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# Aieee pt 5 2012

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### Aieee pt 5 2012

2. 2. Vidyamandir Classes PART - I (PHYSICS) 30 × 4 = 120 MARKS1. Dimensions of resistance in an electrical circuit, in terms of dimension of mass M of length L of time T and of current I would be : (A)  ML2T 3 I 1  (B)  ML2T 1 A1  (C)  ML2T 1 I 1  (D)  ML2T 3 I 2            2. Two vectors A and B are inclined at an angle  . Now if the vectors are interchanged then the resultant turns through an angle  . Which of the following relation is true : 2   A B    A  B  (A) tan   tan (B) tan   tan 2  A B  2 2  A  B 2 2   A B    A  B  (C) tan    cot (D) tan   cot 2  A B  2 2  A  B 23. A metro train starts from rest and in five seconds achieves 108 kmh 1 . After that it moves with constant velocity and goes to rest after traveling 45 m with uniform retardation. If total distance traveled in 395m, find total time of traveling. (A) 12.2 s (B) 15.3 s (C) 9s (D) 17.17 s4. Two paper screen A and B are separated by a distance of 200 m. A bullet pierces A and then B. The hole in B is 40cm below the hole in A. If the bullet is traveling horizontally at the time of hitting A, then the velocity of the bullet at A is : (A) 200 ms 1 (B) 400ms 1 (C) 600ms 1 (D) 700ms 15. A road of 10 m width has radius of curvature 50 m. Its outer edge is raised above the inner edge by a distance of 1.5 m. The road is most suited for vehicle moving with velocity of (A) 8.5 ms 1 (B) 10 ms 1 (C) 10 2 ms 1 (D) 5 2 ms 16. Two elastic blocks P and Q of equal masses m and connected by a massless spring rest on a smooth horizontal surface, as shown in R P Q the figure. A third block R of the same mass M strikes the block P. After the collision, P and Q will (A) Always move in same direction (B) Sometimes move in same direction and sometime move in opposite directions (C) Always move in opposite directions (D) be at rest with respect to each other7. A force F = Ay2 + By + C acts on a body in the y-direction. The work done by this force during a displacement from y   a to y  a is : 2 Aa 3 2 Aa 3 2 Aa 3 Ba 2 (A) (B)  2Ca (C)   Ca (D) None of these 3 3 3 2 SPACE FOR ROUGH WORK VMC/IITJEE-2012 2 AIEEE Practice Test
3. 3. Vidyamandir Classes8. Two spherical bodies of masses M and 5M in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is : (A) 2R (B) 4.5 R (C) 7.5 R (D) 10 R9. Three rod each of length L and mass M are placed along X, Y and Z area in such a way that one end of each rod is at the origin. The moment of inertia of the system about Z-axis is : ML2 2 ML2 3ML2 2 ML2 (A) (B) (C) (D) 3 3 2 1210. A ring of radius R is first rotated with an angular velocity ω0 and then carefully placed on a rough horizontal surface. The coefficient of friction between the surface and the ring is  . Time after which its angular speed is reduced to half is : ω0  R 2ω 0 R ω0 R ω0 g (A) (B) (C) (D) 2g g 2 g 2 R11. Two simple harmonic motions act on a particle. These harmonic motions are x  A cos ωt  y  A cosωt then (A) an ellipse and the actual motion is counter clockwise (B) an ellipse and the actual motion is clockwise (C) A circle and the actual motion is counter clockwise (D) A circle and the actual motion is clockwise12. An organ pipe P1 closed at one end vibrating in its first harmonic and another pipe P2 open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is : (A) 1/3 (B) 1/6 (C) 3/8 (D) 8/313. The bulk modulus of a metal is 8  109 Nm 2 and its density is 11 gcm 3 . The density of this metal under a pressure of 20,000 N cm 2 will be (in gcm 3 ) 440 431 451 40 (A) (B) (C) (D) 39 39 39 3914. The work done in increasing the size of a rectangular soap film with dimension 8cm  3.75 cm to 10cm  6cm is 2  104 J . The surface tension of the film in Nm 1 is : (A) 1.65  102 (B) 3.3  102 (C) 6.6  102 (D) 8.25  10215. N molecules, each of mass m of gas A and 2N molecular each of mass 2m of gas B are contained in the same vessel which is maintained at a temperature T. The mean square velocity of molecules of B type is denoted by V2 and the V means square velocity of A type is denoted by V1, then 1 . V2 (A) 2 (B) 2 (C) 1/3 (D) 2/316. There are 10 condensers each of capacity 5 F . The ratio between maximum and minimum capacities obtained from these condensers will be : (A) 25 : 5 (B) 40 : 1 (C) 60 : 3 (D) 100 : 1 SPACE FOR ROUGH WORK VMC/IITJEE-2012 3 AIEEE Practice Test
4. 4. Vidyamandir Classes17. A full wave rectifier circuit along with the input and output are shown in the figure, the contribution from the diode I is (are) (A) C (B) A, C (C) B, D (D) A, B, C, D18. A potential difference of V is applied at the ends of a copper wire of length  and diameter d. On doubling only d, the drift velocity. (A) becomes two time (B) becomes half (C) does not change (D) becomes one – fourth19. Two identical cells of emf E. and internal resistance r are connected in parallel with an external resistance R. To get maximum power developed across R, the value of R is : (A) R = r/2 (B) R=r (C) R = r/3 (D) R = 2r20. The deflection in a moving coil galvanometer is : (A) directly proportional to the torsional constant (B) directly proportional to the number of turns in the coil (C) inversely proportional to the area of the coil (D) inversely proportional to the current flowing21. The magnetic moment of a magnet is 0.1 amp  m2. It is suspended in a magnetic field of intensity 3  104 Wbm 2 . The couple acting upon it when deflected by 30 from the magnetic field is : (A) 1  105 Nm (B) 1.5  105 Nm (C) 2  105 Nm (D) 2.5  105 Nm22. Two coil have mutual inductance 0.005 H. The current changes in the first coil according to equation i  i0 sin t where i0  10 A and   100 rads 1 . The maximum value of emf in 2nd coil is: (A) 2 (B) 5 (C)  (D) 423. Two plane mirror are inclined at an angle  . It is found that a ray incident on one mirror at any angle is rendered parallel to itself after reflection from both the mirrors. The value of  is : (A) 30 (B) 60 (C) 90 (D) 12024. Light of wavelength  is incident on a slit of width d. The resulting diffraction pattern is observed on a screen at a distance D. The linear width of the principal maximum is equal to the width of the slit, if D equal. d2 d 2 2 2 (A) (B) (C) (D) 2  d d SPACE FOR ROUGH WORK VMC/IITJEE-2012 4 AIEEE Practice Test
5. 5. Vidyamandir Classes25. An electromagnetic wave going through vacuum is described by : E  E0 sin  kx  ωt   B  B0 sin  kx  ωt  . Which of the following equation is true? (A) E0k  B0ω (B) E0ω  B0k (C) E0 B0  ωk (D) None of these26. The variation of photoelectric current given by the photocell, with the intensity of light, is given by a graph, which is a straight line with : (A) +ve slop with intercept on current axis (B)  ve slope with intercept of current axis (C) +ve slop passing through origin (D)  ve slope passing through origin27. A radioactive sample with half-life of 1 month has the level “Activity = 2 Ci on 1-8-1991”. What was its activity two month earlier? (A) 1.0 Ci (B) 0.5Ci (C) 4 Ci (D) 8 Ci28. To get an output Y = 1 from the circuit shown in figure the inputs A, B and C must be respectively. (A) 1, 0, 1 (B) 1, 1, 0 (C) 0, 1, 0 (D) 1, 0, 029. The antenna current of an AM transmitter is 8 A when only the carrier is sent, but it increases to 8.903 A when the carrier is sinusoidal modulated. The percentage modulation is nearly. (A) 90% (B) 80% (C) 75% (D) 70%30. For CE configuration of a transistor, mark the correct statement(s). (A) Input characteristic is plotted between base current and base to emitter voltage keeping collector current constant. (B) Input characteristic is plotted between base current and base to emitter voltage keeping collector to emitter voltage constant. (C) Input characteristic is plotted between emitter current and base to emitter voltage keeping collector to emitter voltage constant. (D) Any of the above may be correct. PART - II (CHEMISTRY) 30 × 4 = 120 MARKS31. Pure ammonia is placed in a vessel at a temperature at which its dissociation constant is appreciable. At equilibrium : (A) Kp does not change significantly with pressure (B) the degree of dissociation does not change with pressure (C) the concentration of NH3 does not change with pressure (D) the concentration of H2 is less than that of N232. The gas-phase reaction 2NO 2  O2  N 2 O  O2 has the rate constant k  2.0  104 dm3 mol 1 s1 at 300 K.  The order of the reaction is : (A) 1 (B) 2 (C) 3 (D) 0 SPACE FOR ROUGH WORK VMC/IITJEE-2012 5 AIEEE Practice Test
6. 6. Vidyamandir Classes33. For an exothermic reaction, (A) the activation energy of the backward reaction is greater than the activation of the forward reaction (B) the activation energy of the backward reaction is lower than the activation energy of the forward reaction (C) the activation energy of the reactants is greater than the energy of the intermediate state (D) the total activation energy of the reactants must be equal to the total activation of the products34. For the precipitation reaction of Ag+ ion with NaI, which of the following statements is correct ? (A) H for the reaction is zero (B) G for the reaction is zero (C) G for the reaction is negative (D) G  H 35. Which of the following pairs of solutions constitutes a buffer having pH = pKa ? (A) 0.1 M HCl and 0.1 M NaCl (B) 0.1 M HAc and 0.1 M NaAc (C) 0.1 M HAc and 0.2 M NaAc (D) 0.2 M HAc and 0.1 M NaAc36. Fe 2   2e  Fe ; E 0   0.44 V  Fe3   3e  Fe ; E 0   0.036 V  Considering the above data, the standard electrode potential (E0) for Fe3   e  Fe2  is :  (A) 0.476 V (B) 0.404 V (C) 0.404 V (D) + 0.771 V37. In a lead storage battery : (A) Pb is oxidized to PbSO4 at the anode (B) PbO2 is reduced to PbSO4 at the cathode (C) both electrodes are immersed in the same aqueous solution of H2SO4 (D) All the above are true38. The vapour pressure of a solution containing 5.0 g of a non-electrolyte in 100.0 g of water at a particular temperature is 298.5 N m 2 . If the vapour pressure of pure water is 300 N m 2 , the molecular weight of the solute is : (A) 60.0 (B) 120.0 (C) 180.0 (D) 380.039. Which of the following aqueous solutions will have the lowest freezing point ? (A) 0.10 M potassium sulphate (B) 0.10 M sodium chloride (C) 0.10 M urea (D) 0.10 M glucose40. The mathematical expression for Kb is given by : 2 2 RTb RTb (A) Kb  (B) Kb  1000 L vap 1000 H vap 2 2 Tb RTb H vap (C) Kb  (D) Kb  1000 L vap 100041. Human blood is isotonic with 0.9% NaCl solution at 27C . What is the osmotic pressure ? (A) 8.6 atm (B) 3.8 atm (C) 15.2 atm (D) 7.6 atm SPACE FOR ROUGH WORK VMC/IITJEE-2012 6 AIEEE Practice Test
7. 7. Vidyamandir Classes42. Sodium thiosulphate is prepared by : (A) boiling Na2SO3 solution with S in alkaline medium (B) reducing Na2SO4 solution with S in with H2S (C) boiling Na2SO3 solution with S in acidic medium (D) neutralising H2S2O3 solution with NaOH43. Gypsum, CaSO4.2H2O on heating to about 120C forms a compound which has the chemical composition represented by : (A) CaSO4.H2O (B) 2CaSO4.3H2O (C) 2CaSO4.H2O (D) CaSO444. Aluminium vessels should not be washed with materials containing washing soda since : (A) washing soda reacts with aluminium to form soluble aluminate (B) washing soda reacts with aluminium to form insoluble aluminium oxide (C) washing soda is expensive (D) washing soda is easily decomposed45. Oxalic acid when heated with conc. H2SO4, gives out : (A) CO and CO2 (B) CO2 and H2S (C) H2O and CO2 (D) oxalic sulphate46. The two isomers given below are : COOH HOOC | | H  C  OH H  C  OH I. | II. | HO  C  H H  C  OH | | COOH HOOC (A) enantiomers (B) diastereomers (C) mesomers (D) position isomers47. Total possible structural isomers (not stereo) of C4H6 are : (A) 4 (B) 6 (C) 9 (D) 1248. Acetaldehyde is not obtained in the reactions : 3 1. O (A) CH 2  CH  CH  CH 2  (B) 2. Zn, H 2 O 4 HgSO 4 Pd-BaSO (C) HC  CH  H 2O  (D) CH 3COCl  H 2   H 2SO 449. [Pt(NH3)4Cl2]Br2 and [Pt(NH3)4Br2]Cl2 are related to : (A) optical isomer (B) linkage isomers (C) coordinate isomers (D) ionisation isomers SPACE FOR ROUGH WORK VMC/IITJEE-2012 7 AIEEE Practice Test
8. 8. Vidyamandir Classes50. Among [Fe(H 2O)6 ]3 , [Fe(CN)6 ]3 , [Fe(Cl)6 ]3  species, the hybridisation state of the Fe atom are, respectively : (A) d2 sp3 , d 2sp3 , sp3d 2 (B) sp3d2 , d 2sp3 , d 2sp3 (C) sp3d 2 , d 2 sp3 , sp3d 2 (D) None of these51. The H  of O3, CO2, NH3 and HI are 142.2,  393.3,  46.2 and 25.9 kJ per mole respectively. The order of their f increasing stabilities will be : (A) O3, CO2 , NH 3 , HI (B) CO2 , NH 3, HI, O3 (C) O3, HI, NH 3 , CO2 (D) NH 3 , HI, CO2 , O352. A cylinder of gas is assumed to contain 11.2 kg of butane (C4H10). If a normal family needs 20000 kJ of energy per day. The cylinder will last (Given that H for combustion of butane is 2658 kJ ) (A) 20 days (B) 25 days (C) 26 days (D) 24 days53. The number of atoms in 100 g of an fcc crystal with density, d = 10g/cm3 and cell edge equal to 100 pm, is equal to (A) 1  1025 (B) 2  1025 (C) 3  1025 (D) 4  102554. A gas is heated in such a way so that its pressure and volume both becomes double. Again by lowering temperature, one fourth of initial number of moles of air has been taken in, to maintain the double volume and pressure. By what fraction, the temperature must have been raised finally? 1 4 16 8 (A) times (B) times (C) times (D) times 5 5 5 555. A particle ’A’ moving with a certain velocity has the de-Broglie wavelength of 1Å . For particle B with mass 25% of A and velocity 75% of A, calculate the de-Broglie wavelength. (A) 3Å (B) 5.33 Å (C) 6.88 Å (D) 0.48 Å56. The number of  and  -particles emitted in the nuclear reaction 228 90 Th  83 Bi 212 are  (A) 4 and1  (B) 3 and 7 (C) 8 and 1 (D) 4 and 757. Iso-electric point is a (A) specific temperature (B) suitable concentration of amino acid (C) hydrogen ion concentration that does not allow migration of amino acid under electric field (D) melting point of an amino acid under the influence of electric field.58. Proteins when heated with conc. HNO3 give yellow colour. This is : (A) Hopper’s test (B) acid-base test (C) biuret’s test (D) xanthoprotic test59. Bakelite is an example of (A) elastomer (B) fibre (C) thermoplastic (D) thermosetting polymer60. Caprolactam used for manufacturer of nylon-6 is obtained by Beckmann rearrangement of (A) benzophenone oxime (B) acetophenone oxime (C) cylohexanone oxime (D) cyclopentanone oxime SPACE FOR ROUGH WORK VMC/IITJEE-2012 8 AIEEE Practice Test
9. 9. Vidyamandir Classes PART - III (MATHEMATICS) 30 × 4 = 120 MARKS61. If a, b, c are in A.P. then a variable line. ax  by  c  0 , will always pass through the point : (A) (2, 1) (B)  2,  1 (C)  2 ,  1 (D)  2, 162. The range of  for which tan 2   sec    holds for some  is : (A) 1,   (B) 1,   (C)  1,   (D)  1,   7 1 7  163. The coefficient of in the expansion of 1  x  .  1   is : x  x 14! 14! 14! 14! (A) (B) (C) (D) 7!8! 6!8! 7!7! 6!7!  x2  1   64. If lim   ax  b   2 then : x   x  1    (A) a  1, b  3 (B) a  1, b  3 (C) a  1, b  3 (D) a  1, b  365. Statement 1 : If a polygon has 45 diagonals, then its number of sides is 10. Statement 2 : Number of ways of selecting 2 points from n non collinear points is nC2. (A) Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True66. If y  f  x  is an odd differentiable function defined on   ,   such that f   3  2 , then f   3 equals : (A) 4 (B) 2 (C) 2 (D) 067. The solution of the differential equation  x  y  dx  dy   dx  dy is : (A) x  y  ke x  y (B) x  y  ke x  y (C) x  y  k  x  y  (D) x  y  ke x  y68. Statement 1 : A   x, y   R  R : y  x is an even integer . Statement 2 : B   x, y   R  R : x   y for some integer   . (A) Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True x log t 1 If f  x   f  x   f   is equal to :69. 1 1  t dt then x 2 1 1 (A)  loge x 2 (B) loge x (C) loge x (D)  loge x 2 3 2 2 SPACE FOR ROUGH WORK VMC/IITJEE-2012 9 AIEEE Practice Test
10. 10. Vidyamandir Classes70. If z is a complex number such that equation z  a 2  z  2a  3 always represents an ellipse, then a belongs to : (A) (0, 3) (B)  3,   (C)   , 3 (D)   , 0   3,  71. The letters of the word ‘PROBABILITY’ are written down at random in a row. Let E1 denotes the event that two Is  E1  are together and E2 denotes the event that two Bs are together then p  is : E    2 1 1 1 1 (A) (B) (C) (D) 2 3 5 672. Let S   0,   denotes the set of values of x satisfying the equation 1  cos x  cos 2 x  cos 3 x  . . . .  8  43 then S =     2    2    2  (A)   (B)  ,  (C)  ,  (D)  ,  3 3 3   3 3  3 3 73. If f : R  R , g : R  R be two functions, and h  x   2 min  f  x   g  x  , 0 then h (x) = (A) f  x  g  x  g  x  f  x (B) f  x  g  x  g  x  f  x (C) f  x  g  x  g  x  f  x (D) f  x  g  x  g  x  f  x  x 1 y 3 z 274. The distance of the point (3, 8, 2) from the line   measured parallel to the plane 2 4 3 3 x  2 y  2 z  15  0 is : (A) 6 (B) 7 (C) 3 (D) 2                    75. Let r , a , c and c be four non zero vectors such that r . a  0, r  b  r b and  a b c   0 , then if           r  c  k r c then k will be : 1 (A) 1 (B) 0 (C) (D) cannot be determined 276. The straight lines x  3 y  3m and x  3 y  3 m intersect in a curve. Let an ellipse with eccentricity x2 y2 reciprocal to that of curve is   1 . If the ellipse passes through a focus of the curve, then the ellipse will be : a2 b2 x2 y2 x2 y2 (A)  1 (B) x2  4 y 2  4 (C) 4x2  y2  4 (D)  1 3 2 2 3 2 sin x dy  77. If y  y  x  and   cos x, y  0   1 , then y   equal : y  1 dx 2 1 2 1 (A) (B) (C) (D) 1 3 3 3 SPACE FOR ROUGH WORK VMC/IITJEE-2012 10 AIEEE Practice Test
11. 11. Vidyamandir Classes        78. If a , b are non zero and non-collinear vectors then j j ˆ ˆ  a b i  i   a b ˆ  ˆ   a b k  k is : ˆ ˆ                (A) a b (B) a b (C) a b (D) b a79. If the circumference of the circle x 2  y 2  2 x  8 y    0 is bisected by the circle x 2  y 2  4 x  22 y    0 then  will be : (A) 15 (B) 20 (C) 25 (D) 30 1 180. If A and B are independent events of a random experiment such that P  A  B   6  and P A  B   3 then P(A) is equal to : 1 1 1 2 (A) (B) (C) (D) 4 6 3 381. Consider the system of equations in x, y, z as : x sin 3  y  z  0 x cos 2  4 y  3z  0 2x  7 y  7z  0 If this system has a non trivial solution, then for any integer n, values of  are given by :  n   1n    n   1n   n  n   1n   (A) (B) (C) (D)  3   4  2  6       82. Negation of the statement P   q  r  is : (A) ~ P  ~  q  r  (B) ~ P  ~  q  r  (C) q  r  P (D) P   ~ q ~ r   x 3  x 2  10 x  7 , x  1 83. Let f  x    2   2 x  log2 b  4 , x  1   The set of values of b for which f (x) has greatest value at x = 1 is : (A)  6 ,  2  (B) (2, 6) (C)  6,  2    2, 6 (D)  6 ,  6 84. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b ? (A) a  1, b  6 (B) a  3, b  4 (C) a  0, b  7 (D) a  5, b  2 SPACE FOR ROUGH WORK VMC/IITJEE-2012 11 AIEEE Practice Test
12. 12. Vidyamandir Classes85.     If  2  2 x 2     6  y 2   3 z 2  4 x  3 2  4 y  2 3 z  1  0 , represents a sphere, the centre and radius of sphere is respectively : 34  1  (A)  1, 1,  1 , (B)  , 1,  1 , 34 2  2   1  1 34 (C)  , 1,  1 , 34 (D)  1, 2,  2  ,  2  4 2 n86. Statement 1 : If A is a matrix of order n  n then det  KA  K det  A . Statement 1 : If B is matrix obtained from A by multiplying any row or column by a scalar K then det B  K det A . (A) Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True87. If z1 lies on curve 2 z  11  10i  6 and z2 lies on z  1  z then minimum value of z1  z2 will be : (A) 2 (B) 4 (C) 6 (D) 8  1 , x  0 88. Let f  x    0 , x  0 and g  x   sin x  cos x then points of discontinuity of f g  x  in  0, 2  is : 1 , x0    3   3 7   2 5   5 7  (A)  ,  (B)  ,  (C)  ,  (D)  ,  2 4   4 4   3 3   4 3 89. Let R1 is the area bounded by f  x    x  , x-axis, x = 0 and x = 10 and R2 be the area bounded by g  x   x , x-axis, x = 0 and x = 10, then : (A) 9R1  R2 (B) 10R1  R2 (C) R1  10R2 (D) R1  9 R2 x x2  90. If e tf  t  dt  sin x  x cos x  for all x  R  0 then the value of f   will be equal to : 2 6 1 (A) 0 (B) 1 (C) (D) None of these 2 SPACE FOR ROUGH WORK VMC/IITJEE-2012 12 AIEEE Practice Test
13. 13. Vidyamandir Classes SPACE FOR ROUGH WORKVMC/IITJEE-2012 13 AIEEE Practice Test
14. 14. Vidyamandir Classes SPACE FOR ROUGH WORK * * * * Vidyamandir wishes you the very best for AIEEE-2012 * * * *VMC/IITJEE-2012 14 AIEEE Practice Test