1 Full Length Practice Paper AIEEE- 2009 Physics 1. If E denotes the electric field and 0 ε is the permittivity of free space, the dimensional formula of 2 0 21 E ε is a) [ ] 2 2 − T ML b) [ ] 1 2 − T ML c) [ ] 2 1 − − T ML d) [ ] 2 − MLT 2. A particle of mass m moves along z-axis in such a way that its distance from the origin varies with time t as 1 2 2 + = t z . The acceleration of the particle at time t is a) z1 b) 3 1 z c) 5 3 z d) z 4 3. If f is the number of degree of freedom of the molecules of a gas, CP & CV are the specific heats at constant pressure and constant volume respectively and R is the universal gas constant, then a) R R f CV + = 2 b) 2R f CV = c) R R f CP + = 2 d) (b) and (c) are correct Directions: Question numbers 4 & 5 are based on the following paragraph. One of the moons of the planet Mars, phobos, has a period of 7 hours, 39 minutes and an orbital radius of 3 10 4 . 9 × km. Further, assume that the Earth and Mars move in circular orbits around the Sun, with the martian orbit being 1.52 times the orbital radius of the Earth. 2 2 11 10 67 . 6 kg Nm G − × = 4. What is the mass of the Mars? a) kg 23 10 48 . 6 × b) kg 24 10 48 . 6 × c) kg 23 10 24 . 3 × d) kg 24 10 24 . 3 × 5. What is the length of the martian year in days? a) ( ) days 3 52 . 1 365× b) ( ) days 2 52 . 1 365× c) ( ) days 2 3 52 . 1 365× d) ( ) days 3 2 52 . 1 365× 6. What type of the waves are formed in air column of resonance apparatus? a) Longitudinal waves b) Transverse waves c) Longitudinal stationary waves d) None of these 7. What is the ratio between the kinetic energy K and the potential energy U of a harmonically oscillating point for the moment 12 T t = , where T is the period? a) 1 = UK b) 2 = UK c) 3 = UK d) 4 = UK Direction : Questions 8-9 contain statement-1 and statement-2. Of the four choices given, choose the one that best describes the two statements. a) Statement-1 is true, Statement-2 is false b) Statement-1 is true, Statement-2 is true c) Statement-1 is true, Statement-2 is true. Statement-2 is a correct explanation for Statement-1 d) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1 2 8. Statement-1: Thin films such as soap bubble or a thin layer of oil on water show beautiful colours when illuminated by monochromatic light. Statement-2: The colours are obtained by dispersion of light. 9. Statement-1: The electron passing through crossed magnetic and electric field is always deflected from its path. Statement-2: If velocity of electron is equal to ratio of electric and magnetic field applied then electron beam remains undeflected. 10. Equation of a stationary wave is t x y π π 20 cos 4 sin 10 = where y is in m and t is in second. Distance between two consecutive nodes is a) 4m b) 2m c) 1m d) 8m 11. In the figure given, the equivalent resistance between A & B is a) 90Ω b) 45Ω c) 20Ω d) 12Ω 12. A vernier calipers has 20 divisions on the vernier scale, which coincide with 19 on the main scale. The least count of the instrument is 0.1 mm. The main scale divisions are of a) 0.5 mm b) 1 mm c) 2 mm d) 3 mm 13. A radioactive element emits 2 alpha particles and 3 beta particles. Then the new element will have the value of A & Z as a) ( ) ( ) 1 , 5 − + Z A b) ( ) ( ) 1 , 5 − + Z A c) ( ) ( ) 1 , 8 − − Z A d) ( ) ( ) 1 , 8 + − Z A 14. If 0 0 & μ ε are the electric permittivity and the magnetic permeability in a free space, μ ε& are the corresponding quantities in the medium, the index of refraction of the medium is a) 0 0 εμμ ε b) 0 εε c) εμμ ε 0 0 d) 0 0 μ εεμ 15. The shape of the graph between 1/u and 1/v in case of convex lens is a) b) c) d) 16. 27 identical drops of mercury are charged simultaneously to the same potential of 10 volt. What will be the potential if all of charged drops are made to combine to form one large drop? (Assume the drop to be spherical) a) 45 V b) 90 V c) 120 V d) 180 V 17. Which of the following substance has negative magnetic susceptibility? a) Ferromagnetic b) Paramagnetic c) Diamagnetic d) None of these B A 15Ω 10Ω 5Ω 20Ω 10Ω 10Ω 20Ω 30Ω 1/v O 1/u X Y O Y X 1/u 1/v OY X 1/u 1/v O Y X 1/u 1/v 3 18. A weight lifter lifts 300 kg from ground to a height of 2 m in 3 second, the average power generated by him is a) 5580 W b) 4410 W c) 2205 W d) 1960 W 19. A hallow sphere of mass M and radius R is rotating with an angular frequency ω. It suddenly stops rotating and 75 % of the kinetic energy is converted into heat energy. If s joule/kg-kelvin is the specific heat of the material of the sphere, the rise of temperature of the sphere is a) s R4 2 2 ω b) s R20 3 2 2 ω c) s R 2 2 ω d) s R3 2 2 2 ω 20. 2 condensers of capacitance 2 F μ and 3 F μ are connected in series and another condenser of capacity (4/5) F μ is connected in parallel to the combination. The effective capacity is a) F μ 20 29 b) F μ 29 20 c) F μ 2 d) F μ 1 21. The moment of inertia of a body (initially at rest) about a given axis is 1.2 kg-m2. In order to produce a rotational kinetic energy of 1500 J, and angular acceleration of 25 rad/sec2 must be applied about that axis for a period of a) 8 sec b) 2 sec c) 1 sec d) 10 sec 22. The angles of incidence and emergence of an equilateral prism are 500 & 400. The angle of deviation is a) 400 b) 500 c) 600 d) 300 23. The given circuit represents a) OR gate b) AND gate c) NAND gate d) NOR gate 24. If two soap bubbles of different radii are in communication with each other a) air flows from the larger bubble into the smaller one until the two bubbles are of equal size b) the size of the bubbles remains the same c) air flows from the smaller bubble into the larger one and larger bubble grows at the expense of the smaller one d) the air flows from the larger into the smaller bubble until the radius of the smaller on becomes equal to that the large one and of large one equal to that of the small one 25. A block slides with a velocity of 10 ms−1 on a rough horizontal surface. It comes to rest after covering a distance of 50 metre. If g is 10 ms−2, then coefficient of dynamic friction between the block and the surface is a) 0.1 b) 0.5 c) 0.6 d) 1 26. The temperature of an ideal gas is increased from 270C to 9270C. The root mean square speed of its molecules becomes a) twice b) half c) four times d) one-fourth Y B A 4 27. The wavelength of α K line for an element of a atomic number 43 is λ. Then the wavelength of α K line for an element of atomic number 29 is a) λ 29 43 b) λ 28 42 c) λ 49 d) λ 94 28. A rocket expels gas at the rate of 0.5 kg/s. If the force produced by the rocket is 1000 N, what is the velocity with which the gas is expelled? a) 1 20 − ms b) 1 200 − ms c) 1 2000 − ms d) 1 5 − ms 29. How many number of wires are used in Searle’s experiment for determining Young’ modulus of elasticity? a) 3 b) 1 c) 2 d) 4 30. A galvanometer (G) gives full scale deflection with 0.1 mA. The resistance of the coil is 1000 ohm. This has to be converted into an ammeter to read current upto 10 A. Then the following is to be done a) 0.01 ohm is to be connected in series to G b) 0.01 ohm is to be connected in parallel to G c) 10,000 ohm is to be connected in parallel to G d) 10,000 ohm is to be connected in series to G Direction: Questions 31,32 & 33 are based on the following paragraph. Figure shows a metal rod PQresting on the rails A & B and positional between the poles of a permanent magnet. The rails, the rod and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 mΩ. 31. Suppose K is open and the rod moves with a speed of 12 cms−1 in the direction as shown in the figure. The magnitude of the induced e.m.f. is a) 5 mV b) 7 mV c) 9 mV d) 11 mV 32. What is the retarding force on the rod when K is closed? a) N 3 10 75 − × b) N 3 10 100 − × c) N 3 10 120 − × d) N 3 10 140 − × 33. How much power is required (by an external agent) to keep the rod moving at the same speed (i.e. 12 cms−1) when Kis closed? a) W 3 10 9 − × b) W 3 10 12 − × c) W 3 10 14 − × d) W 3 10 16 − × Q K G S N B A P 5 34. A stone thrown at an angle θ to the horizontal reaches a maximum height h. The time of flight of the stone is a) gh 2 2 b) g h θ sin 2 2 c) g h θ sin 2 d) gh 2 35. Light is incident from a medium into air at two possible angles of incidence (1) 200 & (2) 400. In the medium, the light travels 3 cm in 0.2 ns. The ray will: a) suffer total internal reflection in both cases 1 & 2 b) suffer total internal reflection in case 2 only c) have 100 % transmission in case 1 d) have partial reflection and partial transmission in case 2 CHEMISTRY 36. An experiment requires 100 cm3 of 20.0 % H2SO4, density 1.14 g/cm3. How much concentrated acid of density 1.84 g/cm3 and containing 98 % H2SO4 by weight, must be diluted with water to prepare 100 cm3 acid of the required solution? a) 8.1 cm3 b) 12.7 cm3 c) 18.1 cm3 d) 21.3 cm3 37. An aqueous soution contains 1 mole of − 2 3 2O S ions and this reduces 4 mole of Cl2 molecules. What is the sulphur-containing product of this reaction? a) − 2 4 SO b) − 2 6 4O S c) − 2 3 SO d) SO2 38. For , 2 2 2 − − → + I e I standard reduction potential = + 0.54 V. For , 2 2 2 − − + → e Br Br standard oxidation potential = –1.09 V. For , 2 2 − + + → e Fe Fe standard oxidation potential = + 0.44V. Which of the following reaction is non-spontaneous? a) 2 2 2 2 I Br I Br + → + − − b) 3 c) − + + → + I Fe I Fe 2 2 2 d) 2 2 2 2 Br I Br I + → + − − 39. An electron is continuously accelerated in a vacuum tube by applying potential difference. If the de-Broglie’s wavelength is decreased by 10 % , the change in the kinetic energy of the electron is nearly a) decreased by 11 % b) increased by 23.4 % c) increased by 10 % d) increased by 11.1% 40. Which of the following will loose optical activity on treatment with divide HN = NH ? a) b) c) d) 41. Mark out the structure which has all formal charge zero. a) N ≡ C – C ≡ N b) c) d) N = N = O CH3 H H CH3 CH3 H CH3 H C – O Cl Cl B – H BH – NH BH = NH HN 6 42. Product. The main product is a) b) c) d) 43. Which of the following set of reagents is the most appropriate to perform the above conversion? a) HCl Hg Zn OH HIO , ; ; 4 − − b) Cold alkaline ( ) 3 4 4 . ; ; ; NH liq Li OH OAc Pb KMnO − c) ( ) 3 2 3 3 . ; ; ; NH liq Li OH S CH O − d) C OH NH NH OH H KMnO 0 2 2 4 150 ; ; ; ; ; − − + − 44. When a vapour, at atmospheric pressure, was gradually heated from 250C, its colour was found to deepened at first and then to fade as the temperature was raised above 1600C. At 6000C the vapour was almost colourless, but its colour deepended when the pressure was raised at this temperature. Which one of the following could have been the vapour? a) Pure bromine b) Pure hydrogen iodide c) Pure nitrogen dioxide d) A mixture of nitrogen dioxide and dinitrogen tetraoxide 45. For the indicator thymol blue, the value of pH is 2.0 when half of the indicator is present in the unionized form. Which of the following is the percentage of the indicator in the unionized form in a solution of + − × MH 3 10 0 . 4 concentration? a) 15.5 b) 28.5 c) 27.3 d) 36.1 46. White lead is a) PbO PbCO . 3 b) PbCO3 c) Pb(OH)2.2PbCO3 d) PbSO4.PbO 47. In the following reaction, the structure of the major product X is a) b) c) d) O Cl3C – C – ONa + Cl Cl Cl Cl Cl O O – C – CH3 Cl conc.H2SO4 conc.HNO3 O N H NO2 O N H O2N O N H NO2 O N H O2N O N H7 48. In presence of a catalyst, the activation energy is lowered by 2 kcal at 1270C. Hence, the rate as compared to the old rate is a) e2 times b) e−2 times c) e2.5 times d) e−2.5 times 49. Heat of combustion of C, H2 & C2H6 are z y x − − − & , respectively. Hence, heat of formation of C2H6 is a) ( ) z y x + + − 3 2 b) z y x − + 3 2 c) ( ) y x z 3 2 + − d) z y x + + 3 2 50. The correct order of magnetic moments (spin only values in BM) among the following, is a) [ ] [ ] ( ) [ ]− − − > > 4 6 2 4 2 4 CN Fe CoCl MnCl b) [ ] ( ) [ ] [ ] − − − > > 2 4 4 6 2 4 CoCl CN Fe MnCl c) ( ) [ ] [ ] [ ]− − − > > 2 4 2 4 4 6 CoCl MnCl CN Fe d) ( ) [ ] [ ] [ ] − − − > > 2 4 2 4 4 6 MnCl CoCl CN Fe (Atomic numbers : Mn = 25, Fe = 26, Co = 27) 51. Which of the following represents correct relationship of bond lengths? a) 2 2 N N < + while NO O N < + b) 2 2 N N < + while O N NO + < c) + < 2 2 N N while NO O N < + d) + < 2 2 N N while O N NO + < 52. In which of the following the oxidation number of oxygen has been arranged in increasing order? a) OF2 < KO2 < BaO2 < O3 b) BaO2 < KO2 < O3 < OF2 c) BaO2 < O3 < OF2 < KO2 d) KO2 < OF2 < O3 < BaO2 53. Compound A, C5H10O5, gives a tetraacetate with (CH3CO)2O and oxidation of A with Br2 – H2O gives an acid, C5H10O6. Reduction of A with HI gives iso-pentane. There are two possible structures for compound A which can be distinguished by using a) HIO4 b) Excess of P, HI c) Phenylhydrazine d) Tollen’s reagent 54. In the reaction The major product is a) b) c) d) 55. When 25 g of a non-volatile solute is dissolved in 100 g of water, the vapour pressure is lowered by . 10 25 . 2 1mm − × If the vapour pressure of water at 200C is 17.5 mm, what is the molecular weight of the solute? a) 206 b) 302 c) 350 d) 276 Heat OH CH – CH3 + HBr Br CH – CH3 CH2CH3 Br Br CH3 Br CH3 8 56. Which type of graph gives straight line in Langmuir adsorption isotherm? a) p mx 1 → b) p xm 1 → c) p mx 1 log → d) p mx → log 57. Compound A & B are a) b) c) d) none of these 58. If AgI crystallizes in zinc blende structure with iodide ions at lattice points, what fraction of tetrahedral voids is occupied by Ag+ ions? a) 25 % b) 50 % c) 100 % d) 75 % 59. An electric current is passed through silver voltameter connected to a water voltameter. The cathode of the silver voltameter weighed 0.108 g more at the end of the electrolysis. The volume of O2 evolved at STP is a) 56 cm3 b) 550 cm3 c) 5.6 cm3 d) 11.2 cm3 Direction : Questions 60-63 contain Statements-1 and Statement-2. Of the four choices given, choose the one that best describes the two statements. a) Statement-1 is true, Statement-2 is false. b) Statement-1 is false, Statement-2 is true. c) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1 d) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1 60. Statement-1 : When Zn is placed in a magnetic field, it is feebly magnetized in a direction opposite to that of the magnetizing field. Statement-2 : Zn has completely filled atomic orbitals. 61. Statement-1 : Enthalpy of combustion is always negative but enthalpy of oxidation (involving combination with oxygen) may be negative or positive. Statement-2 : Oxidation reaction involving combination with oxygen is always a combustion reaction. 62. Statement-1 : Alcohols containing active H can be acetylated in presence of acid scavenger. Statement-2 : The reaction is known as Schotten-Baumann reaction. 63. Statement-1 : Helium and beryllium have similar outer electronic configuration of the type ns2. Statement-2 : Both are chemically inert. A NaBH4 B H2/Ni H , OH O , OH , OH OH 9 Directions : Questions 64, 65 & 66 are based on the following paragraph. Consider the following reaction sequence. 64. Which of the following is reagent (A) ? a) HCrO4 b) CrO3/Ac2O c) PCC/DCM d) CrO2Cl2 65. Compound (C) is a) b) c) d) none of these 66. Compound (F) on treatment with Br2/Fe mainly gives a) b) c) d) (F) + C6H5NH2 + C6H5COO−-C6H5NH2 O C C6H5COOH + (E) (C) + (CH3)2NH2+Cl− (D) (CH3)2NH C – Cl (B) COH (A) CH3 O O O Cl CH3 N N(CH3)2 Cl – CO CN(CH3)2 O Br O C – NH NH C – Br O Br O C – NH CNH Br O 10 Directions : Questions 67,68, & 69 are based on the following paragraph. The gas molecules randomly move in all directions and collide with each other and with the wall of the container. It is difficult to determine the speed of an individual molecule but it has become possible to work out the distribution of molecules among different molecular speeds. This is known as Maxwell Boltzmann distribution. Consider the following graph about Maxwell’s distribution of speeds at two different temperatures T1 & T2. 67. The shaded area represents a) number of molecules having speed between 2 1 &u u b) number of molecules having speed less than the most probable speed c) number of molecules having 1 T at vrms d) fraction of total molecules having average speed 68. The point Qrefers to a) number of molecules with speed at P b) fraction of total molecules with speed at P c) root mean square speed d) total kinetic energy of molecules at P 69. Relation between T1 & T2 is a) T1 = T2 b) T1 > T2 c) T1 < T2 d) cannot be predicted 70. Product. The main product is a) C6H5 – CH2 – C6H5 b) c) d) MATHEMATICS 71. If two distinct chords of a parabola ax y 4 2 = passing through the point ( ) a a 2 , are bisected by the line , 1 = + y x then the length of the latus-rectum can be a) 2 b) 7 c) 4 d) 5 ⎟⎠ ⎞ ⎜⎝ ⎛ nn Δ Fraction of total molecules Q S Speed u1 u2 P R T1 T2 II. H+ I. Me3COK CH2 -COOEt CH2 -COOEt O18 C6H5 – C – C6H5 + C6H5 – C – C6H5 EtOOC – CH EtOOC – C – CH2COO18H C6H5 – C – C6H5 C6H5 – C – C6H5 EtOOC – C – CH2COOH 11 72. If β α, are the roots of δ γ, & 0 1 2 = + + px x are the roots of ( )( ) δ β γ α + − = + + then qx x , 0 1 2 ( )( ) α β δ α − + is divisible by a) δ γ β α + + + b) δ γ β α − + − c) δ γ β α − + + d) δ γ β α − − − 73. If ∈ ≥ + x then x x , 1 1 log 2 . 0 a) ⎟⎠ ⎞ ⎢⎣ ⎡− 0 , 45 b) ⎥⎦ ⎤ ⎢⎣ ⎡ − − 1 , 45 c) ⎟⎠ ⎞ ⎢⎣ ⎡ − − 1 , 45 d) ⎟⎠ ⎞ ⎜⎝ ⎛ − − 1 , 45 74. The coefficient of 50 x in the series ( ) ∑= − − + = 1011 101 1 1 r r r x rx S is a) ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛50 100 b) ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛50 101 c) ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛50 102 d) ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛50 103 75. The number of 3-digt numbers which contain not more two different digits is a) 216 b) 252 c) 264 d) 288 76. If (2,4) is a point interior to the circle 0 10 6 2 2 = + − − + λ y x y x and the circle does not cut the axes at any point, then λlies in the interval a) (25,32) b) (9,32) c) (32,∞) d) (4,25) 77. OABC is a regular tetrahedron of unit edge. Its volume is a) 3 1 b) 6 1 c) 231 d) 2 6 1 78. The value of ∑= ⎟⎠ ⎞ ⎜⎝ ⎛ − 61 7 2 cos 7 2 sin r r i r π π is a) 0 b) 1 c) –1 d) i 79. A straight line with negative slope passes through the point P(8,2) and ends the coordinate axes at the points A & B. The minimum value of OA + OB is a) 12 b) 16 c) 18 d) 24 80. If ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = = = − + = − ∫ ∫ 12 0 0 2 1 , , , 2 & II then dx x g x f I dx x f I x a g x g x f x a f a a a) 1 b) 2 c) a d) 2 a 81. The vector a is equally inclined to the plane determined by j i ˆ 4 & ˆ 3 and to the plane determined by k i ˆ 4 & ˆ 3 at angle θ. Then ∈ θ a) ⎥⎦ ⎤ ⎢⎣ ⎡ 2 , 0 π b) ⎥⎦ ⎤ ⎢⎣ ⎡ π π, 2 c) ⎥⎦ ⎤ ⎢⎣ ⎡ 3 2 , 3 π π d) ⎥⎦ ⎤ ⎢⎣ ⎡ ∪ ⎥⎦ ⎤ ⎢⎣ ⎡ π π π , 4 3 4 , 0 82. The greatest slope of a tangent to the curve, 2 1 x x y + = is a) 2 1 b) 2 − c) 1 d) –1 12 83. = ⎟⎠ ⎞ ⎜⎝ ⎛∑= → x n r x ec x r 2 2 sin 1 cos 0 lim a) 0 b) ∞ c) n d) 1/n 84. If 2005 2005 1 & 1 1 z z a z z + = = + and b is the last digit of the number 1 22 − n , when the integer n > 1, then = + 2 2 b a a) 23 b) 24 c) 26 d) 27 85. Let ⎥⎦ ⎤ ⎢⎣ ⎡ = 2 3 4 1 A . If θ is the angle between the two non zero column vectors X such that X AX λ = for some scalar λ, then = θ tan a) 2 b) 3 c) 5 d) 7 86. A group of 10 boys are randomly divided into two teams containing 5 boys each. The probability that the two tallest boys are in different teams is a) 5/9 b) 4/9 c) 11 4 d) 11 5 87. Three numbers c b a , , are between 2 and 18 such that their sum is 25, 2, , ,b a are in A.P. and , ,c b 18 are in G.P., then = abc a) 360 b) 420 c) 480 d) 540 88. With 17 consonants and 5 vowels, the number of words of 4 letters, that can be formed having 2 different vowels in the middle 1 consonant (repeated or different) at each end, is a) 3680 b) 4540 c) 5780 d) 6210 89. If ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − = ∀ + − − = − x a f Then f y x y a f x a f y f x f y x f 2 . 1 0 & , , a) ( ) x f b) ( ) x f − c) ( ) x f − d) ( ) ( ) x a f a f − + 90. The number of discontinuous functions ( ) x y on [–2,2] satisfying 4 2 2 = + y x is a) 0 b) 1 c) 2 d) > 2 91. If , 2 , 2 , 2 , 2 21 4 10 3 10 2 10 1 3 2 3 2 dx I dx I dx I dx I x x x x ∫ ∫ ∫ ∫ = = = = then a) I1 > I2 b) I1 < I2 c) I3 < I4 d) I3 = I4 92. The area between the curve , 2 2 4 x x y − = the x -axis and the ordinates of the two minimum points on the curve is a) 12 7 b) 30 7 c) 60 7 d) 120 7 93. If ( ) ( ) = ⎟⎠ ⎞ ⎜⎝ ⎛ = − = − 3 , 1 0 , cos sin 1 cos 2 π y then y x x y dx dy x y a) 1 b) 2 c) 1/2 d) 3 13 94. In a c b a if ABC , , , Δ are in A.P. and the largest angle exceeds the smallest by 900, then cos B = a) 1/2 b) 2/3 c) 3/4 d) 3/5 95. If ( ) = − × = × − = = = = b c then b a c a c b c b a 2 , 2 ,& 43 . , 3 , 1 a) 1 b) 2 c) 3 d) 4 96. The locus of ( ) y x P , such that 5 16 8 9 6 2 2 2 2 = + + + + + − + − y y x x y x is a) hyperbola b) circle c) finite line segment d) infinite ray 97. If a line makes angles δ γ β α , , , with the four diagonals of a cube, then = + + + δ γ β α 2 2 2 2 cos cos cos cos a) 1 b) 2 c) 2/3 d) 4/3 98. The normal at t on the parabola ax y 4 2 = subtends a right angle at the vertex. The value of t2 is a) 1 b) 2 c) 3 d) 4 99. Let c b a , , be distinct real numbers. If c b a , , are in G.P. and ∈ = + + x then bx c b a , a) ( ) ∞ , 0 b) ( ) 0 , ∞ − c) ( ) 3 , 1 − d) ( ) 3 , 1 − − R 100. The coefficient of 6 x in the expansion of ( )6 2 1 x x + + is a) 131 b) 141 c) 151 d) 167 101. If ( ) ( ) x f x dz z x f x ′ ≥ ∀ = ∫− 0 , 1 equals a) x b) 2 1 2 x + c) 2 1 2 x − d) x − 102. If dx dy then x x y , 1 2 cos 2 1 ⎟⎠ ⎞ ⎜⎝ ⎛ − = − equals a) 1 1 22 > ∀ +− x x b) 1 1 1 2 2 < < − ∀ + x x c) ∞ < < ∞ − ∀ +− x x2 1 2 d) None of these 103. ( ) ( ) = = → x f where xx f t x , 2 1 0 minimum [ ] { } [] . & , sin x x m represents greatest integer function, then a) { } 4 ∈ m b) [ ] 5 , 4 ∈ m c) [ ) 5 , 4 ∈ m d) { } 5 = m 104. If (h,k) be the point on the axis of the curve ( ) ( ) ( )2 2 2 2 1 2 1 2 + + = − + − y x y x from where three distinct normal can be drawn, then h satisfies the condition a) h < 4 b) h > 6 c) h < 8 d) h > 2 105. If ( ) ( ) ∫ ∫ − − + = x x x f then dz z dz z x f 2 2 cos0 1 sin0 1 , cos sin is a/an a) constant function b) odd function c) even function d) none of these