IIT JEE-Advanced 2011 Solved papers by Triumph Academy
Triumph Academy IIT–JEE-11 / Paper I [1] CHEMISTRY IIT JEE - 2011 Paper 1 Time: 3 hours Max. Marks: 240 A. General: 1. This booklet is your Question Paper containing 60 questions. The booklet has 28 pages. 2. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers, and electronic gadgets in any form are not allowed to be carried inside the examination hall. 3. The answer sheet, Objective Response Sheet (ORS), is provided separately. B. Question paper format and Marking Scheme: 4. The question paper consists of 3 parts (Mathematics, Chemistry and Physics). Each part has FOUR sections. 5. For each question in Section I, you will be awarded 3 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. 6. For each question in Section II, you will be awarded 4 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, zero (0) mark will be awarded. 7. For each question in Section III, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer, and zero mark if no bubble is darkened. In all other cases, minus one (–1) mark will be awarded. 8. For each question in Section IV, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer, and zero mark if no bubble is darkened. In all other cases, minues one (–1) mark will be awarded. Name: 81-B/3, Lohagal Road, Ajmer-305 001 Telefax: 0145-2628805, 2628178 Reg. No.: 1 2 J E E e-mail: [email protected] website: www.triumphacademy.com Triumph Academy IIT–JEE-11 / Paper I [2] CHEMISTRY Part I Section–I Straight Objective Type This section contains 7 multiple choice questions numbered 1 to 7. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. Geometrical shapes of the complexes formed by the reaction of Ni 2 with Cl , CN and H 2 O, respectively, are (A) octahedral, tetrahedral and square planar (B) tetrahedral, sqaure planar and octahedral (C) square planar, tetrahedral and octahedral (D) octahedral, square planar and octahedral Ans. (B) Sol. NiCl 4 2 b g Nib H Og Ni CN 2 2. Tetrahedral 2 4 Square planar 2 6 Octahedral AgNO3 (aq.) was added to an aqueous KCI solution gradually and the conductivity of the solution was measured. The plot of conductance ( ) versus the volume of AgNO3 is (A) (P) Ans. (D) (B) (Q) (C) (R) (D) (S) Triumph Academy 3. CHEMISTRY Bombardment of aluminum by particle leads to its artificial disintegration in two ways, (i) and (ii) as shwon. Products X, Y and Z respectively are (A) proton, neutron, positron (C) proton, positron, neutron Ans. (A) Sol. 4. IIT–JEE-11 / Paper I [3] 4 2 He 27 13 Al 4 2 He 27 13 Al 30 15 Si 4 2 He 27 13 Al 30 14 Si e 30 15 P 0 (B) neutron, positron, proton (D) positron, proton, neutron n1 b Y g neutron 1 P1 b X g proton b positron g Extra pure N2 can be obtained by heating (A) NH3 with CuO (C) (NH4)2Cr2O7 (B) NH4NO3 (D) Ba(N3)2 Ans. (D) Sol. 5. b g Ba N 3 2 Ba 3N 2 Among the following compounds, the most acidic is (A) p-nitrophenol (B) p-hydroxybenzoic acid (C) o-hydroxybenzoic aicd (D) p-toluic acid Ans. (C) Triumph Academy IIT–JEE-11 / Paper I [4] CHEMISTRY O–H O OH C COOH Sol. because its carboxylate ion is stabilised due to intramolecular hydrogen bonding O and due to ortho effect. 6. The major product of the following reaction is (A) (B) (C) (D) Ans. (A) O O C NH Sol. (i) KOH (ii) Br N – CH 2 CH2Cl Br C O 7. O 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 the solution is (A) 1.78 M (B) 2.00 M (C) 2.05 M (D) 2.22 M Triumph Academy IIT–JEE-11 / Paper I [5] CHEMISTRY Ans. (C) Sol. Total mass of the solution = 1000 + 120 = 1120 g V 1120 0.973 L 115 . n urea M 120 2 mol 60 2 2.05 M 0.973 Section–II Multiple Correct Answer Type This section contains 5 multiple choice questions numbered 8 to 14. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is / are 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 Ans. (A, D) Sol. Cassiterite contains impurity of FeWO4 bSnO g 2 SnO 2 2C Sn 2CO 9. Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any), is (are) (A) (B) (C) H 2 C C O (D) H 2 C C CH 2 Ans. (B, C) 10. The correct statement (s) pertaining to the adsorption of a gas on a solid surface is (are) (A) Adsorption is always exothermic (B) Physisorption maytransform 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. Ans. (A, B, D) Triumph Academy IIT–JEE-11 / Paper I [6] CHEMISTRY 11. According to kinetic theory of gases (A) collision 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 collision, the molecules move in straight lines with constant velocities. Ans. (A, C, D) Section–III Paragraph Type This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 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 solution turns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate O. Addition of aqueous NH3 dissolves O and gives an intense blue solution. 12. The metal rod M is (A) Fe (B) Cu (C) Ni (D) CO (B) Zn(NO3)2 (C) Al(NO3)3 (D) Pb(NO3)2 2 (B) Al NH 3 Ans. (B) 13. The compound N is (A) AgNO3 Ans. (A) 14. The final solution contains b g Agb NH g (A) Pb NH 3 (C) Ans. (C) 2 4 3 2 and CoCl 4 b g and Cu NH 3 2 4 (D) b g Agb NH g 3 4 3 2 b g Nib NH g and Cu NH 3 and 2 4 3 6 2 Triumph Academy IIT–JEE-11 / Paper I [7] CHEMISTRY Sol. b g 2 AgNO 3 Cu Cu NO 3 2 2 Ag N M Light blue AgNO 3 NaCl AgCl NaNO3 White ppt O b g AgbNH g Cu 2 4 NH 3 Cu NH 3 AgCl 2 NH 3 2 4 3 2 Cl Paragraph for Question Nos. 15 to 16 An acyclic hydrocarbon P, having molecular formula C6H10 gave acetone as the only organic product through the following sequence of reactions, in which Q is an intermediate organic compoud. 15 16. The structure of compound P is (A) CH 3CH 2 CH 2 C C H (B) H 3CH 2 C C C C CH 2 CH 3 (C) (D) The structure of the compound Q is (A) S (B) (C) (D) Ans. (D, B) Triumph Academy IIT–JEE-11 / Paper I [8] CHEMISTRY CH 3 Sol. CH 3 CH 3 CH 3 C–C CH (D) (1) H2SO4|HgSO4 CH 3– C – C – CH 3 CH 3 O CH 3 CH 3 | | H 4 / C 2 H 5OH NaBH CH 3 C CH CH 3 CH 3 C CH CH 3 dil . acid | | | | CH 3 OH CH 3 OH 2 CH 3 CH3 CH3 CH3 | | | | (i) O CH 3 C CH CH 3 CH 3 C CH CH 3 CH3 C C CH3 3 CH 3COCH3 | CH 3 a ii f Zu / H O 2 | CH 3 Section – IV Integer Answer Type This section contains 8 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the SORS have to be darkened. 17. Reaction of Br2 with Na 2 CO 3 in aqueous solution gives sodium bromide and sodium bromatewith evolution of CO2 gas. The number of sodium bromide molecules involved in the balanced chemical euqation is Ans. (5) Sol. 3Br2 3CO 32 5Br BrO 3 3CO 2 18. The difference in the oxidation numbers of the two types of sulphur atoms in Na 2S 4 O 6 is Ans. (5 ) Sol. O O +– NaO – S – S – S – S – O Na O +5 0 0 +5 O Triumph Academy [9] IIT–JEE-11 / Paper I CHEMISTRY 19. The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum 1 number, ms , is 2 Ans. (9) Sol. Number of orbital for n = 3 is = n2 = 9 Number of electron n = 3 and m s 20. 1 =9 2 A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylanine. Glycine contributes 47.0% to the total weight of the hydrolysed prdoucts. The number of glycine units present in the decapeptide is Ans. (6) Sol. Let number of glycine units = n mass of decapeptide = 796 mass of H2O needed = 162 g Total mass = 958 g 958 n 47 75 n 100 958 47 6 100 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 an unknown compound (vapour pressure 0.68 atm. at 00C) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 00C is close to Ans. (7) Sol. Let unknown is X. b g p He p total p x 1 0.68 atm 0.32 atm Now p He n He v 7 RT V RT 010 . 0.082 273 p He 0.32 Triumph Academy IIT–JEE-11 / Paper I [10] CHEMISTRY 22. The total number of alkenes possible bydehydromination of 3-bromo-3-cyclopentylhexane using alcoholic KOH is Ans. (5) Sol. (Cis + trans) 23. (Cis + trans) bg The work function of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is Metal b g eV Li Na K Mg Cu Ag Fe Pt W 2.4 2.3 2.2 3.7 4.8 4.3 4.7 6.3 4.75 Ans. (4) Sol. For photoelectric effect to occur E 4.14 eV Li, Na, Ka, Mg will show photoelectronic effect when light g 300 nm wavelength falls on the metal is (4). [11] IIT 2011 / Paper I PHYSICS Part II Section – I (Total Marks : 21) Single Correct Answer Type This section contains 7 multiple choice questions numbered 24 to 30. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 24. 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. The maximum tension that the string can bear is 324 N. The maximum possible vlaue of angular velocityof ball (in radian / s) is (A) 9 Sol.: (D) 25. (B) 18 (C) 27 (D) 36 m max 2 r Tmax max Tmax mr 324 1296 36 rad / s 0.5 0.5 A meter bridge is set-up as shown, to determine an unknown resistance 'X' using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of 'X' is (A) 10.2 ohm (B) 10.6 ohm (C) 10.8 ohm (D) 11.1 ohm [12] IIT 2011 / Paper I PHYSICS Sol.: (B) 26. X 53 53 X 10 10.6 (include the end corrections as well in the calculated length) 10 50 50 A 2 F capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is (A) 0% (B) 20% (C) 75% (D) 80% bg 1 2 Sol.: (D) U i 2 V 2 U loss lost 27. U loss 4 80% Ui 5 A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km / hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m / s. The frequencyof the siren heard by the car driver is (A) 8.50 kHz (B) 8.25 kHz (C) 7.75 kHz (D) 7.50 kHz Sol.: (A) 28. bg bg 1 2 8 V 2 2 10 f final 8 LM 320 10 OP 8 33 8.5 kHz N 320 10 Q 31 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T1 , the work done in the prcess is (A) Sol.: (A) 9 RT1 8 3 RT1 2 (C) TV 1 constant b g T1 5.6 (B) 2/3 T2 0.7 2/3 T2 T1 8 2/ 3 FG IJ H K 4T1 RT1 1 3R Wad U nCv T 3T1 4 2 8 15 RT1 8 (D) 9 RT1 2 [13] IIT 2011 / Paper I PHYSICS 29. Consider an electric field E E0 x , where E 0 is a constant. The flux through the shaded area (as shown in the figure) due to this field is (A) 2 E0a 2 Sol.: (C) (B) 2 E0a 2 (C) E0a 2 (D) E 0a 2 2 A ai ak aj a 2 k a 2i j d i e E A E 0i a 2 k a 2i E 0 a 2 30. The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly-ionized helum atom is (A) 1215 Å (B) 1640 Å (C) 2430 Å (D) 4687 Å Sol.: (A) LM N OP Q 1 1 1 5 R R 1 4 9 36 LM N OP Q 1 1 1 3 4R R 2 4 9 4 2 5 4 5 5 2 6561 1215 Å 1 36 3 27 27 [14] IIT 2011 / Paper I PHYSICS Section–II (Total Marks : 16) Multiple Correct Answer Type This section contains 4 multiple choice questions numbered 31 to 34. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is / are correct. 31. b g A spherical metal shell A of radius R A and a solid metal sphere B of radius RB R A are kept far apart and each is given charge +Q. Now they are connected by a thin metal wire. Then (A) E Ainside 0 Sol.: (A, B, C, D) (B) QA QB A RB (C) R B A (D) E Aon surface E Bon surface On connecting V A VB kQ A kQB RA RB . also R constant 32. A RB B RA An electron and a proton are moving on straight parallel paths with same velocity. They enter a semiinfinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s0 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. Sol.: (B, D) As shown in the figure they will come out after describing a semicircle along parallel paths. Also time taken t m which will be different for both. qB [15] IIT 2011 / Paper I PHYSICS 33. b g A metal rod of length L and mass m is pivoted at one end. A thin disk of mass M and radius R L is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A). The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is/are true? (A) (B) (C) (D) Restoring torque in case A = Restoring torque in case B Restoring torque in case A < Restoring torque in case B Angular frequency for case A > Angular frequency for case B Angular frequency for case A < Angular frequency for case B Sol.: (A, D) In both the situations, net restoring torque is same. In first case when the disk is not free to rotate about its centre its moment of inertia is mR 2 mL2 about the axis where as in second case its moment of inertia is mL2 . 2 So from I 2 , the angular frequency in case A is lesser than that in B. 34. A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat Q flows only from left to right through the blocks. Then in steady state (A) (B) (C) (D) heat flow through A and E slabs are same. heat flow through slab E is maximum. temperature difference across slab E is smallest. heat flow through C = heat flow through B + heat flow through D. Sol.: (A, C, D) Slabs A and E are in series and thus heat flow through them is same and maximum. Treating slabs B, C, D as a joint block and since it is in series with A and E temperature difference across slab E is smallest as it has the least resistance. Also for slabs B, C, D heat current H kA and thus H C H B H D . L [16] IIT 2011 / Paper I PHYSICS Section–III (Total Marks : 15) Paragraph Type This section contains 2 paragraphs. Based upon the first paragraph, 3 multiple choice questions and based upon the second paragraph 2 multiple choice questions have to be answered. Each of these question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 35 to 37 Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along bg bg horizontal axis and momentum is plotted along vertical axis. The phase space diagram is x t vs. p t curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative. 35. The sphase space diagram for a ball thrown vertically up from ground is (A) (B) [17] IIT 2011 / Paper I PHYSICS (C) 36. (D) The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, E1 and E 2 are the total mechanical energies respectively. Then (A) E1 2 E 2 (B) E1 2 E 2 (C) E1 4 E 2 (D) E1 16 E 2 [18] IIT 2011 / Paper I PHYSICS 37. 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) (B) (C) (D) Sol.: (D, C, B) For a ball thrown upward, the magnitude of position first increases and then decreases. The magnitude of momentum for upward flight decreases and then for downward flight increases so correct option is B. The amplitude of SHM for second case is double that of first and other factors (mass frequency) are same so from 1 m 2 a 2 , E 2 4 E1 2 During the downward motion (from upper extreme to lower extreme) of block, the momentum is negative and its magnitude first increases then decreases. For upward motion (from lower extreme to upper extreme), the magnitude of momentum first increases and then decreases, the sign is +ve here. Further due to the damping the upper extreme for the upward phase is lower from previous one. So correct option is B. E [19] IIT 2011 / Paper I PHYSICS Paragraph for Question Nos. 38 to 39 A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let N be the number density of free electrons, each of mass m. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons being to 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 are set to resonance together and all the energy is reflected. This is the explanation of high reflectivityof metals. 38. Taking the electronic charge as é and the permittivity as ' 0 ' , use dimensional analysis to determine the correct expression for p . (A) 39. Ne m 0 (B) m 0 Ne (C) Ne 2 m 0 (D) m 0 Ne 2 Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N 4 1027 m 3 . Take 0 1011 and m 10 30 , where these quantities are in proper SI units. (A) 800 nm (B) 600 nm (C) 300 nm Sol.: (C, B) By checking dimension of each option, the correct option is p LM MN Ne 2 m 0 OP PQ The frequency of light reflected is c P/ 2 2 3 108 P so wavelength is 2 10 30 10 11 4 10 27 1.6 16 . 10 38 600 nm (D) 200 nm [20] IIT 2011 / Paper I PHYSICS Section – IV Integer Answer Type This section contains 7 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. 40. The activity of a freshly prepared radioacitve sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10–25 kg. The mass (in mg) of the radioactive sample is Sol.: (1) A N N so 41. A A M mN mA 10 25 1010 109 10 6 kg 1 mg Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side 'a'. The surface tension of the soap film is . The system of charges and planar film are in equilibrium, and Lq O a kM P N Q 2 Sol.: (3) 1/ N , where 'k' is a constant. Then N is b g The force due to surface tension on any side is 2 and the force electrostatic force on any side is 2 kq 2 a2 . For equlibrium, q q q q F kq I 2b ga GH a JK LF q I O a k MG J P MNH K PQ 2 2 2 2 42. 1/ 3 Steel wire of length L at 40 oC is suspended from the ceiling and then a mass m is hung from its free end. The wire is coolled down from 40 oC to 30 oC to regain its original length L. The coefficient of linear thermal expansion of the steel is 10–5 / oC, Young's modulus of steel is 1011 N / m2 and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of m in kg is nearly Sol.: (3) mgL L T AY m AY T g 10 6 1011 10 5 10 10 [21] IIT 2011 / Paper I PHYSICS 43. Four solid spheres each of diameter 5 cm and mass 0.5 kg are placed with their centers atthe corners of a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is N 10 4 kg m2 , then N is Sol.: (9) LM MN 2 2 mR 2 T 2 mr 2 2 mr 2 5 5 2 OP PQ R r LM N OP Q 8 2 1 8 5 mr mR 2 16 10 4 9 10 4 5 2 5 4 44. A long circular tube of length 10 m radius 0.3 m carries a current I along its curved surface as shown. A wrie-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with b g the axis of the tube. The current varies as I I 0 cos 300t where I 0 is constant. If the magnetic moment b g of the loop is N 0 I 0 sin 300t , then 'N' is Sol.: (6) The given tube is equivalent to a solenoid. The current per unit length of the solenoid is is B 0 i I . The flux through the coil is Br 2 so current induced is L FG IJ H K r 2 dI 1 d 1 d 0I Br 2 r 2 0 R R dt R dt L RL dt So magnetic moment of coil is M r 2i 0 2 r 4 dI 0 10 10 4 300 I 0 sin 300t 6 0 I 0 sin 300t RL dt 5 10 3 10 b g I . So field produced L [22] IIT 2011 / Paper I PHYSICS 45. 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 a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m / s2. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P / 10). The value of P is Sol.: (4) Writing torque about instantaneous axis of rotation a = 0.3 m / s2 2N f (2)P/10 FG P IJ R I H 10 K P a 2 R R e2mR j 5 R 2R 2 or 46. IAOR 2 b g or 2 2 2 0.3 P 5 or P 4 A block is moving on an inclined plane making an angle 45o 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 from sliding down. If we defined N = 10 , then N is Sol.: (5) bmg sin mg cos g 3 mg sin mg cos 2mg sin 4 mg cos 1 1 tan 2 2 N 10 10 1 5 2 Triumph Academy IIT–JEE-11 / Paper I [23] MATHEMATICS PART III Section–I Straight Objective Type This section contains 7 multiple choice questions numbered 47 to 53. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 47. Let and be the roots of x 2 6x 2 0 , with . If a n n n for n 1 , then the value of a 10 2a 8 is 2a 9 (A) 1 (B) 2 (C) 3 (D) 4 is a roots of of equation 2 6 2 0 ; 2 6B 2 0 Sol: (C) 2 6 2 0 2 2 6 e j e 10 10 2 8 8 a 10 2a 8 2a 9 2 9 9 e j e 2 e j 6 e j 3 e 8 2 2 8 2 2 9 9 j j 9 j b g b g 2 e j 8 6 8 6 9 9 9 2( 9 9 ) 48. A Straight line L through the point (3, 2) is inclined at an angle 60o to the line 3x y 1 . If L also intersects the x axis , then the equation of L is (A) y 3x 2 3 3 0 (B) y 3x 2 3 3 0 (C) 3y x 3 2 3 0 (D) Sol: (B) Inclination of line 3x y 1 is 150o Inclination of line L = 150o 60o 210o , 90o Slope of line L = tan 210 o tan 30 o Equation of = Line L y2 1 3 bx 3g 3y x 3 2 3 0 1 3 3y x 3 2 3 0 Triumph Academy IIT–JEE-11 / Paper I [24] MATHEMATICS 49. Let ( x 0 , y 0 ) be the solution of the following equations b g (2 x) ln 2 3y ln 3 3ln x 2 ln y Then x 0 is (A) Sol: (C) 1 6 (B) 1 3 (C) 1 2 (D) 6 Let ln x p, ln y q ln 2 a, ln 3 b (3y) ln 3 Now, (2 x) ln 2 a (a p) b( b q ) . . . (1) 3ln x 2 ln y (ln x) (ln 3) (ln y) (ln 2) pb qa . . . (2) From (1) a 2 b 2 bq pa b. pb pa a e j p 2 b a2 a p a ln x ln 2 x 1 2 z ln 3 50. x sin x 2 dx is The value of 2 2 sin x sin(ln 6 x ) ln 2 (A) 1 3 ln 4 2 (B) z ln 3 Ans: (A) I x sin x 2 sin x 2 sin(ln 6 x 2 ) ln 2 z ln 3 I ln 2 I 1 2 1 3 ln 2 2 z ln 2 3 2 dx sin t dt sin t sin(ln 6 t ) 2 ln 3 (C) ln sin(ln 6 t ) dt sin(ln 6 t ) sin t Put x 2 t (D) 1 3 ln 6 2 Triumph Academy IIT–JEE-11 / Paper I [25] MATHEMATICS Adding 51. I 1 2I 2 z ln 3 dt 1 3 ln 2 2 ln 2 1 3 ln 4 2 Let a i j k , b i j k and c i j k be three vectors. A vector v in the plane of a and b , 1 whose projection on c is , is given by 3 (A) i 3j 3k Sol: (C) 52. (B) 3i 3j k (D) i 3j 3k (C) 3i j 3k v a b vc 1 c 3 c a . c ( b . c) 3 1 (a b) . c c 3 1 c a. c 1 ( 1) 3 2 1 b.c v a 2b 2i j 3i o t o t Let P : sin cos 2 cos and Q : sin cos 2 sin be two sets. Then (A) P Q and Q P (C) P Q Ans: (D) sin cos 2 cos sin ( 2 1) cos tan 1 2 1 2 1 sin cos 2 sin ( 2 1) sin cos tan 2 1 (B) Q P (D) P Q Triumph Academy 53. IIT–JEE-11 / Paper I [26] MATHEMATICS Let the straight line x b divide the area enclosed by y (1 x) , y 0 and x 0 into two parts 2 R1 (0 x b) and R 2 ( b x 1) such that R 1 R 2 (A) Ans: (B) 3 4 R1 R 2 z z z z 1 (1 x) 2 dx (1 x) 2 dx 0 b b 1 2 (1 x) 2 dx (1 x) 2 dx 0 0 2 (1 x ) 3 3 e (C) 1 4 b 1 2 (B) b 0 (1 x) 3 3 j FGH 1 0 1 4 1 4 1 4 IJ K 2 1 1 (1 b) 3 1 0 3 3 4 2 2 1 1 1 1 1 (1 b) 3 3 3 3 4 3 4 12 (1 b) 3 1 1 1 1 b b 8 2 2 1 . Then b equals 4 1 3 (D) 1 4 Triumph Academy IIT–JEE-11 / Paper I [27] MATHEMATICS Section–II Straight Objective Type This section contains 4 multiple choice questions numbered 54 to 57. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is / are correct. 54. Let M and N be two 3 3 non-singular skew-symmetric matrices such that MN NM . If p T denotes the transpose of P, then M 2 N 2 ( M T N ) 1 ( MN 1 ) T is equal to (C) M 2 (B) N 2 (A) M 2 (D) MN Ans: (Bouns) M 2 N 2 ( M T N ) 1 ( MN 1 ) T e M 2 N 2 ( N 1 ( M T ) 1 ) ( N 1 ) T M T j 2 2 1 T T 1 M N N ( M ) ( N ) ( M) 55. M 2 N ( N N 1 ) ( M) 1 ( N ) 1 ( M) M 2 N ( I) ( N ) ( M ) M 2 N ( NM) 1 ( M) M ( MN ) ( MN ) 1 ( M) M (I) ( M) M2 b g 1 ( M) The vectors(s) which is/are coplanar with vectors i j 2 k and i 2 j k , and perpendicular to the vectors i j k is/are j k SOL: ( A, D) a i j 2k b i 2j k c i j k (A) (B) i j (C) i j vector coplanar with a and b and perpendicular to c is given by c (a b) (c . b) a ( c . a) b 4 a 4b 4(a b) 4( j k) (D) j k Triumph Academy 56. [28] IIT–JEE-11 / Paper I MATHEMATICS x2 y2 Let the eccentricity of the hyperbola 2 2 1 be reciprocal to that of the ellipse x 2 4 y 2 4 . If the a b hyperbola passes through a focus of the ellipse, then x2 y2 1 (A) the equation of the hyperbola 3 2 (C) the eccentricity of the hyperbola is SOL: ( B, D) Equation of ellipse x2 y2 1 4 1 eccentricity of ellipse 1 1 3 4 2 eccentricity of hyperbola 2 3 Foci of ellipse ( 3 , 0) . 3 a 2 3 a2 0 b2 1 1 a2 3 b2 a2 1 3 Equation of Hyperbola : x2 y2 1 3 1 x 2 3y 2 3 Foci of hyperbola : ( 2, 0) 5 3 (B) a focus of the hyperbola is (2, 0) (D) the equation of the hyperbola is x 2 3y 2 3 Triumph Academy IIT–JEE-11 / Paper I [29] MATHEMATICS 57. Let f : R R be a function such that f ( x y) f ( x) f ( y), x, y 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 x R (C) f ' ( x) is constant x R (D) f ( x) is differentiable except at finitely many points Ans: (B, C or B, C, D ) f ( x) lim h0 f ( x h) f ( x) f ( x) f ( h) f ( x) lim h 0 h h f ( h) f ( h) f (0) lim lim h 0 h h0 h f (0) = A const = k (say) f ( 0) kx c but f (0) 0 k 0 f ( x) kx f ( x 0) f ( x) f (0) f (0) 0 Triumph Academy IIT–JEE-11 / Paper I [30] MATHEMATICS Section–III Linked Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 58 to 59 Let U1 and U 2 be two urns such that U1 contains 3 white and 2 red balls, and U 2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is dawn at random from U1 and put into U 2 . However , if tail appears then 2 balls are drawn at random from U1 and put into U 2 . Now 1 ball is drawn at random from U 2 . 58. The probability of the drawn ball from U 2 being white is (A) 13 30 23 30 (B) (C) W 19 30 (2 W) (D) W 1 3/ 5 H 2/5 1/ 2 SOL: ( B) 3/10 Coin 1/ 2 T 6 /10 1/10 P(W) LM N 1/ 2 R 2W OP 23 Q 30 (3W) 1R) (2W, 1R) 2(1W W,1R 2R 1 3 1 2 1 1 3 1 6 2 1 1 1 2 5 2 5 2 2 10 2 10 3 2 10 3 1 9 1 9 3 6 30 2 2 (1W 1R) (1W, 2R) W 1 W 2/ 3 1/ 3 W W 11 30 Triumph Academy IIT–JEE-11 / Paper I [31] MATHEMATICS 59. Given that the drawn ball from U 2 is white, the probability that head appeared on the coin is (A) 17 23 11 23 (B) (C) 15 23 (D) 12 23 SOL: ( D) F Head appear on coin I PG H ball drawn from U is white JK = 2 1 3 1 2 1 12 2 5 2 5 2 1 3 1 6 2 1 1 1 23 2 10 2 10 3 2 10 3 FG IJ H K Paragraph for Question Nos. 60 to 62 Let a, b and c be three numbers satisfying a 60. b LM1 c 8 MN7 OP PQ 9 2 3 7 7 0 7 0 0 . . . (E) If the point P (a , b, c) , with reference to (E), lies on the plane 2 x y z 1 , then the value of 7a b c is (A) 0 (B) 12 (C) 7 (D) 6 a 8b 7c 0 UV W SOL: ( D) 9a 2 b 3c 0 . . . (E) 7a 7 b 7c 0 1 8 7 Now, D 9 2 3 0 7 7 7 system (E) has infinite solutions a b c k (say) 1 6 7 2a b c 1 2 k 6k 7 k 1 k 1 7a b c 7 k 6k 7 k 6k 6 Triumph Academy IIT–JEE-11 / Paper I [32] MATHEMATICS 61. Let be a solution of x 3 1 0 with Im( ) 0 . If a 2 with b and c satisfying (E), then the value of 3 1 3 b c a is equal to (A) 2 (B) 2 (C) 3 (D) 3 a 2, k 2 , b 12, c 14 Sol: (A) 3 2 1 12 3 4 3 1 3 2 3 ( 2 ) 1 3( 1) 1 2 62. Let b 6 , with a and c satisfying (E). If and are the roots of the quadratic equation ax 2 bx c 0 , then F 1 1I GH JK n n0 is (A) 6 (B) 7 (C) 6 7 b 6 k 1 a 1, c 7 Sol: (B) quadratic Equation is x 2 6x 7 0 ( x 7) ( x 1) 0 x 7, 1 F 1 1I F 1 1 I GH JK GH 1 (7) JK F 6I 1 7 G J H 7K 1 6 n n0 n0 n 0 n 7 n (D) Triumph Academy IIT–JEE-11 / Paper I [33] MATHEMATICS Section – IV Integer Answer Type This section contains 10 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. 63. The minimum value of the sum of real numbers a 5 , a 4 , 3a 3 , 1, a 8 and a10 with a 0 is e j a 5 a 4 3 a 3 1 a 8 a 10 Sol : [8] 64. 1 1 3 1 1 1 F H e j b1gea jea jIK a 5a 4 a 3 3 8 10 1/ 8 1 (using AM GM ) a 5 a 4 3a 3 1 a 8 a 10 8 FG H bg 1 Let f sin tan FG H IJ IJ ,where . Then the value of KK 4 4 d b f ( ) g db tan g sin cos 2 is FG H bg 1 Sol: [1] f sin tan IJ sinFG sin cos 2 K H sin sin e sin 2 cos2 sin 2 j I J cos 2 K sin 1 sin 2 sin sin tan cos cos b g b g b g b g d tan d f 1 d tan d tan 65. If z is any complex number satisfying z 3 2i 2 , then the minimum value of 2 z 6 5i is FG H Sol: [5] 2 z 6 5i 2 z 3 FG H 2 3 3 =2 FG 5 IJ 5 H 2K IJ K 5 i 2 5 2 IJ K (corresponding Pt A) Triumph Academy 66. IIT–JEE-11 / Paper I [34] g MATHEMATICS g Let f : 1, 2, be a differentiable function such that f (1) 2 . If z x 6 f ( t )dt 3x f ( x) x 3 1 for all x 1 , then the value of f ( 2) is z bg x bg 3 SOL [6] 6 f t dt 3 f x x 1 differenciating both sides bg bg bg xf ' b xg f b xg x F 1I f ' b xg f b xgG J x H xK 6f x 3f x 3xf ' x 3x 2 2 integration factor bg f x e 1 dx x 1 x solution is given by z b g FGH IJK f b xg x cx f b1g 2 c 1 f b xg x x f b2g 6 1 1 f x x dx c x c x x Now 67. 2 2 The positive integer value of n 3 satisfying the equation 1 sin is FG IJ H nK 1 1 2 3 sin sin n n FG IJ H K FG IJ H K Triumph Academy IIT–JEE-11 / Paper I [35] MATHEMATICS SoL [7] 1 sin n 1 1 2 3 sin sin n n 1 1 1 sin sin 2 sin 3 sin 3 sin sin 4 sin 3 7 2 2 7 sin sin 3 sin 2 (Let ) n 1 1 1 sin 3 sin sin 2 sin sin 3 sin .sin 3 2 cos 2 sin 7 2 sin cos 0 2 2 sin sin 3 sin 2 sin 0 cos 7 0 2 p 68. Let a1 , a 2 , a 3 , ..., a100 be an arithmetic progression with a1 3 and S p a i , 1 p 100 . For any i 1 Sm integer n with 1 n 20 , let m 5n . If S does not depend on n, then a 2 is n b g b g m 2a 1 m 1 d m 6 md d 5 6 d 5nd Sm 5n 6 5nd d 2 SoL [3, 9 or 3 and 9 ] S n n n 6 nd d n 6 nd d 6 d nd is free from n 2a 1 n 1 d 2 g g b b g b g b g g d6 6d 0 a 2 a1 d 3 6 9 69. b b Consider the parabola y 2 8x . Let 1 be the area of the triangle formed by the end points of its latus rectum and the point P FG 1 , 2IJ on the parabola, and H2 K 2 be the area of the triangle formed by drawning tangents at P and at the end points of the latus rectum. Then 1 is 2 SoL [2] Area of formed by three pts to to parabola is twice the area of formed by tangents at these pts. Triumph Academy IIT–JEE-11 / Paper-II [7] PHYSICS Part II Section–I (Total Marks : 24) (Single Correct Answer Type) This section contains 8 multiple choice questions numbered 21 to 28. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 21. A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence . The reflected (R) and transmitted (T) intensities, both as function of , are plotted. The correct sketch is (A) (B) (C) (D) Triumph Academy IIT–JEE-11 / Paper-II [8] PHYSICS 22. A wooden block performs SHM on a frictionless surface with frequency, v0 . The block carries a charge +Q on its surface. If now a uniform electric field E is switched-on as shown, then the SHM of the block will be (A) on the same frequency and with shifted mean position. (B) of the same frequency and with the same mean position. (C) of changed frequency and with shifted mean position. (D) of changed frequency and with the same mean position. 23. The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is (A) 0.9% (B) 2.4% (C) 3.1% (D) 4.2% 24. A ball of mass 0.2 kgrests 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 the collision, the ball and bullet ravel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The intial velocity V of the bullet is (A) 250 m / s (B) 250 2 m / s (C) 400 m / s (D) 500 m / s Triumph Academy IIT–JEE-11 / Paper-II [9] PHYSICS 25. 26. Which of the file patterns given below is valid for electric field as well as for magnetic field? (A) (B) (C) (D) bg F 2 I x bt g A sinG t J . Adding a third sinusoidal displacement x bt g B sinbt g brings the mass H 3K A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x1 t A sin t and 3 2 to a complete rest. The values of B and are (A) 2 A, 3 4 (B) A, 4 3 (C) 3 A, 5 6 (D) A, 3 Triumph Academy IIT–JEE-11 / Paper-II [10] PHYSICS 27. 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 sprial lies in the X-Y plane and a steady current 'I ' flows through the wire. The Zcomponent of the magnetic field at the center of the sprial is (A) 28. FG IJ b g HK 0N I b ln 2 ba a (B) FG b g H 0 N I ba ln 2 ba ba IJ K (C) FG IJ HK 0 N I b ln 2b a (D) FG H 0N I ba ln 2b ba IJ K A satellite is moving with a constant speed 'V'in a circular orbit about the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is (A) 1 mV 2 2 (B) mV 2 (C) 3 mV 2 2 2 (D) 2mV Triumph Academy IIT–JEE-11 / Paper-II [11] PHYSICS Section–II Multiple Correct Answer Type This section contains 4 multiple choice questions numbered 29 to 32. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is / are correct. 29. Two solid spheres A and B of equal volumes but of different densities d A and d B are connected by a string. They are fully immersed in a fluid of density d F . They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if (A) d A d F 30. (B) d B d F (C) d A d F (D) d A d B 2 d F 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 the same. (D) The work done by the external force in moving a unit positive charge from point A at potential V A to b point B at potential V B is VB V A g Triumph Academy IIT–JEE-11 / Paper-II [12] PHYSICS 31. A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current I R through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true? (A) I RA I RB 32. (B) I RA I RB (C) VCA VCB (D) VCA VCB A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with 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 velocity 10 m / s. Immediately after the collision (A) (B) (C) (D) the ring has pure rotation about its sitationary CM. the ring comes to a complete stop. friction between the ring and the ground is to the left. there is no friction between the ring and the ground. Triumph Academy [13] IIT–JEE-11 / Paper-II PHYSICS Section–III Integer Type This section contains 6 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled. 33. Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is 34. A series R-C combination is connected to an AC voltage of angular frequency 500 rad / s. If the impedance of the R-C circuit is R 1.25 , the time constant (in millisecond) of the circuit is 35. A train is moving along a straight line with a constant acceleration 'a'. A body standing in the train throws a ball forward with a speed of 10 m / s, at an angle of 60o to the horizontal. The body has to move forward by 1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m / s2, is 36. Water (with refractive index 4 7 ) in a tank is 18 cm deep. Oil of refractive index lies on water making 3 4 a convex surface of radius of curvature 'R = 6 cm' as shown. Consider oil to act as a thin lens. An object 'S' is placed 24 cm above water surface. The location of its image is at 'x' cm above the bottom of the tank. Then 'x' is Triumph Academy [14] IIT–JEE-11 / Paper-II PHYSICS 37. 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 is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m / s is V = N / 10. Then N is 38. A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in freespace. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photelectrons emitted from the sphere is A 10 z (where 1 A 10 ). The value of 'Z' is Triumph Academy [15] IIT–JEE-11 / Paper-II PHYSICS Section – IV 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, s and t) in Column II. Any given statement in Column I can have correct mathcing with ONE or MORE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question, against statement B, darken the bubbles corresponding to q and r in the ORS. 39. One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the p-V diagram. Column II gives the characteristic 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. Triumph Academy IIT–JEE-11 / Paper-II [16] PHYSICS 40. Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequencyof a system is called its fundamental frequency, whose wavelength is denoted as f . Match each 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 and at mid-point (s) f 2L (t) f 4L Triumph Academy IIT–JEE-11 / Paper II [1] CHEMISTRY IIT JEE - 2011 Paper 2 Time: 3 hours Max. Marks: 240 A. General: 1. This booklet is your Question Paper containing 60 questions. The booklet has 28 pages. 2. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers, and electronic gadgets in any form are not allowed to be carried inside the examination hall. 3. The answer sheet, Objective Response Sheet (ORS), is provided separately. B. Question paper format and Marking Scheme: 4. The question paper consists of 3 parts (Mathematics, Chemistry and Physics). Each part has FOUR sections. 5. For each question in Section I, you will be awarded 3 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. 6. For each question in Section II, you will be awarded 4 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, zero (0) mark will be awarded. 7. For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer, and zero mark if no bubble is darkened. In all other cases, minues one (–1) mark will be awarded. 8. For each question in Section IV, you will be awarded 2 marks for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, the question in this section carries a maximum of 8 makrs. There is no negative marking for incorrect answer(s) for this section. Name: 81-B/3, Lohagal Road, Ajmer-305 001 Telefax: 0145-2628805, 2628178 Reg. No.: 1 2 J E E e-mail: [email protected] website: www.triumphacademy.com Triumph Academy IIT–JEE-11 / Paper II [2] CHEMISTRY Part I Section–I Straight Objective Type This section contains 6 multiple choice questions numbered 1 to 6. Each question has 4 choices (A), (B), (C) and (D), 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 (B) II, III in haematite and II in magnetitie (C) II in haematite and II, III in magnetite (D) III in haematite and II, III in magnetitie 2. Among the following complexes (K - P), b g b Kg, CobNH g Cl bLg, Na Coboxalateg bM g, NibH Og Pt b CN g bQ g and Znb H O g b NO g b P g K 3 Fe CN 6 3 6 K2 4 2 3 6 3 b g Cl 2 N , (B) K, M, O, P (D) L, M, N, O Passing H2S gas into a mixture of Mn 2 , Ni 2 , Cu2 and Hg 2 ions in an acidified aqueous solution precipitates (A) (B) MnS and CuS CuS and HgS (C) MnS and NiS 4. 6 3 2 the diamagnetic complexes are (A) K, L, M, N (C) L, M, O, P 3. 2 3 (D) NiS and HgS Consider the following cell reaction bg 2 Fe b sg O 2 b g g 4 H baq g 2 Fe b2aq g 2 H 2 O l E 0 167 . V b g . atm pH = 3, the cell potential at 250C is At Fe 2 103 M, P O 2 01 (A) 1.47 V 5. (B) 1.77 V (C) 1.87 V (D) 1.57 V b g bMol. Wt. 329g in 100 g of The freezing point (in 0C) of a solution containing 0.1 g of K 3 Fe CN c 6 h . kg mol 1 is water K f 186 (A) 2.3 102 (B) 5.7 102 (C) 5.7 103 (D) 12 . 102 Triumph Academy IIT–JEE-11 / Paper II [3] CHEMISTRY 6. 7. Amongst the compounds given, the one that would form a brilliant colored dye on treatment with NaNO2 in dil. HCl followed by addition to an alkaline solution of naphtol is (A) (B) (C) (D) The major product of the following reaction is (A) a hemiacetal 8. (B) an acetal (C) an ether (D) an ester (C) an furanose (D) an pyranose The following carbohydrate is (A) a ketohexose (B) an aldohexose Triumph Academy IIT–JEE-11 / Paper II [4] CHEMISTRY Section–II Multiple Correct Answer Type This section contains 5 multiple choice questions numbered 8 to 14. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is / are correct. 9. Reduction of the metal centre in aqueous permagnetic ion involves (A) 3 electron in neutral medium (B) 5 electrons in neutral medium (C) 3 electron in alkaline medium (D) 5 electrons in acidic medium 10. Theequilibrium 2Cu I Cu 0 Cu II in aqueous medium at 25 0C shifts towards the left in the presence of (A) NO 3 11. (B) Cl For the first order reaction bg bg (C) SCN (D) CN bg 2 N 2 O5 g 4 NO 2 g O 2 g (A) the concentration of the reactant 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 reaction (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 (A) X COOCH 3 , Y H 2 / Ni / heat (B) X CONH 2 , Y H 2 / Ni / heat (C) X CONH 2 , Y Br2 / NaOH (D) X CN , Y H 2 / Ni / heat Triumph Academy [5] IIT–JEE-11 / Paper II CHEMISTRY Section–III Integer Answer Type This section contains 5 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the SORS have to be darkened. 13. Among the following, the number of compounds than can react with PCl5 to give POCl3 is O 2 , CO 2 , SO 2 , H 2 O, H 2SO 4 , P4 O 10 14. The volume (in mL) of 0.1 M AgNO3 required for complete precitation of chloride ions present in 30 mL b g of 0.01 M solution of Cr H 2 O 5 Cl Cl 2 , as silver chloride is close to 15. b g . 1010 , 0.1 mol of CuCl In 1L saturated solution of AgCl K sp AgCl 16 b g K sp CuCl 1.0 106 is added. The resultant concentration of Ag+ in the solution is 16 . 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 the following compounds is 18. The total number of contributing structures showing hyperconjugation (involving C - H bonds) for the following carbocation is Triumph Academy IIT–JEE-11 / Paper II [6] CHEMISTRY Section–IV Matrix-Match Type This section contains 2 questions. The question contains statements given in two columns, which have to be matched. The Statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. 19. Match the transformations in Column I with appropriate options in Column II Column I Column II (C) bg bg CaCO bsg CaObsg CO bg g 2H H bg g (D) Pb white , solid g Pb red , solid g (A) (B) CO 2 s CO 2 g 3 2 2 (p) phase transition (q) allotropic change (r) H is positive (s) S is positive S is negative (t) 20. Match the reactions in Column I with appropriate types of steps/reactive intermediante involved in these reactions as given in Column II. Column I Column II (A) (p) Nucleophilic substitution (B) (q) Electrophilic substitution (C) (r) Dehydration (D) (s) Nucleophilc addition (t) Carbanion Triumph Academy IIT–JEE-11 / Paper II [17] MATHEMATICS Section–I Straight Objective Type This section contains 6 multiple choice questions numbered 20 to 23. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 41. Let f :[ 1, 2] [0, ) be a continuous function such that f ( x) f (1 x) for x [ 1, 2] . Let z 2 R1 x f ( x) dx , and R be the area of the region bounded by y f ( x) , x 1 , x 2 , and the x2 1 axis. Then (A) R1 2 R 2 42. (B) R1 3R 2 (D) 3R1 R 2 Let f ( x) x 2 and g( x) sin x for all x R . Then the set of all x satisfying ( f og og of ) ( x) ( g og of ) ( x) , where ( f og)( x) f ( g( x)) is (A) n , n {0, 1, 2,...} (C) 43. (C) 2 R1 R 2 (B) n , n {1, 2,...} 2 n , n {...,2, 1, 0, 1, 2,...} 2 (D) 2 n, n {...,2, 1, 0, 1, 2,...} Let ( x, y) be any point on the parabola y 2 4 x . Let P be the point that divides the line segment from (0, 0) to ( x, y) in the ratio 1 :3 . Then the locus of P is (A) x 2 y 44. (B) y 2 2 x (C) y 2 x (D) x 2 2 y x2 y2 1 . If the normal at the point P intersects the x axis a 2 b2 at (9, 0), then the eccentricity of the hyperbola is Let P(6, 3) be a point on the hyperbola (A) 5 2 (B) 3 2 (C) 2 (D) 3 Triumph Academy IIT–JEE-11 / Paper II [18] MATHEMATICS 45. A value of b for which the equations x 2 bx 1 0 x2 x b 0 have one root in common is (A) 2 46. (B) i 3 (C) i 5 (D) 2 Let 1 be a cube root of unity and S be the set of all non singular matrices of the form LM 1 MM N a 1 2 b c 1 OP PP Q where each of a, b, and c is either or 2 . Then the number of distinct matrices in the set S is (A) 2 (B) 6 (C) 4 (D) 8 47. The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point FG H IJ K FG H 3 (A) , 0 2 48. 1 x ln(1 b 2 ) If lim x0 (A) 4 IJ K 5 (B) , 2 2 1/ x FG H 3 5 (C) , 2 2 IJ K b g (D) 4, 0 b 2 b sin 2 , b 0 and , , then the value of is (B) 3 (C) 6 (D) 2 Triumph Academy IIT–JEE-11 / Paper II [19] MATHEMATICS Section–II Straight Objective Type This section contains 4 multiple choice questions numbered 54 to 57. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is / are correct. 49. Let E and F be two independent events. The probability that exactly one of them occurs is probability of none of them occuring is 11 and the 25 2 . If P(T) denotes the probability of occurrence of the event T, 25 then (A) P( E ) 50. 4 3 1 2 2 1 3 4 , P( F) (B) P( E ) , P( F) (C) P( E ) , P( F) (D) P( E ) , P( F) 5 5 5 5 5 5 5 5 If R| x , | 2 f b xg S cos x, || x 1, T ln x, x 2 x 0, 2 0 x 1 x 1 then (A) f ( x) is continuous at x 2 (D) f (x) is differentiable at x 3 2 (A) f is not invertiable on (0, 1) (B) f f 1 on (0, 1) and f ( b) 1 f (0) 1 (C) f f 1 on (0, 1) and f ( b) f (0) (D) f 1 is differentiable on (0, 1) (C) f(x) is differentiable at x 1 51. (B) f (x) is not differentiable at x 0 f : ( 0, 1) R be defined by f ( x) bx 1 bx where b is a constant such that 0 b 1 . Then 52. Let L be a normal to the parabola y 2 4 x . If L passes through the point (9, 6) , then L is given by (A) y x 3 0 (C) y x 15 0 (B) y 3x 33 0 (D) y 2 x 12 0 Triumph Academy [20] IIT–JEE-11 / Paper II MATHEMATICS Part II Section–III Integer Answer Type This section contains 5 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the SORS have to be darkened. 53. The straight line 2 x 3y 1 divides the circular region x 2 y 2 6 into two parts. If S RSFG 2, 3IJ , FG 5 , 3IJ , FG 1 , 1 IJ , FG 1 , 1 IJ UV TH 4 K H 2 4 K H 4 4 K H 8 4 K W then the number of point(s) in S lying inside the smaller part is 54. Let e i / e and a , b, c, x, y, z be non zero complex numbers such that abc x a b c 2 y a b 2 c z x y z 2 a b c 2 2 Then value of 2 2 2 is 55. The number of distinct real roots of x 4 4 x 3 12 x 2 x 1 0 56. Let y ( x) y( x)g ( x) g x g ( x) , y(0) 0, x R where f ( x) denotes 57. Let M be a 3 3 matrix satisfying bg d f ( x) and g( x) is a given dx non-constant differentiable function on R with g(0) g(2) 0 . Then the value of y(2) is LM0OP LM1OP L 1 O L 1 O LM1OP LM 0 OP M P M P M M1P M 2 P , M M1P M 1 P and M M1P M 0 P MN0PQ MN 3 PQ MN 0 PQ MN1PQ MN1PQ MN12PQ The the sum of the diagonal entries of M is 58. Let a i k , b i j and c i 2 j 3k be three given vectors. If r is a vector such that r b c b and r a 0 then the value of r b is Triumph Academy IIT–JEE-11 / Paper II [21] MATHEMATICS Section–IV Matrix-Match Type This section contains 2 questions. The question contains statements given in two columns, which have to be matched. The Statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to the question have to be darkened as illustrated in the following example: 59. Match the statements in Column I with those in Column II. [Note: Here z takes values in the complex plane and Im z and Re z denote, respectively, the imaginary part and the real part of z.] Column I Column II (A) The set (p) ( , 1) (1, ) (q) ( , 0) (0, ) (r) 2, RSReFG 2iz IJ: z is a complex number, z 1, z 1UV T H 1 z K W 2 is (B) The domain of the function f ( x) sin 1 FG 8(3) IJ is H 1 3 K x 2 2 ( x 1) 1 tan 1 (C) If f () tan 1 tan , then 1 tan 1 RS T the set f () : 0 (s) b, 1 1, g (t) b, 0 2, g UV W is 2 (D) If f ( x) x 3/ 2 (3x 10) , x 0 , then f ( x) is increasing in g Triumph Academy [22] IIT–JEE-11 / Paper II MATHEMATICS 38. Match the statements in Column I with the values in Column II. Column I Column II (A) If a j 3 k , b j 3 k and c 2 3 k form (p) 6 (q) 2 3 (r) 3 (s) (t) 2 a triangle, then the internal angle of the triangle between a and b is z b (B) If ( f ( x) 3x)dx a 2 b 2 , then the value of a f FG IJ is H 6K (C) The value of z 5 6 sec( x) dx is. ln 3 7 6 (D) The maximum value of Arg z 1 , z 1 is given by FG 1 IJ for H 1 z K IIT JEE - 2011 (Paper I) CHEMISTRY 1. (B) 8. (A, D) 12. (B) 17. 5 2. (D) 9. (B, C) 13. (A) 18. 5 3. (A) 4. (D) 5. (C) 10. (A, B, D) 11. (A, C, D) 14. (C) 19. 9 20. 6 21. 7 6. (A) 7. (C) 15. (D) 22. 5 16. (B) 23. 4 PHYSICS 24. (D) 25. (B) 31. (A, B, C, D) 35. (D) 36. (C) 40. 1 41. 3 26. (D) 27. (A) 28. (A) 32. (B, D) 33. (A, D) 37. (B) 42. 3 43. 9 44. 6 29. (C) 30. (A) 34. (A, B, C, D) 38. (C) 39. (B) 45. 4 46. 5 MATHEMATICS 47. (C) 48. (B) 54. (Marks to all) 58. (B) 59. (D) 63. 8 64. 1 49. (C) 50. (A) 51. (C) 52. (D) 53. (B) 55. (A, D) 56. (B, D) 57. (B, C OR B, C, D) 60. (D) 61. (A) 62. (B) 65. 5 66. Marks to all 67. 7 68. 3, 9 OR 3 & 9 (Paper II) CHEMISTRY 1. (D) 2. (C) 3. (A) 4. (D) 5. (A) 6. (C) 9. (A, C, D) 10. (B, C, D) 11. (A, B, D) 12. (C, D) 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 7. (B) 8. (B) 27. (A) 28. (B) PHYSICS 21. (C) 22. (A) 23. (C) 24. (D) 25. (D) 26. (B) 29. (A, B, D) 30. (C, D) 31. (B, C) 32. (A, C) 33. 5 34. 4 35. 5 36. 2 37. 4 38. 7 39. [A] p, r, t ; [B] p, r ; [C] q, s ; [D] r, t 40. [A] p, t ; [B] p, s ; [C] q, s ; [D] q, r MATHEMATICS 41. (C) 42. (A) 43. (C) 44. (B) 45. (B) 46. (A) 47. (D) 48. (D) 49. (A, D) 50. (A, B, C, D) 51. (A) 52. (A, B, D) 53. 2 54. Marks to all 55. 2 56. 0 57. 9 58. 9 59. [A] s ; [B] t ; [C] r ; [D] r 60. [A] q ; [B] p OR p, q, r, s, t ; [C] s ; [D] t 69. 2
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