid sphere is rotating in fr ee s pace. If the radius of s phere is increased keeping mass same which one of the following will not beaffected?

[A] Angular velocity[B] Angular momentum[C] Moment of inertia[D] Rotational kinetic energy

Question 61.

If two curves whose equations are

and intersect in four concy clic points, then :

[A]

[B]

[C]

[D]

Question 62.

Tangents are drawn to from any arbitrary points P on the line . The corr esponding chord of contact

passes through a fixed point whose coordinates are

[A]

[B]

[C]

[D]

Question 63.

The number of common tangents to the circles and is :

[A] 0[B] 1[C] 3

[D] 4

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Question 64.

Circles are drawn through the points (2, 0) to cut intercept of length 5 units on thex-axis. If their centres lie in the first quadrant, then theirequation is:

[A]

[B]

[C]

[D]

Question 65.

The range of values of r for which the point is an interior point of the major segment of the circle

, cut off by the line , is :

[A]

[B]

[C]

[D] None of these

Question 66.

Tangents PA and PB are drawn to from the point P(4, 4). Area of the triangle OAB, 'O' being the origin, is equal to :

[A]

[B]

[C]

[D]

Question 67.

Locus of mid-point of chords of that pass through the origin, is :

[A]

[B]

[C]

[D]

Question 68.

Tangents PA and PB drawn to from any arbitrary point 'P' on the line . Locus of mid-point of chord AB is :

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[A]

[B]

[C]

[D] None of these

Question 69.

The domain of the function,

[A]

[B]

[C]

[D]

Question 70.

The range of the function is :

[A]

[B]

[C]

[D] None of these

Question 71.

A function whose graph is sy mmetrical about the y-axis is given by :

[A]

[B]

[C]

[D] sin(sin(sinx))

Question 72.

If then domain of f (x) is :

[A] R

[B]

[C]

[D]

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Question 73.

If is a function satisfy ing the property , then the period of f (x) is :

[A] 2[B] 4[C] 8[D] 12

Question 74.

then the number of solutions of is :

[A] 1[B] 2[C] 3[D] 4

Question 75.

f : where , (where [.] denotes the G.I.F.), is an odd func tion. Complete

set of values of 'a' is :

[A]

[B]

[C]

[D]

Question 76.

The minimum value of is equal to :

[A] 1[B] 2[C] 3[D] Zero

Question 77.

Let . Then :

[A]

[B]

[C]

[D] None of these

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Question 78.

If the function f (x) is defined by and (repeated r times), then is equal to :

[A]

[B]

[C]

[D]

Question 79.

The value of is :

[A] - 1[B] 0

[C]

[D]

Question 80.

Let z and wbe two non-zero complex number such that and . Then z equal

[A] w[B] - w

[C]

[D]

Question 81.

If , where z is a complex number, then values of

is :

[A] 12[B] 18[C] 54[D] 6

Question 82.

Let , and a, b, c, x, y, z be non-zero complex numbers such that :

,

Then the value of

[A] 1

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[B] 2[C] 3[D] 4

Question 83.

If then value of cannot exceed :

[A]

[B]

[C]

[D]

Question 84.

If then equals :

[A]

[B]

[C] 1[D] 0

Question 85.

If are the roots of , and is a cube root of unity, then value of

is :

[A]

[B] 3q

[C]

[D]

Question 86.

If is an imaginary cube root of unity, then the value of is :

[A]

[B]

[C]

[D]

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Question 87.

If are complex numbers such that . Then is :

[A] Equal to 1[B] Less than 1[C] Greater than 3[D] Equal to 3

Question 88.

Complex number is equal to :

[A]

[B]

[C]

[D]

Question 89.

If , then reduces to :

[A] 2[B] 3[C] 4[D] 5

Question 90.

If , forx> 2 then f(11) is equal to :

[A] 7/6[B] 5/6[C] 6/7[D] 5/7

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