JEE(Advanced) PAPER - II

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1 JEE(Advanced) MDEL PAPER Time : Hrs JEE(Advanced) PAPER - II Max. Marks : 40 PART I : CHEMISTRY SECTIN I (Total Marks:1) (Single answer type) This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which NLY NE is correct. Each correct answer carries Marks. Each wrong answer carries -1 mark. 1. When a certain photoelectric substance was exposed to light with kinetic energy twice when a substance was exposed to substance is A) 10 /s B) 4 10 /s C) ν= / s photoelectrons had ν=.0 10 / s. The threshold ν of photoelectric 10 /s D) 6 10 /s. Which of the following is incorrect statement? A) Ketones are more polar than aldehydes B) Ethers are more volatile than alcohols C) Boiling point of alcohols is more than water D) Alkynes are more reactive than alkenes in nucleophilic addition reaction. Peroxide linkage does not exist in A) HS 5 B) Cr 5 C) Ba D) Mn 4. A metal X on heating in nitrogen gas gives compound Y. Y on treatment with H gives a colourless gas which when passed through CuS 4 solution gives a blue colour. The metal X is A) Na B) K C) Mg D) Zn SECTIN II (Total Marks:0) (Multiple correct answer(s) type) This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which NE or MRE may be correct. Each correct answer carries 4 Marks. Each wrong answer carries -1 mark. 5. Which of the following will not show tautomerism? CH A) B) C) D) 6. Which of the following statements is/are correct? C H Pb is not an organometallic compound A) ( 5) 4 B) ( ) K Pt en Cl gives white ppt. with AgN NiCl, V, Mn have tetrahedral geometry C) [ ] D) Co( NH ) ( N ) has geometrical isomers. 7. Which of the following has spin multiplicity equal to 6? A) Fe + B) Co + D) Fe + D) Mn + 8. Which of the following is/are correct? A) Dipole moment of C is equal to CS B) Hybridization of central nitrogen in N is sp C) Dipole moment of C is more than CS D) Dipole moment of BF is less than NF

2 9. Carnallite on electrolysis gives A) K B) Mg C) Cl D) H SECTIN III (Total Marks:16) (Matrix-Match type) 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 matching with NE or MRE 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 the particular question, against statement B, darken the bubbles corresponding to q and r in the RS. Each correct matching carries Marks. There is no negative marking. 10. Match the following: A) K, specific conductance P) Increases with dilution B) Λ m, molar conductance Q) C) α, degree of dissociation R) Decreases with dilution I Increases with increasing the distance between parallel plates D) Resistance S) Decreases with increase in concentration of electrolyte T) Λm α Λ 11. Match the following: I A) Nitrobenzene azobenzene P) LiAlH 4 B) Aniline phenyl isocyanide Q) NaN + HCl + CuCl C) Aniline chlorobenzne R) CHCl m + KH D) Ethylamine ethanol S) NaN + HCl( aq) T) Zn + NaH + CHH SECTIN IV (Total Marks:) (Integer Answer type) This section contains 8 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the RS. Each correct answer carries 4 Marks. Each wrong answer carries -1 mark. 1. When 1.8 gm of the hydrate CaCr 4.xH was heated at 00 C, gm of anhydrous CaCr 4 was obtained. The value of x is 1. Consider a reaction ax + by Products. When concentration of both the reactants X and Y is doubled, the rate increases by 8 times. However, when concentration of X is doubled keeping the concentration of Y fixed, the rate is doubled. The overall order of the reaction is 14. The total number of α and β particles emitted in the nuclear reaction A B is. The coordination number of each cation in alums is 16. When pure AgCl ( s) is added to 0.01M AgN and 0.05 M KCl then the ratio of Cl ion conc. to the Ag + ion conc. in the second solution will be 17. For the reaction NCl( g) N( g) + Cl( g), Then the value a is 6 KC = 10 L/mole at 47 C. K P is nearly a 10 4.

3 4 18. Liquid ammonia ionizes to a slight extent. At 75 C its self ionization constant is 10. The number of amide ions present per cm of pure liquid ammonia is The ratio of coordination number of cation to anion in ZnS is PART II : MATHEMATICS SECTIN I (Total Marks:1) (Single answer type) This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which NLY NE is correct. Each correct answer carries Marks. Each wrong answer carries -1 mark. ASSERTIN REASNING 0. Let f(x) = x ax + (a + a ). The roots of the equation f(x) = 0 are distinct and both are less than. Then St-1 : < a <. St- : f() > 0 and discriminant of f(x) = 0 is positive A) Both the statements are true and St- is the correct explanation of St-1 B) Both the statements are true and St- is not the correct explanation of St-I C) St -1 is true and St- is false D) St-1 is false and St- is true 1 1. Given S = , where [x] denotes greatest integer less than or equal to x. Then St-1: The value of S is. 1 k St-: If k is an integer, takes only two possible values for 0 k 99. A) Both the statements are true and St- is the correct explanation of St-1 B) Both the statements are true and St- is not the correct explanation of St-I C) St -1 is true and St- is false D) St-1 is false and St- is true. Given the point P(6, 10) and the ellipse x + 4y = 5. St-1 : The point P is nearest to the ellipse at (, ). St- : Normal to the ellipse at (, ) is 8x y = 18. A) Both the statements are true and St- is the correct explanation of St-1 B) Both the statements are true and St- is not the correct explanation of St-I C) St -1 is true and St- is false D) St-1 is false and St- is true. The point P is one extremity of the latus rectum of a parabola and PT, PN are the tangent and normal to the parabola drawn at P. If S is the focus of the parabola. Then St-1 : SPT = SPN. St- : In a parabola focal distance of any point bisects the angle between the tangent and normal at the point. A) Both the statements are true and St- is the correct explanation of St-1 B) Both the statements are true and St- is not the correct explanation of St-I C) St -1 is true and St- is false D) St-1 is false and St- is true SECTIN II (Total Marks:0) (Multiple correct answer(s) type) This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which NE or MRE may be correct. Each correct answer carries 4 Marks. Each wrong answer carries -1 mark. 4. The centre of the largest circle passing through (1, 1), (, ) and lying in the first quadrant is A) (, 0) B) (, 1) C) 5 1 D) (1, ), 5. The solution of the differential equation dy + ytanx = sinx passing through (π/, 0) has dx A) a local minimum -1 B) a local maximum 1/8 C) a global minimum - D) fundamental period π 6. If A = a b c, abc = 1 and A T is the inverse of A, then a + b + c is b c a c a b

4 A) 0 B) C) D) 4 7. Let f(x) = x[x] for 0 x < = ( x 1 ) [x] for x < and let g(x) = f o f(x) then A) Domain of g(x) is 5 0, B) g(x) is continuous at x = C) g(x) is differentiable at x = D) g(x) has a local minimum at x =. 8. If ω is a complex cube root of unity such that (aω + b + cω) + (aω + b + cω ) = 0 where a, b, c are real, then it is possible that A) a, c, b are in A.P B) The line ax + by + c = 0 passes through (1, ) C) The equation 6ax bx c = 0 has a root in (0, 1). D) none of these. SECTIN III (Total Marks:16) (Matrix-Match type) 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 matching with NE or MRE 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 the particular question, against statement B, darken the bubbles corresponding to q and r in the RS. Each correct matching carries Marks. There is no negative marking. 9. In triangle ABC, if C = Sin -1 (4/5) + Sin -1 (5/1) + Sin -1 (16/65) I A) and cot A, cot B are the roots of the equation px + qx + r = 0 P) (8, 9) B) C) D) then the line px + qy + r = 0 passes through The image of the point A(, 4) with respect to the line x y + 10 = 0 is B and the image of B with respect to x y + 1 = 0 is C. Then the circumcentre of triangle ABC is Normals are drawn from the point (, 6) to the hyperbola xy = 1 and (x i, y i ), i = 1,,, 4 be the feet of the co-normal points. If the algebric sum of perpendicular lengths drawn from (x i, y i ), on to a variable line vanishes, then the line passes through 4 + sinx + a sinx + b cosx If the function f(x) = when x # 0, is x continuous at x = 0, then the order pair (b/a, f(0) ) is equal to Q) ( 1, 1) R) (, ) S) vertex of the conic z + 1 i = Im z 0. A) B) C) D) 1 x 1 x Cos + Tan 1+ x 1 x dx is equal to x 1+ e 1/ 1/ If A ( 1 /, 0), B ( /, 0) and C ( 5 /, 0), the area of the region(in square units) of the point P satisfying maximum {PA + PB, PB + PC} <, is If f(x) sec x dx = f (x) secx + c then f(6x) is a periodic function with fundamental period If the latus rectum of the hyperbola x tan θ y sec θ = 1 is 1/ and 0 < θ < π then θ can be P) Q) π/ R) π/1 I S) π/ T) 5π/1 π 4 SECTIN IV (Total Marks:) (Integer Answer type)

5 This section contains 8 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the RS. Each correct answer carries 4 Marks. Each wrong answer carries -1 mark. 1. For the series 1,,,.. K 1, K, the A.M. and G.M. of the first and the last number exists in the given series. If K is a three digit number, then find the number of values of K.. If d ( sec x) is equal to + tan x k + cosx ( ) + c, then find k 1+ cosx. Find the value of cosec π 4π 8π + cosec + cosec If ( C 0 ) ( C 0 ) + ( C 1) ( C 1) + + ( C 50 ) ( 00 ) integer n r. C = n C r then find the value of the 5. Find the shortest distance between any two edges of the tetrahedron formed by the planes x + y = 0; y + z = 0; z + x = 0 and x + y + z = Let A = {1,,, 4, 5, 6}. Let the number of bijective functions from A A in which at least three elements have self image be P and let Q be the number of non increasing functions from A A. Then find the integral part of Q/P 7. A plane is parallel to the two vectors iˆ + ˆj + kˆ and î and another plane is parallel to two other vectors iˆ + ˆj and iˆ kˆ. If the acute angle between iˆ ˆj and the line of inter section of the planes is θ, find [tanθ], where [ ] denotes greatest integer function. 8. In an examination an examinee either guesses or copies or knows the answer to a numerical answer question, whose answer is a digit from 1 to 9. The chance that he makes a guess or copies is, each equal to the probability of getting the same number when two identical dies are rolled. The probability that he answers correctly given that he copied it is 1/8. If P is the probability that he knew the answer to the question, given that he answered it correctly, then find 50P 7. PART III : PHYSICS SECTIN I (Total Marks:1) (Single answer type) This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which NLY NE is correct. Each correct answer carries Marks. Each wrong answer carries -1 mark. 9. m g The dimensional formula of the quantity Q B R where m is mass, g gravitational field, B magnetic field, R Radius, Q charge, is A) M 0 L 0 T 0 B) M L -1 T - C) M -1 LT - D) M 0 L 0 T 40. Two transverse waves traveling along a string are describedd by y = y 0 cos (kx ωt) and y = y 0 sin(ωt Y kx + π/). The phase difference between the two waves at any point x on the string is string A) π/ B) π/ C) π/ D) 5π/6 X 41. The figure shows a disc of radius R rotating about centre with a uniform angular velocity ω 0 rad/s. P and Q are two points on ω 0 P Q the circumference of the disc. The acceleration of P with 90 respect to Q is o A) zero B) Rω 0 C) Rω 0 D) Rω 0 4. Half life of a radioactive substance is 4 days. The probability that a nucleus will decay in two half lies is

6 A) 1 B) /4 C) 1/ D) 1/4 SECTIN II (Total Marks:0) (Multiple correct answer(s) type) This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which NE or MRE may be correct. Each correct answer carries 4 Marks. Each wrong answer carries -1 mark. 4. Two bodies A and B have thermal emissivities 0.01 and 0.81 respectively. The outer surface areas of the two bodies are equal. The bodies emit total radiant power at the same rate. The wavelength λ B for maximum spectral radiancy in B is shifted from the wavelength for maximum spectral radiancy in A by 1.00 µm. The temperature of A is 580 K. A) The temperature of B is 194 K B) λ B = 1.5 µm C) The temperature of B is 1160 K D) λ B =.0 µm 44. A disc of mass M and radius R rolls on a horizontal surface. At the instant shown, the velocity of point P is m/s. R = 0.5 m M = kg Q R P 0 o m/s A) Angular velocity of the body is rad/s clockwise 1 B) The instantaneous centre is at a distance m vertically below. C) The velocity of the centre of the disc is 1.5 m/s. D) The velocity of point Q is m/s. 45. A flat coil of n turns, area A and resistance R is placed in a uniform magnetic field B 0 kˆ. The coil is rotated about its diameter by an angle θ and charge Q flows through it. A) θ = π, Q = 0 B) θ = π, Q = 0 C) θ = π/, Q = B 0 An/R D) θ = π, Q = B 0 An/R Y B X 46. In the LCR ac circuit shown, the voltage across the inductance L is V. A) The supply voltage is 5V B) The voltage across the resistor is V C) The supply frequency ω = LC D) The power supplied to the circuit is 4V /R V S ω R X C = R X L = R/ 47. A particle moves along X-axis according to equation x = 4 t 9t + where t is time x X A) Direction of motion remains constant B) In the time interval 0 < t <, the speed of the particle decreases C) In the time interval t >, the speed of the particle increases D) The initial acceleration of the particle is zero SECTIN III (Total Marks:16) (Matrix-Match type) 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 matching with NE or MRE 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 the particular question, against statement B, darken the bubbles corresponding to q and r in the RS. Each correct matching carries Marks. There is no negative marking.

7 48. An object AB is placed on the principal axis in front of a convex mirror of radius of curvature 50 cm. Assume paraxial rays for image formation. B A 0 cm I A) First image by refraction through the glass slab P) Erect with respect to AB 6 cm Glass slab µ = cm B) Image by mirror Q) Inverted with respect to AB C) Final image of the object R) + / D) Magnification of the final image S) + 1 / T) The switch S is closed for a long time and the RC circuit carries a steady current. Let C 1 =.0 µf, C = 6.0 µf, R 1 = 4.0 kω, R = 7.0 kω. The power dissipated in R is.8 W V 0 C 1 R S R 1 C I A) The power dissipated R 1 is watt P) 1.6 B) The charge on capacitor C 1 in µc Q) 1.8 C) The charge on capacitor C in µc R) 40 D) Long time after switch S is opened, the charge on C 1 in µc S) 660 T) 840 SECTIN IV (Total Marks:) (Integer Answer type) This section contains 8 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be darkened in the RS. Each correct answer carries 4 Marks. Each wrong answer carries -1 mark. 50. A diatomic ideal gas undergoes a cyclic process 11 shown on pressure P, temperature T diagram. The ln 4 efficiency of the cycle is. Find the value of n. n ρ 0 ρ ρ 0 1 T 0 T 0 T 51. K α X-ray emitted by an atom (Z = 11) is λ. Find the atomic number of the atom that emits K α X-ray of wavelength 4λ. 5. Light from a discharge tube containing hydrogen atoms falls on sodium surface. The kinetic energy of the fastest photoelectrons emitted from sodium is 0.7eV. The work function for sodium is 1.8eV. The photons emitted from hydrogen involves transition from n to. Find the value of n. 5. The coherent sources of light S 1 and S are placed at (0, 0) and (0, λ). Interference is observed by a detector D placed on X-axis. Find the number of minima observed as D is moved from x = 0 to x =. (λ = wavelength of light). S S 1 Y D X

8 54. A short dipole is oriented along x-axis such that direction of dipole moment is along positive x-axis. It is observed that the magnitude of electric field and electric potential are equal at a point A, r = x m from the centre of the dipole as shown. The value of θ = 45. Find the value of x. Y θ r A X 55. A voltmeter of resistance R 1 and an ammeter of resistance R are connected in series across a battery of negligible internal resistance (fig 1) when a resistance R is connected in V A R 1 R Fig. 1 V R Fig. parallel to voltmeter, the ammeter reading becomes thrice and voltmeter reading becomes one third. (fig ). Then R = nr/. Find the value of n. 56. The lateral magnification of an object placed in front of a convex lens is +. The focal length of the lens is m. Find the distance (in m) by which the object should be moved to obtain a magnification of. A 57. A charged particle q enters a region of uniform magnetic field B. (into the page) as shown in figure and is deflected a distance d along y axis after traveling a distance a along x-axis. Find the magnitude of momentum of the particle in kg-m/s(a = m, d = 4m, qb = 0. SI units) y v a B d x KEY CHEMISTRY 1. A. C. D 4. C 5. AD 6. CD 7. CD 8. ABD 9. BC 10. A-R; B-P,S; C-P,S,T; D-Q,R 11. A-P,T; B-R, C-Q, D-S MATHEMATICS 0. D 1. A. A. C 4. BD 5. ABCD 6. BD 7. AB 8. ABC 9. A QS,B P,C P,D R; 0. A S;B P;C Q;D RT; PHYSICS 9. B 40. D 41. D 4. B 4. A, B 44. A,B,C,D 45. B,C 46. A,B,D 47. B,C,D 48. A-P; B-P; C-P; D-S 49. A-P; B-R; C-T; D-S

JEE(Advanced) 2017 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 21 st MAY, 2017)

JEE(Advanced) 2017 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 21 st MAY, 2017) JEE(Advanced) 17/Paper-/Code-9 JEE(Advanced) 17 TEST PAPE WITH SOLUTION (HELD ON SUNDAY 1 st MAY, 17) PAT-I : PHYSICS SECTION I : (Maximum Marks : 1) This section contains SEVEN questions. Each question