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Question 1.

Which of the following is(are) correct?

[A] Accor ding to molecular orbital theory double bond in consist of two -bonds

[B] In oxidation state of nitrogen is +5 and its hybridization state is

[C] For square planar molecular geometry hybridization state of central atom is

[D] The order of first ionization enthalpy values of group 13 elements is B > Al < Ga > ln < Tl

Question 2.

Consider the reactions of organic compound [X] and identify the correct statement(s).

[A] Product [Y] exist in two stereoisomeric forms[B] Product [Z] exist in two stereoisomeric forms[C] [Y] on acid catalyzed hydration form [Z]

[D] [Z] on acid catalyzed hydration form [Y]

Question 3.

Which of the following statement(s) is(are) correct for Glucose and Fructose?

[A] Glucose and Fructos e are functional isomers[B] Both form silver mirror with Tollen's Reagent[C] Both form same type of osazone on reaction with excess of phenyl hydrazine[D] Glucose and Fructos e are epimers

Question 4.

Which of the following oxoacids of phosphorous is(are) reducing in nature?

[A]

[B]

[C]

[D]

Question 5.

A potential diagram for rhenium at pH = 0 s hows the following Eovalues:

The value of Eo for the reduction of to Re(0) is :

[A] +0.97 V[B] +0.32 V[C] +0.14 V[D] +0.37 V

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Question 6.

Which of the following statement(s) is(are) correct for drug Dopamine having structure as shown?

[A] It is optically active[B] Its one mol reacts with 3 moles of NaOH

[C] It exist as zwitter ion in aq. solution[D] It form hydroxyl derivative on reaction with

Question 7.

The reaction sequence of Friedel-Crafts acylation followed by Clemmensen reduction accomplishes

[A] The transformation of an electron withdrawing group into an electron releasing group[B] The transformation of an electron releasing group into an electron withdrawing group[C] The formal alkylation of benzene with a primary alkyl halide without rearrangement[D] Transfor m deactivated benzene to activated benzene

Question 8.

In which of the following sets of ores, all ores contain same type of anion ?

[A] Cinnabar, Galena, Zinc blende, Argentite[B] Magnetite, Haematite, Cassiterite, Chromite[C] Dolomite, Calamine, Siderite, Calcite[D] Malachite, Carnallite, Cryolite, Fluorspar

Question 9.

Intermolecular forces are stronger in liquid state than in gaseous state. Molecules in liquid are so close that there is very little emptyspace between them and under normal conditions liquids are denser than gases. Molecules of liquids are held together by attractiveintermolecular forces. Some of the physical properties of the liquids such as vapour pressure, surface tension, viscosity and boiling pointare related with strength of these intermolecular forces. The condition of free vapourization throughout the liquid is called boiling. Thetemperature at which vapour pressure of liquid is equal to the external pressure is called boiling temperature at that pressure.

On increasing temperature

[A] vapour press ure of liquid increases[B] surfac e tension of liquid decreases[C] visc osity of liquid decrease[D] density of liquid decreases

Question 10.

Intermolecular forces are stronger in liquid state than in gaseous state. Molecules in liquid are so close that there is very little emptyspace between them and under normal conditions liquids are denser than gases. Molecules of liquids are held together by attractiveintermolecular forces. Some of the physical properties of the liquids such as vapour pressure, surface tension, viscosity and boiling pointare related with strength of these intermolecular forces. The condition of free vapourization throughout the liquid is called boiling. The

temperature at which vapour pressure of liquid is equal to the external pressure is called boiling temperature at that pressure.

Which of the following statement(s) is(are) correct for most of the pure liquids?

[A] Boiling does not occur when liquid is heated in a closed ves sel[B] At critical temperature, density of liquid and density of vapour is same[C] Liquids at high altitudes boil at lower temperatures in comparison to that at sea level

[D] Entropy change of vapourization is almost same for most of the liquid except H-bonded liquid

Question 11.

Potassium permanganate is a strong oxidizing agent, oxidizes quantitatively most of the common reducing agent. The intense purplecolour of permanganate ion serve as a self-indicator, one drop in excess will impart a distinct colour to a large volume of solution.

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Certain amount of a pure iron containing compound was dissolved in sulphuric acid solution and then titrated with standard permanganatesolution. The titration required 34.5 mL of 0.108 M standard permanganate solution. Which of the following is iron containing compound?

[A] 1.356 g

[B] 1.356 g

[C] 2.161 g

[D] 1.356 g

Question 12.

Potassium permanganate is a strong oxidizing agent, oxidizes quantitatively most of the common reducing agent. The intense purplecolour of permanganate ion serve as a self-indicator, one drop in excess will impart a distinct colour to a large volume of solution.

In dilute aqueous , is oxidized by . For this reaction which of the following

statement(s) is(are) correct?

[A] One mole of complex ion on oxidation gives 5 mole of electrons

[B] One mole of ion on reduction gain 5 mole of electrons

[C] One mole of complex ion on oxidation gives 3 mole of electron

[D] The ratio of the rate of change of to the rate of change of is 8 : 1

Question 13.

The sum of number of particle(s), generated in the following radioactive decay proces s, are_________.

Question 14.

How many isomers (excluding stereoisomers) of the alkane having molecular mass 100 can be prepared by catalytic hydrogenation of

alkene?

Question 15.

How many of the following disproportionate when treated with NaOH ?

Question 16.

Find the number of lone pair of electrons in main organic product of the reaction given below :

Question 17.

The kinetics of the reaction in liquid bromine medium was measured independently for three different

concentr ations of , 0.11, 0.07 and 0.05 mol L-1. The half-life of the reaction was found to be 4.5 hours for all these

concentrations. The order of the reaction is________.

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Question 18.

The sum of coordination number and oxidation number of the metal M in the complex is _______.

Question 19.

How many monoadducts of HCl and penta-1, 3-diene are possible?

Question 20.

Find the number of hydroxyl group in product [A] formed in following conversion.

Question 21.

In the diagram shown, a light ray is incident on the lower medium boundary at an angle if with the normal. Which of the following

statements is(are) true ?

[A] If , then angle of deviation is

[B] If , then angle of deviation is

[C] If , then angle of deviation is

[D] If , then angle of deviation is

Question 22.

A trans parent s lab of thickness tand refractive index is inserted in front of upper slit of YDSEapparatus. The wavelength of light

used is . Assume that there is no absorption of light by the slab. Mark the corr ect statement(s) .

[A] The intensity of dark fringes will be 0, if slits are identical.

[B] The change in optical path due to insertion of plate is .

[C] The change in optical path due to insertion of plate is

[D] For making intensity zero at centre of sc reen, the thick ness can be

Question 23.

A driver in a stationary car blows a horn which produces monochromatic sound waves of fr equency 1000 Hznormally towards areflecting wall. The wall approaches the car with speed of 3.3 m/s. Speed of sound is 340 m/s.

[A] The frequency of sound reflected from wall and heard by the driver is 1020 Hz[B] The frequency of sound reflected from wall and heard by the driver is 980 Hz

[C] The percentage increase in frequency of sound after reflection from wall is

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[D] The percentage decrease in frequency of sound after reflection from wall is

Question 24.

A s pring of spring constant kstores 5 J of energy when stretched by 25 cm. It is kept vertical with one end fixed. A mass m is attachedto the other end. It makes 5 oscillations per second. Then :

[A] m= 0.16 kg[B] m= 0.32 kg[C] k= 160 N/m[D] k= 320 N/m

Question 25.

A ball 'A' collides elastically with an identical ball B with velocity 10 m/sat an angle of from the line joining their centres C1and C2.

Select the correct alternative(s) :

[A] velocity of ballAafter collision is 5 m/s

[B] velocity of ballBafter collision is m/s

[C] both the balls move at right angles after collision[D] kinetic energy will not be conserved here, because collision is not head on

Question 26.

A 100 Hz sinusoidal wave is travelling in the positivex-direction along a string with a linear mass density of and a

tension of 35 N. At time t= 0, the pointx= 0 has zero displacement and the slope of the string is . Then select the wrong

alternative(s) :

[A] Velocity of wave is 100m/s

[B] Angular velocity is rad/s

[C] Amplitude of wave is 0.025 m[D] None of these

Question 27.

A positively c harged thin metal ring of radius Ris fixed in thexyplane with its centre at the origin O. A negatively charged particle P isreleased from rest at the point (0, 0, z0) where z0> 0. Then the motion of P is :

[A] Periodic for all values of z0 satisfying

[B] Simple harmonic for all values of z0 satisfying

[C] Approximately simple harmonic provide z0

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[C]distance moved by particle in time

[D] velocity of particle after time

Question 29.

In the adjacent figure, the two capacitors each of equal capacitance Chave charges CE/2 and CEas shown initially

As soon as the s witch is closed, the c urrent in res istance Ris.

[A]

[B]

[C]

[D]

Question 30.

In the adjacent figure, the two capacitors each of equal capacitance Chave charges CE/2 and CEas shown initially

Heat dissipated in the circuit after closing the switch is :

[A]

[B]

[C]

[D]

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Question 31.

The current through resistance is zero and through is 2A.

The value of Ris :

[A]

[B]

[C]

[D]

Question 32.

The current through resistance is zero and through is 2A.

The emf Eof the ideal cell is :

[A] 14 V[B] 8 V[C] 10 V[D] 12 V

Question 33.

A c ylindrical tube of length 6.93 cmand inner and outer radii of 2.5 cmand 5 cm respectively are covered with two identical hemisphericallids of same inner and outer radii. The materials of lids and the tube is same of thermal conductivity of 0.5 cal/s-mK. An energy source

radiating 1256 cal/s is placed inside. The steady state inside temperature is and surrounding temperature is .

Find the value , given

Question 34.

As shown in figure string PQR is stretc hed by force F = (3 -10 Kt) N, where k is a constant and t is time in second. At time t= 0, a pulseis generated at the end P of the string. For the value of K (in N/s) if the value of force become zero as the pulse reaches point Q.

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Question 35.There are two liquids of different densities. A solid body can be completely submerged in liquid 1,by applying 1.36 N downward forces andthe same body can be completing submerged in liquid 2 by applying 0.82 N in other liquid. These liquid are mixed in volume proportionVliqui 1: Vliquid 2= 4 :x. For what value ofx, the solid can be completely submerged in mixture liquid by applying downward force of 1 N.

Question 36.

Water is flowing in varying cross-section pipe. Area of cross section 1, 2 and 3 are 1 cm2, 2 cm2and A cm2 respectively. Water levels

are shown in different vertical tubes. Speed of water at cros s-s ection 3 is . The value ofxis __________.

Question 37.

Potentiometer wire AB has length = 100 cm. Total resistances , when the jocky is connected at D (AD =x cm), ammeter reading

is 0.5 amp. The value ofx is __________. (Resistance of ammeter is ).

Question 38.

A glass spherical shell of radius R has a point sourc e of monochromatic light of wav elength . Thicknes s of glass wall is t(

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A s olid sphere of r adius Rhas a charge Qdistributed in its volume with a charge density , where k and a are positive

constants and r is the distance from its centre. If the electric field at r= R/2 is 1/8 times that at r= R, find the value of a.

Question 41.

If , where a, b, c, dare real and non real cube root of unity, then :

[A] abc+ acd+ abd+ bcd= 2

[B]

[C] a+ b+ c+ d= 2abcd

[D]

Question 42.

LetA and Bbe two independent events such that and , then :

[A]

[B]

[C]

[D]

Question 43.

If both satisfy and , then :

[A]

[B]

[C] also satisfy

[D] is an even integer

Question 44.

IfAbe a non - singular matrix, then :

[A] adj(adjA) =

[B]

[C]

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[D]

Question 45.

A c urve passes through origin is such that slope of the tangent at any point is reciprocal of sum of abs ciss a and ordinate of point oftangency then :

[A] Slope of tangent at ordinate is

[B] Area bounded by curv e, y= 0, y= 1 and y-axis is

[C] ([.] denote greatest integer function)

[D]

Question 46.

If two distinct circ les and , cut equal intercepts on

a straight line whose slope is , then the line is tangent to :

[A]

[B]

[C]

[D]

Question 47.

If

then :

[A] range of

[B] domain of

[C] domain of (I is set of integers)

[D] range of is [1, 2]

Question 48.

Let and then :

[A]

[B]

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[C]

[D] f (x) has more points of discontinuities then g(x) in

Question 49.

P is arbitrary point lying on the ellipse is one of focus of the ellipse whose abscissa is positive, R is the

mid point of PS (e denotes the eccentricity of ellipse)

Locus of Ris an ellipse,

[A] whose directrices are

[B] whose Foci are at (ae, 0) and (0, 0)

[C] whose directrices are

[D] whose Foci are at and

Question 50.

P is arbitrary point lying on the ellipse is one of focus of the ellipse whose abscissa is positive, R is the

mid point of PS (e denotes the eccentricity of ellipse)

Which of the following is (are) true about locus of R

[A] Second focus of given ellipse (other than S) lies outside of Rif

[B] Second focus of given ellipse (other then S) lies on locus of R if

[C] probability any point selected inside given ellipse lies inside locus of R is

[D] eccentricity of locus of R is

Question 51.

Let a dice be thrown 3 times we get values a, b, cand polynomial is formed . Let Sbe set of all such

possible polynomials.Abe subset of Sconsisting of all polynomials having exactly two distinct points of extrema. Bbe subset of Scontaining polynomials having no point of extrema.

Which of the following is/are true ?

[A] A consists of all polynomials having negative point of local minima

[B]

[C] All polynomials in Shave one negative root[D] Number of polynomials inAhaving rational points of extrema is 5

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Question 52.

Let a dice be thrown 3 times we get values a, b, cand polynomial is formed . Let Sbe set of all such

possible polynomials.Abe subset of Sconsisting of all polynomials having exactly two distinct points of extrema. Bbe subset of Scontaining polynomials having no point of extrema.

Probability that a randomly selected polynomial from S

[A] is strictly increasing is

[B] is strictly increasing is

[C] has integral point of inflection is

[D] has no point of inflection is

Question 53.

If roots of unity. Then value of is ____________.

Question 54.

Let . Ifpbe the sum of all possible integers in the domain of function

f (x) and qbe sum of all possible integers in the range of function f(x), then is ___________. ({.] denotes greatest

integer function, {.} denotes fractional part).

Question 55.

LetA= {1, 2, 3, 4, 5} and B= {0, 1, 2, 3, 4, 5, 6}, if number of one - one function from A to Bwhich are not strictly increasing is , then

number of factors of of the form 3kis ________ .

Question 56.

If the range of the function (where {.} denotes fractional part), then is

__________.

Question 57.

If are non coplanar vectors such that then value of is

____________.

Question 58.

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is __________. ([.] denotes greatest integer function)

Question 59.

then is _________ .

Question 60.

Let function f(x) be such that and , then is ________. ([.] denotes

greatest integer function)