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IIT JEE (Advanced) 2014 : Paper 1 (Solved with Answer Key)

25 pages, 60 questions, 60 questions with responses, 96 total responses,

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JEE(ADVANCED) 2014 PAPER-1 Code-1 Questions with Answers PART 1 PHYSICS SECTION 1 (One or More Than One Options Correct Type) This section contains 10 multiple choice type questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct. At time = 0, terminal A in the circuit shown in the figure is connected to B by a keyand an ( ), with 0 = 1Aand = 500 rad s-1 starts flowing in it with alternating current ( ) = 0 cos 1. the initial direction shown in the figure. At t = 7 6 , the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C=20 F, R= 10 and the battery is ideal with emf of 50V, identify the correct statement (s). B D A 50 V C=20 F R=10 (A) Magnitude of the maximum (B) The current (C) 7 charge on the capacitor before = 6 is 1 10 3 C. 7 in the left part of the circuit just before = 6 is clockwise. Immediately after A is connected to D, the current in R is 10A. (D) Q = 2 10 3 C. Answer (C) and (D) A light source, which emits two wavelengths 1 = 400 and 2 = 600 , is used in a Young s double slit experiment. If recorded fringe widths for 1 and 2 are 1 and 2 number of fringes for them within a distance yon one side of the central maximum are m1 and m2, respectively, then 2. (A) 2 > 1 (B) 1 > 2 (C) From (D)The the central maximum, 3rdmaximum of 2 overlaps with 5th minimum of 1 angular separation of fringes for 1 is greater than 2 Answer: (A), (B) and (C) One end of a taut string of length 3m along the x axis is fixed at x=0.The speed of the waves in the string is 100 1 . The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is(are) 3. 50 cos 3 6 100 (B) ( ) = sin cos 3 3 5 250 (C) ( ) = sin cos 3 6 5 (D) ( ) = sin cos 250 2 (A) ( ) = sin Answer: (A) , (C) and (D) A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is C1. When the capacitor is charged, the plate area covered by the dielectric gets charge Q1 and the rest of the area gets charge Q2. The electric field in the dielectric is E1 and that in the other portion is E2. Choose the correct option/options, ignoring edge effects. 4. Q1 Q2 (A) (B) (C) (D) 1 2 1 2 1 2 1 E1 E2 =1 = 1 = 2+ = 3 Answer: (A) and (D) Let 1 ( ), 2 ( ) and 3 ( ) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density , and an infinite plane with uniform surface charge density . If 1 ( 0 ) = 2 ( 0 ) = 3 ( 0 ) at a given distance r0, then 5. 2 (A) = 4 0 (B) 0 = 2 (C) 1 ( 0 2)= 2 2 ( 0 2) (D) 2 ( 0 2)=4 3 ( 0 2) Answer: (C) A student is performing an experiment using a resonance column and a tuning fork of frequency 244 1 . He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 0.005) , the gas in the tube is 6. (Useful information: 167 = 640 1 2 mole 1 2 ; 140 = 590 1 2 mole 1 2 .The molar 10 masses Min grams are given in the options. Take the values of for each gas as given there.) ( (A)Neon = 20, ( 10 20 = (B) Nitrogen = 28, ( (C) Oxygen = 32, ( (D)Argon = 36, 10 28 10 32 10 36 7 10 ) 3 = = = 5 ) 9 16 17 32 ) ) Answer: (D) Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5kgwater by 40K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d.The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K? 7. (A)4 if wires are in parallel (B) 2 if wires are in series (C)1 if wires are in series (D)0.5 if wires are in parallel Answer : (B) and (D) In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle with the horizontal floor. The coefficient of friction between the wall and the ladder is 1 and that between the floor and the ladder is 2 . The normal reaction of the wall on the ladder is N1 and that of the floor is N2. If the ladder is about to slip, then 8. 1 2 (B) 1 0 2 0and 2 tan = 2 2 = 0and 1 tan = 2 (D) 1 = 0 2 0and 1 tan = (A) 1 = 0 (C) 1 0 2 0and 2 = 1+ 1 2 2 Answer: (C) and (D) A transparent thin film of uniform thickness and refractive index n1= 1.4 is coated on the convex spherical surface of radius Rat one end of a long solid glass cylinder of refractive index n2 = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f1 from the film, while rays of light traversing from glass to air get focused at distance f2 from the film. Then 9. n1 Air n2 (A) | 1 | =3R (B)| 1 | = 2.8R (C)| 2 | =2R (D)| 2 | = 1.4R Answer: (A) and (C) Two ideal batteries of emfV1 and V2 and three resistancesR1, R2 andR3 are connected as shown in the figure. The current in resistanceR2 would be zero if 10. V1 R1 R2 V2 R3 (A) 1 = 2 and 1 = 2 = 3 (B) 1 = 2 and 1 = 2 2 = 3 (C) 1 = 2 2 and 2 1 = 2 2 = 3 (D)2 1 = 2 and2 1 = 2 = 3 Answer: (A), (B) and (D) SECTION 2 (One Integer Value Correct Type) This section contains 10 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive). Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively as shown in figure. The speed of A is 100 3 1 . At time = 0 , an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at = 0 , A just escapes being hit by B, 0 in seconds is 11. A B 30o 60o Answer: 5 During Searle s experiment, zero of the Vernier scale lies between 3.20 10 2 and 3.25 10 2 of the main scale. The 20th division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 10 2 and 3.25 10 2 of the main scale but now the 45th division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 10 7 2 . The least count of the Vernier scale is 1.0 10 5 . The maximum percentage error in the Young s modulus of the wire is 12. Answer: 4 A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in 1 is 13. F X o Y F Z F Answer: 2 Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X1 from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R1. In contrast, if the currents I in the two wires have directions opposite to 14. each other, the radius of curvature of the path is R2. If Answer: 3 0 1 = 3, the value of 1 2 is To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density of the fog, intensity (power/area) of the light from the signal and its frequency f. The engineer finds that isproportionalto 1 . The value of is 15. Answer: 3 16. A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 resistance, it can be converted into a voltmeter of range 0 30 V. If connected to a resistance, it becomes an ammeter of range 0 1.5 A. The value of is Answer: 5 2 249 Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is ( 10)Joules. The value of n is (take acceleration due to gravity = 10 2 ) 17. Q 4m 90o O 3m P Answer : 5 A rocket is moving in a gravity free space with a constant acceleration of 2 2 along +x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in +x direction with a speed of 0.3 1 relative to the rocket. At the same time, another ball is thrown in x direction with a speed of 0.2 1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is 18. a = 2 ms 2 0.2 ms 1 0.3 ms 1 4m Answer : 2 OR 8 x A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of 9 1 with respect to the ground. The rotational speed of the platform in 1 after the balls leave the platform is 19. Answer: 4 A thermodynamic system is taken from an initial state i with internal energy = 100 to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are = 200 , = 50 and = 100 respectively. The heat supplied to the system along the path iaf, ib and bf are , and respectively. If the internal energy of the system in the state b is = 200 and = 500 , the ratio / is 20. a f P i b V Answer : 2 PART 2 CHEMISTRY SECTION 1 (One or More Than One Options Correct Type) This section contains 10 multiple choice type questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct. 21. The correct combination of names for isomeric alcohols with molecular formula C4H10O is/are (A) tert-butanol and 2-methylpropan-2-ol (B) tert-butanol and 1, 1-dimethylethan-1-ol (C) n-butanol and butan-1-ol (D) isobutyl alcohol and 2-methylpropan-1-ol Answer: (A), (C) and (D) he reactivity of compound Z with different halogens under appropriate conditions is given below: 22. The observed pattern of electrophilic substitution can be explained by (A) the steric effect of the halogen (B) the steric effect of the tert-butyl group (C) the electronic effect of the phenolic group (D) the electronic effect of the tert-butyl group Answer: (A), (B) and (C) 23. In the reaction shown below, the major product(s) formed is/are (A) (B) (C) (D) Answer : (A) An ideal gas in a thermally insulated vessel at internal pressure = P1, volume = V1 and absolute temperature = T1 expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P2, V2 and T2, respectively. For this expansion, 24. (A) q=0 (B) T2 = T1 (C) P2V2 = P1V1 (D) P2V2 = P1V1 Answer (A), (B) and (C) 25. Hydrogen bonding plays a central role in the following phenomena: (A) Ice floats in water. (B) Higher Lewis basicity of primary amines than tertiary amines in aqueous solutions. (C) Formic acid is more acidic than acetic acid. (D) Dimerisation of acetic acid in benzene. Answer : (A), (B) and (D) 26. In a galvanic cell, the salt bridge (A) does not participate chemically in the cell reaction. (B) stops the diffusion of ions from one electrode to another. (C) is necessary for the occurrence of the cell reaction. (D) ensures mixing of the two electrolytic solutions. Answer: (A) and (C) or only (A) 27. Upon heating with Cu2S, the reagent(s) that give copper metal is/are (A) CuFeS2 (B) CuO (C) Cu2O (D) CuSO4 Answer: (B), (C) and (D) 28. The correct statement(s) for orthoboric acid is/are (A) It behaves as a weak acid in water due to self ionization. (B) Acidity of its aqueous solution increases upon addition of ethylene glycol. (C) It has a three dimensional structure due to hydrogen bonding. (D) It is a weak electrolyte in water. Answer: (B) and (D) 29. For the reaction: I + ClO3 + H2SO4 Cl + HSO4 + I2 The correct statement(s) in the balanced equation is/are: (A) Stoichiometric coefficient of HSO4 is 6. (B) Iodide is oxidized. (C) Sulphur is reduced. (D) H2O is one of the products. Answer: (A), (B) and (D) OR (A) and (D)* *- Due to a minor error in option (B) in the Hindi Version, Answer (A) and (D) will also be accepted as correct. 30. The pair(s) of reagents that yield paramagnetic species is/are (A) Na and excess of NH3 (B) K and excess of O2 (C) Cu and dilute HNO3 (D) O2 and 2-ethylanthraquinol Answer : (A), (B) and (C) Consider all possible isomeric ketones, including stereoisomers, of MW = 100. All these isomers are independently reacted with NaBH4 (NOTE: stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s) is/are 31. Answer: 5 32. A list of species having the formula XZ4 is given below. XeF4, SF4, SiF4, BF4 , BrF4 , [Cu(NH3)4]2+, [FeCl4]2 , [CoCl4]2 and [PtCl4]2 . Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar shape is Answer: 4 Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi2S3 and SnS2, the total number of BLACK coloured sulfides is 33. Answer: 6 OR 7 The total number(s) of stable conformers with non-zero dipole moment for the following compound is (are) 34. Answer: 3 35. Consider the following list of reagents: Acidified K2Cr2O7, alkaline KMnO4, CuSO4, H2O2, Cl2, O3, FeCl3, HNO3 and Na2S2O3. The total number of reagents that can oxidise aqueous iodide to iodine is Answer: 7 The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the peptide shown below is 36. Answer: 1 In an atom, the total number of electrons having quantum numbers = 4, | | = 1 and = 1 2 is 37. Answer: 6 If the value of Avogadro number is 6.023 1023 mol 1 and the value of Boltzmann constant is 1.380 10 23J K 1, then the number of significant digits in the calculated value of the universal gas constant is 38. Answer: 4 39. A compound H2X with molar weight of 80 g is dissolved in a solvent having density of 0.4 g ml 1. Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is Answer: 8 MX2 dissociates into M2+ and X ions in an aqueous solution, with a degree of dissociation ( ) of 0.5. The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is 40. Answer: 2 PART 3 MATHEMATICS SECTION 1 (One or More Than One Options Correct Type) This section contains 10 multiple choice type questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE are correct. 41. Let and be two 3 3 matrices such that = . Further, if 2 and 2 = 4 , then (A) determinant of ( 2 + 2 ) is 0 (B) there is a 3 3 non-zero matrix such that ( 2 + 2 ) is the zero matrix (C) determinant of ( 2 + 2 ) 1 (D) for a 3 3 matrix , if ( 2 + 2 ) equals the zero matrix then is the zero matrix Answer: (A), (B) 42. For every pair of continuous functions , : [0, 1] such that max { ( ): [0,1]} = max { ( ): [0,1]}, the correct statement(s) is(are) : (A) ( ( )) 2 + 3 ( ) = ( ( )) 2 + 3 ( ) for some [0, 1] (B) ( ( )) 2 + ( ) = ( ( )) 2 + 3 ( ) for some [0, 1] (C) ( ( )) 2 + 3 ( ) = ( ( )) 2 + ( ) for some [0, 1] (D) ( ( )) 2 = ( ( )) 2 for some [0, 1] Answer: (A), (D) 43. Let : (0, ) be given by 1 ( ) = + 1 Then . (A) ( ) is monotonically increasing on [1, ) (B) ( ) is monotonically decreasing on (0, 1) 1 (C) ( ) + = 0, for all (0, ) (D) (2 ) is an odd function of on Answer: (A), (C), (D) 44. Let and let : be given by Then ( ) = 5 5 + . (A) ( ) has three real roots if > 4 (B) ( ) has only one real root if > 4 (C) ( ) has three real roots if < 4 (D) ( ) has three real roots if 4 < < 4 Answer: (B), (D) 45. Let : [ , ] [1, ) be a continuous function and let : be defined as ( ) = Then 0 ( ) ( ) if < , if , if > . (A) ( ) is continuous but not differentiable at (B) ( ) is differentiable on (C) ( ) is continuous but not differentiable at (D) ( ) is continuous and differentiable at either or but not both Answer: (A), (C) 46. Let : ( , 2 2 ) be given by Then ( ) = (log(sec + tan ))3 . (A) ( ) is an odd function (B) ( ) is a one-one function (C) ( ) is an onto function (D) ( ) is an even function Answer: (A), (B) and (C) 47. From a point ( , , ), perpendiculars and are drawn respectively on the lines = , = 1 and = , = 1. If is such that is a right angle, then the possible value(s) of is(are) (A) 2 (B) 1 (C) 1 (D) 2 Answer: (C) 48. Let , and be three vectors each of magnitude 2 and the angle between each pair of them is If is a nonzero vector perpendicular to and and is a nonzero vector perpendicular to and , then (A) = ( )( ) (B) = ( )( ) (C) = ( ) ( ) (D) = ( )( ) Answer: (A), (B) and (C) 49. A circle passes through the point (0, 1) and is orthogonal to the circles ( 1)2 + 2 = 16 and 2 + 2 = 1. Then (A) radius of is 8 (B) radius of is 7 (C) centre of is ( 7, 1) (D) centre of is ( 8, 1) Answer: (B), (C) 3 . 50. Let be a 2 2 symmetric matrix with integer entries. Then is invertible if (A) the first column of is the transpose of the second row of (B) the second row of is the transpose of the first column of (C) is a diagonal matrix with nonzero entries in the main diagonal (D) the product of entries in the main diagonal of is not the square of an integer Answer: (C), (D) 51. Let , , be positive integers such that is an integer. If , , are in geometric progression and the arithmetic mean of , , is + 2, then the value of is 2 + 14 + 1 Answer: 4 52. Let 2 be an integer. Take distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of is Answer: 5 53. Let 1 < 2 < 3 < 4 < 5 be positive integers such that 1 + 2 + 3 + 4 + 5 = 20. Then the number of such distinct arrangements ( 1 , 2 , 3 , 4 , 5 ) is Answer: 7 54. Let : and : by : be respectively given by ( ) = | | + 1 and ( ) = 2 + 1. Define ( ) = max { ( ), ( )} min { ( ), ( )} if 0, if > 0. The number of points at which ( ) is not differentiable is Answer: 3 55. The value of 1 4 3 0 2 (1 2 )5 2 is Answer: 2 56. The slope of the tangent to the curve ( 5 )2 = (1 + 2 )2 at the point (1, 3) is Answer: 8 57. The largest value of the nonnegative integer for which 1 is + sin( 1) + 1 1 = lim 1 + sin( 1) 1 4 Answer: 0 (zero) 58. Let : [0, 4 ] [0, ] be defined by ( ) = cos 1 (cos ). The number of points [0, 4 ] satisfying the equation Is ( ) = 10 10 Answer: 3 59. For a point in the plane, let 1 ( ) and 2 ( ) be the distances of the point from the lines = 0 and + = 0 respectively. The area of the region consisting of all points lying in the first quadrant of the plane and satisfying 2 1 ( ) + 2 ( ) 4 , is Answer: 6 and 60. Let , , be three non-coplanar unit vectors such that the angle between every pair of them is + . If + = + , where , and are scalars, then the value of Answer: 4 2 + 2 2 + 2 2 is 3

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