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1 Time : Hours Maximum Marks : 40 Please read the instructions carefully. You are allotted 5 minutes specifically for th purpose. A. General : INSTRUCTIONS. The question paper CODE printed on the right hand top corner of th sheet and on the back page of th booklet.. No additional sheets will be provided tor rough work.. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets are NOT allowed. 4. Write your name and regtration number in the space provided on the back page of th booklet. 5. The answer sheet, a machine gradable Optical Response Sheet (ORS), provided separately. 6. DO NOT TAMPER WITH/MUTILATE THE ORS OR THE BOOKLET. 7. Do not break the seals ofthe question paper booklet before being instructed to do so by the lnvigilators. 8. Th Question Paper contains 6 pages having 69 questions. 9. On breaking the seals, please check that all the questions are legible. B. Filling the Right Part of the ORS : 0. The ORS also has a CODE printed on its Lelt and Right parts.. Make sure the CODE on the ORS the same as that on th booklet. If the codes do not match, ask for a change of the booklet. 54 E. Write your Name, Regtration No. and the name of centre and sign with pen in the boxes provided. Do not write them anywhere else. Darken the appropriate bubble UNDER each digit of your Regtration No. with a good quality HB pencil. C. Question paper format and Marking Scheme :. The question paper consts of parts (Chemtry, Physics and Mathematics). Each part consts of four sections. 4. In Section I (Total Marks: ), for each question you will be awarded marks if you darken ONLY the bubble corresponding to the correct answer and zero marks if no bubble darkened. In all other cases, minus one ( ) mark will be awarded. 5. In Section II (Total Marks: 6), 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 otherwe. There are no negative marks in th section. 6. In Section lll (Total Marks: 5), tor each question you will be awarded marks if you darken ONLY the bubble corresponding to the correct answer and zero marks if no 'bubble darkened. In all other cases, minus one (-) mark will be awarded. 7. In Section IV (Total Marks: 8), for each question you will be awarded 4 marks it you, darken ONLY the bubble corresponding to the correct answer and zero marks otherwe. There are no negative marks in th section. South Delhi: 65 Kalusarai, Sarvpriya Vihar, Hauz Khas, N.D. 6, Ph: ,

2 PART I : CHEMISTRY SECTION I (Total Marks : ) (Single Correct Answer Type) Th section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE correct.. Bombardment of aluminium by -particle leads to lt artificial dintegration in two ways, (i) and (ii) as shown. Products X, Y and Z respectively are, (ii) 7 Al 0 5 P Y (i) (iii) 0 4 Si X 0 4 Si Z proton, neutron, positron b. neutron, positron, proton c. proton, positron, neutron d. positron, proton, neutron. a. AgNO (aq) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance (A) versus the volume of AgNO. P b. Q c. R d. S. d. The major product of the following reaction b. c. d.. a East Delhi: Pratap Nagar, Mayur Vihar Phase -, Delhi - 9, Ph: 40798,

3 4. Geometrical shapes of the complexes formed by the reaction of Ni + with Cl, CN and H O, respectively, are octahedral, tetrahedral and square planar b. tetrahedral, square planar and octahedral c. square planar, tetrahedral and octahedral d. octahedral, square planar and octahedral 4. b 5. Extra pure N can be obtained by heating NH with CuO b. NH 4 NO c. (NH 4 ) Cr O 7 d. Ba (N ) 5. d 6. Dsolving 0g of urea (mol. wt. 60) in 000g of water gave a solution of density.5g/ml. The molarity of the solution.78 M b..00 M c..05 M d.. M 6. c 7. Among the following compounds, the most acidic p- nitrophenol b. p-hydroxybenzoic acid c. o-hydroxybenzoic acid d. p-toluic acid 7. c SECTION ll (Total Marks : 6) (Multiple Correct Answers Type) Th section contains 4 multiple choice questions.each question has four choices (A), (B), (C) and (D) out of which ONE or MORE may be correct 8. The correct statement(s) pertaining to the adsorption of a gas on a solid surface (are) Adsorption always exothermic b. Physorption may transform into chemorption at high temperatures. c. Physorption increases with increasing temperature but chemorption decreases with increasing temperature. d. Chemorption more exothermic than physorption, however it very slow due to higher energy of activation. 8. a, b, d 9. According to kinetic theory of gases collions 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 collions, the molecules move in straight lines with constant velocities. 9. a, b, c, d, 0. Extraction of metal from the ore cassiterite involves Carbon reduction of an oxide ore b. Self- reduction of a sulphide ore c. removal of copper impurity d. removal of iron impurity 0. a, d. Amongst the given options, the compound (s) in which all the atoms are in one plane in all the possible conformations (if any), (are) b.. a, b, c c. d. H C = C = CH South Delhi: 65 Kalusarai, Sarvpriya Vihar, Hauz Khas, N.D. 6, Ph: ,

4 SECTION III (Total Marks : 5) (Paragraph Type) Th section contains paragraphs. Based upon one of the paragraphs multiple choice questions and based on the other paragraph multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE correct. Paragraph for question Nos. and An acyclic hydrocarbon P, having molecular formula C 6 H 0, gave acetone as the only organic product through the following sequence of reactions, in which Q an intermediate organic compound.. The structure of compound P CH CH CH CH C C H b. H CH C C C CH CH c. d.. d. The structure of the compound Q b. c. d.. b Paragraph for question Nos. 4 and 6 When a metal rod M 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 NH dsolves O and gives an intense blue solution. 4. The metal rod M Fe b. Cu c. Ni d. Co 4. b East Delhi: Pratap Nagar, Mayur Vihar Phase -, Delhi - 9, Ph: 40798,

5 5. The compound N AgNO b. Zn (NO ) c. Al(NO ) d. Pb (NO ) 5. a 6. The final solution contains [Pb(NH ) 4 ] + and [CoCl 4 ] b. [Al(NH ) 4 ] + and [Cu(NH ) 4 ] + 6. c c. [Ag(NH ) ] + and [Cu(NH ) 4 ] + d. [Ag(NH ) ] + and [Ni(NH ) 6 ] + SECTION IV (Total Marks : 8) (Integer Answer Type) Th section contains 7 questions. The answer to each of the questions a single-digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer to be darkened in the ORS. 7. The maximum number of electrons that can have principal quantum number, n =, and spin quantum number, m s = ½, Reaction of Br with Na CO in aqueous solution gives sodium bromide and sodium bromate with evolution of CO gas. The number of sodium bromide molecules involved in the balanced chemical equation The total number of alkenes possible by dehydrbromination of -bromo--cyclopentylhexane using alcocholic KOH The work function () of some metals lted below. The number of metals which will show photoelectric effect when light of 00 nm wavelength falls on the metal 0. 4 Metal Li Na K Mg Cu Ag Fe Pt W (ev) A decapeptide (Mol. Wt. 796) on complete hydrolys gives glycine (Mole.Wt. 75), alanine and phenylalanine. Glycine contributes 47.0% to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide.. 5. The difference in the oxidation numbers of the two types of sulphur atoms in Na S 4 O To an evacuated vessel with movable pton under external pressure of atm., 0. mol of He and.0 mol of an unknown compound (vapour pressure 0.68 atm.0 C) are introduced. Considering the idea gas behaviour, the total volume (in litre) of the gases at 0 C close to.. 7 litre South Delhi: 65 Kalusarai, Sarvpriya Vihar, Hauz Khas, N.D. 6, Ph: ,

6 PART II : PHYSICS SECTION I (Total Marks : ) (Single Correct Answer Type) Th section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE correct. 4. Consider an electric filed E E xˆ, where E 0 a constant. The flux through the shaded area (as shown in the figure) due to th field z 0 (a, 0, a) (a, a, a) E 0 a b. 4. c flux = area to x-ax field x 0 (0, 0, 0) (0, a, 0) E a c. E 0 a d. y E a 0 5. A ball of mass (m) 0.5 kg attached to the end of string having length (L) 0.5 m. The ball rotated on a horizontal circular path about vertical ax. The maximum tension that the strincan bear 4 N. The maximum possible value of angular velocity of ball (in radian/s) 9 b. 8 c. 7 d d In the case of conical pendulum g l cos and also T cos = mg 6. A F capacitor charged as shown in figure. The percentage of its stored energy dsipated after the switch S turned to position. 0% b. 0% c. 75% d. 80% 6. d East Delhi: Pratap Nagar, Mayur Vihar Phase -, Delhi - 9, Ph: 40798,

7 liter of helium gas at STP adiabatically compressed to 0.7 liter. Taking the temperature to be T, the work done in the process 9 RT 8 7. a r 5 b. RT 5 c. RT 8 r r T V T V T 4 T and T = T n mole n R T R T 9 4 W RT r 4 / 8 9 d. RT 8. A police car with a siren of frequency 8 khz moving with uniform velocity 6 km/ hr towards a tall building which reflects the sound waves. The speed of sound waves. The speed of sound in air 0m/s. The frequency of the siren heard by the car driver 8.50 khz b. 8.5 khz c khz d khz 8. a khz 0 9. The wavelength of the first spectral line in the Balmer series of hydrogen atom 656 Å. The wave length of the second spectral line in the Balmer series of singly ionized helium atom 5Å b. 640Å c. 40Å d. 4687Å 9. a 4 4R E R E R E Å A meter bridge set up as shown, to determine an unknown restance X using a standard 0 ohm restor. The galvanometer shows null point when tapping key at 5 cm mark. The end corrections are cm and cm respectively for the ends A and B. The determined value of X 0. ohm b. 0.6 ohm c. 0.8ohm d..ohm 0. b/d 5 0 x 46 South Delhi: 65 Kalusarai, Sarvpriya Vihar, Hauz Khas, N.D. 6, Ph: ,

8 SECTION ll (Total M-arks : 6) (Multiple Correct Answers Type) Th section contains 4 multiple choice questions.each question has four choices (B), (C) and (D) out of which ONE or MORE may be correct (A),. An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi infinite region of uniform magnetic filed perpendicular to the velocity. Which of the following statement(s) /are true? They will never come out of the magnetic filed 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.. d. A composite block made of slabs A, B, C, D and E of different thermal conductivities (Given in terms of a constant K) and size (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 steady state. heat flow through A and E slabs are same. b. heat flow through slab E maximum. c. temperature difference across slab E smallest d. heat flow through C = heat flow through B + heat through D.. a, c. 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 each given charge +Q. Now they are connected by a thinmtela wire. Then c. inside E 0 b. Q A A > Q B A B. a, b, c, d R R B A East Delhi: Pratap Nagar, Mayur Vihar Phase -, Delhi - 9, Ph: 40798, d. E on surface A E on surface B 4. A metal rod of length L and mass m pivoted at one end. A thin dk of mass M and radius R (< L) attached at its center to the free end ofthe rod. Consider two ways the dc attached: (case A) The dc not free to rotate about its center and (case B) the dc free to rotate about its center. The rod-dc system performs SHIVI in vertical plane after being released from the same dplaced position. Which of the following statement(s) (are) true?

9 Restoring torque in case A = Restoring torque in case B b. Restoring torque in case A < Restoring torque in case B c. Angular frequency for case A > Angular frequency for case B. d. Angular frequency for case A < Angular frequency for case B. 4. a, d SECTION III (Total Marks : 5) (Paragraph Type) Th section contains paragraphs. Based upon one of the paragraphs multiple choice questions and based on the other paragraph multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE correct. Paragraph for Question Nos. 5 and 6 A dense collection of equal number of electrons and positive ions called neutral plasm Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasm Let N be the number densityof free electrons, each of mass m. When the electrons are subjected to an electric field, they are dplaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency p,which 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 absorbed and a part of it reflected. As approaches p, all the free electrons are set to resonance together and all the energy reflected. Th the explanation of highreflectivity of metals. 5. Taking the electronic charge as e and the permittivity as 0, use dimensional analys to determine the correct expression for mp. Ne m b. 0 m 0 Ne c. 5. c Ne m 0 d. m Ne 0 6. Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N = m. Take o = 0 and m = 0 0, where these quantities are in proper Sl units. 800 nm b. 600 nm c. 00 nm d. V 00 nm 6. b South Delhi: 65 Kalusarai, Sarvpriya Vihar, Hauz Khas, N.D. 6, Ph: ,

10 Paragraph for Question Nos. 7 to 9 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 andmomentum are changed. Here we consider some simple dynamical systems in one dimension. For such systems, phase space a plane in which position plottedalong horizontal ax and momentum plotted along vertical ax. The phase spacea diagram x(t) vs. p(t) curve in th plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) positive and downwards (or to left) negative. 7. The phase space diagram for a bail thrown vertically up from ground b. Momentum c. Position d. 7. d East Delhi: Pratap Nagar, Mayur Vihar Phase -, Delhi - 9, Ph: 40798,

11 8. The phase space diagram for simple harmonic motion a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E and E are the total mechanical energies respectively. Then 8. c E E b. E = E c. E = 4E d. E = 6E 9. Consider the spring mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of th system b. c. d. 9. a South Delhi: 65 Kalusarai, Sarvpriya Vihar, Hauz Khas, N.D. 6, Ph: ,

12 SECTION IV (Total Marks : 8) (Integer Answer Type) Th section contains 7 questions. The answer to each of the questions a singledigit integer, ranging from 0 to 9. The bubble corresponding to the correct answer to be darkened in the ORS. 40. 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. The system of charges 40. and planar film are in equilibrium, and /N q a k, where k a constant. Then N 4. A block moving on an inclined plane making an angle 45º with the horizontal and the coefficient of friction. The force required to just push it up the inclined plane times the force required to just prevent it from sliding down. If we define N = 0, then N A long circular tube of length 0 m and radius 0. m carries a current I along its curved surface as shown. A wire Ioop of restance ohm and of radius 0. m placed inside the tube with its ax coinciding with the ax of the tube. The current varies as I = I 0 cos (00t) where I 0 constant. If the magnetic moment of the loop N 0 I 0 sin (00t), then N Steel wire of length L at 40 C suspended from the ceiling and then a mass m hung from its free end. The wire cooled down from 40ºC to 0ºC to regain its original length L. The coefficient of linear thermal expansion of the steel 0 5 / ºC, Young s modulus of steel 0 N/m and radius of the wire mm. Assume that L >> diameter of the wire. Then the value of m in kg nearly 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 N 0 4 kg m, then N A boy pushing a ring of mass kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of N on the ring and rolls it without slipping with an acceleration of 0. m/s. The coefficient of friction between the ground and the ring large enough that rolling always occurs and the coefficient of friction between the stick and the ring (P/0). The value of P East Delhi: Pratap Nagar, Mayur Vihar Phase -, Delhi - 9, Ph: 40798,

13 The activity of a freshly prepared radioactive sample l0 0 dintegrations per second,whose mean life 0 9 s. The mass of an atom of th radiootope l0 5 kg. The mass (in mg) of the radioactive sample 46. PART III : MATHEMATICS SECTION I (Total Marks : ) (Single Correct Answer Type) Th section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE correct. 47. Let a iˆ ˆj k, ˆ b i ˆ ˆj kˆ and c ˆi ˆj kˆ be three vectors. A vector v in the plane of a and b, whose projection on c, given by ˆi j ˆ kˆ b. i ˆ j ˆ kˆ c. i ˆ ˆj kˆ d. ˆi j ˆ kˆ 48. Let the straight line x = b divide the area enclosed by y = ( x), y = 0, and x = 0 into two parts R (0 x b) and R (b x ) such that R R. Then 4 b equals b. c. d A straight line L through the point (, ) inclined at an angle 60 to the line x y. If L also intersects the x-ax, then the equation of L y x 0 b. y x 0 c. y x 0 d. y x 0 South Delhi: 65 Kalusarai, Sarvpriya Vihar, Hauz Khas, N.D. 6, Ph: ,

14 50. The value of ln 4 ln x sin x dx sin x sin (ln 6 x ) ln b. ln c. ln d. ln 6 5. Let (x 0, y 0 ) be the solution of the following equations Then x 0 6 b. (x) ln = (y) ln ln x = ln y c. d Let P { : sin cos cos } and Q { : sin cos sin } be two sets. Then P Q and Q P b. Q P c. P Q d. P = Q 5. Let and be the roots of x 6x 0, with >. If n n a n for n, a then the value of 0 a8 a9 b. c. d. 4 SECTION ll (Total Marks : 6) (Multiple Correct Answers Type) Th section contains 4 multiple choice questions.each question has four choices (B), (C) and (D) out of which ONE or MORE may be correct (A), 54. Let M and N be two non-singular skew-symmetric matrices such that MN = NM. If P T denotes the transpose of P, then M N (M T N) (MN ) T equal to M b. N c. M d. MN 55. Let the eccentricity of the hyperbola x 4y 4 x y a b be reciprocal to that of the ellipse. If the hyperbola passes through a focus of the ellipse, then x y the equation of the hyperbola b. a focus of the hyperbola (, 0) 5 c. the eccentricity of the hyperbola d. the equation of the hyperbola x y East Delhi: Pratap Nagar, Mayur Vihar Phase -, Delhi - 9, Ph: 40798,

15 56. The vectors(s) which /are coplanar with vectrors ˆi ˆj kˆ and ˆi j ˆ kˆ, and perpendicular to the vector ˆi ˆj kˆ /are ˆj kˆ b. i ˆ ˆj c. ˆi ˆj d. ˆj kˆ 57. Let f : be a function such that f (x y) f (x) f (y), x, y. If f(x) differentiable at x = 0, then f (x) differentiable only in a finite interval containing zero b. f (x) continuous x c. f (x) constant x d. f (x) differentiable except at finitely many points SECTION III (Total Marks : 5) (Paragraph Type) Th section contains paragraphs. Based upon one of the paragraphs multiple choice questions and based on the other paragraph multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE correct. Paragraph for Question Nos. 58 and 59 Let U and U two urns such that U contains white and red balls, and U contains only white ball. A fair coin tossed. If head appears then ball drawn at random from U and put into U. However, if tail appears then balls are drawn at random from U and put into U. Now ball drawn at random from U. 58. The probability of the drawn ball from U being white 9 b. c d Given that the drawn ball from U white, the probability that head appeared on the coin 7 5 b. c. d. Paragraph for Question Nos. 60 to 6 Let a, b and c be three real numbers satfying 9 7 [a b c] 8 7 [0 0 0]...(E) If the point P(a, b, c), with reference to (E), lies on the plane x + y + z =, then the value of 7a + b + c 0 b. c. 7 d Let be a solution of x = 0 with Im() > 0. If a = with b and c satfying (E), then the value of a b c equal to South Delhi: 65 Kalusarai, Sarvpriya Vihar, Hauz Khas, N.D. 6, Ph: ,

16 b. c. d. 6. Let b = 6, with a and c satfying (E). If and are the roots of the quadratic equation n ax bx c 0, then n b. 7 c. d. 7 SECTION IV (Total Marks : 8) (Integer Answer Type) Th section contains 7 questions. The answer to each of the questions a singledigit integer, ranging from 0 to 9. The bubble corresponding to the correct answer to be darkened in the ORS. 6. The positive integer value of n > satfying the equation sin sin sin n n n p 64. Let a, a, a,..., a 00 be an arithmetic progression with a = and SP ai, S i m p 00. For any integer n with n 0, let m = 5n. If S does not depend n on n, then a 65. The minimum value of the sum of real numbers a, a, a,, a and 0 a with a > Let f : [, ) [, ) be a differentiable function such that f () =. If A 6 f (t) dt x f (x) x for all x, then the value of f () 67. Let sin f ( ) sin tan, where. Then the value of cos Consider the parabola y d (f ( )) d (tan ) 8x. Let be the area of the triangle formed by the end points of its latus rectum and the point P, on the parabola, and be the area of the triangle formed by drawing tangents at P and at the end points of the latus rectum. Then 69. If z any complex number satfying z i, then the minimum value of z 6 + 5i East Delhi: Pratap Nagar, Mayur Vihar Phase -, Delhi - 9, Ph: 40798,

Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , PART II Physics

Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , PART II Physics R Prerna Tower, Road No, Contractors rea, istupur, Jamshedpur 8311, Tel (657)189, www.prernaclasses.com IIT JEE 11 Physics Paper I PRT II Physics SECTION I (Total Marks : 1) (Single Correct nswer Type)