2013_JEE-ADVANCED_MODEL PAPER PAPER-2. No.of Qs Sec I(Q.N : 1 5) Questions with Single Correct Choice Questions with Multiple Correct Choice

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1 PYSICS: Section 01_JEE-ADVANCED_MODEL PAPER PAPER- Question Type +Ve Marks - Ve Marks Max Marks : 5 No.of Qs Sec I(Q.N : 1 5) Questions with Single Correct Choice Sec II(Q.N : 6 11) Questions with Multiple Correct Choice Total marks Sec III(Q.N : 1 1) Matrix Match Type Questions Sec IV(Q.N : 14 18) Integer Type Questions CEMISTRY: Section Total Question Type +Ve Marks - Ve Marks No.of Qs Sec I(Q.N : 19 ) Questions with Single Correct Choice Sec II(Q.N : 4 9) Questions with Multiple Correct Choice Total marks Sec III(Q.N : 0 1) Matrix Match Type Questions Sec IV(Q.N : 6) Integer Type Questions MATEMATICS: Section Total Question Type +Ve Marks - Ve Marks No.of Qs Sec I(Q.N : 7 41) Questions with Single Correct Choice Sec II(Q.N : 4 47) Questions with Multiple Correct Choice Total marks Sec III(Q.N : 48 49) Matrix Match Type Questions Sec IV(Q.N : 50 54) Integer Type Questions Total 18 75

2 01_JEE-Advanced_ Model_Paper- PYSICS: Max.Marks:75 SECTION I Single Correct Answer Type This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1 The coordinates and potentials at different points in a region of uniform electric field are shown. Find the electric field strength in the region: 0 V (, ) 6V 'A A) iˆ 4 ˆj B) ( iˆ ˆj ) C) iˆ 4 ˆj D) iˆ ˆj (4, 0) C 6V (+, -) V. A sphere of mass M is suspended symmetrically from two wires of natural length L each and cross-sectional area A with Young s modulus Y1 and Y. The elastic potential energy of the system when it finally stops at equilibrium will be (The diagram shows the situation just after the release) : A,L A,L Y Y1 A) M g L A( Y Y ) 1 B) M g L A( Y Y ) 1 M g L C) A( Y Y ) 1 M g L( Y1 Y ) D) 8AYY 1. The gravitational field strength at point P P due to uniform solid hemisphere of mass M and radius R (as shown in R figure) is E. Then the gravitational field strength at point Q is R GM (A) E R (B) GM R E R GM (C) E R (D) GM E R Q Paper- Page

3 01_JEE-Advanced_ Model_Paper- 4. Find the reading of voltmeter across the resistance and ammeter in the circuit L C 100 A V 00V V 00V ~ 500V, 50 z V (A) 500V, 5A (B) 50V, 5A (C) 50V, 10A (D) 500V,.5A 5. A flying disc of radius r is moving with constant speed 'V 0 ' along a curve with respect to an inertial frame. Radius of curvature of the curve at the instant shown in the figure is 4r. Angular velocity of the disc about its centre perpendicular to plane V0 is constant equal to. Acceleration of point A at the instant with respect to the r inertial frame is. V 0 = 4r A V 0 w = r A) V 0 4r B) V 0 r C) V 0 r D) Zero Paper- Page

4 01_JEE-Advanced_ Model_Paper- SECTION II Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 6. Two equilateral triangles ACE and BDF have common centre O and are taken symmetrically in the same plane as shown in figure. Six point charges are placed at the vertices. Choose the correct of the following. (Given OA = L) -q A -q F O -q B E +q +q C D +q q A) Magnitude of net field at the centre O is 0 L B) Net electric potential at O is zero C) Electrostatic potential energies of charges at B and E are equal D) Electrostatic potential energies of charges at C and F are equal 7. A sphere is rolled on a rough horizontal surface. It gradually slows down and stops. The force of friction tries to A) Increase the angular velocity B) Increase the linear momentum C) Decrease the angular velocity C) Decrease the linear momentum 8. A wire shaped as a semicircle of radius a is rotating about an axis PQ with constant angular velocity 1 with the help of an external agent. A uniform magnetic field LC B exist in the space and directed into the plane of the figure (circuit part remains at rest) (A) (B) (C) (D) The rms value of current in the circuit is R Ba LC The rms value of current in the circuit is R Ba LC The maximum energy stored in the capacitor is B a 4 8R C The maximum power delivered by external agent is 4 B a 4LCR C X R B L P Q a 1 LC Paper- Page 4

5 01_JEE-Advanced_ Model_Paper- 9. A unknown solid sphere of mass m and radius r is kept on rough horizontal surface 1 with coefficient of friction as shown in the figure. An impulse J = MV 0 is applied tangentially on the sphere at an angle 7 with the horizontal as shown in the figure. (Assuming J >> Mgdt, g = 10 m/s ) R 7 = 1 J (A) The velocity of centre of mass of the sphere just after impulse applied is V 0 (B) The angular velocity of sphere just after impulse applied is 0 (C) The velocity of centre of mass of the sphere just after impulse applied is 0 V0 (D) The angular velocity of sphere just after impulse applied is R 10. In YDSE, the separation between two slits is d and wavelength of light is. The intensity of light falling on slit I is four times the intensity of light falling on slit II. Choose the correct choice. A) If d, the screen will contain only one maximum B) If d, at least one more maximum (beside central maximum) will be observed on the screen C) If the intensity of light falling on slit I is reduced so that it becomes equal to that of slit II, the intensities of the observed dark and bright fringes will increases D) if the intensity of light falling on slit II is increased so that it become equal to that of slit I, the intensities of the observed dark and bright fringes will increase 11. A particle of mass m and charge q moving with a velocity V enters region II normal to the boundary as shown in figure. Region II has a uniform magnetic field B perpendicular to the plane of paper and length of region II is. Choose the correct choice Region I v Region II x x x x x x x x x x x x x x x x x x x x Region III B q A) Particle enters region III only if its velocity v m B q B) Particle enters region III only if its velocity v m B q C) Path length of particle in region II is maximum when v m D) Time spent in region II is same for any velocity as long as particle returns to region I Paper- Page 5 V R 4V 5

6 01_JEE-Advanced_ Model_Paper- SECTION III ( MATRIX MATC TYPE) This section contains questions. Each questions contains statements given in columns which have to be matched. The statements in Column I or labeled choices A, B, C and D, while the statements Column- II are labeled p,q,r,s & t. 1. For the situation shown in Fig, match the entries of Column I with entries of Column II. q q Column I Column II A) If we displace the inside charge p) distribution of charge on inner surface of conductor is uniform. B) If we displace the outside charge q) distribution of charge on inner surface of keeping the inside charge at center. conductor is non-uniform. C) If both the charges are displaced. r) distribution of charge on outer surface of conductor is uniform. D) If outside charge is not present and s) distribution of charge on outer surface of inside charge is at center, conductor is non-uniform. 1. Match the standing waves formed in column II due to plane progressive SM waves in Column I Column-I Column-II A) Incident wave is y Asin kx wt p) y ACos kxsin wt B) Incident wave is y Acos kx wt q) y ASin kx Sin wt C) x 0 is rigid support r) y A Sin kx Cos wt D) x 0 is flexible support s) y ACos kxcos wt Paper- Page 6

7 01_JEE-Advanced_ Model_Paper- SECTION IV Integer Answer Type This section contains 5 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive). 14. A simple LR circuit is connected to a battery at time t = 0. The energy stored in the nl inductor reaches half its maximum value at time l n R 1 then the value of n is 15. A rod of length l with uniformly distributed charge Q is rotated about one end with a n fql constant frequency f. Its magnetic moment is. What is the value of n 16. Two wires AO and OC carry equal currents I as shown in figure. One end of both the wires extends to infinity. Angle AOC is. A P O > C The magnitude of magnetic field at a point P on the bisector of these two wires at a 1 cos P0I distance r from point O is then what is value of P 4 r sin 17. A conducting wire bent in the form of a parabola y x carries a current I = A as shown in figure. This wire is placed in a uniform magnetic field B 4Kˆ Tesla. The magnitude of magnetic force on the wire is (in Newton) is 8x then what is the value of x y(m) (0, 0) A x(m) B 18. A circular current loop of radius a is placed in a radial field B as shown. The net force acting on the loop carrying current I is x BaI sin. Then what is the value of x B I a Paper- Page 7

8 01_JEE-Advanced_ Model_Paper- CEMISTRY: Max.Marks :75 SECTION I Single Correct Answer Type This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 19. The product of the following I and II sequence are related as (I) (i) /Pd/CaCO (ii) Br /CCl 4? C C C C (II) (i) Br (1 eq.)/ CCl 4 (ii) / Pt;5 0 C A) Diastereomers B)Identical C) Enantiomers D) Geometrical isomers 0. An aldehyde, ( P) which does not undergo self aldol condensation gives benzaldehyde and two moles of ( Q) on ozonolysis. Compound ( Q), on oxidation with silver ions gives oxalic acid. The structure of ( P) is given as? A) B) C) D) 1. The hybridizations of Ni atom in NiCl, Ni CN & Ni CO are respectively A) sp, sp & dsp B) sp, dsp & sp C) dsp, dsp & sp D) dsp, sp & dsp. Which of the following sequences the increasing order of polarizing power of the cations K, Ca, Mg, Be? A) Be K Ca Mg B) K Be Ca Mg C) K Ca Mg Be C) Mg K Ca Be ) When an electron makes a transition from (n+1) th state to n th state, the frequency of emitted radiations is related to n according to (n >> 1) A) CRZ B) n CRZ C) n CRZ CRZ D) 4 n n Paper- Page 8

9 01_JEE-Advanced_ Model_Paper- SECTION II Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 4. The correct statement(s) about the following sugars X and Y is/are C O O O O O O X C O O O O C O C O O O O O O C O O O A) X is a non-reducing sugar and Y is a reducing sugar B) Both X and Y shows mutarotation. C) X does not show mutarotation and Y shows mutarotation. D) X show mutarotation and Y does not shows mutarotation. 5. In a hydrogen like atom, electron is in nd excited state, the binding energy of fourth state of this atom is 1.6 ev, then A) A 5 ev photon can set free the electron from the second excited state of this sample. (Y) B) different types of photon will be observed if electrons make transition up to ground state from the second excited state C) If ev photon is used then K.E. of the ejected electron is 1 ev. D) nd line of balmer series of this sample has same energy value as 1 st excitation energy of -atoms 6. The following rearrangements involve the formation of isocyanate intermediate A) offmann rearrangement B) Curtius rearrangement C) Wolff rearrangement D) Lossen rearrangement 7. Which of the following statements are true in case of attacked electrodes (active electrodes) in Electrolytic cells A) Metal dissolves at anode i.e. reduction B) Metal dissolves at anode. i.e. oxidation C) Metal ion deposit at cathode i.e. reduction D) There is change in conc. of solution during electrolysis. O O Paper- Page 9

10 01_JEE-Advanced_ Model_Paper- 8. Which of the following compounds undergo solvolysis (SN 1 ) with methanol and heat Br Br Br A) C B) C C) C D) C Br 9. The temperature coefficient of the e.m.f of cell, de dt p is given A) n F S B) S nf C) S nft D) nfe SECTION III ( MATRIX MATC TYPE) This section contains questions. Each questions contains statements given in columns which have to be matched. The statements in Column I or labeled choices A, B, C and D, while the statements Column- II are labeled p,q,r, s & t. 0. Match each of the compounds given Column I with the reaction (s), that they can undergo, given in Column II. Column-I Column-II Br a) O O p) Nucleophilic substitution b) CO q) Elimination c) Br O r) Nucleophilic addition d) NO s) Esterification with aacetic anhydride t) Dehydrogenation Paper- Page 10

11 01_JEE-Advanced_ Model_Paper Match the following : Column I Column II Fe CN A) 4 6 p) paramagnetic B) Fe O 6 q) Diamagnetic C) Cu N 6 D) NiCN 4 6 r) Inner orbital complex s) Outer orbital complex SECTION IV Integer Answer Type This section contains 5 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive).. The number of P-O-P bonds in PO 4 10 is. What is the number of stereoisomer/s of major product formed in the following reaction? Ph C C C Cl alc.ko excess Cl? C Cl Ph 4. For a gas A x the ratio of specific heats is found to be 1.66 then x is 5. Bond order ratio of NO and O is 6. ow many moles of acetyl chloride are used per mole of sucrose for esterification Paper- Page 11

12 01_JEE-Advanced_ Model_Paper- MATEMATICS: Max.Marks :75 SECTION I Single Correct Answer Type This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 7) If P is point inside the equilateral triangle ABC such that PA = 1 cm, PB cm and PC cm. Then the side of the triangle ABC (in cm) is A) 6 B) 6 C) 6 D) 6 8) A circle of radius 6 units is having arc lengths,5, 4 in first, second and third quadrants respectively. Then centre of the circle is A), 1 B), 1 C), 1 D), 1 9) ABCD is a square of unit side. It is folded along the diagonal AC, so that the plane ABC is perpendicular to the plane ACD. The shortest distance between AB and CD is A) B) 1 C) D) 40) If the equation 4sin x.cos x a sin x cos x has no solution then the 6 range of a is A) a B) a C) a 0, D) a,0 41. Four identical oranges and six distinct apples (each a different variety) are distributed randomly into five distinct boxes. The probability that each box gets a total of two objects is A) B) C) 4750 D) Paper- Page 1

13 01_JEE-Advanced_ Model_Paper- SECTION II Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 4. Let f x be a real valued function defined by min imumf t : t x, x,0 f x x x and g x then max imumf t : 0 t x, x 0, A) g(x) is not continuous at x = 0 B) g(x) is not derivable at x = 0, C) Number of integral ciritical points of g(x) is 4 D) Absolute maximum of g(x) is n 4) If three numbers are chosen randomly from the set 1,,,... without replacement, then the probability that they form an increasing geometric progression is n N, n A) if n is even B) if n is odd n n n n C) if n is even D) if n is odd n 1 n 1 44 If α = x1 x x and β = y1 y y be two three digits numbers, the number of pairs of α and β can be formed so that α can be subtracted from β without borrowing is A)!10!10! B) C).5.11 D) If f - x =f + x and f 4- x = f 4+ x for all x and 0 f xdx = 5, then 50 0 f xdx is equal to f x is a function for which A) 15 B) f xdx C) f xdx D) -4 1 f x dx 46 Let unit vectors a and b are perpendicular and unit vector c be inclined at an angle to both a and b. If c a b a b, then cos A) B) 1 C) D) a x ab ac ab b x bc ac bc c x is divisible by A) x B) x C) x D) x 4 Paper- Page 1

14 01_JEE-Advanced_ Model_Paper- SECTION III ( MATRIX MATC TYPE) This section contains questions. Each questions contains statements given in columns which have to be matched. The statements in Column I or labeled choices A, B, C and D, while the statements Column- II are labeled p,q,r, s & t. 48. Let a, b, c and d be four real numbers satisfying the system of equations a b 8, ab c d, ad bc 8 and cd 1. Now match the following Column I Column II A) a b c d equals p) 15 B) ab cd equals q) 16 C) ac bd equals r) 7 D) ab equals s) Column-I Column-II A. The minimum value of ab if roots of the equation p. 4 x ax bx 0 are positive, is B. The number of divisors of the form 1 6 N of the q. number 500 are C. The number of quadrilaterals formed in an octagon having r. 1 two adjacent sides common with the polygon are D. The number of solutions of the equation x where [.] denotes GIF, x 0,6 are cos tan x, s. 18 Paper- Page 14

15 01_JEE-Advanced_ Model_Paper- SECTION IV Integer Answer Type This section contains 5 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive). 50) The planes px 4y z 0, y z 1 0,x qz 0 meet on a line and f a is minimum value of the function psin q cos a then the value of f 6 is ( where [. ] is g.i.f.) 51) Let be a regular hexagon, with two consecutive vertices (0, 0) and (1, 0). If C i,i 1to6 are circles having centres at vertices of and each circle touches its adjacent circles and P (x,y) is a point on the circle of maximum area which touches all C i 's,i 1to6, then the largest possible value that x y can have is. x cos 5) If 1 cos x 6 dx k and dx mk 1 x 6 x then m is 0 6 5) P(x) is a 4 th degree polynomial and has extreme values at x = 1,. If P x lim1 x0 x then the value of P () is 54) Consider the equation x y x y 0, where. denotes Greatest integer function. Number of the points of intersection between all the possible lines on which the non-integral solutions of the given equation lies, is Paper- Page 15

JEE-ADVANCED MODEL PAPER PAPER-2. No.of Qs Sec I(Q.N : 1 5) Questions with Single Correct Choice Questions with Multiple Correct Choice

JEE-ADVANCED MODEL PAPER PAPER-2. No.of Qs Sec I(Q.N : 1 5) Questions with Single Correct Choice Questions with Multiple Correct Choice PYSICS: Section JEE-ADVANCED MDEL PAPER PAPER- Question Type +Ve Marks - Ve Marks Max Marks : 5 No.of Qs Sec I(Q.N : 1 5) Questions with Single Correct Choice -1 5 15 Sec II(Q.N : 6 11) Questions with