iit jee 2011 paper 2 question answer

8/3/2019 IIT JEE 2011 Paper 2 Question Answer

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~RT I : CHEMISTRY 1SECTION -I (Total Marks: 24)(Single Correct Answer Type)

This section contains 8 multiple choice questions. Each question has four choices(A), (8), (C) and (0) out of which ONLY ONE is correct.

1. Oxidation states of the metal in the minerals haematite and magnetite, respectively, are(A) II, III in haematite and III in magnetite(8) II, III in haematite and II in magnetite(C) II in haematite and II, III in magnetite(0) III in haematite and II, III in magnetite

ANSWER:D2. Among the following complexes (K-P),

K3[Fe(CN)6] (K), [Co(NH3)6]CI3 (L), Na3[Co(oxalate)3] (M), [Ni(H20)6]CI2 (N),K2[Pt(CN)4] (0) and [Zn(H20)6](N03)2 (P)the diamagnetic complexes are

(8) K, M, 0, P (C) L, M, 0, PANSWER:C

3. Passing H2S gas into a mixture of Mn2+,Ni2+,Cu2+and Hg2+ions in an acidified aqueoussolution precipitates

(A) K, L, M, N (0) L, M, N,0

(A) GuS and HgS(C) MnS and NiS

(8) MnS and GuS(0) NiS and HgS

ANSWER: A4. Consider the following cell reaction:

+ 2+ 2Fe(S)+ 02(Q)+ 4H (aq) ~ 2Fe (aq) + 2H20(l) E = 1.67 VAt [Fe2+]= 10-3 M, P(02) = 0.1 atm and pH = 3, the cell potential at 25C is(A) 1.47V (8) 1.77 V

ANSWER:D(C) 1.87 V (0) 1.57 V


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CHEMISTRY

5. The freezing point (in C) of a solution containing 0.1 g of K3[Fe(CN)61 (Mol. Wt. 329) in-1100 g of water (K,= 1.86 K kg mol ) is-2 -2 -3(A) -2.3 x 10 (8) -5.7 x 10 (C) -5.7 x 10

ANSW ER: A6. Amongst the compounds given, the one that would form a brilliant colored dye on

treatment with NaN02 in dil. Hel followed by addition to an alkaline solution of~-naphthol is

-2(0) -1.2 x 10

(C )

ANSWER:C7. The major product of the following reaction is

o(A) a hemiacetal(C) an ether H G > (anhydrous)(8) an acetal(0) an esterANSWER:B

8. The following carbohydrate is

OH

(A) a ketohexose(C) an a-furanose

(8) an aldohexose(0) an a-pyranose

ANSWER:B


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( CHEMISTRY)SECTION - II (Total Marks: 16)(Mulltiple Correct Answer(s) Type)

This section contains 4 multiple choice questions. Each question has four choices(A), (8), (C) and (D) out of which ONE or MORE may be correct.

9. Reduction of the metal centre in aqueous permanganate ion involves(A) 3 electrons in neutral medium(C) 3 electrons in alkaline medium

(8) 5 electrons in neutral medium(D) 5 electrons in acidic medium

ANSWER:ACD

10. The equilibrium2 CU i . . . . . . . -in aqueous medium at 25C shifts towards the left in the presence of

(8) Cl (C) SCN (D) eNANSW ER: BCD


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CHEMISTRY11. For the first order reaction

(A ) the concentration of the reactant decreases exponentially with time.(8) the half-life of the reaction decreases with increasing temperature.(C) the half-life of the reaction depends on the initial concentration of the reactant.(D) the reaction proceeds to 99.6 % completion in eight half-life duration.

ANSWER:ABD12. The correct functional group X and the reagent/reaction conditions Y in the following

scheme are(i) Y condensation polymero 0(ii) ~-(CH )- 8/ 24 \HO OH

heat(A) X = COOCH3, Y = H/Ni/heat(C) X = CONH2, Y = 8r/NaOH

(8) X = CONH2, Y = H/Nilheat(D) X = CN , Y = H/Nilheat

ANSW ER: CD


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( CHEMISTRY)SECTION -III (Total Marks: 24)

(Integer Answer Type)This section contains 6 questions. The answer to each of the questions is a single-digitinteger, ranging from 0 to 9. The bubble corresponding to the correct answer is to bedarkened in the ORS.

-10In 1 L saturated solution of AgCl [Ksp(AgCl) = 1.6 x 10 ], 0.1 mol of CuCl[Ksp(CuCl) = 1.0 x 10-6] is added. The resultant concentration of Ag + in the solution is

-x1.6 x 10 . The value of "x" isANSWER: 7

The number of hexagonal faces that are present in a truncated octahedron isANSWER: 8

The maximum number of isomers (including stereoisomers) that are possible on mono-chlorination of the following compound, isCH3I/C,CH3CH2 I CH2CH3H

ANSWER: 818. The total number of contributing structures showing hyperconjugation (involving

C-H bonds) for the following carbocation isH3C c > CH2CH3

13.

14.

15.

16.

17.

Among the following, the number of compounds than can react with PCls to give POC13is02' CO2, S02' H20, H2S04, P4010

ANSWER: 4The volume (in mL) of 0.1 M AgN03 required for complete precipitation of chloride ionspresent in 30 mL of 0.01 M solution of [Cr(H20)sCl]C12, as silver chloride is close toANSWER: 6

ANSWER: 6


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( CHEMISTRY)SECTION - IV (Total Marks: 16)

(Matrix-Match Type)This section contains 2 questions. Each question has four statements (A, B, C and D)given in Column I and five statements (p, q, r, sand t) in Column II. Any givenstatement in Column I can have correct matching with ONE or MORE statement(s) givenin Column II. For example, if for a given question, statement B matches with thestatements given in q and r, then for the particular question, against statement B, darkenthe bubbles corresponding to q and r in the DRS.

19. Match the transformations in column I with appropriate options in column II

Column I Column II(p) phase transition

(t) ~S is negative

ANSWER A : p, rand 5B: rand 5C: tD: p, q and t


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CHEMISTRY )2 0 . Match the reactions in column I with appropriate types of steps/reactive intermediate

involved in these reactions as given in column II

Column I Column II(A ) H3C 0 (p) Nucleophilic0 substitution

aq NaOH " ' . : : : : : :~

(q ) Electrophilic(8) 0 substitution

~CH2CH2CH2ClCH3MgI " ' . : : : : : :

~(r) Dehydration

(C) 0 180~ 18 H2SO4 ~CH2CH2CH2OH (s) Nucleophilic

addition(0) VCH2CH2CH29(CHsh H2SO4 coH (t) CarbanionH3C CH3

ANSWER A : r, 5and tB: p and 5C: rand 5D: q and r


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[ PART II : PHYSICS 1SECTION -I (Total Marks: 24)

(Single Correct Answer Type)This section contains 8 multiple choice questions. Each question has four choices(A), (8), (C) and (0) out of which ONLY ONE is correct.

21. A light ray traveling in glass medium is incident on glass-air interface at an angle ofincidence e . The reflected ( R ) and transmitted ( T ) intensities, both as function of e ,are plotted. The correct sketch is

100%( 8 ). . . . . . . . . . . . . . . . . . . . . '1

T II/

_ . B _ _ . . . . .

(A)

R

a 90- - -o e e(0)

-~--100% .................... ~ -

---( C )100 r _._- _._

TT

R--_ . . . . . .900 oe e

ANSWER: C22. A satellite is moving with a constant speed 'V' in a circular orbit about the earth. An objectof mass em ' is ejected from the satellite such that it just escapes from the gravitational pullof the earth. At the time of its ejection, the kinetic energy of the object is

(8) ( C ) 3 V2-m2 (0) 2mV2ANSWER: B


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( PHYSICS23. A long insulated copper wire is closely wound as a spiral of 'N' turns. The spiral has inner

radius 'a' and outer radius 'b'. The spiral lies in the X-V plane and a steady current 'I'flows through the wire. The Z-component of the magnetic field at the center of the spiralis

v

-x-

(A) f . 1 o N I 1 ( b )2(b-a) n -;;f . 1 o N I In ( ! ! _ )2b a

(8) f . 1 o N I I(b+a)2(b-a) n b-af . 1 o N I In(b+a)2b b-a(C) (0)

ANSWER: A24. A point mass is subjected to two simultaneous sinusoidal displacements in x-direction,

Xl (t ) = A sinwt and X2 (r) = A S i n ( on + 2 ; ) . Adding a third sinusoidal displacementx3(t) =B sin(wt+~) brings the mass to a complete rest. The values of 8 and ~are

(A) J2A , 3: (8) A 4 1 Z ", 3 (C) J3A , 5 : (0) A,~ANSWER: B


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PHYSICS25. Which of the field patterns given below is valid for electric field as well as for magneticfield?

(A) (8) ~l/--+0+----/~(C) (0)

ANSWER: C


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( PHYSICS )26. A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg,

traveling with a velocity V m /s in a horizontal direction, hits the centre of the ball. After thecollision, the ball and bullet travel independently. The ball hits the ground at a distance of20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity Vof the bullet is

\\\, '",,\\

\o 20 100

(A) 250 m /s (8) 250.[i m /s (C) 400 m /s (0) 500 m /sANSWER: D

27. The density of a solid ball is to be determined in an experiment. The diameter of the ballis measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on thecircular scale. The reading on the main scale is 2.5 mm and that on the circular scale is20 divisions. If the measured mass of the ball has a relative error of 2%, the relativepercentaqs error in the density is(A) 0.9% (8) 2.4% (C) 3.1% (0) 4.2%

ANSWER: C


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PHYSICS )28. A wooden block performs SHM on a frictionless surface with frequency, V o . The block

--tcarries a charge +0 on its surface. If now a uniform electric field E is switched-on asshown, then the SHM of the block will be

(A) of the same frequency and with shifted mean position.(8) of the same frequency and with the same mean position.(C) of changed frequency and with shifted mean position.(0) of changed frequency and with the same mean position.

ANSWER: A


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( PHYSICSSECTION - II (Total Marks: 16)(Multiple Correct Answer(s) Type)

This section contains 4 multiple choice questions. Each question has four choices(A), (8), (C) and (0) out of which ONE or MORE may be correct.

29. Two solid spheres A and 8 of equal volumes but of different densities dA and dB areconnected by a string. They are fully immersed in a fluid of density dF. They get arrangedinto an equilibrium state as shown in the figure with a tension in the string. Thearrangement is possible only if

(A) dA < dF(C) dA> dF

(8) dB> dF(0) dA + dB= 2 dF

ANSWER:ABD30. A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C

is without a dielectric medium and (8) when C is filled with dielectric of constant 4. Thecurrent I R through the resistor and voltage Vc across the capacitor are compared in thetwo cases. Which of the following is/are true?

(8)(0)

ANSWER: Be

(A )(C)


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( PHYSICS ]31. Which of the following statement(s) is/are correct?

(A) If the electric field due to a point charge varies as r -25 instead of r -2, then theGauss law will still be valid.(8) The Gauss law can be used to calculate the field distribution around an electric

dipole.(e) If the electric field between two point charges is zero somewhere, then the sign ofthe two charges is the same.(0) The work done by the external force in moving a unit positive charge from point A atpotential V A to point B at potential V B is ( V B - V A ) .

ANSWER: CD32. A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal planewith velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the

opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity10 m/s. Immediately after the collision

10mls

(A) the ring has pure rotation about its stationary eM.(8) the ring comes to a complete stop.(e) friction between the ring and the ground is to the left.(0) there is no friction between the ring and the ground.

ANSWER: A OR AC


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PHYSICSSECTION - III (Total Marks: 24)

(Integer Answer Type)This section contains 6 questions. The answer to each of the questions is a single-digitinteger, ranging from 0 to 9. The bubble corresponding to the correct answer is to bedarkened in the ORS.

33. A train is moving along a straight line with a constant acceleration' a'. A boy standing inthe train throws a ball forward with a speed of 10 mis, at an angle of 60 to the horizontal.The boy has to move forward by 1.15 m inside the train to catch the ball back at the initialheiqht. The acceleration of the train, in rn/s", is

ANSWER: 534. A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of

friction between the block and the floor is 0.1. Initially the block is at rest and the spring isuri-stretched. An impulse is given to the block as shown in the figure. The block slides adistance of 0.06 m and comes to rest for the first time. The initial velocity of the block inm /s is V = N/10 . Then N is

ANSWER: 435. Two batteries of different ernfs and different internal resistances are connected as shown.The voltage across AS in volts is6V- - - 1 1 Q B3V 2Q

ANSWER: 5


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PHYSICS36. Water (with refractive index = 4) in a tank is 18 ern deep. Oil of refractive index 2 lies on3 4

water making a convex surface of radius of curvature 'R = 6 cm' as shown. Consider oilto act as a thin lens. An object'S' is placed 24 cm above water surface. The location ofits image is at 'x' cm above the bottom of the tank. Then 'x' is

S: J .l = 1.0

ANSWER: 237. A series R-C combination is connected to an AC voltage of angular frequency

co = 500 radian/so If the impedance of the R-C circuit is R .J1.25 , the time constant(in millisecond) of the circuit is

ANSWER: 438. A silver sphere of radius 1 cm and work function 4.7 eV is suspended from aninsulating thread in free-space. It is under continuous illumination of 200 nm wavelength

light. As photoelectrons are emitted, the sphere gets charged and acquires apotential. The maximum number of photoelectrons emitted from the sphere is A x 102(where 1 < A < 10). The value of 'Z' is

ANSWER: 7


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( PHYSICSSECTION - IV (Total Marks: 16)

(Matrix-Match Type)This section contains 2 questions. Each question has four statements (A, 8, C and D)given in Column I and fiive statements (p, q, r, sand t) in Column II. Any givenstatement in Column I can have correct matching with ONE or MORE statement(s) givenin Column II. For example, if for a given question, statement 8 matches with thestatements given in q and r, then for the particular question, against statement 8, darkenthe bubbles corresponding to q and r in the ORS.

39. One mole of a monatomic ideal gas is taken through a cycle A8CDA as shown in theP-V diagram. Column II gilves the characteristics involved in the cycle. Match them witheach of the processes given in Column I.P

3P

1P

I II II I I18 IA I~ - - - ~ - - - - - - - - - - - - - - ~ - - - - - - -IIIIII

II..L-. -'-~------~___;~ _: e : 0I II I

o 1V 3V vColumn I

(A) Process A ---7 8

(8) Process 8 ---7 C

(C) Process C ---7 0

(D) Process 0 ---7 A

9V

Column II(p) Internal energy decreases.(q) Internal energy increases.(r) Heat is lost.(s) Heat is gained.(t) Work is done on the gas.

ANSWER A : p, rand tB: p and rC: q and sD: rand t


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PHYSICS )40. Column I shows four systems, each of the same length L, for producing standing waves.

The lowest possible natural frequency of a system is called its fundamental frequency,whose wavelength is denoted as A f . Match each system with statements given inColumn II describing the nature and wavelength of the standing waves.

Column I Column II

(A) Pipe closed at one end

o(8) Pipe open at both ends

L

(p) Longitudinal waves

(q) Transverse waves

0 L (r) A t = L(C) Stretched wire clamped at both ends

1 0 I -l(0) Stretched wire clamped at both ends and at (s) A t = 2Lmid-point

L

ANSWER A: p and tB: p and 5C: q and 5D: q and r

(t) A t = 4L


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[ PART III : MATHEMATICS 1SECTION -I (Total Marks: 24)(Single Correct Answer Type)

This section contains 8 multiple choice questions. Each question has four choices(A), (8), (C) and (0) out of which ONLY ONE is correct.

2 241 . Let P (6,3) be a point on the hyperbola ~ - 4 = 1. If the normal at the point P intersectsa- bthe x - axis at (9 , 0) , then the eccentricity of the hyperbola is(A) J % (8) J % (C) . J 2 (0) .J 3

ANSWER: B42. A value of b for which the equationsx2 +bx-l =0x2 +x+b =0,

have one root in common is(A) - . J 2 (8 ) - i . J 3 (C) i . J 5 (0) . J 2

ANSWER: B43. Let (J) * 1 be a cube root of unity and S be the set of all non-singular matrices of the form

[1 a b l(J) 1 C,{J)2 (J) 1

where each of a, b, and c is either (J) or (J)2. Then the number of distinct matrices in theset S is(A) 2 (8) 6 (C) 4 (0) 8

ANSWER: A44. The circle passing through the point (-1,0) and touching the y-axis at (0,2) also

passes through the point(A) (- ~ , 0 ) (8) ( - % , 2 ) (0) (-4 , 0 )

ANSWER: D


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MATHEMATICS)45. I f

}lim [1+xln(1+b2)];=2bsin2e , b>O and eE(-1l,1l],


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MATHEMATICSSECTION - II (Total Marks: 16)(Multiple Correct Answer(s) Type)

This section contains 4 multiple choice questions. Each question has four choices(A), (8), (C) and (0) out of which ONE or MORE may be correct.

49. IfJr Jr-x-- x$--2' 2

Jrf(x)= -cosx, --


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MATHEMATICS

51. Let L be a normal to the parabola / = 4x. If L passes through the point (9,6), then Lis given by

(8 ) y + 3x- 33 = (0) y - 2x + 12 =

ANSWER:ABD52. Let f: (0,1)~ lR . be defined by

(A ) y-x+3=0(C) y + x -15 =

b-xf(x)=I_bx'where b is a constant such that 0< b < 1. Then(A) f is not invertible on (0, 1)(8) Ir' on (0,1) and f'(b) =_1_f '(O)(C) f = f-I on (0,1) and f'(b) =_1_f '(O)(0) f-I is differentiable on (0, 1)

ANSWER: A


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MATHEMATICS)

SECTION - III (Total Marks: 24)(Integer Answer Type)

This section contains 6 questions. The answer to each of the questions is a single-digitinteger, ranging from 0 to '9 . The bubble corresponding to the correct answer is to bedarkened in the ORS.

53. '~Let {J} = e 3, and a, b, e, x, y, z be non-zero complex numbers such thata+b+c = x

a + bai+ col = ya+bar +e{J)= z.

I A I ~ + I y l ' + I z l 2 .Then the value of l a l 2 + I b l ' + l e l 2 ISANSWER: MARKS TO ALL

54. The number of distinct real roots of X4 - 4x3 + 12x2 + x-I = 0 isANSWER: 2

55. Let y'(x) + y(x)g'(x) = g(x)g'( x), yeO) = 0, XE IR, where f'(x) denotes d ~ ; X ) and g(x) isa given non-constant differentiable function on l R with g(O) = g(2) = O . Then the value ofy(2) is

ANSWER: 0


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( MATHEMATICS)56. Let M be a 3x3 matrix satisfying

Then the sum of the diagonal entries of M isANSWER: 9

57. Let a = -i- k , b = . ; + ] and c = i+ 2] + 3 k be three given vectors. If r is a vector suchthat r x b = c : band r . a = 0, then the value of r .b is

ANSWER: 958. The straight line 2x - 3y = 1 divides the circular region x2 +ls 6 into two parts. If

then the number of point(s) in S lying inside the smaller part isANSWER: 2


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SECTION - IV (Total Marks: 16)(Matrix-Match Type)

( MATHEMATICS)

This section contains 2 questions. Each question has four statements (A, 8, C and 0)given in Column I and five statements (p, q, r, sand t) in Column II. Any givenstatement in Column I can have correct matching with ONE or MORE statement(s) givenin Column II. For example, if for a given question, statement 8 matches with thestatements given in q and r, then for the particular question, against statement 8, darkenthe bubbles corresponding to q and r in the DRS.

59. Match the statements given in Column I with the values given in Column IIColumn I

(A) If ii = ] + 1 3 k , b = - ] + 1 3 k and c = 2 1 3 k forma triangle, then the internal angle of thetriangle between a and b is

(8) If J : (f(x)-3x)dx = a2 -b", then the value off ( ~ ) is

1[2 . %(C) The value of - f sectzr) dx isIn 3 X(0) The maximum value of Arg ( _ 1 _ ) for1-zI z I = 1, z * - 1 is given by

ANSWERA: qB : p or p, q, r, 5and tC:sD: t

Column II(p) 6

(q) 21[3

(r) 3

(s) 1[

(t ) 2


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( MATHEMATICS J60. Match the statements given in Column I with the intervals/union of intervals given in

Column IIColumn I

(A ) The set{ R e C = i ~ , : Z is a complex number, I z l ~1, z= 1}is

(8) The domain of the function. -I ( 8(3r-2 J ' .fCx) = sin 1-32(X-I) IS

1 tan 0 1(C) If fCO) = -tanO 1 tan 0 , then the set

-1 -tanO 1{ f (0) :0 ~ 0 < ~ } is

(D ) If fC x)= x%C3x-1O ), x~O , thenincreasing in

fCx) is

ANSWERA:sB: tC: rD: r

Column II(p ) ( -00 , -1)uO, 00 )

(q ) ( -00 , 0)u (0, 0 0 )

(r ) [2, 00 )

(s) ( -00 , -l]u[l, 00 )

(t ) ( -00 , 0]u [2, 00 )

iit jee 2011 paper 2 question answer

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