VIEWS: 2 PAGES: 13 CATEGORY: High School POSTED ON: 9/14/2012 Public Domain
Today’s Mathiitians..... Tomorrow’s IITians. IIT-JEE 2004 Screening Question Paper PHYSICS 1. White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains A ir G reen (a) yellow, orange, red G lass (b) violet, indigo, blue W h ite (c) all colours (d) all colours except green 2. Liquid oxygen at 50 K is heated to 300 K at constant pressure of 1 atm. The rate of heating is constant. Which of the following graphs represents the variation of temperature with time? T em p . T em p . T em p . T em p . (a) T im e (b) T im e (c) T im e (d) T im e 3. A ray of light is incident on an equilateral glass prism placed on a horizontal Q R table. For minimum deviation which of the following is true? S P (a) PQ is horizontal (b) QR is horizontal (c) RS is horizontal (d) Either PQ or RS is horizontal 4. An ideal gas expands isothermally from a volume V1 to V2 and then compressed to original volume V1 adiabatically. Initial pressure is P1 and final pressure is P3. The total work done is W. Then (a) P3 > P1, W > 0 (b) P3 < P1, W < 0 (c) P3 > P1, W < 0 (d) P3 = P1, W = 0 5. A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected k Q µs to the wall with the help of a spring of spring constant k as shown in the figure. µ s is the coefficient of friction between P P S m o oth and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is kA (a) kA (b) (c) zero (d) µ s mg 2 6. After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample in dps is (a) 6000 (b) 9000 (c) 3000 (d) 24000 7. The energy of a photon is equal to the kinetic energy of a proton. The energy of the photon is E. Let λ1 be the de-Broglie wavelength of the proton and λ 2 be the wavelength of the photon. The λ1 ratio is proportional to λ2 (a) E0 (b) E 1/2 (c) E-1 (d) E-2 Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #1# 8. A closed organ pipe of length L and an open organ pipe contain gases of densities ρ1 and ρ 2 respectively. The compressibility of gases are equal in both the pipes. Both pipes are vibrating in their first overtone with same frequency. The length of the open organ pipe is L 4L 4L ρ1 4L ρ2 (a) (b) (c) 3 ρ2 (d) 3 ρ1 3 3 αZ α − kθ 9. In the relation P = e β P is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be (a) [M0L2T0] (b) [M1L2T1] (c) [M1L0T-1] (d) [M0L2T-1] 10. A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U(0) = 0, the graph of U(x) versus x will be (where U is the potential energy function) u(x ) u(x) u(x ) u (x ) (a) x (b) x (c) x (d) x 11. Consider the charge configuration and a spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface, the q2 + q1 electric field will be due to (a) q2 (b) only the positive charges -q 1 (c) all the charges (d) +q1 and -q1 12. The variation of induced emf ( ε ) with time (t) in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as ε ε ε ε (a) (b) t (c) (d) t t t 13. Six equal resistances are connected between points P, Q and R as P shown in the figure. The net resistance will be maximum between (a) P and Q (b) Q and R (c) P and R (d) any two points Q R 14. Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at P Q O is double the electric field when only one positive charge of same magnitude is placed at R. Which of the following arrangements of charges is possible for O R U P, Q, R, S, T and U respectively? (a) +, -, +, -, -, + (b) +, -, +, -, +, - (c) +, +, -, +, -, - (d) -, +, +, -, +, - T S Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #2# 15. A source of sound of frequency 600 Hz is placed inside water. The speed of sound in water is 1500 m/s and in air it is 300 m/s. The frequency of sound recorded by an observer who is standing in air is (a) 200 Hz (b) 3000 Hz (c) 120 Hz (d) 600 Hz 16. A point object is placed at the centre of a glass sphere of radius 6 cm and refractive index 1.5. The distance of the virtual image from the surface of the sphere is (a) 2 cm (b) 4 cm (c) 6 cm (d) 12 cm 17. In a YDSE bi-chromatic light of wavelengths 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distance between the plane of the slits and the screen is 1 m. The minimum distance between two successive regions of complete darkness is (a) 4 mm (b) 5.6 mm (c) 14 mm (d) 28 mm 18. A particle starts from rest. Its acceleration ( α ) versus time (t) is as shown α in the figure. The maximum speed of the particle will be 1 0m /s2 (a) 110 m/s (b) 55 m/s (c) 550 m/s (d) 660 m/s 11 t(s) 19. Two identical conducting rods are first connected independently to two vessels, one containing water at 1000C and the other containing ice at 00C. In the second case, the rods are joined end to end and connected to the same vessels. Let q1 and q2 g/s be the rate of melting of ice in the two cases q1 respectively. The ratio is q2 1 2 4 1 (a) (b) (c) (d) 2 1 1 4 20. Three discs, A, B and C having radii 2m, 4m and 6m respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm respectively. The power radiated by them are QA, QB and QC respectively (a) QA is maximum (b) QB is maximum (c) QC is maximum (d) QA = QB = QC P h o to 21. The figure shows the variation of photocurrent with anode cu ren t potential for a photo-sensitive surface for three different radiations. Let Ia, Ib and Ic be the intensities and fa, fb and c a fc be the frequencies for the curves a, b and c respectively b (a) fa = fb and Ia ≠ Ib (b) fa = fc and Ia = Ic (c) fa = fb and Ia = Ib (d) fb = fc and Ib = Ic O A node p o ten tial 22. A disc is rolling (without slipping) on a horizontal surface C is its centre and Q and P are two points equidistant from C. Let Vp,Vq and Vc be the magnitude of velocities of points P, Q and C respectively, then C Q (a) VQ > VC > VP (b) VQ < VC < VP P 1 (c) VQ = VP, VC = VP (d) VQ < VC > VP 2 23. An electron moving with a speed u along the positive x-axis y × × × × r ˆ at y = 0 enters a region of uniform magnetic field B = −B0 k × × × × which exists to the right of y-axis. The electron exits from e- u × × × × the region after some time with the speed v at ordinate y, then × × × × x (a) v > u, y < 0 (b) v = u, y > 0 × × × × (c) v > u, y > 0 (d) v = u, y < 0 Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #3# 24. A wire has a mass 0.3 ± 0.003 g, radius 0.5 ± 0.005 mm and length 6 ± 0.06 cm. The maximum percentage error in the measurement of its density is (a) 1 (b) 2 (c) 3 (d) 4 25. A small block slides without friction down an inclined plane starting from rest. Let sn be the distance sn travelled from time t = n - 1 to t = n. Then is s n +1 2n − 1 2n + 1 2n − 1 2n (a) (b) (c) (d) 2n 2n − 1 2n + 1 2n + 1 26. A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is K K (a) 2K (b) (c) (d) 4K 2 4 27. In an RC circuit while charging, the graph of ln I versus time is as ln I shown by the dotted line in the adjoining diagram where I is the current. S When the value of the resistance is doubled, which of the solid curves best represents the variation of ln I versus time? R (a) P (b) Q Q (c) R (d) S P t B C D 28. For the post office box arrangement to determine the value of unknown resistance, the unknown resistance should be connected between (a) B and C (b) C and D (c) A and D (d) B1 and C1 A B1 C1 Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #4# IIT - JEE 2004 PHYSICS ANSWER KEY 1. a 2. c 3. b 4. c 5. b 6. d 7. b 8. c 9. a 10. a 11. c 12. b 13. a 14. d 15. d 16. c 17. d 18. b 19. c 20. b 21. a 22. a 23. d 24. d 25. c 26. b 27. b 28. c Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #5# Today’s Mathiitians..... Tomorrow’s IITians. IIT-JEE 2004 Screening Question Paper CHEMISTRY 29. 2-phenyl propene on acidic hydration gives (a) 2-phenyl-2-propanol (b) 2-phenyl-1-propanol (c) 3-phenyl-1-propanol (d) 1-phenyl-2-propanol CH 3 H H 3 30. 2 H CH H 3 C2 is rotated anticlockwise 1200 about C2 - C3 bond. The resulting conformer is (a) Partially eclipsed (b) Eclipsed (c) Gauche (d) Staggered 31. Benzamide on treatment with POCl3 gives (A) Aniline (b) Benzonitrile (c) Chlorobenzene (d) Benzyl amine 32. The methods chiefly used for the extraction of lead and tin from their ores are respectively (a) Self reduction and carbon reduction (b) Self reduction and electrolytic reduction (c) Carbon reduction and self reduction (d) Cyanide process and carbon reduction H O N H 3C CH 3 33. → 2Fe / Br Product on monobromination of this compound is H O H O N N H 3C CH 3 H 3C CH 3 (a) (b) Br Br H O H O N N H 3C CH 3 H 3C CH 3 (c) (d) Br Br Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #6# 34. The order of reactivity of phenyl magnesium bromide with the following compounds is O O O H 3C CH 3 H 3C H Ph Ph (I) (II) (III) (a) (II) > (III) > (I) (b) (I) > (III) > (II) (c) (II) > (I) > (III) (d) All react with the same rate 35. (NH4)2Cr2O7 on heating gives a gas which is also given by (a) Heating NH4NO2 (b) Heating NH4NO3 (c) Mg3N2 + H2O (d) Na(comp.) + H2O2 36. Zn |Zn2+ (a = 0.1 M) || Fe2+ (a = 0.01 M)| Fe. The emf of the above cell is 0.2905 V. Equilibrium constant for the cell reaction is (a) 10 0.32/0.0591 (b) 10 0.32/0.0295 (c) 10 0.26/0.0295 (d) e 0.32/0.295 37. HX is a weak acid (Ka = 10-5). It forms a salt NaX (0.1 M) on reacting with caustic soda. The degree of hydrolysis of NaX is (a) 0.01% (b) 0.0001% (c) 0.1% (d) 0.5% 38. Spontaneous adsorption of a gas on solid surface is an exothermic process because: (a) ∆H increases for system (b) ∆S increases for gas (c) ∆S decreases for gas (d) ∆G increases for gas 39. For a monoatomic gas kinetic energy = E. The relation with rms velocity is 1/ 2 1/ 2 1/ 2 1/ 2 2E 3E E E (a) u = (b) u = (c) u = (d) u = m 2m 2m 3m 40. The pair of compounds having metals in their highest oxidation state is (a) MnO2, FeCl3 (b) [MnO4]-, CrO2Cl2 (c) [Fe(CN)6]3-, [Co(CN)3] (d) [NiCl4]2-, [CoCl4]- 41. The compound having tetrahedral geometry is (a) [Ni(CN)4]2- (b) [Pd(CN)4]2- (c) [PdCl4]2- (d) [NiCl4]2- 42. Spin only magnetic moment of the compound Hg[Co(SCN)4] is (a) 3 (b) 15 (c) 24 (d) 8 43. A sodium salt of an unknown anion when treated with MgCl2 gives white precipitate only on boiling. The anion is (a) SO2− 4 − (b) HCO3 (c) CO2 − 3 − (d) NO3 44. Which hydrogen like species will have same radius as that of Bohr orbit of hydrogen atom? (a) n = 2, Li+2 (b) n = 2, Be3+ (c) n = 2, He+ (d) n = 3, Li2+ H 3N + +N H 3 Z Y 45. COOH X Arrange in order of increasing acidic strength (a) X > Z > Y (b) Z < X > Y (c) X > Y > Z (d) Z > X > Y 46. 0.004 M Na2SO4 is isotonic with 0.01 M glucose. Degree of dissociation of Na2SO4 is (a) 75% (b) 50% (c) 25% (d) 85% 47. ∆H vap = 30 kJ / mole and ∆Svap = 75 J mol−1 K −1 . Find temperature of vapour, at one atmosphere (a) 400 K (b) 350 K (c) 298 K (d) 250 K Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #7# 48. 2 mol of an ideal gas expanded isothermally and reversibly from 1 litre to 10 litres at 300 K. What is the enthalpy change? (a) 4.98 k.J (b) 11.47 k.J (c) -11.47 k.J (d) 0 k.J 49. (A) follows first order reaction. (A) → product Concentration of A, changes from 0.1 M to 0.025 M in 40 minutes. Find the rate of reaction of A when concentration of A is 0.01 M. (a) 3.47 × 10-4 M min-1 (b) 3.47 × 10-5 M min-1 (c) 1.73 × 10-4 M min-1 (d) 1.73 × 10-5 M min-1 50. 2-hexyne gives trans-2-hexene on treatment with (a) Li/NH3 (b) Pd/BaSO4 (c) LiAlH4 (d) Pt/H2 51. How many chiral compounds are possible on mono chlorination of 2-methyl butane? (a) 2 (b) 4 (c) 6 (d) 8 52. Which of the following pairs give positive Tollen's test? (a) Glucose, sucrose (b) Glucose, fructose (c) Hexanal, acetophenone (d) Fructose, sucrose 53. Which of the following has - O - O - linkage (a) H2S2O6 (b) H2S2O8 (c) H2S2O3 (d) H2S4O 6 54. When I- is oxidised by MnO4- in alkaline medium, I- converts into (a) IO-3 (b) I2 (c) IO4- (d) IO- 55. Number of lone pair(s) in XeOF4 is/are (a) 0 (b) 1 (c) 2 (d) 3 56. According to MO Theory, (a) O+2 is paramagnetic and bond order greater than O2 (b) O+2 is paramagnetic and bond order less than O2 (c) O+2 is diamagnetic and bond order less than O2 (d) O2+ is diamagnetic and bond order is more than O2 Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #8# IIT - JEE 2004 CHEMISTRY ANSWER KEY 29. a 30. c 31. b 32. a 33. b 34. c 35. a 36. b 37. a 38. c 39. a 40. b 41. d 42. b 43. b 44. b 45. a 46. a 47. a 48. d 49. a 50. a 51 b 52. b 53. b 54. a 55. b 56. a Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #9# Today’s Mathiitians..... Tomorrow’s IITians. IIT-JEE 2004 Screening Question Paper MATHEMATICS 57. The sides of a triangle are in the ratio 1 : 3 : 2 , then the angles of the triangle are in the ratio (a) 1 : 3 : 5 (b) 2 : 3 : 4 (c) 3 : 2 : 1 (d) 1 : 2 : 3 58. Area of triangle formed by the lines x + y = 3 and angle bisectors of the pair of straight lines x2 - y2 + 2y = 1 is (a) 2 sq. units (b) 4 sq. units (c) 6 sq. units (d) 8 sq. units 59. If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is 4 4 4 4 (a) (b) (c) (d) 55 35 33 1155 60. The area enclosed between the curves y = ax2 and x = ay2 (a > 0) is 1 sq. unit. Then the value of 'a' is 1 1 1 (a) (b) (c) 1 (d) 3 2 3 1 1 61. Given both θ and φ are acute angles sin θ = , cos φ = , then the value of θ + φ belongs to 2 3 π π π 2π 2π 5π 5π (a) 3 , 2 (b) 2 , 3 (c) 3 , 6 (d) 6 , π 62. If tangents are drawn to the ellipse x2 + 2y2 = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is 1 1 1 1 x2 y2 x2 y2 (a) 2x 2 + 4y 2 = 1 (b) 4x 2 + 2y 2 = 1 (c) + =1 (d) + =1 2 4 4 2 t2 ∫ xf (x)dx = t 5 then f 4 equals 2 63. If f(x) is differentiable and 0 5 25 2 −5 5 (a) (b) (c) 1 (d) 5 2 2 64. The value of x for which sin(cot-1(1 + x)) = cos (tan-1 x) is 1 1 (A) (b) 1 (c) 0 (d) − 2 2 65. If f(x) = x3 + bx2 + cx + d and 0 < b2 < c, then in (−∞, ∞) (a) f(x) is strictly increasing function (b) f(x) has a local maxima (c) f(x) is strictly decreasing function (d) f(x) is bounded 66. If ω (≠ 1) be a cube root of unity and (1 + ω2 ) n = (1 + ω 4 ) n , then the least positive value of n is (a) 2 (b) 3 (c) 5 (d) 6 α 67. If f(x) = x log x and f(0) = 0, then the value of α for which Rolle's theorem can be applied in [0, 1] is (a) -2 (b) -1 (c) 0 (d) ½ Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #10# 68. For all 'x', x2 + 2ax + (10 - 3a) > 0, then the interval in which 'a' lies is (a) a < -5 (b) -5 < a < 2 (c) a > 5 (d) 2 < a < 5 69. The angle between the tangents drawn from the point (1, 4) to the parabola y2 = 4x is π π π π (a) (b) (c) (d) 6 4 3 2 70. If one root is square of the other root of the equation x2 + px + q = 0, then the relation between p and q is (a) p3 - (3p - 1)q + q2 = 0 (b) p3 - q(3p + 1) + q2 = 0 (c) p3 + q(3p - 1) + q2 = 0 (d) p3 + q(3p + 1) + q2 = 0 1 1− x 71. The value of the integral ∫ 0 1+ x dx is π π (a) +1 (b) −1 (c) -1 (d) 1 2 2 r rr r r r 72. i j ˆ j ˆ If a = (ˆ + ˆ + k ), a. b = 1 and a × b = ˆ − k, then b is (a) ˆ − ˆ + k i j ˆ j ˆ (b) 2ˆ − k (c) ˆ i (d) 2ˆ i 73. If n-1 Cr = (k2 - 3)nCr+1, then K ∈ (a) (−∞, − 2] (b) [2, ∞) [ (c) − 3, 3 ] (d) ( 3, 2] 2 74. If f(x) = sin x + cos x, g(x) = x - 1 then g(f(x)) is invertible in the domain π π π π π (a) 0, 2 (b) − 4 , 4 (c) − 2 , 2 (d) [0, π] 2 + sin x dy π 75. If y = y(x) and = − cos x, y(0) = 1 , then y equals y + 1 dx 2 1 2 1 (a) (b) (c) − (d) 1 3 3 3 x −1 y +1 z −1 x−3 y−k z 76. If the lines = = and = = intersect, then the value of k is 2 3 4 1 2 1 3 9 2 3 (a) (b) (c) − (d) − 2 2 9 2 77. Given 2x - y + 2z = 2, x - 2y + z = -4, x + y + λ z = 4, then the value of λ such that the given system of equation has no solution, is (a) 3 (b) 1 (c) 0 (d) -3 78. If the line 2x + 6 y = 2 touches the hyperbola x2 - 2y2 = 4, then the point of contact is 1 1 (a) (−2, 6 ) (b) (−5, 2 6 ) (c) 2 , (d) (4, − 6 ) 6 α 2 79. If A = and |A | = 125 then the value of α is 3 2 α (a) +1 (b) +2 (c) +3 (d) +5 j ˆ 80. The unit vector which is orthogonal to the vector 3ˆ + 2ˆ + 6k and is coplanar with the vectors i i j ˆ i j ˆ 2ˆ + ˆ + k and ˆ − ˆ + k is Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #11# j ˆ 2 ˆ − 6ˆ + k i 2 ˆ − 3ˆ i j 3ˆ − k j ˆ i j ˆ 4ˆ + 3ˆ − 3k (a) (b) (c) (d) 41 13 10 34 lim f ( x 2 ) − f ( x) 81. If f(x) is differentiable and strictly increasing function, then the value of x→0 is f ( x) − f ( 0) (a) 1 (b) 0 (c) -1 (d) 2 82. An infinite G.P. has first term 'x' and sum 5, then x belongs to (a) x < -10 (b) -10 < x < 0 (c) 0 < x < 10 (d) x > 10 2 2 83. If one of the diameters of the circle x + y - 2x - 6y + 6 = 0 is a chord to the circle with centre (2, 1) then the radius of the circle is (a) 3 (b) 2 (c) 3 (d) 2 84. If y is a function of x and log(x + y) = 2xy, then the value of y'(0) is equal to (a) 1 (b) -1 (c) 2 (d) 0 Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #12# IIT - JEE 2004 MATHEMATICS ANSWER KEY 57. d 58. a 59. d 60. a 61. b 62. a 63. a 64. d 65. a 66. b 67. d 68. b 69. c 70. a 71. b 72. c 73. d 74. b 75. a 76. b 77. b 78. d 79. c 80. c 81. c 82. c 83. c 84. a Kochi Branch: Bldg.No.41/352, Mulloth Ambady lane, Chittoore Road, Kochi - 11, Ph: 0484-2370094, 9388465944 Trivandrum Branch: TC.5/1703/30, Golf Links Road, Kowdiar Gardens, Housing Board Colony, Ph: 0471- 2438271, Mobile: 9387814438. www.mathiit.com #13#