iit-jee 2011 question paper with answer key

8/13/2019 IIT-JEE 2011 Question Paper With Answer Key

1/35

1 IIT-JEE 2011 Paper

IIT-JEE 2011 TEST PAPERPHYSICS

PAPER - 1

Time : 1.00 Hr Max. Marks : 80

GENERAL INSTRUCTIONS

1. There are 23 Questions.

2. In Section I (Total Marks: 21), for each question you will be awarded 3 marks if you darken ONLY the bubble

corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one

(-1) mark will be awarded.

3. In Section Il (Total Marks: 16), for each question you will be awarded 4 marks if you darken ALL the

bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. There are no negative

marks in this section.

4. In Section III (Total Marks: 15), for each question you will be awarded 3 marks if you darken ONLY the bubble

corresponding to the correct answer and zero marks if no

bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

5. In Section IV (Total Marks: 28), for each question you will be awarded 4 marks if you darken ONLY the

bubble corresponding to the correct answer and zero marks otherwise. There are no negative marks in this

section.

SECTION - I (Total Marks : 21)(Single Correct Answer Type)

This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out ofwhich ONLY ONE is correct.

1. A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall buildingwhich reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by thecar driver is(A) 8.50 kHz (B) 8.25 kHz

(C) 7.75 kHz (D) 7.50 kHz


2/35


2. 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T 1,the work done in the process is :

(A) 1RT89 (B) 1RT2

3

(C) 1RT815

(D) 1RT29

3. Consider an electric field xEE 0!!

, where E 0 is a constant.

The flux through the shaded area (as shown in the figure)due to this field is :

(A) 2E 0a2 (B) 2 E0a

2

(C) E 0a2 (D)

2

aE 20

4. The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 . The wavelength of thesecond spectral line in the Balmer series of singly ionized helium atom is :(A) 1215 (B) 1640 (C) 2430 (D) 4687

5. A ball of mass (m) 0.5 kg is attached to the end of a string having length (L)0.5 m. The ball is rotated on a horizontal circular path about vertical axis. Themaximum tension that the string can bear is 324 N. The maximum possible

value of angular velocity of ball (in radian/s) is :

(A) 9 (B) 18(C) 27 (D) 36

6. A meter bridge is set-up as shown, to determine an unknownresistance X using a standard 10 ohm resistor. Thegalvanometer shows null point when tapping-key is at 52cm mark. The end-corrections are 1 cm and 2 cmrespectively for the ends A and B. The determined value ofX is (A) 10.2 ohm (B) 10.6 ohm

(C) 10.8 ohm (D) 11.1 ohm

7. A 2"F capacitor is charged as shown in figure. The percentage of itsstored energy dissipated after the switch S is turned to position 2 is

(A) 0%

(B) 20%

(C) 75%

(D) 80%


3/35


SECTION II (Total Marks : 16)

(Multiple Correct Answers Type) This section contains 4 multiple choice questions . Each question has four choices (A), (B), (C) and (D) outof which ONE or MORE may be correct.

8. A spherical metal shell A of radius R A and a solid metal sphere B of radius R B (< R A) are kept far apart and eachis given charge +Q. Now they are connected by a thin metal wire. Then

(A) 0E insideA ! (B) Q A > Q B (C) AB

B

A

RR!

##

(D) surfaceonBsurfaceon

A EE $

9. An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infiniteregion of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

(A) They will never come out of the magnetic field region.

(B) They will come out travelling along parallel paths.

(C) They will come out at the same time.

(D) They will come out at different times.

10. A composite block is made of slabs A, B, C, D and E ofdifferent thermal conductivities (given in terms of a constantK) and sizes (given in terms of length, L) as shown in thefigure. All slabs are of same width. Heat Q flows only fromleft to right through the blocks. Then in steady state

(A) heat flow through A and E slabs are same(B) heat flow through slab E is maximum

(C) temperature difference across slab E is smallest

(D) heat flow through C = heat flow through B + heat flow through D.

11. A metal rod of length L and mass m is pivoted at one end. A thin disk of mass M and radius R (


4/35


5/35


13. The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the twocircles represent the same oscillator but for different initial conditions, and E 1 and E 2 are the total mechanicalenergies respectively. Then :

(A) 21 E2E ! (B) 21 E2E !

(C) 21 E4E ! (D) 21 E16E !14. Consider the spring-mass system, with the mass submerged in water,

as shown in the figure. The phase space diagram for one cycle of this

system is :

(A)Position

Momentum

(B)

(C) (D)


6/35


Paragraph for Question Nos. 15 and 16A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solidscontaining fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let N be thenumber density of free electrons, each of mass m. When the electrons are subjected to an electric field, theyare displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons beginto oscillate about the positive ions with a natural angular frequency %p , which is called the plasma frequency.To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency %,where a part of the energy is absorbed and a part of it is reflected. As % approaches %p all the free electrons areset to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

15. Taking the electronic charge as e and the permitlivity as &0, use dimensional analysis to determine thecorrect expression for %p.

(A)0m

Ne& (B) Ne

m 0&

(C)0

2

mNe

& (D) 20

Ne

m&

16. Estimate the wavelength at which plasma reflection will occur for a metal having the density of electronsN ' 4 x 10 27 m 3. Take &0 ' 10

111 and m ' 10 30, where these quantities are in proper SI units. s.(A) 800 nm (B) 600 nm(C) 300 nm (D) 200 nm

SECTION IV (Total Marks : 28)

(Integer Answers Type) This sections contains 7 questions . The answer to each of the questions is a single-digit integer , rangingfrom 0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.

17. A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies aforce of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m/s 2. The coefficient of frictionbetween the ground and the ring is large enough that rolling always occurs and the coefficient of frictionbetween the stick and the ring is (P/10). The value of Pis

18. A block is moving on an inclined plane making an angle 45 with the horizontal and the coefficient of friction is" . The force required to just push it up the inclined plane is 3 times the force required to just prevent it fromsliding down. If we define N = 10 " , then N is


7/35


19. Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side a .Thesurface tension of the soap film is (. The system of charges and planar film are in equilibrium, and

a = k

N / 12q

))*+

,,-.

( , where k is a constant. Then N is

20. Steel wire of length L at 40C is suspended from the ceiling and then a mass m is hung from its free end. Thewire is cooled down from 40 C to 30C to regain its original length L. The coefficient of linear thermal expansionof the steel is 10 5 / C, Youngs modulus of steel is 10 11 N/m 2 and radius of the wire is 1 mm. Assume that L >>diameter of the wire. Then the value of m in kg is nearly.

21. The activity of a freshly prepared radioactive sample is 10 10 disintegrations per second, whose mean life is 10 9

s. The mass of an atom of this radioisotope is 10 25 kg. The mass (in mg) of the radioactive sample is

22. A long circular tube of length 10 m and radius 0.3 m carries a current / along its curved surface as shown. A

wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with theaxis of the tube. The current varies as / = /0 cos (300 t) where /0 is constant. If the magnetic moment of the loopis N " 0 /0 sin (300 t), then N is

23. Four solid spheres each of diameter 5 cm and mass 0.5 kg are placed with their centers at the corners of a

square of side 4cm. The moment of inertia of the system about the diagonal of the square isN 10 4 kg-m 2, then N is


8/35


IIT-JEE 2011 TEST PAPER

PHYSICSPAPER - 2




2. In Section I (Total Marks: 24), for each question you will be awarded 3 marks it you darken ONLY thebubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases,minus one (-1) mark will be awarded.

3. In Section II (Total Marks: 16), for each queshon you will be awarded 4 marks if you darken ALL thebubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. There are no negativemarks in this section.

4. In Section Ill (Total Marks: 24), for each question you will be awarded 4 marks if you darken ONLY thebubble corresponding to the correct answer and zero marks otherwise. There are no negative marks inthis section.

5. In Section IV (Total Marks: 16), for each question you will be awarded 2 marks for each row in which youhave darkened ALL the bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise.Thus, each question in this section carries a maximum of 8 marks . There are no negative marks in this

section.

SECTION - I (Total Marks - 24)(Single Correct Answer Type)

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

1. A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence 1. The reflected(R ) and transmitted (T) intensities, both as function of 1, are plotted. The correct sketch is

(A)

100%

(B)

100%

(C)

100%

(D)


9/35


2. A satellite is moving with a constant speed 'V in a circular orbit about the earth. An object of mass m is ejectedfrom the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, thekinetic energy of the object is

(A) 2mV21

(B) mV 2

(C) 2mV23

(D) 2mV 2

3. 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 inthe X-Y plane and a steady current / flows through the wire. TheZ-component of the magnetic field at the center of the spiral is

(A) 2 3 45

6 7

8/"

ab

n)ab(2

N0 " (B) 2 3 45

6 7

89

8/"

abab

n)ab(2

N0 "

(C) 2 3 45

6 7 /"

ab

nb2N0 " (D) 2 3

456 7

89/"

abab

nb2N0 "

4. A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x 1 (t) = A sin %t and

x2 (t) = A sin 2 3 45

6 7 :9%

32

t . Adding a third sinusoidal displacement x 3 (t) = B sin ( %t + ; ) brings the mass to acomplete rest. The values of B and ; are

(A) 4

3,A2 :

(B) 3

4,A :

(C) 65

,A3 :

(D) A, 3:

5. Which of the field patterns given below is valid for electric field as well as for magnetic field?

(A) (B)

(C) (D)


10/35


6. 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 ahorizontal direction, hits the centre of the ball. After thecollision, the ball and bullet travel independently. The ballhits the ground at a distance of 20 m and the bullet at adistance of 100 m from the foot of the post. The initial velocityV of the bullet is

(A) 250 m/s (B) 250 2 m/s

(C) 400 m/s (D) 500 m/s

7. The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with ascrew gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the mainscale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relativeerror of 2%, the relative percentage error in the density is(A) 0.9% (B) 2.4%(C) 3.1% (D) 4.2%

8. A wooden block performs SHM on a frictionless surfacewith frequency, d F(C) d A > d F (D) d A + d B = 2d F

10. A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectricmedium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage V Cacross the capacitor are compared in the two cases. Which of the following is/are true?

(A) BRAR /=/ (B) BRAR /$/

(C)BC

AC VV = (D)

BC

AC VV $


11/35


11. Which of the following statement(s) is/are correct?(A) If the electric field due to a point charge varies as r 2.5 instead of r 2, then the Gauss law will still be valid.(B) The Gauss law can be used to calculate the field distribution around an electric dipole.(C) If the electric field between two point charges is zero somewhere, then the sign of the two charges is thesame.(D) The work done by the external force in moving a unit positive charge from point A at potential V A to point Bat potential V B is (V B

VA).

12. A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on ahorizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving withvelocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 mand goes vertically up with velocity 10 m/s. Immediately after the collision(A) The ring has pure rotation about its stationary CM(B) The ring comes to a complete stop.(C) Friction between the ring and the ground is to the left.(D) There is no friction between the ring and the ground.

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

This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.

13. A train is moving along a straight line with a constant acceleration a . A boy standing in the train throws a ballforward with a speed of 10 m/s, at an angle of 60 to the horizontal. The boy has to move forward by 1.15 minside the train to catch the ball back at the initial height. The acceleration of the train, in m/s 2, is

14. A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the blockand the floor is 0.1. Initially the block is at rest and thespring is un-stretched. An impulse is given to the block asshown in the figure. The block slides a distance of 0.06 mand comes to rest for the first time. The initial velocity of theblock in m/s is V= N/10. Then N is

15. Two batteries of different emfs and different internal resistances are connected as shown. The voltage acrossAB in volts is


12/35


16. Water (with refractive index = 34

) in a tank is 18 cm deep.

Oil of refractive index 47

lies on water making a convexsurface of radius of curvature R = 6 cm as shown. Consider oil to act as a thin lens. An object S is placed 24 cm abovewater surface. The location of its image is at x cm abovethe bottom of the tank. Then x is

17. A series R-C combination is connected to an AC voltage of angular frequency % = 500 radian/s. If the impedance

of the R-C circuit is 25.1R , the time constant (in millisecond) of the circuit is

18. A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space.

It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere getscharged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is A 10Z

(where 1 < A < 10). The value of Z is

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 andfive statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching withONE or MORE statement(s) given in Column II. For example, if for a given question, statement B matches withthe statements given in q and r, then for the particular question, against statement B, darken the bubblescorresponding to q and r in the ORS.

19. One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column IIgives the characteristics involved in the cycle. Match them with each of the processes given in Column I.

Column I Column II(A) Process A > B (p) Internal energy decreases(B) Process B > C (q) Internal energy increases(C) Process C > D (r) Heat is lost(D) Process D > A (s) Heat is gained

(t) Work is done on the gas.


13/35


20. Column I shows four systems, each of the same length L, for producing standing waves. The lowest possiblenatural frequency of a system is called its fundamental frequency, whose wavelength is denoted as ?f. Matcheach system with statements given in Column II describing the nature and wavelength of the standing waves.

Column I Column II

(A) Pipe closed at one end (p) Longitudinal waves

(B) Pipe open at both ends (q) Transverse waves

(C) Stretched wire clamped at both ends (r) ?f = L

(D) Stretched wire clamped at both ends (s) ?f = 2L and at mid-point

(t) ?f = 4L


14/35


ANSWER KEY TO IIT-JEE 2011 PAPER

PAPER - 11. (A) 2. (A) 3. (C) 4. (A) 5. (D)

6. (B) 7. (D) 8. (A),(B),(C),(D) 9. (B),(D) 10. (A),(C),(D)

11. (A),(D) 12. (D) 13. (C) 14. (B) 15. (C)

16. (B)lish 4 a 17. P = 4 18. N = 5 19. N = 3 20. 3

21. 1 22. N = 6 23. N = 9

45. 6 46. 9

PAPER - 21. (C) 2. (B) 3. (A) 4. (B) 5. (C)

6. (D) 7. (C) 8. (A) 9. (A), (B), (D) 10. (B), (C)

11. (C) 12. (C) 13. 5 14. 4 15. 5

16. 2 17. 4 18. 7

19. (A) p,r,t; (B) p,r ; (C) q,s; (D) r, t 20. (A) p; (B) p,s; (C) q,s; (D) q, r


15/35


IIT-JEE 2011 TEST PAPERCHEMISTRY

PAPER - 1




2. In Section I (Total Marks: 21), for each question you will be awarded 3 marks if you darken ONLY the bubble

corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one

(-1) mark will be awarded.

3. In Section Il (Total Marks: 16), for each question you will be awarded 4 marks if you darken ALL the

bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. There are no negative

marks in this section.

4. In Section III (Total Marks: 15), for each question you will be awarded 3 marks if you darken ONLY the bubble

corresponding to the correct answer and zero marks if no

bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

5. In Section IV (Total Marks: 28), for each question you will be awarded 4 marks if you darken ONLY the

bubble corresponding to the correct answer and zero marks otherwise. There are no negative marks in this

section.


This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out

of which ONLY ONE is correct.

1. Extra pure N 2 can be obtained by heating

(A) NH3 with CuO (B) NH 4NO3(C) (NH 4)2Cr2O7 (D) Ba(N 3)2

2. Geometrical shapes of the complexes formed by the reaction of Ni 2+ with Cl , CN and H 2O, respectively, are

(A) octahedral, tetrahedral and square planar (B) tetrahedral, square planar and octahedral

(C) square planar, tetrahedral and octahedral (D) octahedral, square planar and octahedral


16/35


3. Bombardment of aluminum by ! -particle leads to its artificialdisintegration in two ways, (I) and (ii) as shown. Products X, Y and Zrespectively are,(A) proton, neutron, positron(B) neutron, positron, proton(C) proton, positron, neutron(D) positron, proton, neutron

4. Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of thesolution is :(A) 1.78 M (B) 2.00 M(C) 2.05 M (D) 2.22 M

5. AgNO 3 (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured.The plot of conductance ( " ) versus the volume of AgNO 3 is :

(A) (P) (B) (Q)(C) (R) (D) (S)

6. Among the following compounds, the most acidic is :(A) p-nitrophenol (B) p-hydroxybenzoic acid(C) o-hydroxybenzoic acid (D) p-toluic acid

7. The major product of the following reaction is :

(A) (B)

(C) (D)


17/35


SECTION II (Total Marks : 16)

(Multiple Correct Answers Type)This section contains 4 multiple choice questions . Each question has four choices (A), (B), (C) and (D) outof which ONE or MORE may be correct.

8. Extraction of metal from the ore cassiterite involves :(A) carbon reduction of an oxide ore (B) self-reduction of a sulphide ore(C) removal of copper impurity (D) removal of iron impurity

9. The correct statement(s) pertiaining to the adsorption of a gas on a solid surface is (are)(A) Adsorption is always exothermic(B) Physisorption may transform into chemisorption at high temperature

(C) Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature(D) Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation.

10. According to kinetic theory of gases(A) collisions are always elastic(B) heavier molecules transfer more momentum to the wall of the container(C) only a small number of molecules have very high velocity(D) between collisions, the molecules move in straight lines with constant velocities.

11. Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possibleconformations (if any), is (are)

(A) (B) H C #

(C) H 2C=C=O (D) H 2C=C=CH 2

SECTION III (Total Marks :15)(Paragraph Type)

This section contains 2 paragraphs. Based upon one of the paragraphs 3 multiple choice questions andbased on the other paragraph 2 multiple choice questions have to be answered. Each of these questions hasfour choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Question Nos. 12 to 14

When a metal rod M is dipped into an aqueous colourless concentrated solution of compound N the solutionturns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate O. Addition of aqueousNH3 dissolves O and gives an intense blue solution.

12. The metal rod M is :(A) Fe (B) Cu(C) Ni (D) Co


18/35


13. The compound N is :(A) AgNO 3 (B) Zn(NO 3)2(C) Al(NO

3)

3(D) Pb(NO

3)

2

14. The final solution contains :(A) [Pb(NH 3)4]

2+ and [CoCl 4]2 (B) [Al(NH3)4]

3+ and [Cu(NH 3)4]2+

(C) [Ag(NH 3)2]+ and [Cu(NH 3)4]

2+ (D) [Ag(NH 3)2]+ and [Ni(NH 3)6]

2+

Paragraph for Question Nos. 15 and 16

An acyclic hydrocarbon P , having molecular formula C 6H10 , gave acetone as the only organic product throughthe following sequence of reactions, in which Q is an intermediate organic compound.

15 . The structure of compound P is :(A) CH3CH2CH2CH2 C#C H (B) H3CH2C C#C CH2CH3

(C) (D)

16. The structure of the compound Q is

(A) (B)

(C) (D)

SECTION IV (Total Marks : 28)(Integer Answers Type)

This sections contains 7 questions . The answer to each of the questions is a single-digit integer , rangingfrom 0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.

17. The difference in the oxidation numbers of the two types of sulphur atoms in Na 2S 4O6 is

18. Reaction of Br 2 with Na 2CO 3 in aqueous solution gives sodium bromide and sodium bromate with evolution ofCO 2 gas. The number of sodium bromide molecules involved in the balanced chemical equation is

19. The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum number,m s = 1/2, is


19/35


20. The work function ( $) of some metas is listed below. The number of metals which will show photoelectric effectwhen light of 300 nm wavelength falls on the metal is

Metal Li Na K Mg Cu Ag Fe Pt W

f (eV) 2.4 2.3 2.2 3.7 4.8 4.3 4.7 6.3 4.75

21. To an evacuated vessel with movable piston under external pressure of 1 atm, 0.1 mol of He and 1.0 mol of anunknown compound (vapour pressure 0.68 atm. at 0 C) are introduced. Considering the ideal gas behaviour,the total volume (in litre) of the gases at 0 C is close to

22. The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholicKOH is

23. A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine.Glycine contributes 47.0 % to the total weight of the hydrolysed products. The number of glycine units presentin the decapeptide is


20/35


21/35


4. Consider the following cell reaction :

2Fe (s) + O 2 (g) + 4H+ (aq) %& % 2Fe 2+ (aq) + 2H 2O (l) E = 1.67 V

At [Fe 2+] = 10

3 M, P (O 2) = 0.1 atm and pH = 3, the cell potential at 25 C is :(A) 1.47 V (B) 1.77 V(C) 1.87 V (D) 1.57 V

5. The freezing point (in C) of a solution containing 0.1 g of K 3[Fe(CN) 6] (Mol. Wt. 329) in 100 g of water(Kf = 1.86 K kg mol

1) is :(A) 2.3 10 2 (B) 5.7 10 2

(C) 5.7 10 3 (D) 1.2 10 2

6. Amongst the compounds given, the one that would form a brilliant colored dye on treatment with NaNO 2 indilute HCl followed by addition to an alkaline solution of ' -naphthol is :

(A) (B)

(C) (D)

7. The major product of the following reaction is

)anhydrous(HOHRCH 2

( % % % % & %

(A) a hemiacetal (B) an acetal(C) an ether (D) an ester

8. The following carbohydrate is

(A) a ketohexose (B) an aldohexose(C) an ! -furanose (D) an ! -pyranose

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

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

9. Reduction of the metal centre in aqueous permanganate ion involves :

(A) 3 electrons in neutral medium (B) 5 electrons in neutral medium(C) 3 electrons in alkaline medium (D) 5 electrons in acidic medium


22/35


10. The equilibrium2Cu I Cu 0 + Cu II

in aqueous medium at 25 C shifts towards the left in the presence of :(A) NO 3

(B) Cl

(C) SCN (D) CN

11. For the first order reaction2N 2O 5 (g) & 4NO 2(g) + O 2 (g)

(A) The concentration of the reaction decreases exponentially with time(B) 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

12. The correct functional group X and the reagent/reaction conditions Y in the following scheme are

condensation polymer :

(A) X = COOCH 3, Y = H 2 /Ni/heat (B) X = CONH 2, Y = H 2Ni/heat(C) X = CONH 2, Y = Br 2 /NaOH (D) X = CN, Y = H 2 /NI/heat

Section Ill (Total Marks : 24)(Integer Answer Type)

This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from0 to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.

13. Among the following, the number of compounds that can react with PCl 5 to give POCl 3 isO2, CO 2, SO 2, H2O, H 2SO 4, P 4O10 .

14. The volume (in mL) of 0.1 M AgNO 3 required for complete precipitation of chloride ions present in 30 mL of 0.01M solution of [Cr(H 2O) 5Cl]Cl2, as silver chloride is close to

15. In 1 L saturated solution of AgCl [K sp (AgCl) = 1.6 10 10 ], 0.1 mol of CuCl

[Ksp (CuCl) = 1.0 10 6] is added. The resultant concentation of Ag + in the solution is 1.6 10 x. The value of "x"

is :

16. The number of hexagonal faces that are present in a truncated octahedron is

17. The maximum number of isomers (including stereoisomers) that are possible on monochlorination of thefollowing compound, is


23/35


18. The total number of contributing structures showing hyperconjugation (involving C H bonds) for the followingcarbocation is

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


19. Match the transformation in column I with appropriate options in column IIColumn I Column II

(A) CO 2(s) %& % CO 2(g) (p) phase transition

(B) CaCO 3(s) %& % CaO(s) + CO 2(g) (q) allotropic change

(C) 2H ) %& % H2(g) (r) * H is positive

(D) P (white, solid) %& % P (red, solid) (s) * S is positive

(t) * S is negative

20. Match the reactions in column I with appropriate type of steps/reactive intermediate involved in these reactionsas given in column II

Column I Column II

(A) % % % % & % NaOHaq (p) Nucleophilic substitution

(B) % % % % & % MgICH3 (q) Electrophilic substitution

(C) % % % % & % 42SOH (r) Dehydration

(D) % % % % & % 42SOH

(s) Nucleophilic addition

(t) Carbanion


24/35



PAPER - 11. (D) 2. (B) 3. (A) 4. (C) 5. (D) 6. (C) 7. (A)

8. (AD) or (ACD) 9. (AB) 10. (ABCD) 11. (BC) 12. (B) 13. (A)

14. (C) 15 . (D) 16. (B) 17. 5 18. 5 19. 9 20. 4

21. 7 22. 5 23. 69

PAPER - 21. (D) 2. (C) 3. (A) 4. (D) 5. (A) 6. (C) 7. (B)

8. (B) 9. (ACD) or (AD) 10. (BCD) 11. (ABD) 12. (ABCD) 13. 4

14. 6 15. 7 16. 8 17. 8 18. 6

19. (A p, r, s) ; (B r, s) ; (C t) ; (D p, q, t) 20. (A-r, s, t) ; (B-p, s) ; (C-r, s) ; (D-q, r)


25/35


IIT-JEE 2011 TEST PAPERMATHEMATICSPAPER - 1




2. In Section I (Total Marks: 21), for each question you will be awarded 3 marks if you darken ONLY the bubblecorresponding to the correct answer and zero marks if no bubble is darkened. In all other cases, minus one(-1) mark will be awarded.

3. In Section Il (Total Marks: 16), for each question you will be awarded 4 marks if you darken ALL the bubble(s)corresponding to the correct answer(s) ONLY and zero marks otherwise. There are no negative marks in thissection.

4. In Section III (Total Marks: 15), for each question you will be awarded 3 marks if you darken ONLY the bubblecorresponding to the correct answer and zero marks if nobubble is darkened. In all other cases, minus one (-1) mark will be awarded.

5. In Section IV (Total Marks: 28), for each question you will be awarded 4 marks if you darken ONLY the bubblecorresponding to the correct answer and zero marks otherwise. There are no negative marks in this section.


This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONLY ONE is correct.

1. Let (x 0, y0) be the solution of the following equations(2x) ! n2 = (3y) ! n3

3 ! nx = 2 ! ny .Then x 0 is

(A) 61

(B) 31

(C)2

1(D) 6


26/35


2. The value of ! "#3n

2n

22

2

dx)x6nsin(xsin

xsinx!

!! is

(A)41

! n23

(B)21

! n23

(C) ! n23

(D) 61

! n23

3. Let k

j

i

a ##$"

, k

j

i

b #"$"

and k

j

i

c ""$"

be three vectors. A vector %"

in the plane of a"

and b"

, whose

projection on c"

is3

1, is given by

(A) k

3 j

3i #" (B) k j3i3 """

(C) k

3 j

i

3 #" (D) k3 j3i "#

4. Let P = { & : sin & cos & = 2 cos &} and Q = { & : sin & + cos & = 2 sin &} be two sets. Then(A) P ' Q and Q P ( ) (B) Q '* P(C) P '* Q (D) P = Q

5. Let the straight line x = b divide the area enclosed by y = (1 x)2, y = 0, and x = 0 into two parts R 1 (0 + x + b)

and R 2(b + x + 1) such that R 1 R 2 = 41

. Then b equals

(A)43

(B)21

(C) 31

(D)41

6. Let , and - be the roots of x 2 6x 2 = 0, with , > - . If a n = , n - n for n . 1, then the value of9

810

a2a2a "

is

(A) 1 (B) 2(C) 3 (D) 4

7. A straight line L through the point (3, 2) is inclined at an angle 60 to the line 1yx3 $# . If L also intersects

the x-axis, then the equation of L is

(A) y + 3 x + 2 3 3 = 0 (B) y 3 x + 2 + 3 3 = 0

(C) 3 y x + 3 + 2 3 = 0 (D) 3 y + x 3 + 2 3 = 0

SECTION II (Total Marks : 16)(Multiple Correct Answers Type)

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


27/35


8. The vector(s) which is/are coplanar with vectors k

2 j

i ## and k j2i ## , and perpendicular to the vector

k

j

i

## is/are

(A) k

j " (B) ji #"

(C) j

i " (D) k j #"

9. Let M and N be two 3 3 non-singular skew-symmetric matrices such that MN = NM. If P T denotes thetranspose of P, then M 2 N2 (MT N) 1 (MN 1)T is equal to(A) M2 (B) N2

(C) M2 (D) MN

10. Let the eccentricity of the hyperbola 22

ax

22

by

= 1 be reciprocal to that of the ellipse x2

+ 4y2

= 4. If the

hyperbola passes through a focus of the ellipse, then

(A) the equation of the hyperbola is3x2

2y 2

= 1

(B) a focus of the hyperbola is (2, 0)

(C) the eccentricity of the hyperbola is 35

(D) the equation of the hyperbola is x 2 3y 2 = 3

11. Let f : R / R be a function such that f(x + y) = f(x) + f(y), 0 x, y 1 R. If f(x) is differentiable at x = 0, then(A) f(x) is differentiable only in a finite interval containing zero(B) f(x) is continuous 0 x 1 R(C) f2(x) is constant 0 x 1 R(D) f(x) is differentiable except at finitely many points

SECTION III (Total Marks :15)(Paragraph Type)

This section contains 2 paragraphs. Based upon one of the paragraphs 3 multiple choice questions and basedon the other paragraph 2 multiple choice questions have to be answered. Each of these questions has fourchoices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Questions Nos. 12 to 14

Let a, b and c be three real numbers satisfying

[a b c]

333

4

5

666

7

8

737

728791

= [0 0 0] ...........(E)


28/35


12. If the point P(a, b, c), with reference to (E), lies on the plane 2x + y + z = 1, then the value of 7a + b + c is(A) 0 (B) 12

(C) 7 (D) 613. Let 9 be a solution of x 3 1 = 0 with :m ( 9) > 0. if a = 2 with b and c satisfying (E), then the value of

a

39 + b

19 + c

39 is equal to

(A) 2 (B) 2(C) 3 (D) 3

14. Let b = 6, with a and c satisfying (E). If , and - are the roots of the quadratic equation ax 2 + bx + c = 0, then

n

0n

11; ?

@@A B

-#

, is

(A) 6 (B) 7

(C)76

(D) ?

@A B

2,2

1

P on the parabola, and C2 be the area of the triangle formed by drawing tangents at P and at

the end points of the latus rectum. Then2

1

CC

is

18. Let a 1, a 2, a 3,....., a 100 be an arithmetic progression with a 1 = 3 and S p = ;$

p

1iia , 1 + p + 100.

For any integer n with 1 + n + 20, let m = 5n. Ifn

m

SS

does not depend on n, then a 2 is

19. The positive integer value of n > 3 satisfying the equation= > ?@

A B D

#= > ?@

A B D

$= > ?@

A B D

n3sin

1

n2sin

1

nsin

1 is

20. Let f : [1,


30/35


IIT-JEE 2011 TEST PAPERMATHEMATICS

PAPER - 2Time : 1.00 Hr Max. Marks : 80



2. In Section I (Total Marks: 24), for each question you will be awarded 3 marks it you darken ONLY thebubble corresponding to the correct answer and zero marks if no bubble is darkened. In all other cases,minus one (-1) mark will be awarded.

3. In Section II (Total Marks: 16), for each queshon you will be awarded 4 marks if you darken ALL thebubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise. There are no negativemarks in this section.

4. In Section Ill (Total Marks: 24), for each question you will be awarded 4 marks if you darken ONLY thebubble corresponding to the correct answer and zero marks otherwise. There are no negative marks inthis section.

5. In Section IV (Total Marks: 16), for each question you will be awarded 2 marks for each row in which youhave darkened ALL the bubble(s) corresponding to the correct answer(s) ONLY and zero marks otherwise.Thus, each question in this section carries a maximum of 8 marks . There are no negative marks in thissection.

SECTION - I (Total Marks - 24)(Single Correct Answer Type)

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

1. Let P(6, 3) be a point on the hyperbola 1by

ax

2

2

2

2

$" . If the normal at the point P intersects the x-axis at

(9, 0), then the eccentricity of the hyperbola is

(A)25

(B)23

(C) 2 (D) 32. A value of b for which the equations

x2 + bx 1 = 0x2 + x + b = 0have one root in common is

(A) 2 (B) 3i

(C) i 5 (D) 2


31/35


3. Let 9 ( 1 be a cube root of unity and S be the set of all non-singular matrices of the form

3334

5

6667

8

999

1c1ba1

2 ,

where each of a, b and c is either 9 or 92. Then the number of distinct matrices in the set S is(A) 2 (B) 6(C) 4 (D) 8

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

(A) =

>

?@

A

B " 0,23

(B) =

>

?@

A

B " 2,25

(C) = > ?@

A B "

25

,23

(D) ( 4, 0)

5. If0x

lim/ E Fx

12 )b1ln(x1 ## = 2b sin 2 &, b > 0 and & 1 ( D, D], then the value of & is

(A) 4D

(B) 3D

(C) 6D (D) 2D

6. Let f : [ 1, 2] / [0,


32/35


SECTION II (Total Marks: 16)

(Multiple Correct Answer(s) Type)This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) outof which ONE or MORE may be correct.

9. If f(x) =

G

GG

H

GGG

I

J

K

+L"+LD""

D"+D""

1x,xn

1x0,1x

0x2

,xcos

2x,

2x

!

, then

(A) f(x) is continuous at x = 2D

(B) f(x) is not differentiable at x = 0

(C) f(x) is differentiable at x = 1 (D) f(x) is differentiable at x = 23

10. Let E and F be two independent events. The probability that exactly one of them occurs is 2511

and the

probability of none of them occurring is 252

. If P(T) denotes the probability of occurrence of the event T, then

(A) P(E) = 54 , P(F) = 5

3 (B) P(E) = 51 , P(F) = 5

2

(C) P(E) = 52

, P(F) = 51

(D) P(E) = 53

, P(F) = 54

11. Let L be a normal to the parabola y 2 = 4x. If L passes through the point (9, 6), then L is given by(A) y x + 3 = 0 (B) y + 3x 33 = 0(C) y + x 15 = 0 (D) y 2x + 12 = 0

12. Let f : (0, 1) / R be defined by f(x) = bx1xb

""

, where b is a constant such that 0 < b < 1. Then

(A) f is not invertible on (0, 1) (B) f ( f 1 on (0, 1) and f 2(b) = )0(f12

(C) f = f 1 on (0, 1) and f 2(b) = )0(f12 (D) f

1 is differentiable on (0, 1)

Section Ill (Total Marks : 24)(Integer Answer Type)

This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0to 9. The bubble corresponding to the correct answer is to be darkened in the ORS.


33/35


13. Let 9 = 3i

eD

, and a, b, c, x, y, z be non-zero complex numbers such that a + b + c = xa + b 9 + c 92 = ya + b 92 + c 9 = z.

Then the value of 222222

|c||b||a||z||y||x|

####

is

14. The number of distinct real roots of x 4 4x 3 + 12x 2 + x 1 = 0 is

15. Let y2(x) + y(x) g 2(x) = g(x) g 2(x), y(0) = 0, x 1 R , where f 2(x) denotes dx)x(df

and g(x) is a given non-constant

differentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is

16. Let M be a 3 3 matrix satisfying

M333

4

5

666

7

8

010

=333

4

5

666

7

8"

321

, M333

4

5

666

7

8"01

1

=333

4

5

666

7

8

" 111

, and M333

4

5

666

7

8

111

=333

4

5

666

7

8

1200

. Then the sum of the diagonal entries of M is

17. Let k

i

a ""$"

, j

i

b #"$"

and k

3 j

2i

c ##$"

be three given vectors. If r"

is a vector such that bcbr""""

M$M and

0a.r $""

, then the value of b.r""

is

18. The straight line 2x 3y = 1 divides the circular region x 2 + y2 + 6 into two parts.

If S = NOP

HIJ

= > ?@

A B =

> ?@

A B "=

> ?@

A B =

> ?@

A B

41

,81

,41

,41

,43

,25

,43

,2 ,

then the number of point(s) in S lying inside the smaller part is

SECTION IV (Total Marks : 16)

(Matrix-Match Type)



34/35


19. Match the statements given in Column-I with the values given in Column-IIColumn-I Column-II

(A) If k3 ja #$" , k3 jb #"$" and k32c $" form a triangle, (p) 6D

then the internal angle of the triangle between a"

and b"

is

(B) If ! "b

a

dx)x3)x(f( = a 2 b 2, then the value of = > ?@

A B D

6f is (q) 3

2D

(C) The value of ! DD6 / 5

6 / 7

2

dx)x(sec

3ln is (r)

3

D

(D) The maximum value of = > ?@

A B

" z11

Arg for |z| = 1, z ( 1 is given by (s) D

4

20. Match the statements given in Column-I with the intervals/union of intervals given in Column-IIColumn-I Column-II

(A) The setNOP

HIJ Q($=

> ?@

A B

"1z,1|z|,numbercomplexaisz:

z1iz2

Re 2 is (p) (


35/35



PAPER - 11. (C) 2. (A) 3. (C) 4. (D) 5. (B) 6. C 7. (B)

8. (AD)

9. Bonus (there is no non-singular 3 3 skew symmetric matrix).

10. (BD) 11. (BC) 12. (D) 13. (A) 14. (B) 15. (B) 16. (D)

17. (2)

18. 3 or 9, both 3 and 9 (The common difference of the arithmatic progression can be either 0 or 6, and accordinglythe second term can be either 3, or 9 ; thus the answers 3, or 9, or both 3 and 9 are acceptable.)

19. (7)

20. Bonus (Taking x = 1, the integral becomes zero, whereas the right side of the equation gives 5.

Therefore, the function f does not exist.)

21. (5) 22. (8) 23. (1)

45. 6 46. 9

PAPER - 21. (B) 2. (B) 3. (A) 4. (D) 5. (D) 6. (C) 7. (A)

8. (C) 9. (ABCD) 10. (AD) 11. (ABD) 12. (A)

13. Bonus (w = 3 / ie D is a typographical error, because of this the answer cannot be an integer.)

14. (2) 15. (0) 16. (9) 17. (9) 18. (2)

19. (A) / (q), (B) / (p,q,r,s,t) (C) / (s), (D) / (t)

20. (A) / (s), (B) / (t), (C) / (r), (D) / (r)

iit-jee 2011 question paper with answer key

Documents