Vidyamandir Classes 1 AIEEE HOME PRACTICE TEST -2010 19/04/2010 M.M. : 480 09.30 A.M. to 12.30 P.M. TIME : 3.00 Hrs Read the following Instructions very carefully before you proceed. The paper contains a total of 120 questions & 16 Printed Pages. [We have intentionally given 120 questions as you never know how many questions will be actually asked] Section : I -Chemistry 1 -40, Section : II -Physics 41 – 80, Section : III -Mathematics 81 – 120. Each question carries 4 Marks. 1 will awarded for every wrong answer (Negative Marking). For answering a question an ANSWER SHEET is provided separately. Please follow the directions in the question paper. Please darken the entire circle that corresponds to your answer for each question. Use only Black/Blue pen to fill the BUBBLES. Do not scribble anything on the answer sheet. Please Fill your Roll Number & Personal Information Properly in the space provided in the ANSWER SHEET. Wrong way of filling Right way of filling A B C D A B C D A B C D Please fill the following information carefully. REGISTRATION NO. NAME ROLL NUMBER Invigilator’s Signature 2 Vidyamandir Classes SECTION -I (Chemistry) M. Marks : 160 For Questions : 1 – 40 1. A mixture of aluminium and zinc weighing 1.67 g was completely dissolved in acid and evolved 1.69 litre of H2 at NTP. The weight of aluminium at the original mixture is : (A) 2.24 g (B) 1.24 g (C) 6.8 g (D) 4.2 g 2. Which combination is best explained by the coordinate covalent bond ? (A) 2HHO (B) Cl + Cl (C) 21MgO2 (D) H2 + I2 3. If ‘a’ is the initial concentration of the reactant, the half life period of the reaction of nth order is proportional to : (A) n1a (B) an (C) 1na (D) an + 1 4. Plot of AA11vsXY (XA mole fraction of A in liquid and YA in vapour) is linear whose slope and intercept respectively are given : (A) BABABppp/p,p (B) ABBABppp/p,p (C) BAABBppp/p,p (D) ABABBppp/p,p 5. In the sequence of following nuclear reactions. 2382189284nXYZLM The value of n will be : (A) 3 (B) 4 (C) 5 (D) 6 6. Borax structure contains : (A) two BO4 groups and two BO3 groups (B) four BO4 groups only (C) four BO3 groups only (D) three BO4 and one BO3 groups 7. In an isobaric process the ratio of heat supplied to the system d and work done by the system (dW) for diatomic gas is : (A) 1 : 1 (B) 7 : 2 (C) 7 : 5 (D) 5 : 7 8. The azeotropic mixture of water (b. pt. 100C) and HCl (b.pt. 85C) boils at 108.5C. When this mixture is distilled it is possible to obtain : (A) pure HCl (B) pure water (C) pure water as well as HCl (D) neither HCl nor H2O in their pure states 9. For the reaction 33BrOBrO2Br, in alkaline solution, the value of the second order (in BrO) rate constant at 80C in the rate law for BrO/t was found to be 110.056Lmols. Then 3BrO/t is : (A) 110.019Lmols (B) 110.112Lmols (C) 110.168Lmols (D) 110.056Lmols 10. The solubility of AgCl will be minimum in a sample of water containing : (A) AgNO3 (B) pure water (C) CaCl2 (D) Na Vidyamandir Classes 3 11. 3864NHCHOXY The compound X is : (A) o-xylene (B) phthalic acid (C) phthalic anhydride (D) salicyclic acid 12. A, B and C are respectively : (A) A = Raney Ni, H2, B = Sn/HCl (B) A = 2222NHNH,HOBSn/HCl C = 2222NHNH,HO C = Raney Ni, H2 (C) A = Sn/HCl, B = Raney Ni, H2 (D) A = 2222NHNH,HO, B = Raney Ni, H2 C = 2222NHNH,HO C = Sn/HCl 13. Which shows the least dipole moment ? (A) CHCl3 (B) CH3CH2OH (C) CH3COCH3 (D) CCl4 14. Which of the following is most stable ? (A) Na3N (B) Li3N (C) K3N (D) Rb3N 15. The compound reacts with MeMgI to give A and with Me2CuLi to give B. What are A and B (A) (B) (C) (D) 16. Which of the following attacks glass ? (A) HF (B) HBr (C) HCl (D) HI 17. For a gas in equilibrium with a liquid, the ratio of the concentration of the gas in the solution phase to that in the gaseous phase is constant at constant temperature only if molecules undergo : (A) ionization (B) dissociation (C) isolation (D) reaction with solvent 18. Number of optical isomers of lactic acid are : (A) 1 (B) 2 (C) 3 (D) 4 19. Which of the following reactions would convert 2-butanol into deuterated compound323CHCHCHCH|D ? (A) (B) (C) (D) CH3 – CH = CH – CH2 – NO2 CH3 – CH2 – CH2 – CH2 – NO2 CH3 – CH = CH – CH2 – NH2 CH3 – CH2 – CH2 – CH2 – NH2 A B C O Cl O Me O Me Me Me Me Cl OMgI Me Cl OMgI Me O Me Me OMgI Me Cl OLi Me OH H2SO4 heat 1. BD3/THF 2. H2O2, NOOH OH H2SO4 heat D2/Pt OH PBr3 1. Mg, diethyl ether 2. D2O OH PBr3 NaOD, D2O 4 Vidyamandir Classes 20. Equal weights of zinc metal and iodine are mixed together and the iodine is completely converted to zinc iodide. The fraction of the original zinc remains unreacted (Zn = 65.0) : (A) 0.744 (B) 0.647 (C) 0.372 (D) 0.451 21. The precipitate of 102spCaFK1.710 is obtained when equal volumes of the following are mixed : (A) 42410MCa10MF (B) 22310MCa10MF (C) Both (A) and (B) (D) None of these 22. In a cubic closed packed structure of mixed oxides, the lattice a made up of oxide ions, one eighth of tetrahedral voids are occupied by divalent ions (A2+), while one half of the octahedral voids are occupied by trivalent ions (B3+). What is the formula of the oxide ? (A) A3B2O4 (B) A2B2O4 (C) AB2O5 (D) AB2O4 23. Which of the following represents the correct sets of the four quantum numbers of a 4d electron ? (A) 4, 2, 1, 0 (B) 14,2,1,2 (C) 14,3,2,2 (D) 14,3,2,2 24. Reddish-brown (chocolate) ppt. are formed with (A) 246CuandFe(CN) (B) 224BaandSO (C) 2PbandI (D) None 25. A mixture of benzaldehyde and formaldehyde on heating with aqueous NaOH solution gives : (A) Benzyl alcohol and sodium formate (B) Sodium benzoate and methyl alcohol (C) Sodium benzoate and sodium formate (D) Benzyl alcohol and methyl alcohol 26. 3222NOClCH.CH.CH,NHA. Here ‘A’ is : (A) CH3CH2CH2Cl (B) CH3CH2CH2OH (C) 322CHCHCHNH|OH (D) 322CHCHCHNHCl 27. The bond dissociation energies of gaseous H2, Cl2 and HCl are 104.58 and 103 kcal respectively. The enthalpy of formation of HCl gas would be : (A) 44kcal (B) 44 kcal (C) 22kcal (D) 22 kcal 28. Which of the following molecular orbitals has two nodal planes ? (A) 2s (B) 2py (C) *2py (D) *2px 29. Action of concentrated nitric acid (HNO3) on metallic tin produces : (A) stannic nitrate (B) stannous nitrite (C) meta stannic acid (D) stannous nitrate 30. The major product obtained in the reaction : 23OHO||CHCHCCHHCN is : (A) |23OHCHCHC(CN)CH (B) 223O||NCCHCHCCH (C) |23COOHCHCHC(OH)CH (D) None of these Vidyamandir Classes 5 31. When phenolic ether is heated with HI it yields : (A) alkyl halide + aryl halide + water (B) (C) alcohol + aryl halide (D) None of these 32. Consider gaseous equilibrium of 22H(g)I(g)2HI(g) In the following graphs, the three gases are at equilibrium in a container. At some time t, extra I2 is added. Which of following sets will respond to this situation ? (A) (B) (C) (D) 33. What is the product of the following series of reactions ? (A) (B) (C) (D) 34. Cu+ ion is not stable in aqueous solution because of disproportionation reaction.E value for disproportionation of Cu+ is (given, 22Cu/CuCu/CuE0.15,E0.34V) : (A) + 0.38 V (B) 0.38V (C) + 0.49 V (D) 0.49V 35. When AgNO3 is added to a solution of 353Co(NH)Cl, the precipitate of AgCl shows two ionizable chloride ions. This means : (A) two chlorine atoms satisfy primary valency and one secondary valency (B) one chlorine atom satisfies primary as well secondary valency (C) three chlorine atoms satisfy primary valency (D) three chlorine atoms satisfy secondary valency 36. The order of activity of the various o-and p-direction is : (A) 33OOHOCOCHCOCH (B) 33OHOOCOCHCOCH (C) 33OHOCOCHOCOCH (D) 33OCOCHOCOCHOH alkyl halide + OH P HI I2 H2 t P HI I2 H2 t P HI I2 H2 t P HI I2 H2 t Cl O = C – CH3 Cl COOCH3 Cl HO – CH – CH3 Cl CH2CN Cl NH2 NaNO2, HCl H2O, 0C CuCN 1. CH3MgBr 2. H2O, H+ 6 Vidyamandir Classes 37. In the extraction of silver from argentite ore the ore is treated with dilute solution as NaCN in water in the presence of Y, whereby the following reaction takes place 2224AgX4NaCN2Y2NaAg(CN)NaXO X and Y in this reaction are represented by : (A) Cl and S (B) S and O2 (C) O and O2 (D) O and S 38. Ortho and para hydrogen differ in : (A) nuclear charge (B) nuclear reaction (C) electron spin (D) proton spin 39. Specific conductance of 0.1 M CH3COOH at 25C is 4113.910Ohmcm. If 3(HO) and 3(CHCOO) at 25C are 349.0 and 12141.0Ohmcmmol respectively degree of ionisation of CH3COOH at the given concentration is : (A) 1.0 % (B) 4.0 % (C) 5.0 % (D) 2.0 % 40. Which of the following is not the step-growth polymer ? (A) Nylon-66 (B) Nylon-6 (C) Bakelite (D) Dacron SECTION – II (Physics) M. Marks : 160 For Questions : 41 – 80 41. The kinetic energy of particle moving along a circle of radius R depends upon the distance covered S and is given by K = aS where a is a constant. Then the force acting on the particle is : (A) aSR (B) 22aSR (C) 22aSR (D) 2aSR 42. In case A, when an 80 kg skydiver falls with arms and legs fully extended to maximize his surface area, his terminal velocity is 60 m/s. In Case B, when the same skydiver falls with arms and legs pulled in and body angled downward to minimize his surface area, his terminal velocity increased to 80 m/s. In going from Case A to Case B, which of the following statements most accurately describes what the skydiver experiences ? (A) airresistanceF increases and pressure, P increases (B) airresistance F increases and pressure P, decreases (C) airresistance F decreases and pressure, P, increases (D) airresistance F remains the same and pressure, P, increases 43. A cylindrical tank 10 m high has an internal diameter of 4m. How much work would be required to fill the tank with water, if the water were pumped in at the bottom edge ? (A) 12.15 MJ (B) 6.15 MJ (C) 1.23 MJ (D) 3000 kJ 44. A particle is moving in a circle of radius R in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is v0, the time taken to complete the first revolution is : (A) 0Rv (B) 201Rev (C) 20Rev (D) 02Rv Vidyamandir Classes 7 45. A proton moving with velocity v0 strikes another proton at rest, assume impact parameter to be zero i.e., head on collision. How close will the incident proton go to other proton? [Note that both the protons are free to move and take mass of proton as m]. (A) 22004emv (B) 22002emv (C) 2200emv (D) Can’t be determined 46. A current source drivers a current in a coil of resistance R1 for a time t. The same source drives current in another coil of resistance R2 for same time. If heat generated is same, find internal resistance of source (A) 1212RRRR (B) R1 + R2 (C) zero (D) 12RR 47. n moles of an ideal gas undergo a process as shown in figure. Maximum temperature of gas during process is : (A) 003PVnR (B) 004PVnR (C) 006PVnR (D) 009PVnR 48. A particle is moving along a straight line with constant acceleration then its : (A) distance and displacement must be equal, for all the time intervals (B) distance and displacement may be equal for all the time intervals (C) distance and displacement must be different for some of the time intervals (D) distance and displacement may be different for all the time intervals 49. In the given figure : (Take g = m/s2) (A) The acceleration of A and B are same to each other (B) The acceleration of A is 9 m/s2 (C) The acceleration of B, C and D are not same to each other (D) All bodies move with different acceleration 50. A particle of mass 4 m which is at rest explodes into three fragments. Two of the fragments, each of mass m, are observed to move with a speed v each in mutually perpendicular directions. The total energy released in the process of explosion is : (A) mv2 (B) 2mv2 (C) 212mv (D) 232mv 51. Mark correct option of options. (A) Rolling friction always oppose the motion of centre of mass of rolling body (B) Rolling friction depends upon hardness of the surface (C) Rolling friction does not depend upon roughness of the surface (D) All of the above 52. Two parallel and opposite forces, each 4000 N, are applied tangentially to the upper and lower faces of a cubical metal block 25 cm on a side. Find the angle of shear and the displacement of the upper surface relative to the lower surface. The shear modulus for the metal is 80 GPa : (A) 60210.cm (B) 52010.cm (C) 526510.cm (D) 521510.cm 3 1 2 P0 3P0 V0 3V0 A 1kg B 2kg C 3kg D 7kg f = 10 N g = 10 m/s2 1 = 0.1 2 = 0.2 3 = 0.3 4 = 0 8 Vidyamandir Classes 53. Two photons of same frequencies moving in same medium have necessarily : (A) Same linear momenta and wavelengths (B) Same linear momenta and same speeds (C) Same energies and same linear momenta (D) None of these 54. The plane of a dip circle is set in the geographical meridian and the apparent dip is 1. It is then set in a vertical plane perpendicular to the geographical meridian. The apparent dip angle is 2.The declination at the place is : (A) 112tantantan (B) 112tantantan (C) 112tantantan (D) 112tantantan 55. Which of the following is the mT graph for a perfectly black body ? (A) A (B) B (C) C (D) D 56. Cathode rays are made to pass between the poles of a magnet as shown. The effect of the magnetic field is : (A) to deflect then into the plane of the paper (B) to deflect them towards the north pole (C) to deflect them towards the south pole (D) to deflect them out of the plane of the paper 57. Which of the following configurations of electric lines of force is not possible ? (A) (B) (C) (D) Both B and C 58 A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is : (A) 22ugL (B) 2gL (C) 2ugL (D) 22ugL 59. Find the ratio of lengths of an iron rod and aluminium rod for which the difference in the lengths of rod is independent of temperature. 55ironAl1210and2410./C./C (A) 1 : 2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1 60. Which of the following in electricity is analogous to momentum mv in dynamics ? (A) IV (B) IL (C) QL (D) IQ 61. A paper, with two marks having separation d, is held normal to the line of sight of an observer at a distance of 50 m. The diameter of the eye-lens of the observer is 2 mm. Which of the following is the least value of d, so that the marks can be seen as separate ? The mean wavelength of visible light may be taken as 5000Å (A) 1.25 m (B) 12.5 cm (C) 1.25 cm (D) 2.5 mm A B C D T m N S – 2C – 2C +5C – 1C Vidyamandir Classes 9 62. Write down the expression for capacitance of a spherical capacitor whose conductors radii are R1 and R2 (R1 > R2), when inner sphere is grounded : (A) 012214RRRR (B) 201214RRR (C) 202214RRR (D) 20122214RRRR 63. What is the binding energy per nucleon of 126C nucleus ? Given : mass of C12 (mc) = 12.000 u mass of proton (mp) = 1.0078 u mass of neutron (mn) = 1.0087 u and 1 amu = 931.4 MeV (A) 5.26 MeV (B) 10.11 MeV (C) 15.65 MeV (D) 7.68 MeV 64. A and B are two identically spherical charged bodies which repel each other with force F, kept at a finite distance. A third uncharged sphere of the same size is brought in contact with sphere B and removed. It is then kept at mid point of A and B. Find the magnitude of force on C. (A) F/2 (B) F/8 (C) F (D) Zero 65. A particle is projected with initial velocity u at an angle above the horizontal, then variation of torque and angular momentum with time will be : (A) (B) (C) (D) 66. Pick out the correct statements. I. Susceptibility of a diamagnetic substance is high and negative. II. In paramagnetic substance, the intrinsic magnetic moment is not zero. III. When a paramagnetic substance is heated, it becomes ferromagnetic. IV. Spin exchange interaction is present in the absence of external magnetic field. (A) I and II (B) III and IV (C) II and III (D) II and IV 67. Two short magnets of equal dipole moments M are fastened perpendicularly at their centres (figure). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is : (A) 034Md (B) 0324Md (C) 03224Md (D) 0324Md 68. A raw egg and a hard boiled egg are made to spin on a table with the same angular speed about the same axis. The ratio of the time taken by the two to stop is : (A) = 1 (B) < 1 (C) > 1 (D) None of these 69. The graph between distance between source and observer and apparent frequency in the case of Dopplers effect will be : (A) (B) (C) (D) , L L t , L L t , L L t , L L t n S n S n S n S N S S N 45 10 Vidyamandir Classes 70. A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle at the centre. The value of the magnetic induction at the centre due to the current in the ring is : (A) proportional to 2180 (B) inversely proportional to r (C) zero, only if 180 (D) zero for all values of 71. Figure shows two rays A and B being reflected by a mirror and going as A and B. The mirror : (A) is plane (B) is convex (C) is concave (D) may be any spherical mirror 72. In a meter bridge experiment, null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y ? (A) 50 cm (B) 80 cm (C) 40 cm (D) 5 cm 73. In a photoelectric experiment anode potential is plotted against plate current : (A) A and B will have different intensities while B and C will have different frequencies (B) B and C will have different intensities while A and C will have different frequencies (C) A and B will have different intensities while A and C will have equal frequencies (D) A and B will have equal intensities while B and C will have different frequencies 74. The atmospheric temperature is below 0C and its value is , then ice starts forming on the surface of lake. Find the time in which thickness of ice formed gets h m. Let us consider K is the thermal conductivity of ice, is the density of ice. Lf is the latent heat of fusion : (A) 22fLhK (B) 2fLhK (C) 22fLhK (D) None of these 75. Water flows in a stream line manner through a capillary tube of radius a, the pressure difference being P and the rate flow Q. If the radius a reduced to a/2 and the pressure is increased to 2P, the rate of flow becomes : (A) 4Q (B) Q (C) Q/2 (D) Q/8 76. An electric bulb is at a vertical distance of h over the centre of a circular table of radius R as shown in figure. By what factor the intensity of illumination at the centre O is greater than that at the edge of the table ? (A) 32221/Rh (B) 32221/Rh (C) 221Rh (D) 221Rh 77. The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t0 in air. Neglecting frictional force of water and given that the density of the bob is 3410003kg/m. What relationship between t and t0 is true ? (A) t = t0 (B) t = t0/2 (C) t = 2t0 (D) t = 4t0 A B C B A V I Vidyamandir Classes 11 78. Which one of the following curves represents the variation of impedance (z) with frequency f in series LCR circuit (A) (B) (C) (D) 79. What is the plate current in a diode value under the space charge limited operation, when the plate potential is 60 V ? In a diode valve, the plate current is 320 mA, when the plate potential is 240 V : (A) 30 mA (B) 20 mA (C) 40 mA (D) 10 mA 80. A long conducting wire AH is moved over a conducting triangular wire CDE with a constant velocity v in a uniform magnetic field B directed into the paper. Resistance per unit length of each wire is . Then : (A) a constant clockwise induced current will flow in closed loop (B) an increasing clockwise induced current will flow in the closed loop (C) a decreasing anticlockwise induced current will flow in the closed loop (D) a constant anticlockwise induced current will flow in the closed loop SECTION -III (Mathematics) M. Marks : 160 Questions : 81 – 120 81. If ,, are the cube roots of p (p < 0), then for any x, y and z ; xyzxyz equals to : (A) 1132i (B) 1132i (C) 1132i (D) None of these 82. Sum of the series 242424123111222333... up to n terms is equal to : (A) 22121nnnn (B) 2221nnnn (C) 2211nnnn (D) 2221nnnn 83. If 20121nnnxCCxCx...Cx, then the value of 0rsrsnrsCC is : (A) 22nn. (B) 2nn. (C) 222nn. (D) None of these 84. For 0nmxsinxm,nI,Limsinx is equal to : (A) 1 (B) 1 (C) n/m (D) None of these 85. If x1, x2, x3, x4 are four positive real numbers such that 123234111414x,x,xxxx and 4111xx, then : (A) 13xx and 24xx (B) 24xx and 13xx (C) 121xx, 341xx (D) 341xx, 121xx Z f Z f Z f Z f A B F G H v C E D 12 Vidyamandir Classes 86. 2211logxlogx dx is equal to : (A) 21xcx (B) 21xclogx (C) 21xxecx (D) 21logxclogx 87. The equation 22235442logxlogxx has : (A) At least one real solution (B) Exactly three real solutions (C) Exactly one irrational solution (D) All of these 88. Given a, g are the roots of the equation 2410Axx and b, d are the roots of the equation 2610Bxx. If a, b, g, d are in H.P., then the values of A and B are respectively : (A) 3, 5 (B) 8, 5 (C) 5, 8 (D) 3, 8 89. If A and B are two independent events such that 215PAB and 16PAB, then P(B) is : (A) 1/5 (B) 1/6 (C) 2/5 (D) 5/6 90. The difference of the tangents of the angles which the lines 2222220xsecsinxytanysin make with the x-axis, is : (A) 2tan (B) 2 (C) 2cot (D) 2sin 91. If 12zitan, then polar form of the complex number z is : (A) 1cosisincos (B) 1cosisincos (C) 122cosisincos (D) None of these 92. If the tangent at a point acos,bsin on the ellipse 22221xyab meets the auxiliary circle in two points, the chord joining them subtends a right angle at the centre, then the eccentricity of the ellipse is given by : (A) 1221/cos (B) 21sin (C) 1221/sin (D) 21cos 93. The exponent of 3 in 100 ! is : (A) 33 (B) 44 (C) 48 (D) 52 94. Consider a circle with its centre lying on the focus of the parabola y2 = 2px such that it touches the directrix of the parabola. Then a point of intersection of the circle and the parabola is : (A) 2p,p or 2p,p (B) 22pp, (C) 2p,p (D) 22pp, 95. In a triangle ABC, if a = 5, b = 4 and 3132cosAB, then side c is : (A) 6 (B) 7 (C) 9 (D) None of these Vidyamandir Classes 13 96. The greatest and the least values of 3311sinxcosx are respectively : (A) 22, (B) 3388, (C) 337328, (D) None of these 97. In a ABC, if 1101abcabc, then 222sinAsinBsinC is equal to : (A) 9/4 (B) 4/9 (C) 1 (D) 33 98. Number of ordered triplet (p, q, r) where 110p,q,r, such 235pqr is a multiple of 4 ; is p,q,rN (A) 1000 (B) 500 (C) 250 (D) 125 99. Let r be the range and 22111niiSxXn be the SD of a set of observations x1, x2, . . . . , xn, then : (A) 1nSrn (B) 1nSrn (C) 1nSrn (D) None of these 100. A particle begins to move from a distance ‘a’ towards a fixed centre, which repels it with retardation x. If its initial velocity is a then its equation of motion is : (A) txae (B) txae (C) txae (D) txae 101. The centre of the circle passing through (0, 0) and (1, 0) and touching the circle 229xy is : (A) 1122, (B) 122, (C) 3122, (D) 1322, 102. 3271nn is divisible by (for all nN) : (A) 64 (B) 36 (C) 49 (D) None of these 103. In a bolt factory, machines A, B and C manufacture 60%, 25% and 15% respectively. Of the total of their output 1%, 2%, 1% are defective bolts. A bolt is drawn at random from the total production and found to be defective. From which machine, the defective bolt is most expected to have been manufactured (A) A (B) B (C) C (D) Cannot be decided 104. The function 1xfxxtanx has : (A) one point of minimum in the interval 02, (B) one point of maximum in the interval 0 2 , (C) no point of maximum, no point of minimum in the interval 0 2 , (D) two points of maxima in the interval 0 2 , 105. Let f (x) = (1 + b2) x2 + 2 bx + 1 and let m (b) be the minimum value of f (x). As b varies, the range of m(b) is : (A) [0, 1] (B) 102, (C) 112, (D) (0, 1] 106. In a plane there are two families of lines y = x + r,yxr, where 01234r,,,,,. The number of squares of diagonals of the length 2 formed by the lines is : (A) 9 (B) 16 (C) 25 (D) None of these 14 Vidyamandir Classes 107. A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then 2222CPCQCRCS is equal to : (A) 2r (B) 22r (C) 23r (D) 24r 108. 2sinx.logcosxdx is equal to : (A) 212cosxlogcosxk (B) 2cosx.logcosxk (C) 212cosxlogcosxk (D) None of these 109. The angle between the lines whose direction cosines are given by the equations 22200lmn,lmn is : (A) 6 (B) 4 (C) 3 (D) 2 110. For any integer n the integral 23021cosxecosnxdx has the value : (A) (B) 1 (C) 0 (D) None of these 111. The equation of the circle having the lines 22360xxyyy as its normal and having size just sufficient to contain the circle 430xxyy is : (A) 2236400xyxy (B) 2263450xyxy (C) 2284200xyxy (D) 2248200xyxy 112. Area of the rhombus enclosed by the lines 0axbyc is : (A) 12ab sq. unit (B) 212cab sq. unit (C) 22cabsq. unit (D) None of these 113. A weight W can be just supported on a rough inclined plane by a force P either acting along the plane or horizontally. Then P/W for the angle of friction , is : (A) tan (B) sec (C) 3kg (D) 33kg 114. From a point on the ground, the angles of elevation of a bird flying with a constant speed in a horizontal direction at equal intervals of time are ,, and . Then 22cotcot is equal to : (A) 223cotcot (B) 22cotcot (C) 223cotcot (D) 22cotcot 115. Let the unit vectors a and b be perpendicular to each other and the unit vector c be inclined at an angle to both a and b . If cxaybzab, then : (A) 2xcos,ysin,zcos (B) 2xsin,ycos,zcos (C) 22xycos,zcos (D) 22xycos,zcos 116. If xyyxy, then its solution is : (A) 222yxyxc (B) 222yxyxc (C) 222yxyxc (D) 222yxyxc 117. If xabybczca and 18abc, then (x + y + z) is equal to : (A) 8.abc(B) abc(C) 8abc (D) None of these Vidyamandir Classes 15 118. The value of 221100sinxcosxsintdtcostdt is : (A) (B) 2 (C) 4 (D) 1 119. If the solution for0,cospcosq, p > 0, q > 0 are in AP, then the numerically smallest common difference of AP is : (A) pq (B) 2pq (C) 2pq (D) 1pq 120. A uniform beam AB of weight W is standing with the end B on a horizontal floor and end A leaning against a vertical wall. The beam stands in a vertical plane perpendicular to the wall inclined at 45 to the vertical, and is in the position of limiting equilibrium. If the two points of contact are equally rough, then the coefficient of friction at each of them is : (A) 21 (B) 12 (C) 13 (D) None of these * * * * Vidyamandir wishes you the very best for AIEEE -2010 * * * * 16 Vidyamandir Classes Answers to AIEEE Practice Test – 2010 1 2 3 4 5 6 7 8 9 10 B A C C B A B D A C 11 12 13 14 15 16 17 18 19 20 C B D B B A C B C A 21 22 23 24 25 26 27 28 29 30 B D B A A A C C C A 31 32 33 34 35 36 37 38 39 40 B B A A A A B D A B 41 42 43 44 45 46 47 48 49 50 D D B B C D B B B D 51 52 53 54 55 56 57 58 59 60 D B D C B D D D B B 61 62 63 64 65 66 67 68 69 70 B C D C D D C C D D 71 72 73 74 75 76 77 78 79 80 A A A A D B C C C D 81 82 83 84 85 86 87 88 89 90 D B A D A B C D B B 91 92 93 94 95 96 97 98 99 100 B C C A A D A B A A 101 102 103 104 105 106 107 108 109 110 B C A B D A D C C C 111 112 114 114 115 116 116 117 119 120 B C A A D A A C B A