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AIEEE 2011 Exam Papers

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Tags : AIEEE,2003,Paper,Exam,Chemistry,Maths,Physics,IIT,JEE,IIT JEE,Joint Entrance Examination, iit jee solved question paper with answers and detailed solutions, online question paper free,important questions,aieee exam paper, jee mains, iit jee papers. [1] AIEEE 2011 1. Consider 5 independent Bernulli’s trails each with probability of sucess p. If the probability of at least one failure is greater than or equal to 31 32 , then p lies in the interval (1) 11 12 , 1 FH G OQ P (2) 1 2 3 4 , FH G OQ P (3) 3 4 11 12 , FH G OQ P (4) 0 1 2 , FH G OQ P Ans: [4] 2. The coefficient of x7 in the expansion of (1 x  x2  x3 )6 is (1) 132 (2)144 (3) – 132 (4) – 144 Ans: [4] 3. lim cos{ ( )} x x  x    F H GG I K JJ 2 1 2 2 2 (1) equals 1 2 (2) does not exist (3) equals 2 (4) equals  2 Ans: [2] 4. Let R be the set of real numbers Statement -1 A  {(x, y) R  R : y  x is an integer} is an equivalence relation on R. Statement -2 B  {(x, y) R  R : x y for some rational number  } is an equivalence relation on R. (1) Statement -1 is false, Statement -2 is true (2) Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for statement-1 (3) Statement-1 is true, Statement -2 is true, Statement- 2 is not correct explanation for Statement-1 (4) Statement -1 is true, Statement-2 is false Ans: [4] 5. Let  ,  be real and z be complex number. If z2 z    0 has two distinct roots on the line Re z  1, then it is necessary that (1)  (1, ) (2)  (0, 1) (3)  (1, 0) (4)   1 Ans: [1] 6. d x dy 2 2 equal (1) – d y dx dy dx 2 2 3 FH G IK J FH G IK J  (2) d y dx 2 2 1 FH G IK J  (3) – d y dx dy dx 2 2 1 3 FH G IK J FH G IK J   (4) d y dx dy dx 2 2 2 FH G IK JFH GIK J  Ans: [1] 7. The number of values of k for which the linear equations 4x  ky  2z  0 kx  4y  z  0 2x  2y  z  0 possess a non-zero solutoin is (1) zero (2) 3 (3) 2 (4) 1 Ans: [3] 8. Statement -1 The point A (1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line x y z 1 1 2 2 3     Statement -2 The line x y z 1 1 2 2 3     bisects the line segment joining A (1, 0, 7) and B (1, 6, 3) (1) Statement -1 is false, Statement -2 is true (2) Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for statement-1 (3) Statement-1 is true, Statement -2 is true, Statement- 2 is not correct explanation for Statement-1 (4) Statement -1 is true, Statement-2 is false Ans: [2] Mathematics [2] AIEEE 2011 9. Consider the following statements P : Suman is brilliant . Q : Suman is rich R : Suman is honest The negation of the statment “Suman is brilliant and dishonest if and only if sumna is rich” can be expressed as (1) ~ (P ~ R)Q (2) ~ P (Q~ R) (3) ~ (Q(P ~ R)) (4) ~ Q~ P  R Ans: [3] 10. The lines L y x 1 :   0 and L x y 2 : 2   0 intersect the line L y 3 :  2  0 at P and Q respectivley. The bisector of the acute angle between L1 and L2 intersects L3 at R. Statement -1 The ratio PR : RQ equals 2 2 : 5 . Statement -2 In any triangle, bisector an angle divides the trianle into two similar triangles. (1) Statement -1 is false, Statement -2 is true (2) Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for statement-1 (3) Statement-1 is true, Statement -2 is true, Statement- 2 is not correct explanation for Statement-1 (4) Statement -1 is true, Statement-2 is false Ans: [4] 11. A man saves Rs 200 in each of the first three months of his services. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service wil be Rs. 11040 after (1) 21 months (2) 18 months (3) 19 months (4) 20 months Ans: [1] 12. Equations of the ellipse whose axes are the axes of coordinates and which passes through the point (3, 1) and has eccentricity 2 5 is (1) 5×2  3y2  32  0 (2) 3×2  5y2  32  0 (3) 5×2  3y2  48  0 (4) 3×2  5y2 15  0 Ans: [2] 13. If A  sin2 x  cos4 x then for all real x. (1) 3 4 13 16  A  (2) 3 4  A  1 (3) 13 16  A  1 (4) 1 A  2 Ans: [2] 14. The value of 8 1 1 2 0 1 log(  )  z x x dx is (1) log2 (2)  log2 (3)  8 log 2 (4)  2 log 2 Ans: [2] 15. If the angle between the line x y z    1  2 3  and the plane x  2y  3z  4 is cos FH G IK J 1 5 14 (1) 5 3 (2) 2 3 (3) 3 2 (4) 2 5 Ans: [2] 16. For x FH G IK J 0 5 2 ,  , define f x t x ( ) z0 sint dt Then f has (1) local maximum at  and local minimum at 2 (2) lcoal maximum at  and 2 (3) lcoal minimum at  and 2 (4) local minimum at  and local maximum at 2 Ans: [1] [3] AIEEE 2011 22. Let be the purchase value of an equaipment and V (t) be the value after it has been used for t years. The value V (t) depreciates at a rate given by differential euqation dV t dt k T t ( )   (  ) , where k  0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is (1) ekT (2) T k 2 1  (3) I kT  2 2 (4) I k T t  (  )2 2 Ans: [3] 23. If C and D are two events such that C  Dand P(D)  0 , then the correct statement among the following is (1) P C D P D P C ( | ) ( ) ( )  (2) P(C|D)  P(C) (3) P(C|D)  P(C) (4) P(C|D)  P(C) Ans: [3] 24. Let A and B be two symmetric matrices of order 3 Statement -1 A (BA) and (AB) A are symmetric matrices Statement -2 AB is symmetric matrix if matrix multiplication of A with B commutative. (1) Statement -1 is false, Statement -2 is true (2) Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for statement-1 (3) Statement-1 is true, Statement -2 is true, Statement- 2 is not correct explanation for Statement-1 (4) Statement -1 is true, Statement-2 is false Ans: [3] 25. If  ( 1) is a cube root of unity, and (1)7  A  B . Then (A, B) equals (1) P C D P D P C ( | ) ( ) ( )  (2) P(C|D)  P(C) (3) P(C|D)  P(C) (4) P(C|D)  P(C) Ans: [3] 17. The domain of the function (1) f x x x ( )   1 is (2) (, ) {0} (3) (0, ) (4) (, 0) Ans: [4] 18. If the mean deviation about the median of the numbers a, 2a, . . ., 50 a is 50, then a equals (1) 5 (2) 2 (3) 3 (4) 4 Ans: [4] 19. If ra  i  k 1 10 e3$ $j and rb  i  j  k 1 7 e2$ 3$ 6 $j , then the value of 2 2 r r r r r r a  b  a  b a  b LNM OQP e j e j e j is (1) 3 (2) 5 (3) 3 (4) 5 Ans: [2] 20. The value of p and q for which the function f x p x x x q x x x x x x x ( ) sin( ) sin , , ,         R S ||| T ||| 1 0 0 0 2 3 2 is continuous for all x in R, are, (1) p  q  1 2 3 2 , (2) p  q   1 2 3 2 , (3) p  q  5 2 3 2 , (4) p   q  3 2 1 2 , Ans: [4] 21. The two circles x2  y2  ax and x2  y2  c2 (c  0) touch each other if (1) a  2c (2) 2 a  c (3) a  c (4) a  2c Ans: [3] [4] AIEEE 2011 26 Statement -1 The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9 3 C . Statement -2 The number of ways of choosing any 3 places from 9 different places is 9 3 C (1) Statement -1 is false, Statement -2 is true (2) Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for statement-1 (3) Statement-1 is true, Statement -2 is true, Statement- 2 is not correct explanation for Statement-1 (4) Statement -1 is true, Statement-2 is false Ans: [3] 27 The shortest distance between line y  x  1 and curve x  y2 is (1) 4 3 (2) 3 4 (3) 3 2 8 (4) 8 3 2 Ans: [3] 28. The area of the region enclosed by trhe curves y  x, x  e, y  b1/ xg and the positive x-axis is (1) 5/2 square units (2) 1/2 square units (3) 1 square units (4) 3/21 square units Ans: [4] 29. If dy dx  y  3  0 and yb0g  2, the ybln2g is equal to: (1) –2 (2) 7 (3) 5 (4) 13 Ans: [2] 30. The vectors a and  b are no perpendicular and c and  d are two vectors satisfying :     b  c  b  d and   a d  0 . Then the vector  d is equal to: (1)       c a c a b  b   FH G IK J (2)       b b c a b  c   FH GIK J (3)       c b c a b  c   FH G IK J (4)       b b c a b  c   FH G IK J Ans: [1] CHEMISTRY [5] AIEEE 2011 / Code C Part -B Chemistry 1. In context of the lanthanoids, which of the following statements is not correct? (1) Availability of 4f electrons results in the formation of compounds in +4 state for all the members of the series. (2) There is a gardual decrease in the radii of the members with increasing atomic number in the series. (3) All the members exhibit +3 oxidation state. (4) Because of similar properties the separation of lanthanoids is not easy. Ans: [1] 2. In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing form one of the face centred points, the formula of the compound is (1) A2B5 (2) A2B (3) AB2 (4) A2B3 Ans: [1] 3. The magnetic moment (spin only) of NiCl4 4 is (1) 1.41BM (2) 1.82 BM (3) 5.46 BM (4) 2.82 BM Ans: [4] 4. Which of the following facts about the complex Cr NH3 6 Cl3 b g is wrong? (1) The complex gives which precipitate with silver nitrate solution. (2) The complex involves d2sp3 hybridisation and is octahedral in shape. (3) The complex is paramagnetic (4) The complex is an outer orbital complex. Ans: [4] 5. The rate of a chemical reaction doubles for every 10C rise of temperature. If the temperature is sraised by 50C the rate of the reaction increases by aobut: (1) 64 times (2) 10 times (3) 24 times (4) 32 times Ans: [4] 6. ‘a’ and ‘b’ are van der Waals’ constants for gases. Chlorine is more easily liquefied than ethane because (1) a for Cl2  a for C2H6 but b for Cl2  b for C2H6 (2) a and b for Cl2  a and b for C2H6 (3) a and b for Cl2  a and b for C2H6 (4) a for Cl2  a for C2H6 but b for Cl2  b for C2H6 Ans: [2] 7. The hybridisation of orbitals of N atom in NO3 NO2  ,  and NH4  are respectively: (1) sp2 , sp3, sp (2) sp, sp2 , sp3 (3) sp2 , sp, sp3 (4) sp, sp3, sp2 Ans: [3] 8. Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it form freezing at 6C will be: ( Kf foer water  1.86 K kg mol1 and molar mass of ethylene glycol  62 g mol1 ) (1) 304.60 g (2) 804.32 g (3) 204.30 g (4) 400.00 g Ans: [2] 9. The outer electron configuration of Gd (Atomic No : 64) is (1) 4f 7 5d1 6s2 (2) 4f 3 5d5 6s2 (3) 4f 8 5d0 6s2 (4) 4f 4 5d4 6s2 Ans: [1] 10. The structure of IF7 is (1) pentagonal bipyramid (2) square pyramid (3) trigonal bipyramid (4) octahedral Ans: [1] CHEMISTRY [6] AIEEE 2011 / Code C 11. Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of: (1) an acetylenic triple bond (2) two ethylenic double bonds (3) a vinyl group (4) an isopropyl group Ans: [3] 12. The degree of dissociation () of a weak electrolyte, AxBy is related to van’t Hoff factor (i) by the expression: (1)      x y i 1 1 (2)      i x y 1 b 1g (3)      i x y 1 1 (4)      x y i 1 1 Ans: [2] 13. A gas absorbs a photon of 355 nm and emists at two wavelengths. If one of the emissions is at 680 nm, the other is at: (1) 518 nm (2) 1035 nm (3) 325 nm (4) 743 nm Ans: [4] 14. Identify the compound that exhibits tautomerism. (1) Phenol (2) 2-Butene (3) Lactic acid (4) 2-Pentanone Ans: [4] 15. The entropy change involved int he isothermal reversible expansion of 2 moles of an ideal gas form a volume of 10 dm3 to a volume of 100 dm3 at 27C is (1) 42.3 J mol1 K1 (2) 38.3 J mol1 K1 (3) 35.8 J mol1 K1 (4) 32.3 J mol1 K1 Ans: [2] 16. Silver Mirror test is given by which one of the following compounds? (1) Benzophenone (2) Acetaldehyde (3) Acetone (4) Formaldehyde Ans: [2, 4] 17. Trichloroacetaldehyde was subjected to Cannizszaro’s reaction by using NaOH . The mixture of the products contains sodium trichloroacetate and another compound. The other compound is: (1) Chloroform (2) 2, 2, 2-Trichloroethanol (3) Trichloromethanol (4) 2, 2, 2-Trichloropropanol Ans: [2] 18. The reduction potential of hydrogen half cell will be negative if: (1) pbH2 g  2 atm and H  2.0 M (2) pbH2 g  1 atm and H  2.0 M (3) pbH2 g  1 atm and H  1.0 M (4) pbH2 g  2 atm and H  1.0 M Ans: [4] 19. Phenol is heated with a solution of mixture of KBr and KBrO3 . The major product obtained in the above reaction is: (1) 2, 4, 6-Tribromophenol (2) 2-Bromophenol (3) 3-Bromophenol (4) 4-Bromophenol Ans: [1] 20. Among the following the maximum covalent character is shown by the compound: (1) MgCl2 (2) FeCl2 (3) SnCl2 (4) AlCl3 Ans: [4] 21. Boron cannot form which one of the following anions? (1) BO2  (2) BF6 3 (3) BH4  (4) BbOHg4  Ans: [2] CHEMISTRY [7] AIEEE 2011 / Code C 22. Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is (1) Ethyl ethanoate (2) Diethyl ether (3) 2-Butanone (4) Ethyl chloride Ans: [1] 23. Which of the following reagents may be used to distinguish between phenol and benzoic acid (1) Neutral FeCl3 (2) Aqueous NaOH (3) Tollen’s reagent (4) Molisch reagent Ans: [1] 24. A vessel at 1000 K contains CO2 with a pressure of 0.5 atm. Some of the CO2 is converted into CO on the addition of graphite. If the total pressure at equilibrium is 0.8 atm the value of K is (1) 0.18 atm (2) 1.8 atm (3) 3 atm (4) 0.3 atm Ans: [2] 25. The strongest acid amongst the following compounds is (1) ClCH2CH2CH2COOH (2) CH3COOH (3) HCOOH (4) CH3CH2CH Cl CO2H b g Ans: [4] 26. Which one of the following orders presents the correct sequence of the increasing basic nature of the given oxides? (1) K2O Na2O Al2O3 MgO    (2) Al2O3 MgO Na2O K2O    (3) MgO  K O  Al O  Na O 2 2 3 2 (4) MgO  K O  MgO  Al O 2 2 3 Ans: [2] 27. A 5.2 molal aqueous solution of methyl alcohol, CH3OH is supplied. What is the mole fraction of methyl alcohol in the solution? (1) 0.050 (2) 1.100 (3) 0.190 (4) 0.086 Ans: [4] 28. The presence or absence of hydroxy group on which carbon atom of sugar differentiates RNA and DNA? (1) 4th (2) 1st (3) 2nd (4) 3rd Ans: [3] 29. Which of the following statement is wrong? (1) N2O4 has two resonance structures. (2) The stability of hydrides increases form NH3 to BiH3 in group 15 of the periodic table. (3) Nitrogen cannot form d  p bond. (4) Single N– N bond is weaker than the single P  P bond. Ans: [2] 30. Which of the following statements regarding sulphur is incorrect? (1) The oxidation state of sulphur is never less than +4 in its compounds. (2) S2 molecular is paramagnetic (3) The vapour at 200C consists mostly of S8 rings. (4) At 600C the gas mainly consists of S2 Ans: [1] [8] AIEEE 2011 PHYSICS 61. A Carnot engine operating between temperatures T1 and T2 has efficiency 1 6 . When T2 is lowered by 62 K, its efficiency increases to 1 3 . Then T1 and T2 are, respectively: (1) 310 K and 248 K (2) 372 K and 310 K (3) 372 K and 330 K (4) 330 K and 268 K Ans: (2) 62. A pulley of radius 2 m is rotated about its axis by a force F  e20t  5t 2 j newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about is axis of rotationis 10kgm2 , the number of rotations made by the pulley before its direction of motion if reversed, is: (1) more than 9 (2) less than 3 (3) more than 3 but less than 6 (4) more than 6 but less than 9 Ans: (3) 63. Three perfect gases at absolute temperatures T1,T2 and T3 are mixed. The masses of molecules are m1,m2 and m3 and the number of molecules are n1,n2 and n3 respectively. Assuming no loss of energy, the final temperature of the mixtures is: (1) n T n T n T n T n T n T 1 2 1 2 2 2 2 2 3 2 3 2 1 1 2 2 3 3     (2) T1 T2 T3 3 b   g (3) n T n T n T n n n 1 1 2 2 3 3 1 2 3     (4) n T n T n T n T n T n T 1 1 2 2 2 2 3 3 2 1 1 2 2 3 3     Ans: (3) 64. A boat is moving due east in a region where the earth’s magnetic field is 5.0105 NA1 m1 due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is 1.50ms1 , the magnitude of the induced emf in the wire of aerial is: (1) 0.15 mV (2) 1 mV (3) 0.75 mV (4) 0.50 mV Ans: (1) 65. A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a dimater of the disc to reach its other end. During the journey of the insect, the angular speed of the the disc: (1) first increases and then decreases (2) remains unchanged (3) continuously decreases (4) continuously increases Ans: (1) 66. Two identical charged spheres suspneded from a common point by two massless strings of length  are initially a distance dbd  g a part because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them, (1) v  x (2) v  x  1 2 (3) v  x1 (4) v  x  1 2 Ans: (2) 67. 100 g of water is heated fvrom 30 oC to 50 oC. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J / kg / K): (1) 2.1 kJ (2) 4.2 kJ (3) 84 kJ (4) 8.4 kJ Ans: (4) 68. The half life oa radioactive substance is 20 minutes. The approximate time interval t2 t1 b  g between the time t2 when 2 3 of it has decayed and time t1 when 1 3 of it had decayed is (1) 28 min (2) 7 min (3) 14 min (4) 20 min Ans: (4) PART C — PHYSICS [9] AIEEE 2011 PHYSICS 69. Energy required for the electron excitation in Li from the first to the third Bohr orbit is: (1) 122.4 eV (2) 12.1 eV (3) 36.3 eV (4) 108.8 eV Ans: (4) 70. The electrostatic potential inside a charged spherical ball is given by   ar2  b where r is the distance fromt he centre ; a, b, are constants. Then the charge density inside the ball is (1) 6a 0 (2) 24 0  a r (3) 6a 0r (4) 24 0  a Ans: (1) 71. Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution  0.03Nm1 ): (1) 0 4 .  mJ (2) 4 mJ (3) 0 2 .  mJ (4) 2 mJ Ans: (1) 72. A resistor ‘R’and 2 F capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed. blog10 2.5  0.4g (1) 3.3107  (2) 1.3104  (3) 1.7 105  (4) 2.7 106  Ans: (4) 73. A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is: (1)   0 4 I R (2)   0 2 I R (3)   0 2 2 I R (4)   0 2 I R Ans: (2) 74. An object, moving with a speed of 6.25 m / s, is decelerated at a rate given by dv dt  2.5 v where v is the instantaneous speed. The time taken by the object, to come to rest, woudl be: (1) 8 s (2) 1 s (3) 2 s (4) 4 s Ans: (3) 75. Direction: The question has paragraph fllowed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex surface of a plen-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement – 1: When light reflects from the air-lgass plate interface, the reflected wave surfers a phase change of . Statement – 2: The centre of the interference pattern is dark. (1) Statement – 1 is flase, Statement – 2 is true. (2) Statement – 1 is true, Statement – 2 is flase. (3) Statement – 1 is true, Statement – 2 is true and Statement – 2 is the correct explanation of Statement – 1 (4) Statement – 1 is true, Statement – 2 is true and Statement – 2 is not the correct explantion of Statement – 1. Ans: (3) 76. Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is: (1)  9Gm r (2) zero (3)  4Gm r (4)  6Gm r Ans: (1) [10] AIEEE 2011 PHYSICS 77. This equation has Statement – 1 and Statement – 2. Of the four choices given afterthe statements, choose the one that best decrribes the two statements. Statement – 1: Sky wave signals are used for long distance radio communication. These signlas are in gneeral, less table than ground wave signals. Statement – 2: The state of ionosphere varies from hour to hour, day to day and season to season. (1) Statement – 1 is flase, Statement – 2 is true. (2) Statement – 1 is true, Statement – 2 is flase. (3) Statement – 1 is true, Statement – 2 is true and Statement – 2 is the correct explanation of Statement – 1 (4) Statement – 1 is true, Statement – 2 is true and Statement – 2 is not the correct explantion of Statement – 1. Ans: (3) 78. A fully charged capacitor C with iniital charge q0 is connected to a coil of self inductance L at t  0. The imt at which the enrgy is stored equally between the electric and the magnetic fiedls is: (1) LC (2)  LC (3)  4 LC (4) 2 LC Ans: (3) 79. This equation has Statement – 1 and Statement – 2. Of the four choices given afterthe statements, choose the one that best decrribes the two statements. Statement – 1: A metallic surface is irradiated by a monochromatic light of frequency v  v0 (the threshold frequency). The maximum kinetic energy and the stopping potential are Kmax and V0 respectively. If the frequency incident on the surfaceis doubled, both the Kmax and V0 are also doubled. Statement – 2: The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light. (1) Statement – 1 is flase, Statement – 2 is true. (2) Statement – 1 is true, Statement – 2 is flase. (3) Statement – 1 is true, Statement – 2 is true and Statement – 2 is the correct explanation of Statement – 1 (4) Statement – 1 is true, Statement – 2 is true and Statement – 2 is not the correct explantion of Statement – 1. Ans: (1) 80. Water is flowing continuously from a tap having an internal diameter 8 103 m. The water velocity as it leaves the tap is 0.4ms1 . The dimaeter of the water stream at a distance 2 101 m below the tap is close to: (1) 3.6 103 m (2) 5.0103 m (3) 7.5103 m (4) 9.6 103 m Ans: (1) 81. A mass M, attached to a horizontal spring, executes SHM with amplitude A1 . When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A2 . The ratio of A A 1 2 FH G IK J is: (1) M m M  FH G IK J 1 2 (2) M M m (3) M m M  (4) M M  m FH G IK J 1 2 Ans: (1) 82. Two particles are executing simple harmonic motion of the same amplitude A and frequency  along the axaxis. Their mean positionis separated by distance X0 X0 A b  g . If the maximum separation between them is X0 A b  g , the phase difference between their motion is (1)  6 (2)  2 (3)  3 (4)  4 Ans: (3) [11] AIEEE 2011 PHYSICS 83. If a wire is stretched to make it 0.1% longer, its resitance will (1) decrease by 0.05% (2) increase by 0.05% (3) increase by 0.2% (4) decrease by 0.2% Ans: (3) 84. A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is: (1)  v g 2 2 (2)  v g 2 (3)  v g 4 2 (4)  2 4 2 v g Ans: (3) 85. A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats  . It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by: (1)   1 2 2 b g R Mv K (2)     1 2 1 2 b g b gR Mv K (3)    1 2 2 b g R Mv K (4) Mv R K 2 2 Ans: (1) 86. A screw gauge gives the following reading when used to measure the diameter of a wire Main scale reading: 0 mm. Circular scale reading: 52 dividison Given tghat 1 mm on main scale corresponds to 100 dividions of the circular scale. The dimater of wire from the above data is (1) 0.005 cm (2) 0.52 cm (3) 0.052 cm (4) 0.026 cm Ans: (3) 87. A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform ciruclar disc, the acceleration of the mass m, if the string does not slip on the pulley, is (1) g 3 (2) 3 2 g (3) g (4) 2 3 g Ans: (4) 88. The transverse displacement ybx,tg of a wave on a string is given by y x t e ax bt abxt b , g  e j  2  2 2 This represents a: (1) standing wave of frequency 1 b (2) wave moving in +x direction with speed a b (3) wave moving in –x direction with speed b a (4) standing wave of fcrequency b Ans: (3) 89. A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m / s. The speed of the image of the second car as seen in the mirror of the first one is: (1) 15 m / s (2) 1 10 m/ s (3) 1 15 m/ s (4) 10 m / s Ans: (3) 90. Let the x – z plane be the boundary between two transparewnt media. Medium 1 in z  0 has a refractive index of 2 and medium 2 with z < 0 has a refractive index of 3. A ray of light in medium 1 given by the vector A  6 3i 8 3 j 10k is incident on the plane of separation. The angle of refraction in medium 2 is: (1) 75o (2) 30o (3) 45o (4) 60o Ans: (3)