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CODE GREEN NARAYANA GROUP OF EDUCATIONAL INSTITUTIONS ALL INDIA TEST SERIES (AIEEE) NARAYANA PART TEST- 2 Exam date: 20-11-2010 Ti m e : 3 ho ur s M a xi m u m m a r ks : 4 3 2 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS C. Question paper format: A. General: 11. The question paper consists of 3 parts (Part I: Physics:, Part 1. This booklet is your Question Paper containing 90 questions. II: Chemistry, Part III: Mathematics). Each part has 3 2. The question paper CODE is printed on the right hand top sections. corner of this booklet. 12. Section I contains 12 multiple choice questions. Each question 3. Blank papers, clipboards, log tables, slide rules, calculators, has 4 choices (A), (B), (C) and (D), out of which only one is cellular phones, pagers, and electronic gadgets in any form are correct. not allowed to be carried inside the examination hall. 13. Section II contains 6 multiple choice questions. Each question 4. The answer sheet, a machine–readable Objective Response has 4 choices (A), (B), (C) and (D), out of which only one is Sheet (ORS), is provided separately. correct. 5. DO NOT TAMPER WITH / MUTILATE THE ORS OR THE 14. Section III contains 12 multiple choice questions. Each BOOKLET. question has 4 choices (A), (B), (C) and (D), out of which only one is correct. B. Filling the ORS 6. On the lower part of the ORS, write in ink, your name in box L1, your Registration No. in box L2 and Name of the Centre in box D. Marking Scheme L3. Do not write these anywhere else. 15. For each question in Section – I, you will be awarded 3 marks 7. Write your Registration No. in ink, in the box L4 provided in the if you have darkened only the bubble corresponding to the lower part of the ORS and darken the appropriate bubble correct answer and zero mark if no bubble is darkened. In case UNDER each digit of your Registration No. with a good quality of bubbling of incorrect answer, minus one (–1) mark will be HB pencil. awarded. 8. The ORS has a CODE printed on its lower and upper parts. 16. For each question in Section II, you will be awarded 8 marks if you have darkened only the bubble(s) corresponding to the 9. Make sure the CODE on the ORS is the same as that on this correct answer and zero mark if no bubble is darkened. In case booklet and put your signature in ink in box L5 on the ORS of bubbling of incorrect answer, minus one (–2) mark will be affirming that you have verified this. awarded. 10. IF THE CODES DO NOT MATCH, ASK FOR A CHANGE OF 17. For each question in Section III, you will be awarded 4 marks THE BOOKLET. if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. The distribution of marks in each subject is as under FOR CORRECT FOR WRONG SUBJECT QUESTIONS ANSSWER ANSWER 1 to 12 +4 -1 PHYSICS 13 to 18 +8 -2 (144 MARKS) 19 to 30 +4 -1 31 to 42 +4 -1 CHEMISTRY 43 to 48 +8 -2 (144 MARKS) 49 to 60 +4 -1 61 to 72 +4 -1 MATHEMATICS 73 to 78 +8 -2 (144 MARKS) 79 to 90 +4 -1 Name of the Student Roll Number I have read all the instructions and shall abide by them I have verified all the information filled in by the Candidate ……..……………………………………………………… Signature of the Candidate …………………………………………….. Signature of the Invigilator NPT-II (AIEEE MOD) 20-11-2010 PHYSICS 1. Two uniform metal rods of lengths l1 and l2 and linear coefficients of expansion 1 and 2 respectively are connected to form a single rod of length l1 l2 . When the temperature of the combined rod is raised by tºC, the length of each rod increases by the same 2 amount. Then is 1 2 l1 l1 l2 (1) (2) l1 l2 l1 l2 l1 l2 (3) (4) l1 l2 l2 2. A pendulum clock runs fast by 5 seconds per day at 20ºC and goes slow by 10 seconds per day at 35ºC. It shows correct time at a temperature of (1) 27.5ºC (2) 25ºC (3) 30ºC (4) 33ºC 3. A specific gravity bottle contains m grams of liquid of apparent expansion a at 0ºC. When it is heated to tºC the mass of liquid expelled is 1 a t am (1) (2) a mt 1 at mt mt (3) a (4) a 1 at 1 a t 4. When a monoatomic gas expands at constant pressure the percentage of heat supplied that increases the internal energy of the gas and that which is involved in expansion respectively is (1) 75%, 25% (2) 25%, 75 % (3) 60%, 40% (4) 40%, 60% Space for rough work 2 NPT-II (AIEEE MOD) 20-11-2010 5. Match the following Column-I (Process) Column II( Workdone ) (a ) Isothermal process ( p ) W=0 (b ) Adiabatic process (q) 1 W P V P V 1 1 1 2 2 (c ) Isobaric process (r) W P V2 V1 (d ) Isochoric process (s) V W nRT log e 2 V1 (1) a p;b q;c r;d s (2) a q;b s;c r;d p (3) a r;b p;c r;d q (4) a s;b q;c r;d p 7 6. The pressure and density of a given mass of a diatomic gas 5 1 d1 P 1 1 change adiabatically from (p,d) to (p ,d ) . If 32 then is d P ( = ratio of specific heats) 1 1 (1) (2) 128 64 (3) 64 (4) 128 7. 30g of ice at 0ºC and 20g of steam at 100ºC are mixed. The composition of the resultant mixture is (1) 40g of water and 10g steam at 100ºC (2) 10g of ice and 40g of water at 0ºC (3) 50g of water at 100ºC (4) 35g of water and 15g of steam at 100ºC Space for rough work 3 NPT-II (AIEEE MOD) 20-11-2010 8. A Carnots engine whose sink is at a temperature of 300K has an efficiency of 40%. The increase in temperature of the source, so that the efficiency of that engine increases to 60% is (1) 250 K (2) 275 K (3) 300 K (4) 325 K 9. During an experiment an ideal gas is found to obey an additional law V P constant. The gas is initially at a temperature T and 2 volume V. When it expand to a volume 2V, the temperature becomes (1) T (2) 2T T (3) T 2 (4) 2 10. An open pipe is suddenly closed at one end, as a result of which the frequency of the third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is (1) 200 Hz (2) 300 Hz (3) 240 Hz (4) 480 Hz 11. The vibrations of a string of length 600 cm fixed at both ends are x represented by the equation y 4sin cos 90t cm . The 15 maximum displacement of a point at x = 5 cm is (1) 3cm (2) 2 3cm 3 (3) cm (4) 3 3cm 2 Space for rough work 4 NPT-II (AIEEE MOD) 20-11-2010 12. A motor boat with a sound source is moving across the river at 90ºC 1 to the flow of water with a velocity12ms . Width of river is 169m 1 and the velocity of stream in the river is 5ms . Stationary observer is on one bank of the river. At t = 0, the motor boat starts from the other bank. The observer will hear actual frequency released by the source after a time of (1) 10 S (2) 12 S (3) 8 S (4) 6 S 13. On a smooth inclined plane a body of M is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has a force constant K, the period of oscillation of the body is(Assume the springs as massless) M 2M (1) 2 (2) 2 2K K Msin 2Msin (3) 2 (4) 2 2K K Space for rough work 5 NPT-II (AIEEE MOD) 20-11-2010 14. The relation between internal energy U, pressure P and volume V of a gas in an adiabatic process is: U=a + bPV where a and b are constants. The value of the ratio of the specific heats is a b 1 (1) (2) b b a 1 b (3) (4) a a 15. The apparent coefficient of expansion of liquid, when heated in a copper vessel is C and when heated in a silver vessel is S. If A is the linear coefficient of expansion of copper, linear expansion coefficient of silver is C S 3A C 3A S (1) (2) 3 3 S 3A C C S 3A (3) (4) 3 3 16. The length of a potentiometer wire is l. A cell of EMF E is balanced ' l' at a length from the positive end of the wire. If the length of the 5 l wire is increased by , the new balancing length with the same 2 cell is 2 3 (1) l (2) l 15 15 3 4 (3) l (4) l 10 10 Space for rough work 6 NPT-II (AIEEE MOD) 20-11-2010 17. A rectangular coil of single turn, having area A, rotates in a uniform magnetic field B with an angular velocity about an axis perpendicular to the field. If initially the plane of wire is perpendicular to the field, then the average induced emf when rotated through 900 is 2BA BA (1) (2) 4 BA BA (3) (4) 2 18. A rod of length L has a total charge Q distributed along its length, it is bent in the shape of a semicircle. The magnitude of the electric field at the centre of curvature of the semi circle is Q2 Q (1) (2) 2 0 L2 2 0 L Q Q (3) (4) 2 0 L2 0 L2 19. Three charges Q, + q and + q are placed at the vertices of a right angle triangle (isosceles triangle) as shown. The net electrostatic energy of the configuration is zero, if Q is equal to : q 2q (1) (2) 1 2 2 2 (3) 2q (4) q Space for rough work 7 NPT-II (AIEEE MOD) 20-11-2010 20. A parallel plate capacitor filled with a dielectric of relative permittivity 5 between its plates is charged to acquire an energy E and isolated. If the dielectric is replaced by another of relative permittivity 2, its energy becomes (1) E (2) 0.4 E (3) 2.5 E (4) 6.25 E 21. In the part of the circuit given below, potential difference between the points M and N is (1) 8V (2) 7V (3) 6V (4) 9V 22. Six spokes of resistance r each are connected between the axle and the rim of a wheel. If r 2 and a 2V battery is connected between the rim and the axle. The power consumed is (neglect resistance of the rim) (1) 24W (2) 12W (3) 6W (4) 3W 23. In wheat stones bridge in the four arms, four conductors of lengths l1 ,l2 ,l3 ,l4 and areas of cross-section a1 ,a2 ,a3 ,a4 are connected to balance. If their resistivities are 1 , 2 , 3 and 4 respectively, then (1) 1 4 1 4 2 3l2 l3 (2) 1 4l1 l4 a1 a4 2 3l2 l3 a1 a4 (3) 1 4l1 l4 a1 a2 2 3l2 l3 a3 a4 (4) 1 4 l1 l4 a 2 a 3 2 3l2 l3a 1 a 4 24. An ideal inductor draws a current of 12.5A when connected to an alternating source 250V, 50Hz. A pure resistance across the same source draws a current of 25A. If the resistor and inductor are connected in series with same source, then the current in circuit is (1) 8.3A (2) 12.5A (3) 5 5 A (4) 10 5 A Space for rough work 8 NPT-II (AIEEE MOD) 20-11-2010 25. A metal conductor of length 1m rotates vertically about one of its ends at angular velocity 5 rad/sec. If the horizontal component of 4 earth’s magnetic field is 0.2 10 T , then the emf developed between the two ends of the conductor is (1) 5V (2) 50 V (3) 5mV (4) 50mV 26. A transformer has primary, secondary turns ratio 1:2. Its efficiency is 80%. When 50V battery is connected in the primary, then voltage across the secondary is (1) 92V (2) 40V ((3) 80V (4) 0V 27. When a conductor in the form of wire is connected in the left gap and known resistance in the right gap of a metre bridge. The balancing length is 50cm. If the wire is stretched so that its length is increased by 100% then the new balancing length is (in cm) (1) 70 (2) 20 (3) 80 (4) 60 28. An inductor of 1H is connected across a 220 V, 50 Hz supply. The peak value of current is approximately (1) 0.5 A (2) 1 A (3) 4 A (4) 6 A 29. An alternating emf E = 100 sin (100 t) is connected to a choke of negligible resistance and current oscillations with a amplitude 1A are to be produced. The inductance of the choke should be 1 (1) 100 H (2) H (3) 1 H (4) H Space for rough work 9 NPT-II (AIEEE MOD) 20-11-2010 30. When a 30 V dc source is connected to L-R series with ammeter, 2A current is recorded. When 30 V ac source of frequency 100 Hz is connected a current 1.2A is recorded. The inductance reactance is (1)100 (2) 20 (3) 5 34 (4) 40 CHEMISTRY 31. The boiling point of C6 H 6 ,CH 3OH ,C6 H 5 NH 2 and C6 H 5 NO2 are 80 ºC, 65ºC, 184ºC and 212ºC respectively. Which will show highest vapour pressure at room temperature? (1) C6 H 6 (2) CH 3OH (3) C6 H 5 NH 2 (4) C6 H 5 NO2 32. In the electrolysis of Na2 SO4 solution using inert electrodes a) the anodic reaction is 2H 2O O2 g 4e 4H b) H 2 g and O2 g is produced in a molar ratio of 2:1 c) 23 grams of sodium is produced at the cathode d) the cathode reaction is Na e Na (1) a and b are correct (2) c, d are correct (3) Only c is correct (4) All are correct 33. d-block elements form complexes because they have: (1) Vacant orbitals (2) Small sizes (3) Higher nuclear charge (4) All of the above 34. If 20ml of 0.4M – NaOH solution completely neutralized by 40ml of a dibasic acid, the molarity of the acid solution is (1) 0.1 M (2) 0.2 M (3) 0.3 M (4) Space for rough work 0.4 M 10 NPT-II (AIEEE MOD) 20-11-2010 35. Which of the following type of forces are present in natural rubber? (1) Weakest intermolecular forces (2) Hydrogen bonding (3) Three dimensional network of bonds (4) Metallic bonding 36. A metal in its highest oxidation state can acts as (1) A reducing agent (2) An oxidising agent (3) An oxidizing agent and reducing agent (4) Neither oxidising agent nor reducing agent 37. The standard reduction potential of three metals X, Y, Z are 0.52, -3.03 and -1.18V respectively. The order of reducing power of the corresponding metals is (1) Y > Z > X (2) X > Y > Z (3) Z > Y > X (4) Z > X > Y 38. Which of the following monomer in excess makes PHBV more flexible (1) - hydroxy butanoic acid (2) - hydroxy butanoic acid (3) -hydroxy pentanoic acid (4) - hydroxy pentanoic acid 39. Chlorine gas can be dried by passing over (1) Quick lime (2) Soda lime (3) Caustic potash sticks (4) Concentrated sulphuric acid 40. Oxides of sulphur present in the atmosphere are washed down by rain and will result in (1) Lowering of pH of the soil (2) Increase in pH of the soil (3) Increase in O3 quantities (4) Increase in population 41. The important features of genetic code are a) It is universal b) It is comma less c) It is degenerate d) The third base in the codon is not always specific Find the correct one (1) a only (2) Space for rough work b, c only 11 (3) b, c and d only (4) all a, b, c and d NPT-II (AIEEE MOD) 20-11-2010 42. What structural feature distinguishes proline from other natural - amino acids (1) It is optically inactive (2) It contains aromatic group (3) It is a di carboxylic acid (4) It has a secondary amine group 43. Following solutions at the same temperature will be isotonic (1) 3.42 g of cane sugar in one litre water and 0.18 g of glucose in one litre water (2) 3.42 g of cane sugar in one litre water and 0.18 g of glucose in 0.1 litre water (3) 3.42 g of cane sugar in one litre water and 0.585 g of NaCl in one litre water (4) 3.42 g of cane sugar in one litre water and 1.17 g of NaCl in one litre water Equivalent conductance at infinite dilution, of NH4Cl, NaOH 0 44. 1 2 1 and NaCl are 128.0,217.8 and 109.9 ohm cm eq respectively. The equivalent conductance of 0.01 N NH4OH is 9.30 ohm1cm2eq1 , then the degree of ionization of NH4OH at this temperature would be (approximately) (1) 0.04 (2) 0.1 (3) 0.4 (4) 0.62 45. Which of the following is not a draw back of Werners theory (1)Does not explain the valency of metal ions in the complex (2)Does not give any explanation for the colour of complex compounds (3)Does not explain the magnetic behaviour of complex compounds (4)Does not correlate electronic configuration of the metal with the formation of complex. 46. Hypo solution reacts with chlorine gas the products formed are (1) Na2 S4O6 NaCl (2) Na2 SO4 S HCl (3) Na2 SO4 NaCl (4) Na2 SO4 SO2 HCl Space for rough work 12 NPT-II (AIEEE MOD) 20-11-2010 47. The correct statements from the given statements are i) Nalgonda technique is a cheap defluoridation method ii) Dental flourisis and skeletal flourisis results if the fluoride ion concentration in water is less than 3 ppm. iii) Defluoron -1, Defluoron-2, coconut charcoal are used as adsorbent for fluoride ions The correct answer is (1) i, ii (2) ii, iii (3) i, iii (4) All are correct 48. Cimetidine acts as (1) Antibiotic (2) Antifertility (3) Antihistamine (4) Antipyretic 49. Which of the following statement is not correct? (1) La(OH)3, is less basic than Lu(OH)3 (2) In Lanthanoid series ionic radius of Ln 3 ions decreases (3) La is actually an element of transition series (4) Atomic radii of Zr and Hf are same because of Lanthanoid contraction 50. sp3d 2 hybridization is present in (1) CoF6 (2) Ni CO 4 3 4 (3) Fe CN 6 (4) All 51. The effective atomic number of central metal ion is wrongly calculated in the following complexe? (1) In [Ni(CO)4] the EAN of Ni is 36 (2) In [K2 Ni(CN)4] the EAN of Ni is 36 (3) In [K3 Fe(CN)6] the EAN of Fe 35 (4) In[Co(NH3)6] Cl3 the EAN of Cr is 36 Space for rough work 13 NPT-II (AIEEE MOD) 20-11-2010 52. The IUPAC name of the coordination compound K3 {Fe(CN)6] is (1) Potassium hexacyanoferrate (II) (2) Potassium hexacyanoferrate (III) (3) Potassium hexacyanoiron (II) (4) Tripotassium Hexacyanoiron (II) 53. The substances which affect the central nervous system and induce sleep are called. (1) Antipyretics (2) Tranquilizers (3) Analgesics (4) Antibiotics 54. In which of the following statements about halogens is correct? (1) They are all diatomic and form univalent ions (2) They are all capable of exhibiting several oxidation states (3) They are all diatomic and form divalent ions (4) They can mutually displace each other from the solution of their compounds with metals. 55. The TLV values of four pollutants A, B, C and D are 9 ppm, 10ppm, 100 ppm and 500 ppm respectively. The most toxic is (1) A (2) B (3) C (4) D 56. Which of the following statements regarding ozone is not true (1) Ozone is an allotrope of oxygen (2) The ozone layer protects the earths surface from an excessive concentration of harmful ultraviolet radiation (3) The conversion of oxygen in to ozone is an exothermic process (4) Ozone is much more powerful oxidizing agent than molecular oxygen 23 57. 3.01× 10 NaCl ion pairs are dissolved in water and diluted to a volume of 10 liters. The molar concentration of the solution is (1) 0.5M (2) 0.25M (3) 1M (4) 0.05M Space for rough work 14 NPT-II (AIEEE MOD) 20-11-2010 58. The observed magnetic moment value abs is higher than calculated magnetic moment value cal for 3 2 (1) Ti (2) V 2 2 (3) Co (4) Cr 59. The number of electrons required for deposition of one mole of copper on the cathode during the electrolysis of CuSO4 solution is 23 24 (1) 6.0 × 10 (2) 1.2 × 10 24 23 (3) 4.8 × 10 (4) 3 × 10 60. Chemically inert halide of sulphur is (1) S 2Cl2 (2) SF4 (3) SCl2 (4) SF6 MATHEMATICS 61. In, ABC if A:B:C = 3:5:4 then a + b + 2 C = (1) 2b (2) 2c (3) 3b (4) 3a 1 R 62. In ABC, right angled at A, cos is r2 r3 (1) 30º (2) 60º (3) 90º (4) 45º 63. If in ABC, sin4 A sin4 B sin4 C sin 2 B sin 2 C 2 sin 2 C sin 2 A 2 sin 2 Asin 2 B then A = 5 5 (1) , (2) , 6 6 3 6 3 (3) , (4) , 3 2 4 4 Space for rough work 15 NPT-II (AIEEE MOD) 20-11-2010 a b c 64. In a triangle ABC, if r1 = 2r2 = 3r3 then = b c a 75 155 (1) (2) 60 60 176 191 (3) (4) 60 60 1 3 65. If sin x sin 1 y sin 1 z then 2 9 x100 y100 z 100 101 x y101 z 101 (1) 3 (2) 2 (3) 1 (4) 0 66. sin1 sin3 cos 1 cos7 ta n1 ta n5 (1) + 1 (2) (3) 3 - 1 (4) -1 67. A person standing on the bank of a river observes that the angle subtends by a tree on the opposite bank is 60º, when he retires 40 mts from the bank perpendicular to it, he finds the angle to be 30º. The height of the tree and breadth of the river are (1) 20,20 3 (2) 10,20 3 (3) 20 3 ,20 (4) 10,30 3 68. From the top of a cliff ‘x’ meters high, the angle of depression of the foot of a tower is found to be double the angle of elevation of the top of the tower. If the height of the tower is ‘h’ meters, then the angle of elevation is 1 x 1 2h (1) sin h (2) T an 3 2 x 1 2h 1 2h (3) Cos (4) T an 3 x x Space for rough work 16 NPT-II (AIEEE MOD) 20-11-2010 1 69. The total number of solutions of cot x cot x , x 0,3 is sin x equal to (1) 1 (2) 2 (3) 3 (4) Zero 70. The number of solutions of the equation 1 1 sin 5 x cos5 x sin x cos x is cos x sin x (1) 0 (2) 1 (3) Infinite (4) 5 71. The maximum value of cos 1 cos 2 ...... cos n , under the restrictions 0 1 , 2 ,...... n and cot 1 cot 2 2 ...... cot n 1is 1 1 (1) (2) n 2 2n 2 1 (3) (4) 1 2n 72. If x sin n 0 2n , y cos ,z sin 2n cos 2n , then n 0 2n n 0 (1) XYZ = XY + Z (2) XYZ = XZ + Y (3) XYZ = YZ + X (4) XYZ = XY + YZ + ZX cot C 73. In a triangle if a 2 b 2 2011c 2 then cot A cot B (1) 999 (2) 1002 (3) 1000 (4) 1005 Space for rough work 17 NPT-II (AIEEE MOD) 20-11-2010 sin sin 3 sin 9 74. If K1 Tan27 Tan and K 2 then cos3 cos9 cos 27 (1) K1 K 2 (2) K1 2K2 (3) K1 K2 2 (4) K2 2K1 2 4 6 75. If x 270 cos cos cos 3746 , then the value of 7 7 7 (1) 3880 (2) 3881 (3) 3882 (4) 3883 t 76. If f(y)= e , g(y)= Y; y > 0 and F t f t y g y dy, then y 0 t t (1) f(t)= e -(1+ t) (2) f(t)= t e t t (3) f(t)= t e (4) f(t)= 1- e -(1+ t) 77. The slope of the tangent to a curve at any point (x, y) on it in given y y y by cot cos x 0, y 0 and the curve passes through the x x x point 1, the equation of the curve is 4 y x (1) sec log x 2 (2) sec log x 2 x y (3) sec yx log x 2 (4) sec xy log x 2 Space for rough work 18 NPT-II (AIEEE MOD) 20-11-2010 dx 78. 7 9 x 2 x 3 8 8 1 1 8 x 2 8 8 x 2 8 (1) c (2) c 5 x 3 3 x 3 1 1 8 x 2 8 3 x 2 8 (3) c (4) c 5 x 3 8 x 3 79. If polynomials P and Q satisfies 3x 1 cos x 1 2x sin x dx P cos x Qsin x R (ignoring the constant of integration) then (1) P = 3x -2 (2) Q = 2 + x (3) P = 3(x -1) (4) Q = 3(x -1) 80. Let the equation of a curve passing through the point (0, 1) be y x 2 ,ex dx . 3 given by If the equation of the curve is written in the form x = f(y) then f(y) is (1) log e 3y 2 (2) 3 log e 3y 2 (3) 3 log e 2 3y (4) 3 log e 2 y 81. Let f(x) be a function satisfying f ' (x) = f(x) with f(0) = 1 and g(x) be 2 a function that satisfies f(x) + g(x) = x . Then, the value of the 1 integral f x g x dx is 0 2 e 3 e2 3 (1) e (2) e 2 2 2 2 e2 5 e2 5 (3) e (4) e 2 2 2 2 Space for rough work 19 NPT-II (AIEEE MOD) 20-11-2010 6 x 82. The value of the integral 3 9x x dx is 3 (1) (2) 2 2 1 (3) 1 (4) 2 83. Let f(x) = Min x 1; 1 x then area bounded by y = f(x) and x- axis is 7 5 (1) (2) 6 6 1 11 (3) (4) 6 6 The area bounded by curve y x 6x 8x and the x-axis is (in 3 2 84. sq.units) 8 (1) 8 (2) 3 3 (3) (4) 6 8 xdx ydy xsin x y has the solution 2 2 85. ydx xdy y3 y2 (1) log tan x y x y C (2) log tan x y 2 C 2 2 2 2 2 2 x x 2 y2 x 2 (3) log tan x y 2 2 xy C (4) log tan 2 y2 C Space for rough work 20 NPT-II (AIEEE MOD) 20-11-2010 86. If a, x1 , x 2 are in G.P. with common ratio r and b, y1 , y 2 are in G.P. with common ratio s where s - r = 2, , then the area of the triangle with vertices is a,b , x1, y1 and x 2 , y2 (1) ab r 1 2 (2) ab r s 2 2 (3) ab s 1 2 (4) abrs 87. P and Q are two variable points on the axes of x and y respectively such that OP OQ a , then the locus of foot of perpendicular from (0,0) on PQ is (1) x y x y 2 a x y 2 (2) x y x y 2 2 axy (3) x y x y axy (4) x y x y axy 2 2 2 2 88. If P1 , P2 , P3 are lengths of perpendiculars from the points m ,2m, mm ,m m and m 2 2 1 1 1 ,2m1 to the line sin 2 x cos ysin 0 respectively then P1 , P2 , P3 are in cos (1) A.P (2) G.P (3) H.P (4) A.G.P 89. If the line y = 3 x cuts the curve x3 y3 3xy 5x 2 3y2 4x 5y 1 0 at the points A, B, C. Then OA.OB.OC = (1) 4 13 3 3 1 (2) 3 3 1 (3) 2 3 7 1 13 3 3 1 (4) If the pair of lines ax 2 a b xy by 0 lie along diameters of a 2 2 90. circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector, then (1) 3a 2ab 3b 0 (2) 3a 10ab 3b 0 2 2 2 2 (3) 3a 2ab 3b 0 (4) 3a 10ab 3b 0 2 2 2 2 Space for rough work 21