Part I Section I Straight Objective Type

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1 [] Part I Section I Straight Objective Type IIT JEE- / Paper II CHEMISTRY This section contains 6 multiple choice questions numbered to 6. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.. 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 (D). Among the following complexes (K - P), b g b g b g b g b g b g b g b g b g b g b g b g b g K Fe CN K, Co NH Cl L, Na Co oxalate M, Ni H O Cl N, K Pt CN Q and Zn H O NO P the diamagnetic complexes are (A) K, L, M, N (C) L, M, O, P (B) K, M, O, P (D) L, M, N, O (C) 3. Passing H S gas into a mixture of Mn, Ni, Cu and Hg ions in an acidified aqueous solution precipitates (A) CuS and HgS (B) MnS and CuS (C) MnS and NiS (D) NiS and HgS (A) 4. Consider the following cell reaction Fe O 4H Fe H O l At Fe 0 bsg bgg baqg baqg b g E 67. V 3 0 M, PbOg 0. atm ph = 3, the cell potential at 5 0 C is (A).47 V (B).77 V (C).87 V (D).57 V (D)

2 [] IIT JEE- / Paper II b g b CHEMISTRY 5. The freezing point (in 0 C) of a solution containing 0. g of K Fe CN Mol. Wt in 00 g of 6 water ckf 86. kg mol h is (A). 3 0 (B) (C) (D). 0 g (a) 6. Amongst the compounds given, the one that would form a brilliant colored dye on treatment with NaNO in dil. HCl followed by addition to an alkaline solution of naphtol is (A) (B) (C) (D) (C) 7. The major product of the following reaction is (A) a hemiacetal (B) an acetal (C) an ether (D) an ester (B)

3 8. The following carbohydrate is [3] IIT JEE- / Paper II CHEMISTRY (A) a ketohexose (B) an aldohexose (C) an furanose (D) an pyranose (B) Section II Multiple Correct Answer Type This section contains 5 multiple choice questions numbered 8 to 4. 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 (C,D) 0. The equilibrium Cu I Cu 0 Cu II in aqueous medium at 5 0 C shifts towards the left in the presence of (A) NO 3 (B, C, D). For the first order reaction b g b g b g N O g 4NO g O g 5 (B) Cl (C) SCN (D) CN (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. (A, B, D)

4 [4] IIT JEE- / Paper II CHEMISTRY. The correct functional group X and the reagent/reaction conditions Y in the following scheme are (A) X COOCH, Y H / Ni / heat (B) X CONH, Y H / Ni / heat 3 (C) X CONH, Y Br / NaOH (D) X CN, Y H / Ni / heat (A, B, C, D) 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. 3. Among the following, the number of compounds than can react with PCl 5 to give POCl 3 is (3) O, CO, SO, H O, H SO, P O The volume (in ml) of 0. M AgNO 3 required for complete precitation of chloride ions present in 30 ml (6) of 0.0 M solution of Cr H O Cl Cl 5 b g, as silver chloride is close to 0 5. In L saturated solution of AgCl KspbAgClg 6. 0, 0. mol of CuCl KspbCuClg is added. The resultant concentration of Ag + in the solution is x The value of 'x' is (7) 6. The number of hexagonal faces that are present in a truncated octahedron is (8)

5 [5] IIT JEE- / Paper II CHEMISTRY 7. The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the following compounds is (7) 8. The total number of contributing structures showing hyperconjugation (involving C - H bonds) for the following carbocation is (6) Section IV Matrix-Match Type This section contains 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. 9. All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II. Column I b g b g 3b g b g b g Column II (A) CO s CO g (p) phase transition (B) CaCO s CaO s CO g (q) allotropic change (C) H H g b g (r) H is positive (D) Pb P white, solidg bred, solidg (s) S is positive (t) S is negative [A] p, r, s,[b] r, s, [C] t, [D] q, t

6 [6] IIT JEE- / Paper II CHEMISTRY 0. All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II. Column I Column II (A) (p) Nucleophilic (B) (q) Electrophilic (C) (r) Dehydration (D) (s) Nucleophilic addition (t) Carbanion [A] r, s, t, [B] p, s, [C] r, s [D] q, r

7 [7] Part II Section I (Total Marks : 4) (Single Correct Answer Type) IIT JEE- / Paper-II PHYSICS This section contains 8 multiple choice questions numbered to 8. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.. A light ray traveling in glass mediumis 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) Ans: (C)

8 [8] IIT JEE- / Paper-II PHYSICS. A wooden block performs SHM on a frictionless surface with frequency, v 0. 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) (B) (C) (D) on the same frequency and with shifted mean position. of the same frequency and withthe same mean position. of changed frequency andwith shifted mean position. of changed frequency and with the same mean position. Ans: (A) 3. 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.5 mm and that on the circular scale is 0 divisions. If the measured mass of the ball has a relative error of %, the relative percentage error in the density is Ans: (C) (A) 0.9% (B).4% (C) 3.% (D) 4.% 4. A ball of mass 0. kgrests on a vertical post of height 5 m. A bullet of mass 0.0 kg, traveling with a velocity V m / s in ahorizontal 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 0 m and the bullet at a distance of 00 m from the foot of the post. The intial velocity V of the bullet is Ans: (D) (A) 50 m / s (B) 50 m / s (C) 400 m / s (D) 500 m / s

9 [9] IIT JEE- / Paper-II PHYSICS 5. Which of the file patterns given below is valid for electric field as well as for magnetic field? (A) (B) (C) (D) Ans: (D) b g 3b g sin b g 6. A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x t Asint and x t Asin t b g F HG 3 I K J. Adding a third sinusoidal displacement x t B t to a complete rest. The values of B and are brings the mass (A) A, 3 4 (B) A, 4 3 (C) 3A, 5 6 (D) A, 3 Ans: (B)

10 [0] IIT JEE- / Paper-II PHYSICS 7. 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 Z- component of the magnetic field at the center of the sprial is (A) Ans: (A) F bi b g ln HG a K J (B) 0 N I F b ai bb ag ln HG b a K J (C) 0 0 N I b a N I b b a ln F H G I K J (D) 0 N I ln b F HG b a b a I K J 8. 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) Ans: (B) mv (B) mv (C) 3 mv (D) mv

11 [] IIT JEE- / Paper-II Section II Multiple Correct Answer Type PHYSICS This section contains 4 multiple choice questions numbered 9 to 3. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is / are correct. 9. 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 Ans: (A, B, D) d (B) d d (C) d d (D) d d d F B F A F A B F 30. Which of the following statement(s) is/are correct? (A) If the electric field due to a point charge varies as r. 5 instead of r, then the Gauss law will still be valid. (B) (C) (D) Ans: (C, D) The Gauss law can be used to calculate the field distribution around an electric dipole. If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same. The work done by the external force in moving a unit positive charge from point A at potential V A to point B at potential V B is V b B V A g

12 [] IIT JEE- / Paper-II PHYSICS 3. 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 V C across the capacitor are compared in the two cases. Which of the following is/are true? (A) I A R Ans: (B, C) B A B A B A I (B) I I (C) V V (D) V V R R R C C C B C 3. A thin ring of mass kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity m / s. A small ball of mass 0. kg, moving with velocity 0 m / s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 0 m / s. Immediately after the collision (A) the ring has pure rotation about its sitationary 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. Ans: (A, C)

13 [3] IIT JEE- / Paper-II Section III Integer Type PHYSICS 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 Ans: A series R-C combinationis connected to an AC voltage of angular frequency 500 radian/s. If the Ans: 4 impedance of the R-C circuit is R 5., 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 0 m / s, at an angle of 60 o to the horizontal. The body has to move forward by.5 m inside the train to catch the ball back atthe intial height. The acceleration of the train, in m / s, is Ans: 5

14 [4] IIT JEE- / Paper-II PHYSICS 36. Water (with refractive index 4 3 ) in a tank is 8 cm deep. Oil of refractive index 7 4 lies on water making a convex surface of radius of curvature 'R = 6 cm' as shown. Consider oil to act asa thin lens. An object 'S' is placed 4 cm above water surface. The location of its image is at 'x' cm above the bottom of the tank. Then 'x' is Ans: 37. A block of mass 0.8 kg is attached to a spring of force-constant N / m. The coefficient of friction between the block and the floor is 0.. 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 intial velocity of the block in m / s is V = N / 0. Then N is Ans: A silver sphere of radius cm and work function 4.7 ev is suspended from an insulating thread in freespace. It is under continuous illumination of 00 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photelectrons emitted from the Ans: 7 sphere is A 0 z (where A 0 ). The value of 'Z' is

15 [5] IIT JEE- / Paper-II Section IV Matrix-Match Type PHYSICS This section contains 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. Columne II gives the characteristic involved in the cycle. Match them with each of the prcess 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. Ans: [A] p, r, t ; [B] p, r ; [C] q, s ; [D] r, t (t) Work is done on the gas.

16 [6] IIT JEE- / Paper-II PHYSICS 40. Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as 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 L Ans: [A] p, t ; [B] p, s ; [C] q, s ; [D] q, r (t) f 4L

17 [7] Section I Straight Objective Type IIT JEE- / Paper II MATHEMATICS This section contains 6 multiple choice questions numbered 0 to 3. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 4. Let f :[, ] [ 0, ) be a continuous function such that f( x) f( x) for x [, ]. Let z R x f( x) dx, and R be the area of the region bounded by y f( x), x, x, and the x- axis. Then (A) R R (B) R 3R (C) R R (D) 3R R (C) 4. Let f( x) x 3 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,,,...} (B) n, n {,,...} (C) n, n {...,,, 0,,,...} (D) n, n {...,,, 0,,,...} (A) 43. Let ( x, y ) be any point on the parabola y ( 0, 0 ) to ( x, y ) in the ratio :3. Then the locus of P is 4x. Let P be the point that divides the line segment from (A) x y (B) y x (C) y x (D) x y (C)

18 [8] IIT JEE- / Paper II MATHEMATICS 44. Let P( 6, 3 ) be a point on the hyperbola x y. If the normal at the point P intersects the x axis a b at (9, 0), then the eccentricity of the hyperbola is (A) 5 (B) 3 (C) (D) 3 (B) 45. A value of b for which the equations x bx 0 x x b 0 have one root in common is (A) (B) i 3 (C) i 5 (D) (B) 46. Let be a cube root of unity and S be the set of all non singular matrices of the form L NM a b c O QP where each of a, b, and c is either or. Then the number of distinct matrices in the set S is (A) (B) 6 (C) 4 (D) 8 (B) 47. The circle passing through the point (-, 0) and touching the y-axis at (0, ) also passes through the point

19 (A) F HG I K J F HG I K J [9] 3, 0 5 (B), 3 5 (C), (D) 4, 0 F HG I K J IIT JEE- / Paper II MATHEMATICS b g (D) / x 48. If lim xln( b ) bsin, b 0 and, x0 b, then the value of is (A) 4 (B) 3 (C) 6 (D) (D) 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 5 probability of none of them occuring is 5 then and the. If P( T) denotes the probability of occurrence of the event T, 4 3 (A) P( E), P( F) 5 5 (B) P( E), P( F) 5 5 (C) P( E), P( F) 5 5 (D) 3 P( E), P( F) 5 (A, D) If then R S T x, cos x, x, ln x, x x 0 0 x, x (A) f( x) is continuous at x (B) f (x) is not differentiable at x 0

20 [0] IIT JEE- / Paper II MATHEMATICS (C) f(x) is differentiable at x (D) f (x) is differentiable at x 3 (A, B, C, D) 5. f : ( 0, ) R be defined by b x f( x) bx where b is a constant such that 0 b. Then (A) f is not invertiable on (0, ) (B) f f on (0, ) and f ( b) f ( 0) (C) f f on (0, ) and f ( b) f ( 0) (D) f is differentiable on ( 0, ) (A) 5. Let L be a normal to the parabola y 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 5 0 (D) y x 0 (A, B, D) 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 x 3y divides the circular region x y 6 into two parts. If F S RS H G I K J F H G I K J F I HG K J F H G I T 3 5 3,,,,,,, K JUV W then the number of point(s) in S lying inside the smaller part is ()

21 [] 54. Let e i / e and a, b, c, x, y, z be non zero complex numbers such that a b c x a b c y a b c z IIT JEE- / Paper II MATHEMATICS (3) Then value of x y z a b c is 55. The number of distinct real roots of 4 3 x 4x x x 0 () (0) 56. Let y( x) y( x) g( x) g( x), y( 0) 0, x R where f ( x) denotes d f ( x ) and g( x) is a given non- dx constant differentiable function on R with g( 0) g( ). Then the value of y( ) is 57. Let M be a 3 3 matrix satisfying M L0 O NM P Q 0P NM O P Q L 3P, M L NM O P Q L M N O P Q 0P MP and M M The the sum of the diagonal entries of M is (9) L O M L N QP NM 0 0 O QP 58. Let a i k, a i k and c i j 3 k be three given vectors. If r is a vectors such that r b c b and r a 0 then the value of r b is (9)

22 [] Section IV Matrix-Match Type IIT JEE- / Paper II MATHEMATICS This section contains 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) (, ) (, ) RS T F I HG K J UV W iz Re : z is a complex number, z, z z is (B) The domain of the function (q) (, 0) ( 0, ) f( x) sin F HG 8( 3) 3 x ( x) I KJ is (r), g tan (C) If f( ) tan tan tan, then (s),, b g RST the set f( ) : 0 UVW is 3/ (D) If f( x) x ( 3x 0 ), x 0, then f( x) is increasing in (t), 0, (A) s, (B) t, (C) r, (D) r b g

23 [3] IIT JEE- / 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 3k form a triangle, then the internal angle of the triangle between a and b is (p) 6 zb (B) If ( f( x) x) dx 3 a b, then the value of (q) 3 f a F I HG 6 K J is (C) The value of (r) 3 ln 5 z 6 sec( x) dx is (D) The maximum value of Arg z z, z is given by, (A) q, (B) p, (C) s, (D) s F HG I K J for (s) (t)