FIITJEE SOLUTIONS TO JEE(ADVANCED)

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Note:For the benefit of the students, specially the aspiring ones, the question of JEE(advanced), 2014 are also given in thisbooklet. Keeping the interest of students studying in class XI, the questions based on topics from class XI have beenmarked with ‘*’, which can be attempted as a test. For this test the time allocated in Physics, Chemistry &Mathematics are 22 minutes, 35 minutes and 22 minutes respectively.FIITJEECODESOLUTIONS TO JEE(ADVANCED)-20145PAPER-1P1-14-51208625Note: Front and back cover pages are reproduced from actual paper back to back here.Time: 3 HoursMaximum Marks: 180Please read the instructions carefully. You are allotted 5 minutes specifically for this INSTRUCTIONSGeneralThis booklet is your Question Paper. Do not break the seal of this booklet before being instructed to do so by theinvigilators.The question paper CODE is printed on the left hand top corner of this sheet and on the back cover page of this booklet.Blank space and blank pages are provided in the question paper for your rough work. No additional sheets will be providedfor rough work.Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers and electronic gadget of anykind are NOT allowed inside the examination hall.Write your name and roll number in the space provided on the back cover of this booklet.Answers to the questions and personal details are to be filled on an Optical Response Sheet, which is provided separately.The ORS is a doublet of two sheets – upper and lower, having identical layout. The upper sheet is a machine-gradableObjective Response Sheet (ORS) which will be collected by the invigilator at the end of the examination. The upper sheetis designed in such a way that darkening the bubble with a ball point pen will leave an identical impression at thecorresponding place on the lower sheet. You will be allowed to take away the lower sheet at the end of the examination(see Figure-1 on the back cover page for the correct way of darkening the bubbles for valid answers).Use a black ball point pen only to darken the bubbles on the upper original sheet. Apply sufficient pressure so that theimpression is created on the lower sheet. See Figure -1 on the back cover page for appropriate way of darkening thebubbles for valid answers.DO NOT TAMPER WITH / MUTILATE THE ORS SO THIS BOOKLET.On breaking the seal of the booklet check that it contains 28 pages and all the 60 questions and corresponding answerchoices are legible. Read carefully the instruction printed at the beginning of each section.Filling the right part of the ORSThe ORS also has a CODE printed on its left and right parts.Verify that the CODE printed on the ORS (on both the left and right parts) is the same as that on the this booklet and putyour signature in the Box designated as R4.IF THE CODES DO NOT MATCH, ASK FOR A CHANGE OF THE BOOKLET / ORS AS APPLICABLE.Write your Name, Roll No. and the name of centre and sign with pen in the boxes provided on the upper sheet of ORS. Donot write any of this anywhere else. Darken the appropriate bubble UNDER each digit of your Roll No. in such way thatthe impression is created on the bottom sheet. (see example in Figure 2 on the back cover)Question Paper FormatThe question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of two sections.Section 1 contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONEOR MORE THAN ONE are correct.Section 2 contains 10 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9 (bothinclusive)Please read the last page of this booklet for rest of the instructions.FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-2PART I : PHYSICSSECTION – 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) outof which ONE or MORE THAN ONE are correct.*1.A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s-1.He is told that the air in the tube has been replaced by another gas (assume that the column remains filledwith the gas). If the minimum height at which resonance occurs is (0.350 0.005)m , the gas in the tube is(Useful information: 167RT 640 J1/ 2 mole 1/ 2 ; 140RT 590 J1/2 mole 1/ 2 . The molar masses M ingrams are given in the options. Take the values of 107 (A) Neon M 20,20 10 10 9 (C) Oxygen M 32,32 16 2.10for each gas as given there.)M 10 3 (B) Nitrogen M 28,28 5 10 17 (D) Argon M 36,36 32 At time t 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternatingcurrent I(t) I0 cos ( t), with I0 1A and 500 rad/s starts flowing in it with the initial direction shown7 in the figure. At t , the key is switched from B to D. Now onwards only A and D are connected. A6 total charge Q flows from the battery to charge the capacitor fully. If C 20 F, R 10 and the batteryis ideal with emf of 50 V, identify the correct statement(s).BDA 50 VC 20 FR 10 (A) Magnitude of the maximum charge on the capacitor before t 7 is 1 10-3C.6 7 is clockwise.6 (C) Immediately after A is connected to D, the current in R is 10 A.(D) Q 2 10 3C.(B) The current in the left part of the circuit just before t 3.A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates thatcovers 1/3 of the area of its plates, as shown in the figure. The total capacitance of thecapacitor is C while that of the portion with dielectric in between is C1. When the capacitor ischarged, the plate area covered by the dielectric gets charge Q1 and the rest of the area getscharge Q2. The electric field in the dielectric is E1 and that in the other portion is E2. Choosethe correct option/options, ignoring edge effects.EE1(A) 1 1(B) 1 E2E2 K(C)Q1 3 Q2 K(D)Q1E1Q2E2C 2 K C1KFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-3*4.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 stringis 100 ms 1. The other end of the string is vibrating in the y direction so that stationary waves are set up inthe string. The possible waveform(s) of these stationary waves is (are) x50 t x100 t(A) y(t) A sincos(B) y(t) A sincos63335 x250 t5 x(C) y(t) A sincos(D) y(t) A sincos 250 t6325.A transparent thin film of uniform thickness and refractive index n1 1.4 iscoated on the convex spherical surface of radius R at one end of a long solidglass cylinder of refractive index n2 1.5, as shown in the figure. Rays oflight parallel to the axis of the cylinder traversing through the film from airto glass get focused at distance f1 from the film, while rays of lighttraversing from glass to air get focused at distance f2 from the film. Then(A) f1 3R(B) f1 2.8 R(C) f2 2R(D) f2 1.4 Rn1n2Air6.Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise thetemperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the samematerial, 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 40K?(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.7.Two ideal batteries of emf V1 and V2 and three resistances R1, R2 and R3are connected as shown in the figure. The current in resistance R2 wouldbe zero if(A) V1 V2 and R1 R 2 R 3(B) V1 V2 and R1 2R 2 R 3(C) V1 2V2 and 2R1 2R 2 R 3(D) 2V1 V2 and 2R1 R 2 R 3V1R1R2V2R38.Let E1 (r), E 2 (r) and E 3 (r) be the respective electric fields at a distance r from a point charge Q, aninfinitely long wire with constant linear charge density , and an infinite plane with uniform surface chargedensity . If E1 (r0 ) E 2 (r0 ) E 3 (r0 ) at a given distance r0, then(A) Q 4 r02(C) E1 (r0 / 2) 2E 2 (r0 / 2)9. 2 (D) E 2 (r0 / 2) 4E 3 (r0 / 2)(B) r0 A light source, which emits two wavelengths 1 400 nm and 2 600 nm, is used in a Young’s doubleslit experiment. If recorded fringe widths for 1 and 2 are 1 and 2 and the number of fringes for themwithin a distance y on one side of the central maximum are m1 and m2, respectively, then(A) 2 1(B) m1 m2(C) From the central maximum, 3rd maximum of 2 overlaps with 5th minimum of 1(D) The angular separation of fringes for 1 is greater than 2FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-4*10.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 thatbetween the floor and the ladder is 2. The normal reaction of the wall on the ladder is N1 and that of thefloor is N2. If the ladder is about to slip, then 1mg(A) 1 0 2 0 and N2 tan 2mg(B) 1 0 2 0 and N1 tan 2 2mg(C) 1 0 2 0 and N2 1 1 2(D) 1 0 2 0 and N1 tan mg2SECTION – 2: (Only 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).11.During Searle’s experiment, zero of the Vernier scale lies between 3.20 10-2 m and 3.25 10 2 m of themain 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 m and 3.25 10 2 m of the main scale but now the 45th division of Vernier scale coincides with one ofthe main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 10 7m2. The least count of the Vernier scale is 1.0 10 5 m. The maximum percentage error in the Young’smodulus of the wire is*12.Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 withrespect to the horizontal respectively as shown in the figure. The speed of A is 100 3 ms 1. At time t 0s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocityperpendicular to the line of motion of A. If at t t0, A just escapes being hit by B, t0 in seconds isA30 *13.B60 A thermodynamic system is taken from an initial state i with internal energy Ui 100 J to the final state falong two different paths iaf and ibf, as schematically shown in the figure. The work done by the systemalong the paths af, ib and bf are Waf 200 J, Wib 50 J and Wbf 100 J respectively. The heat supplied tothe system along the path iaf, ib and bf are Qiaf , Qib and Qbf respectively. If the internal energy of thesystem in the state b is Ub 200 J and Qiaf 500 J, the ratio Qbf / Qib isafPibVFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-514.Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed ubetween the wires in the same plane at a distance X1 from one of the wires. When the wires carry current ofmagnitude 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 each other, the radius of curvature of the path isXRR2. If 0 3, the value of 1 isX1R215.To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer usesdimensional analysis and assumes that the distance depends on the mass density of the fog, intensity(power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional toS1/n. The value of n is*16.A rocket is moving in a gravity free space with a constantacceleration of 2 ms–2 along x direction (see figure). Thelength of a chamber inside the rocket is 4 m. A ball isthrown from the left end of the chamber in x directionwith a speed of 0.3 ms–1 relative to the rocket. At the sametime, another ball is thrown in x direction with a speed of0.2 ms–1 from its right end relative to the rocket. The time inseconds when the two balls hit each other isa 2 ms–20.3 ms–10.2 ms–1x4m17.A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 resistance, it2ncan be converted into a voltmeter of range 0 – 30 V. If connected to a resistance, it becomes an249ammeter of range 0 – 1.5 A. The value of n is*18.A uniform circular disc of mass 1.5 kg and radius 0.5 m isinitially at rest on a horizontal frictionless surface. Threeforces of equal magnitude F 0.5 N are appliedsimultaneously along the three sides of an equilateraltriangle XYZ with its vertices on the perimeter of the disc(see figure). One second after applying the forces, theangular speed of the disc in rad s–1 isFXOFYZF*19.A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate aboutits axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg areattached to the platform at a distance 0.25 m from the centre on its either sides alongits diameter (see figure). Each gun simultaneously fires the balls horizontally andperpendicular to the diameter in opposite directions. After leaving the platform, theballs have horizontal speed of 9 ms–1 with respect to the ground. The rotational speedof the platform in rad s–1 after the balls leave the platform is*20.Consider an elliptically shaped rail PQ in the vertical plane withOP 3 m and OQ 4 m. A block of mass 1 kg is pulled along therail from P to Q with a force of 18 N, which is always parallel toline PQ (see the figure given). Assuming no frictional losses, thekinetic energy of the block when it reaches Q is (n 10) Joules. Thevalue of n is (take acceleration due to gravity 10 ms–2)Q4m90 O3mPFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-6PART - II: CHEMISTRYSECTION – 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) outof 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*22.An ideal gas in a thermally insulated vessel at internal pressure P1, volume V1 and absolutetemperature T1 expands irreversibly against zero external pressure, as shown in the diagram. The finalinternal pressure, volume and absolute temperature of the gas are P2, V2 and T2, respectively. For thisexpansion,Pext 0Pext 0IrreversibleP2, V2, T2P1, V1, T1Thermal insulation(A) q 0(C) P2V2 P1V1(B) T2 T1(D) P2V2 P1V1 *23.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.24.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.*25.For the reaction:I ClO3 H 2SO 4 Cl HSO 4 I 2The 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.FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-7*26.The reactivity of compound Z with different halogens under appropriate conditions is given below:mono halo substituted derivative when X 2 I 2OHX2di halo substituted derivative when X 2 Br2C(CH3 )3Ztri halo substituted derivative when X 2 Cl 2The 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*27.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.28.Upon heating with Cu2S, the reagent(s) that give copper metal is/are(A) CuFeS2(B) CuO(C) Cu2O(D) CuSO4*29.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- ethylanthraquinol30.In the reaction shown below, the major product(s) formed is/areNH2acetic anhydride product s CH 2 Cl2NH2O(A)H(B)NNH2CH3HOCH3 COOHNNH2CH3CH3 COOHOOO(C)(D)HNCH3NH3 CH3 COOHOHNCH3H2 ONOOCH3OOFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-8SECTION – 2: (Only 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).31.Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi2S3 and SnS2, the total number of BLACK colouredsulphides is*32.The total number(s) of stable conformers with non-zero dipole moment for the following compound is(are)ClBrCH3BrClCH333.Consider the following list of reagents:Acidified K 2Cr2 O7 , alkaline KMnO4 ,CuSO 4 , H 2 O2 ,Cl2 ,O3 , FeCl3 , HNO3 and Na 2S2 O3 .The total number of reagents that can oxidise aqueous iodide to iodine is34.A list of species having the formula XZ4 is given below.XeF4 ,SF4 ,SiF4 , BF4 , BrF4 , Cu NH3 4 2 2 2 , FeCl4 , CoCl4 2 and PtCl 4 .Defining shape on the basis of the location of X and Z atoms, the total number of species having a squareplanar shape is35.Consider all possible isomeric ketones, including stereoisomers of MW 100. All these isomers areindependently reacted with NaBH4 (NOTE: stereoisomers are also reacted separately). The total number ofketones that give a racemic product(s) is/are*36.In an atom, the total number of electrons having quantum numbers n 4, ml 1 and ms –1/2 is*37.If the value of Avogadro number is 6.023 1023 mol–1 and the value of Boltzmann constant is1.380 10 23 JK 1 , then the number of significant digits in the calculated value of the universal gas constantis38.MX2 dissociates in M2 and X ions in an aqueous solution, with a degree of dissociation ( ) of 0.5. Theratio of the observed depression of freezing point of the aqueous solution to the value of the depression offreezing point in the absence of ionic dissociation is39.The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis ofthe peptide shown below isOHOOHONNONNOHNNNCH2HHNOHCH2OO*40.A compound H2X with molar weight of 80g is dissolved in a solvent having density of 0.4 gml –1. Assumingno change in volume upon dissolution, the molality of a 3.2 molar solution isFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-9PART - III: MATHEMATICSSECTION – 1 : (One or More than One Options Correct Type)This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out ofwhich ONE or MORE THAN ONE are correct.x41.Let f : (0, ) R be given by f (x) e 1 t t 1/ xdt, thent(A) f (x) is monotonically increasing on [1, ) 1 (C) f (x) f 0, for all x (0, ) x (B) f (x) is monotonically decreasing on (0, 1)(D) f (2x) is an odd function of x on R42.Let a R and let f : R R be given by f (x) x5 5x a, then(A) f (x) has three real roots if a 4(B) f (x) has only one real roots if a 4(C) f (x) has three real roots if a 4(D) f (x) has three real roots if 4 a 443.For every pair of continuous functions f, g : [0, 1] R such that max{ f (x) : x [0, 1]} max{g(x) : x [0, 1]}, the correct statement(s) is(are)(A) (f (c))2 3f (c) (g(c))2 3g(c) for some c [0, 1](B) (f (c))2 f (c) (g(c))2 3g(c) for some c [0, 1](C) (f (c))2 3f (c) (g(c))2 g(c) for some c [0, 1](D) (f (c))2 (g(c))2 for some c [0, 1]*44.A circle S passes through the point (0, 1) and is orthogonal to the circles (x 1)2 y2 16 and x2 y2 1.Then(A) radius of S is 8(B) radius of S is 7(C) centre of S is ( 7, 1)(D) centre of S is ( 8, 1)45. Let x , y and z be three vectors each of magnitude 2 and the angle between each pair of them is . If3 a is a non-zero vector perpendicular to x and y z and b is a non-zero vector perpendicular to y and z x , then (A) b b z z x (B) a a y y z (C) a b a y b z(D) a a y z y 46.From a point P( , , ), perpendiculars PQ and PR are drawn respectively on the lines y x, z 1 and y x, z 1. If P is such that QPR is a right angle, then the possible value(s) of is(are)(A) 2(B) 1(C) 1(D) 247.Let M be a 2 2 symmetric matrix with integer entries. Then M is invertible if(A) the first column of M is the transpose of the second row of M(B) the second row of M is the transpose of the first column of M(C) M is a diagonal matrix with non-zero entries in the main diagonal(D) the product of entries in the main diagonal of M is not the square of an integerFIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-1048.Let M and N be two 3 3 matrices such that MN NM. Further, if M N2 and M2 N4, then(A) determinant of (M2 MN2) is 0(B) there is a 3 3 non-zero matrix U such that (M2 MN2)U is the zero matrix(C) determinant of (M2 MN2) 1(D) for a 3 3 matrix U, if (M2 MN2)U equals the zero matrix then U is the zero matrix49.Let f : [a, b] [1, ) be a continuous function and let g : R R be defined as 0ifx a, x g x f t dt if a x b, a bx b a f t dt ifThen(A) g(x) is continuous but not differentiable at a(B) g(x) is differentiable on R(C) g(x) is continuous but not differentiable at b(D) g(x) is continuous and differentiable at either a or b but not both 50. Let f : , R be given by f(x) (log(sec x tan x))3. Then 2 2 (A) f (x) is an odd function(B) f (x) is a one-one function(C) f (x) is an onto function(D) f (x) is an even functionSECTION – 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 (bothinclusive).*51.Let n1 n2 n3 n4 n5 be positive integers such that n1 n2 n3 n4 n5 20. Then the number of suchdistinct arrangements (n1, n2, n3, n4, n5) is*52.Let n 2 be an integer. Take n 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 ofred and blue line segments are equal, then the value of n is53.Let f : R R and g : R R be respectively given by f (x) x 1 and g(x) x2 1. Define h : R R by max f x , g x if x 0.h x min f x , g x if x 0Then number of points at which h(x) is not differentiable is*54.Let a, b, c be positive integers such thatbis an integer. If a, b, c are in geometric progression and theaarithmetic mean of a, b, c is b 2, then the value of55.a 2 a 14isa 1 Let a , b , and c be three non-coplanar unit vectors such that the angle between every pair of them is .3 p 2 2q 2 r 2If a b b c pa qb rc , where p, q and r are scalars, then the value ofisq2FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-1156.The slope of the tangent to the curve (y x5)2 x(1 x2)2 at the point (1, 3) is157.58.The value of2 d4 x3 2 1 x 2 dx0 5 dx is 1 xx ax sin x 1 a 1 The largest value of the non-negative integer a for which lim x 1 x sin x 1 1 1is4*59.Let f : [0, 4 ] [0, ] be defined by f (x) cos 1(cos x). The number of points x [0, 4 ] satisfying the10 xequation f (x) is10*60.For a point P in the plane, let d1(P) and d2(P) be the distances of the point P from the lines x y 0 and x y 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the planeand satisfying 2 d1(P) d2(P) 4, is*****FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-12JEE(ADVANCED)-2014PAPER 1 CODE 5ANSWERSPART - I: PHYSICS1.D2.C, D3.A, D4.A, C, D5.A, C6.B, D7.A, B, D8.C9.A, B, C10.C, D11.412.513.214.315.316.217.518.219.420.5PART - II: CHEMISTRY21.A, C, D22.A, B, C23.A, B, D24.A25.A, B, D26.A, B, C27.B, D28.B, C, D29.A, B, C30.A31.632.333.734.435.536.637.438.239.140.8PART - III: MATHEMATICS41.A, C, D42.B, D43.A, D44.B, C45.A, B, C46.C47.C, D48.A, B49.A, C50.A, B, C51.752.553.354.455.456.857.258.259.360.6FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-13HINTS AND SOLUTIONSPART - I: PHYSICS1. 1 RT4 M1 RTfor gases mentioned in options A, B, C and D, work out to be 0.459 m, 0.363 m4 M0.340 m & 0.348 m respectively. As (0.350 0.005)m ; Hence correct option is D.Calculations for2.As current leads voltage by /2 in the given circuit initially, then ac voltage can be represent asV V0 sin t q CV0 sin t Q sin twhere, Q 2 10-3 C3 At t 7 /6 ; I I0 and hence current is anticlockwise.27 Current ‘i’ immediately after t is6 V 50i c 10 AR Charge flow Qfinal – Q(7 /6 ) 2 10 6CHence C & D are correct options.3.As E V/dE1/E2 1 (both parts have common potential difference)Assume C0 be the capacitance without dielectric for whole capacitor.C2Ck 0 0 C33C 2 k C1kQ1 k .Q2 24.Taking y(t) A f(x) g(t) & Applying the conditions:1; here x 3m is antinode & x 0 is node2; possible frequencies are odd multiple of fundamental frequency.v 25where, fundamental Hz4 3The correct options are A, C, D.5.For air to glass1.5 1.4 1 1.5 1.4 f1RR f1 3RFor glass to air.FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-141 1.4 1.5 1 1.4 f2 R R f2 2RV2V2V24 t1 t2RR/2R /8t1 2 min.t2 0.5 min.6.H 7.V1 R 1 (V1 V2 ) V1R 3 V2 R1R1 R 3V2 R 3 (V1 V2 ) V2 R1 V2 R 3R1 R 38.Q 24 0 r0 2 0 r0 2 0Q r r r E1 0 , E2 0 , E3 0 2 2 0 r0 2 0 r0 2 2 0 r r E1 0 2E 2 0 2 2 D d 2 1 2 1 9.10.Also m1 1 m2 2 m1 m2 D D Also 3 (600 nm) (2 5 1) 400 nm d 2d Angular width dCondition of translational equilibriumN1 2N2N2 1N1 MgmgSolving N 2 1 1 2 2 mg1 1 2Applying torque equation about corner (left) point on the floor mg cos N1 sin 1 N1 cos 21 1 2Solving tan 2 2N1 11.FLsince the experiment measures only change in the length of wire A Y 100 100Y From the observation 1 MSR 20 (LC)Y FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-15 2 MSR 45 (LC) change in lengths 25(LC)and the maximum permissible error in elongation is one LC Y(LC) 100 100 4Y25(LC)12.13.14.The relative velocity of B with respect to A is perpendicular to lineof motion of A. VB cos30 VA VB 200 m/sAnd time t0 (Relative distance) / (Relative velocity)500 5 secVB sin 30 Ub 200 J, U i 100 JProcess iafProcessW(in Joule)iaafNet300 Uf 400 JouleProcess ibfProcessW(in Joule)ib100bf200Net300Q bf 300 2Qib 150Case – IX0 VB30 U(in Joule)0200200Q(in Joule) U(in Joule)50100150Q(in Joule)150300450500Case – IIII VAX0IIPX0/3PX0/315.B1 1 0 3I 2 2 x 0 R2 R1 mvqB1 mvqB2R 1 B 2 1/3 3R 2 B1 1/9d x Sy Fz [L] [ML 3 ]x [MT 3 ]y [T 1 ]z x y 0, –3x 1, –3y –z 0FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942website: www.fiitjee.com.60

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-16 11, y , z 1331 y n n 3 x 16.Maximum displacement of the left ball from the left wall of the chamber is 2.25 cm, so the right ball has totravel almost t

JEE(ADVANCED)2014-Paper 1-CHEMISTRY-2 FIITJEE Ltd., FIITJEE House, 29 -A, Kalu Sarai, Sarvapriya Vihar, New Delhi 110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com. SECTION – 1 (One or More Than One Options Correct Type) This section contains 10 multiple choice type ques

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