AIEEE 2002 With Answer Key

1 AIEEE 2002 Paper

AIEEE 2002 TEST PAPERPHYSICS

Time : 1.15 Hours Max. Marks : 225

GENERAL INSTRUCTIONS 1. This question paper has 75 objective type questions. Each question has four choices (1), (2), (3) and (4) out

of which only one is correct.

2. For each question you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer isgiven. In all other cases, minus one (1) Mark will be awarded.

1. The inductance between A and D is :

A D3H 3H 3H

(1) 3.66 H (2) 9 H (3) 0.66 H (4) 1 H2. A ball whose kinetic energy is E, is projected at an angle of 45 to the horizontal. The kinetic energy of the

ball at the highest point of its flight will be :(1) E (2) E/ 2 (3) E/2 (4) zero

3. From a building two balls A and B are thrown such that A is thrown upwards and B downwards with same speed(both vertically). If VA and VB are their respective velocities on reaching the ground, then(1) vB> vA (2) vA =vB(3) vA> vB (4) their velocities depends on their masses

4. If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate morebefore coming to rest?(1) 1 cm (2) 2 cm (3) 3 cm (4) 4 cm

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5. If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero,then the satellite will :(1) continue to move in its orbit with same velocity(2) move tangentially to the original orbit with the same velocity(3) become stationary in its orbit(4) move towards the earth

6. If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a :(1) low resistance in parallel (2) high resistance in parallel(3) high resistance in series (4) low resistance in series

7. If in a circular coil A of radius R, current i is flowing and in another coil B of radius 2R a current 2i is flowing, thenthe ratio of the magnetic fields, BA and BB produced by them will be :(1) 1 (2) 2 (3) 1 / 2 (4) 4

8. f two mirrors are kept at 60 to each other, then the number of images formed by them is -(1) 5 (2) 6 (3) 7 (4) 8

9. A wire when connected to 220 V mains supply has power dissipation P1 . Now the wire is cut into two equal pieceswhich are connected in parallel to the same supply. Power dissipation in this case is P2. Then P2 : P1 is(1) 1 (2) 4 (3) 2 (4) 3

10. f 13.6 eV energy is required to lionize the hydrogen atom, then the energy required to remove an electron fromn = 2 is :(1) 10.2 eV (2) 0 eV (3) 3.4 eV (4) 6.8 eV

11. Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio offundamental frequency of tubes A and B is :(1) 1 : 2 (2) 1: 4 (3) 2 : I (4) 4 : I

12. A tuning fork arrangement (pair) produces 4 beats/sec with one fork of frequency 288 cps. A little Wax is placedon the unknown fork and it then produces 2 beats/sec. The frequency of the unknown fork is :(1) 286 cps (2) 292 cps (3) 294 cps (4) 288 cps

13. A wave y = a sin (t - kx) on a string meets with another wave producing a node at x = O. Then the equation ofthe unknown wave is :(1) y = a sin (t + kx) (2) y = -a sin (t + kx) (3) y = a sin (t - kx) (4) y = -a sin (t - kx)

14. On moving a charge of, 20 coulombs by 2 cm, 2 J of work is done, then the potential difference between the points is :(1) 0.1 V (2) 8 V (3) 2 V (4) 0.5 V

15. If an electron and a proton having same momentum enter perpendicularly to a magnetic field, then :(1) curved path of electron and proton will be same (ignoring the sense of revolution)(2) they will move undeflected(3) curved path of electron is more curved than that of proton(4) path of proton is more curved

16. Energy required to move a body of mass m from an orbit of radius 2R to 3R is :(1) GMm/12R2 (2) GMm/3R2 (3) GMm/8R (4) GMm/6R

17. If a spring has time period T, and is cut into n equal parts, then the time period of each part will be :

(1) nT (2) nT

(3) nT (4) T

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18. A charged particle q is placed at the centre O of cube of length L (ABCDEFGH).Another same charge q is placed at a distance L from O. Then the electricflux through ABCD is -

HA

DE F

C

BG

qO

q

L(1) q/4L (2) zero

(3) q/2L (4) q/3L19. If in the circuit, power dissipation is 150 w, then R is

R

2

15V

(1) 2 (2) 6 (3) 5 (4) 4

20. Wavelength of light used in an optical instrument are 1= 4000 and 2= 5000 , then ratio of their respectiveresolving powers (corresponding to and 2) is -(1) 16 : 25 (2) 9 : 1 (3) 4 : 5 (4) 5 : 4

21. Two identical particles move towards each other with velocity 2v and v respectively. This velocity of centre of mass is -(1) v (2) v/3 (3) v/2 (4) zero

22. If a current is passed through a spring then the spring will :(1) expand (2) compress (3) remain same (4) none of these

23. Heat given to a body which raises its temperature by 1C is :(1) water equivalent (2) thermal capacity(3) specific heat (4) temperature gradient

24. At absolute zero, Si acts as :(1) non-metal (2) metal (3) insulator (4) none of these

25. Electromagnetic waves are transverse in nature is evident by -(1) polarization (2) interference (3) reflection (4) diffraction

26. Which of the following is used in optical fibres ?(1) Total internal reflection (2) Scattering(3) Diffraction (4) Refraction

27. The escape velocity of a body depends upon mass as -(1) m0 (2) m1(3) m2 (4) m3

28. Which of the following are not electromagnetic waves ?(1) Cosmic-rays (2) -rays (3) -rays (4) X-rays

29. If i is the inversion temperature, n is the neutral temperature, c is the temperature of the cold junction then-

(1) i + c = n (2) i + c = 2n (3) nci 2 (4)

c + i = 2n

30. Infrared radiations are detected by :(1) spectrometer (2) pyrometer (3) nanometer (4) photometer

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31. If No is the original mass of the substance of half-life period tl/2 = 5 years, then the amount of substance left after

15 years is :(1) N0 / 8 (2) No / 16 (3) N0 / 2 (4) N0 / 4

32. By increasing the temperature, the specific resistance of a conductor and ~ semiconductor:(1) increases for both (2) decreases for both(3) increases, decreases respectively (4) decreases, increases respectively

33. If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to-

(1) CV (2) 21

nCV2 (3) CV2 (4) n21 CV2

34. Which of the following is more close to a black body ?(1) Black board paint (2) Green leaves (3) Black holes (4) Red roses

35. Which statement is incorrect ?(1) All reversible cycles have same efficiency(2) Reversible cycle has more efficiency than an irreversible one(3) Carnot cycle is a reversible one(4) Carnot cycle has the maximum efficiency in all cycles

36. Length of a string tied to two rigid supports is 40 cm. Maximum length (wavelength in cm) of a stationary waveproduced on it, is :(1) 20 (2) 80 (3) 40 (4) 120

37. The power factor of an A.C. circuit having resistance R and inductance L (connected in series) and an angularvelocity is-(1) R/ L (2) R/(R2 +L2)1/2 (3) L / R (4) R/ (R2 L2)1/2

38. An astronomical telescope has a large aperture to-(1) reduce spherical aberration (2) have high resolution(3) increase span of observation (4) have low dispersion

39. The kinetic energy needed to project a body of mass m from the earth's surface (radius R) to infinity is-(1) mgR/2 (2) 2mgR (3) mgR (4) mgR/4

40. Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas moleculesinside will :(1) increase (2) decrease(3) remain same (4) decrease for some, while increase for others

41. When temperature increases, the frequency of a tuning fork :(1) increases (2) decreases(3) remain same (4) increases or decreases depending on the material

42. If mass energy equivalence is taken into account, when water is cooled to form ice, the mass of water should:(1) increases (2) remain unchanged(3) decrease (4) first increase then decrease

43. The energy band gap is maximum in :(1) metals (2) superconductors (3) insulators (4) semiconductors

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44. The part of a transistor which is most heavily doped to produce large number of majority carriers is :(1) emitter (2) base(3) collector (4) can be any of the above three

45. In a simple harmonic oscillator, at the mean position:(1) kinetic energy is minimum, potential energy is maximum(2) both kinetic and potential energies are maximum(3) kinetic energy is maximum, potential energy is minimum(4) both kinetic and potential energies are minimum

46. Initial angular velocity of a circular disc of mass M is 1

. Then two small spheres of mass m are attached gently to twodiametrically opposite points on the edge of the disc. What is the final angular velocity of the disc ?

(1) 1MmM

(2) 1mmM

(3) 1m4MM

(4) 1m2M

M

47. The minimum velocity (in ms1) with which a car driver must traverse a flat curve of radius 150 m and coefficient offriction 0.6 to avoid skidding is :(1) 60 (2) 30 (3) 15 (4) 25

48. A cylinder of height 20m is completely filled with water. The velocity of efflux of water (in ms1) through a smallhole on the side wall of the cylinder near its bottom, is :(1) 10 (2) 20 (3) 25.5 (4) 5

49. A spring of force constant 800 N/m has an extension of 5cm. The work done in extending it from 5cm to 15cm is :(1) 16 J (2) 8 J (3) 32 J (4) 24 J

50. A child swinging on a swing in sitting position, stands up, then the time period of the swing will :(1) increase (2) decrease(3) remain same (4) increase if the child is long and decrease if the child is short

51. A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ballas observed by the man in the lift and a man standing stationary on the ground are respectively :(1) g, g (2) g a , g a (3) g a, g (4) a, g

52. The mass of a product liberated on anode in an electrochemical cell depends on :(1) (It)1/2 (2) It (3) t (4) 2t(where t is the time period for which the current is passed)

53. At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at 47 C?(1) 80 K (2) 73 K (3) 3 K (4) 20 K

54. The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent ofits :(1) speed (2) mass (3) charge (4) magnetic induction

55. A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that theyslide down the plane. The maximum acceleration down the plane is for (no rolling) :(1) solid sphere (2) hollow sphere (3) ring (4) all same

56. In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primaryis 4 A, then that in the secondary is :(1) 4 A (2) 2 A (3) 6 A (4) 10 A

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57. Even Carnot engine cannot give 100% efficiency because we cannot :(1) prevent radiation (2) find ideal sources(3) reach absolute zero temperature (4) eliminate friction

58. Moment of inertia of a circular wire of mass M and radius R about its diameter is :

(1) 2

MR2 (2) MR2 (3) 2MR2 (4) 4

MR2

59. When forces ' F1, F2, F3 are acting on particle of mass m such that F2 and F3 are mutually perpendicular, then theparticle remains stationary. If the force F1 is now removed then the acceleration of the particle is :(1) F1 / m (2) F2 F3 / mF1 (3) (F2 F3) / m (4) F2 / m

60. Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smallerforce. Then the magnitudes of the forces are :(1) 12 N , 6 N (2) 9 N , 9 N (3) 10N , 8 N (4) 16 N , 2 N

61. Speeds of two identical cars are u and 4u at a specific instant. The ratio of the respective distances at thewhich the two cars are stopped from that instant is :(1) 1 : 1 (2) 1 : 4 (3) 1 : 8 (4) 1 : 16

62. 1 mole of a gas with = 7/5 is mixed with 1 mole of a gas with = 5/3, then the value of for the resultingmixture is :(1) 7/5 (2) 2/5 (3) 24/16 (4) 12/7

63. If a charge q is placed at the centre of the line joining two equal charges Q such that the system is inequilibrium then the value of q is :(1) Q / 2 (2) Q/2 (3) Q / 4 (4) Q/4

64. Capacitance (in F) of a spherical conductor having radius 1m, is :(1) 1.1 1010 (2) 106 (3) 9 109 (4) 103

65. A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If theacceleration of the system is g/8, then the ratio of the masses is :(1) 8 : 1 (2) 9 : 7 (3) 4 : 3 (4) 5 : 3

66. Two spheres of the same material have radii 1 m and 4m and temperatures 4000 K and 2000 K respectively.The ratio of the energy radiated per second by the first sphere to that by the second is :(1) 1 : 1 (2) 16 : 1 (3) 4 : 1 (4) 1 : 9

67. Three identical blocks of masses m = 2 kg are drawn by a force F = 36 N with an acceleration of 6ms2 on africtionless surface, then what is the tension (in N) in the string between the blocks B and C ?

C B A F

(1) 9.2 (2) 7.8 (3) 12 (4) 9.868. One end of massless rope, which passes over massless and frictionless

pulley P is tied to a hook C while the other end is free. Maximum tension thatthe rope can bear is 960 N. With what value of maximum safe acceleration(in ms2) can a man of 60kg climb on the rope

P

C(1) 16 (2) 6(3) 4 (4) 8

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69. A particle of mass m moves along line PC with velocity v as shown .What isthe angular momentum of the particle about P ?

PI

O

rL

C

(1) mvL (2) mvl(3) mvr (4) zero

70. Wires 1 and 2 carrying currents i1 and i2 respectively are inclined at an angle to each other. What is the force on a small element dl of wire 2 at distance rfrom wire 1 (as shown in figure) due to the magnetic field of wire ?

r

i1 i2

dl

1 2

(1) r2

0

i1 i2 dl tan (2) r20

i1 i2 dl sin

(3) r2

0

i1 i2 dl cos (4) r40

i1 i2 dl sin

71. At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound canemit:(i) electrons (ii) protons (iii) He2+ (iv) neutronsThe emission at the instant can be(1) i, ii, iii (2) i, ii, iii, iv (3) iv (4) ii, iii

72. Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. Then the ratio of the wavelengths isnearest to :(1) 1 : 2 (2) 4 : 1 (3) 2 : 1 (4) 1 : 4

73. Formation of covalent bonds in compounds exhibits :(1) wave nature of electron (2) particle nature of electron(3) both wave and particle nature of electron (4) none of these

74. A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicularto one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into theplane at the loop exists everywhere with half the loop outside the field, as shown in figure. The induced emf is:

(1) zero (2) RvB (3) VBL/R (4) VBL

75. Identify the pair whose dimensions are equal(1) torque and work (2) stress and energy (3) force and stress (4) force and work.

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ANSWER KEY TO AIEEE 2002 TEST PAPER (PHYSICS)1. (4) 2. (3) 3. (2) 4. (1) 5. (3) 6. (3) 7. (1)8. (1) 9. (2) 10. (3) 11. (1) 12. (2) 13. (3) 14. (1)15. (1) 16. (4) 17. (2) 18. (2) 19. (2) 20. (4) 21. (3)22. (2) 23. (2) 24. (3) 25. (1) 26. (1) 27. (1) 28. (3)29. (3) 30. (2) 31. (1) 32. (3) 33. (2) 34. (1) 35. (1)36. (2) 37. (2) 38. (2) 39. (3) 40. (3) 41. (2) 42. (1)43. (3) 44. (1) 45. (3) 46. (3) 47. (2) 48. (2) 49. (2)50. (2) 51. (3) 52. (2) 53. (4) 54. (1) 55. (4) 56. (2)57. (3) 58. (1) 59. (1) 60. (3) 61. (2) 62. (3) 63. (4)64. (1) 65. (2) 66. (1) 67. (3) 68. (2) 69. (4) 70. (3)71. (1) 72. (3) 73. (1) 74. (4) 75. (1)

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1. Which of the following is a redox reaction ?(1) NaCl + KNO3 NaNO3 + KCl(2) CaC2O4 + 2 HCl CaCl2 + H2C2O4(3) Ca(OH)2 + 2 NH4Cl CaCl2 + 2 NH3 +2H2O(4) 2K [Ag(CN)2] + Zn 2 Ag + K2[Zn(CN)4]

2. For an ideal gas, number of moles per litre in terms of its pressure P, temperature T, gas constant R is:(1) pT/R (2) pRT (3) p/RT (4) RT/p

3. Number of PO bonds in P4O10 is:(1) 17 (2) 16 (3) 15 (4) 6

4. KO2 (potassium super oxide) is used in oxygen cylinders in space and submarines because it :(1) Absorbs CO2 and increases O2 concentrations.(2) Absorbs moisture.(3) Absorbs CO2.(4) Produces ozone.

5. Which of the following ions has the maximum magnetic moment ?(1) Mn2+ (2) Fe2+ (3) Ti2+ (4) Cr2+.

6. Which of these will not react with acetylene?(1) NaOH (2) ammonical AgNO3(3) Na (4) HCl.

AIEEE 2002 TEST PAPERCHEMISTRY

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7. The compound

OCOCH3COOH

is used as :

(1) Antiseptic (2) Antibiotic (3) Analgesic (4) Pesticide.

8. For the following cell with hydgoren electrodes at two different pressure p1and p2Pt (H2) | H+ (aq)| Pt (H2)p1 1M p2

emf is given by

(1) 2

1e p

plogF

RT (2) 2

1e p

plogF2

RT (3) 1

2e p

plogF

RT (4) 1

2e p

plogF2

RT

9. What is the product when acetylene reacts with hypochlorous acid ?(1) CH3COCl (2) ClCH2CHO (3) Cl2CHCHO (4) ClCH2COOH.

10. A similarity between optical and geometrical isomerism is that :(1) each forms equal number of isomers for a given compound.(2) if in a compound one is present then so is the other.(3) both are included in stereoisomerism.(4) they have no similarity.

11. Which of the following reaction is possible at anode?(1) 2 Cr3+ + 7H2O Cr2O72 + 14H+ (2) F2 2F(3) (1/2) O2 + 2H+ H2O (4) displacement reaction.

12. Which of the following concentration factor is affected by change in temperature ?(1) Molarity (2) Molality (3) Mole fraction (4) Weight fraction

13. Cyanide process is used for the extraction of :(1) barium. (2) silver. (3) boron. (4) zinc.

14. The reaction : (CH3)3CBr OH2 (CH3)3COH is an example of -(1) elimination reaction. (2) substitution reaction.(3) free radical reaction. (4) rearrangement reaction.

15. A metal M readily forms water soluble sulphate MSO4 ,and oxide MO . MO in aqueous solution forms insolubleM(OH)2 soluble in NaOH. Metal M is :(1) Be (2) Mg (3) Ca (4) Sr

16. Half-life of a substance A following first order kinetics is 5 days. Strarting with 100g of A, amount left after 15days is :(1) 25 g (2) 50 g (3) 12.5 g (4) 6.25 g

17. The most stable ion is :(1) [Fe(OH)5]3 (2) FeCl6]3 (3) [Fe(CN)6]3 (4) [ [Fe(H2O)6]3+

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18. When primary amine reacts with chloroform in ethanolic KOH then the product is :(1) an isocyanide. (2) an aldehyde. (3) a cyanide. (4) an alcohol.

19. If Fe3+ and Cr3+ both are present in group IIIrd of qualitative analysis, then distiction can be made by ?(1) addition of NH4OH in presence of NH4Cl when only Fe (OH)3 is precipitated(2) addition of NH4OH in presence of NH4 Cl when Cr(OH)3 and Fe(OH)3 both are precipitated and on adding Br2

water and NaOH, Cr(OH)3 dissolves.(3) Precipitate of Cr(OH)3 and Fe(OH)3 as obtained in (b) are treated with conc. HCl when only Fe(OH)3

dissolves.(4) Both (2) and (3).

20. In an organic compound of molar mass 108 g mol1 C,H and N atoms are present in 9 : 1 : 3.5 by weight.Molecular formula can be :(1) C6H8N2 (2) C7H10N (3) C5H6N3 (4) C4H18N3

21. The solubility of Ca(OH)2 is s moles/litre. The solubility product under the same condition is(1) 4S3 (2) 3S4 (3) 4S2 (4) S3.

22. The heat required to raise the temperature of1 mole of a substance by 1C is called :(1) Specific heat. (2) molar heat capacity.(3) water equivalent. (4) none of these.

23. particle is emitted in a radioactive reaction when:(1) proton changes to neutron. (2) a neutron changes to proton.(3) a neutron change to electron. (4) an electron changes to neutron.

24. In mixture A and B components show - ve deviation as :(1) A B interaction is stronger than A A and B B interaction is.(2) A B interaction is weaker than A A and B B interaction is.(3) V

mix > 0 , S mix > 0.(4)Vmix = 0 , S mix > 0.

25. Refining of impure copper with zinc impurity is to be done by electrolysis using electrodes as : Cathode Anode Cathode Anode(1) pure copper pure zinc (2) pure zinc pure copper(3) pure copper impure copper (4) pure zinc impure zinc

26. Aluminium is extracted by the electrolysis of :(1) alumina (2) bauxite(3) molten cryolite. (4) alumina mixed with molten cryolite

27. Freezing point of an aqueous solution is ( 0.186)0C. Elevation of boiling point of the same solution is Kb =0.512 0 C mol1kg, K = 1.860C mol1kg, find the increase in boiling point.(1) 0.1860C (2) 0.05120C (3) 1.860C (4) 5.12C

28. In which of the following species is the underlined carbon having sp3 hybridisation?(1) CH3 OOHC (2) CH3CH2OH (3) CH3COCH3 (4) CH2= HC CH3

29. Bond angle of 1090 28 found in -(1) NH3, (BF4)1 (2) (NH4)+, (BF3) (3) NH3, BF4 (4) (NH2)1, BF3

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30. For the reaction A + 2B C, rate is given by+ dt]C[d = k [A] [B], hence the order of the reaction is :

(1) 3 (2) 2 (3) 1 (4) 0

31. CH3 Mg Br is an organo metallic compound due to :(1) Mg Br bond (2) C Mg bond (3) C Br bond (4) C H bond

32. One of the following species acts as both Bronsted acid and base -(1) H2PO2 (2) HPO32 (3) HPO42 (4) All of these

33. Hybridisation of the underline atom changes in :(1) AlH3 changes to 4AlH (2) H2O changes to H3O+(3) NH3 changes to 4NH (4) In all cases

34. Racemic mixture is formed by mixing two :(1) isomeric compounds. (2) chiral compounds.(3) meso compounds. (4) optical isomers.

35. In XeF2, XeF4, XeF6 the number of lone pairs on Xe are respectively(1) 3, 2, 1 (2) 2, 4, 6 (3) 1, 2, 3 (4) 6, 4, 2

36. 1 M NaCl and 1 M HCl are present in an aqueous solution. The solution is(1) not a buffer solution with pH < 7 (2) not a buffer solution with pH > 7(3) a buffer solution with pH < 7 (4) a buffer solution with pH > 7

37. Consider following two reactions :

A product dt]A[d

= k1 [A]0 ; B product dt]B[d

= k2 [B]k1 and k2 are expressed in terms of molarity (mol L1) and time (s1) as :(1) s1 Ms1L1 (2) Ms1, Ms1 (3) s1M1s1 (4) Ms1, s1

38. RNA is different from DNA because RNA contains :(1) ribose sugar and thymine. (2) ribose sugar and uracil.(3) deoxyribose sugar and thymine. (4) deoxyribose sugar and uracil.

39. For a cell given below :Ag |Ag+|| Cu2+| Cu +Ag+ + e Ag E = xCu2+ + 2e Cu, E = y

E cell is :(1) x + 2y (2) 2x + y (3) y x (4) y 2x

40. Kinetic theory of gases proves :(1) Only Boyles law. (2) Only Charles law.(3) Only Avagadro's law. (4) All of these.

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41. MnO4 is a good oxidising agent in different medium changing toMnO4 Mn2+

MnO42-

MnO2 Mn2O3

Changes in oxidation numbner respecitively are(1) 1, 3, 4, 5 (2) 5, 4, 3, 2 (3) 5, 1, 3, 4 (4) 2, 6, 4, 3

42. The differential rate law for the reaction H2 + I2 2HI is :

(1) dt]HI[d

dt]I[d

dtHd 22 (2) dt

]HI[d21

dt]I[d

dtHd 22

(3) dt]HI[d

dt]I[d

21

dtHd

21 22 (4) dt

]HI[ddt

]I[d2dtHd2 22

43. Number of atoms in 560g of Fe (atomic mass 56g mol1) is :(1) Twice that of 70g N. (2) Half that of 20g H.(3) Both (1) and (2). (4) None of these.

44. Which of the following does not show geometrical isomerism?(1) 1, 2-Dichloro- 1 -pentene. (2) 1, 3-Dichloro -2-pentene.(3) 1, 1-Dichloro- 1 -pentene. (4) 1, 4-Dichloro -2-pentene.

45. Na and Mg crystallize in BCC and FCC type crystals respectively, then the number of atoms of Na and Mgpresent in the unit cell of their respective crystal is(1) 4 and 2 (2) 9 and 14 (3) 14 and 9 (4) 2 and 4

46. Which of the following compounds has wrong IUPAC name?(1) CH3 CH2 CH2 COO CH2CH3 Ethyl butanoate(2) 3-Methylbutanal

(3) 2-Methyl-3-butanol

(4) 2-Methyl-3-pentanone

47. CH3CH2COOH A B, What is B?

(1) CH3CH2COCI (2) CH3CH2CHO (3) CH2 = CHCOOH (4) CICH2CH2COOH

48. For the reaction CO (g) + (1/2) O2 (g) = CO2 (g), Kc/Kp is :(1) RT (2) (RT)1 (3) (RT)1/2 (4) (RT)1/2

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49. Energy of H-atom in the ground state is 13.6 eV, hence energy in the second excited state is(1) 6.8 eV (2) 3.4 eV (3) 1.51 eV (4) 4.53 eV

50. A square planar complex is formed by hybridization of which atomic orbitals ?(1) s, p

x, py, pz (2) s, px, py, pz,d (3) d, s, px, py (4) s, px, py, pz, d

51. The type of isomerism present in nitropentaamminechromium(III) chloride is :(1) optical. (2) linkage. (3) ionization. (4) polymerization.

52. Change in volume of the system does not alter the number of moles in which of the following equilibriums :(1) N2(g) + O2(g) 2NO(g) (2) PCl5(g) PCl3(g) + Cl2(g)(3) N2(g) + 3H2(g) 2NH3(g) (4) SO2Cl2(g) SO2(g) + Cl2(g)

53. Uncertainity in position of a particle of 25 g in space is 1015 m. Hence, Uncertainity in velocity (m.sec1) is :(planks constant, h = 6.6 1034 Js)(1) 2.1 1018 (2) 2.1 1034 (3) 0.5 1034 (4) 5.0 1024

54. Consider the following reaction at 1100C.(I) 2C + O2 2CO, G = 460 k J mol1(II) 2Zn + O2 2ZnO, G = 360 k J mol1Based on these, select correct alternate.(1) zinc can be oxidised by CO (2) zinc oxide can be reduced by carbon(3) Both (1) and (2) (4) None of the above

55. A reaction is non-spontaneous at the freezing point of water but is spontaneous at the boiling point of water,then

H S H S(1) + ve + ve (2) ve ve(3) ve + ve (4) + ve ve

56. Polymer formation from monomers starts by :(1) condensation reaction between monomers.(2) coordinate bond formation between monomers.(3) conversion of monomer to monomer ions by protons.(4) hydrolysis of monomers.

57. Which of the following are arranged in an increasing order of their bond strengths of(1) O2 < O2 < O2+ < O22 (2) O22 < O2 < O2 < O2+(3) O2 < O22 < O2 < O2+ (4) O2+ < O2 < O2 < O22

58. Most common oxidation state fo Ce (Cerium) are :(1) +3, +4 (2) +2, +3 (3) +2, +4 (4) +3, +5

59. Arrange Ce+3, La+3, Pm+3 and Yb+3 in increasing order of their ionic radii.(1) Yb+3 < Pm+3 < Ce+3 < La+3 (2) Ce+3 < Yb+3 < Pm+3 < La+3(3) Yb+3 < Pm+3 < La+3 < Ce+3 (4) Pm+3 < La+3 < Ce+3 < Yb+3.

60. pH of 0.005 M calcium acetate (pKa of CH3 COOH = 4.74) is(1) 7.04 (2) 9.37 (3) 9.26 (4) 8.37

15 AIEEE 2002 Paper

61. H2 gas is absorbed on the metal suface like tungasten. This follows.......... order reaction.(1) third (2) second (3) zero (4) first

62. Rate constant k of the first order reaction when initial concentration C0 and concentration Ct at time t is given byequation

kt = log C0 log CtGraph is a straight line if we plot(1) t vs log C0 (2) t vs log Ct (3) t1 vs log Ct (4) log C0 vs log Ct

63. Alum is widely used to purify water since(1) it forms complex with clay particles.(2) it coagulates the mud particles.(3) it exchanges Ca2+ and Mg2+ ions present in hard water.(4) its sulphate ion is water purifier.

64. On vigorous oxidation by permagnate solution, (CH3)2C = CH CH2 CHO gives :

(1) 3

323

CH| CHCHCHCCH

|| OHOH(2)

(3) CH3CH3

CH OH + CH3CH2CH2OH (4) CH3CH3

=== O + CH3CH2CHO.

65. Arrangement of (CH3)3C, (CH3)2CH , CH3CH2 when attached to benzyl or an unsaturated group in increasingorder of electron releasing nature is.(1) (CH3)3C < (CH3)2CH < CH3CH2 (2) CH3CH2 < (CH3)2CH < (CH3)3C (3) (CH3)2CH < (CH3)3C < CH3CH2 (4) (CH3)3C < CH3CH2 < (CH3)2CH

66. In case of nitrogen, NCl3 is possible but no NCl5 while in case of phosphorus, PCl3 as well as PCl5 arepossible. It is due to :(1) availability of vacant d-orbital in P but not in N.(2) lower electronegativity of P then N.(3) lower tendency of H bond formation in P than N.(4) occurrence of P in solid while N in gaseous state at room temperature.

67. The functional group, which is found in amino acid is(1) COOH group. (2) NH2 group. (3) CH3 group. (4) both (1) and (2).

68. Conductivity (unit Siemens S) is directly proportional to area of the vessel and the concentration of the solutionin it and is inversely proportional to the length of the vessel then the unit of the constant of proportionality is(1) Sm mol1. (2) Sm2 mol1. (3) S2m2 mol. (4) S2m2 mol1.

69. A heat engine absorbs heat Q1 from a source at temperature T1 and heat Q2 from a source at temperature T2.Work done is found to be J (Q1 + Q2). This is in accordance with :(1) First law of thermodynamics. (2) second law of thermodynamics.(3) Joules equivalent law. (4) None of the above.

16 AIEEE 2002 Paper

70. Select correct statement :(1) when a covalent bond is formed, transfer of electrons takes place.(2) pure H2O does not contain any ion.(3) a bond is formed when attractive forces overcome repulsive forces.(4) HF is less polar than HBr.

71. The metallic sodium dissolves in liquid ammonia to form a deep blue coloured solution.The deep blue colour is due to formation of :(1) solvated electron, electron (NH3)x . (2) solvated atomic sodium, Na(NH3)y .(3) (Na+ + Na). (4) NaNH2 + H2 .

72. Maximum dehydration takes place that of :

(1) (2) (3) (4)

73. SN1 reaction is feasible in :

(1) (CH3)3CCl + KOH (2) + KOH

(3) (4)

74. Oxidation number of Cl in CaOCl2 (bleaching powder) is(1) zero, since it contains Cl2 (2) 1, since it contains Cl(3) + 1, since it contains CIO (4) +1 and 1 since it contains ClO and Cl

75. Pricric acid is :

(1) (2)

(3) (4)

17 AIEEE 2002 Paper

ANSWER KEY TO AIEEE 2002 TEST PAPER (CHEMISTRY)1. (4) 2. (3) 3. (2) 4. (1) 5. (1)

6. (1) 7. (3) 8. (2) 9. (3) 10. (3)

11. (1) 12. (1) 13. (2) 14. (2) 15. (1)

16. (3) 17. (3) 18. (1) 19. (2) 20. (1)

21. (1) 22. (2) 23. (2) 24. (1) 25. (3)

26. (4) 27. (2) 28. (2) 29. (4) 30. (2)

31. (2) 32. (3) 33. (1) 34. (4) 35. (1)

36. (1) 37. (4) 38. (2) 39. (3) 40. (4)

41. (3) 42. (4) 43. (3) 44. (3) 45. (4)

46. (3) 47. (3) 48. (4) 49. (3) 50. (3)

51. (2) 52. (1) 53. (1) 54. (2) 55. (1)

56. (1) 57. (2) 58. (1) 59. (1) 60. (4)

61. (3) 62. (2) 63. (2) 64. (2) 65. (1)

66. (1) 67. (4) 68. (2) 69. (3) 70. (3)

71. (1) 72. (2) 73. (1) 74. (4) 75. (3)

18 AIEEE 2002 Paper

AIEEE 2002 TEST PAPERMATHEMATICS





1. If but 2 = 5 3, 2 = 5 3, then the equation having the roots

and

is.

(1) 3x2 + 19x + 3 = 0 (2) 3x2 19x + 3 = 0 (3) 3x2 19x 3 = 0 (4) x2 16x + 1 = 0

2. If y = (x + 2x1 )n, then (1 + x2) 22

dxyd

+ x dxdy

is -

(1) n2y (2) n2y (3) y (4) 2x2 y

3. If 1, log3 23 x1 , log3(4.3x 1) are in AP, then x equals(1) log3 4 (2) 1 log3 4 (3) 1 log4 3 (4) log4 3

4. A problem in mathematics is given to three students A, B, C and their respectively probability of solving the

problem is 31

,

21

and 41

. Probability that the problem is solved, is

(1) 3/4 (2) 1/2 (3) 2/3 (4) 1/3

5. The fundamental period of sin2 x is -(1) /2 (2) (3) 3/2 (4) 2

19 AIEEE 2002 Paper

6. , m, n are the pth, qth and rth term of a GP and all positive, then 1rnlog1qmlog1plog

equals -

(1) 3 (2) 2 (3) 1 (4) 0

7. 0xim

x2x2cos1

is equal to

(1) 1 (2) 1 (3) 0 (4) does not exist

8. A triangle with vertices (4, 0), (1, 1), (3, 5) is(1) isosceles and right angled (2) isosceles but not right angled(3) right angled but not isosceles (4) neither right angled nor isosceles

9. In a class of 100 students there are 70 boys whose average marks in a subject is 75. If the average marks of thecomplete class is 72, then what is the average marks of the girls?(1) 73 (2) 65 (3) 68 (4) 74

10. tan1

41

+ tan1

92

is equal to -

(1)

53

cos21 1 (2)

53

sin21 1 (3)

53tan

21 1 (4) tan1 2

1

11. The order and degree of the differential equation 3/2

dxdy31

= 4 3

3

dxyd

are

(1)

32

,1 (2) (3, 1) (3) (3, 3) (4) (1, 2)

12. The equation of the plane containing the line

1xx =

m

yy 1 =

n

zz 1 is

a (x x1) + b (y y1) + c (z z1) = 0, where-

(1) ax1 + by1 + cz1 = 0 (2) a + bm + cn = 0 (3) a

= m

b =

n

c (4) x1 + my1 + nz1 = 0

13. The solution of the equation 22

dxyd

= e2x is

(1) 4

e x2 (2) 4

e x2 + cx + d (3) 4

1 e2x + cx2 + d (4) 4

1e2x + c + d

14. xim

x

2x3x

, x R, is equal to

(1) e (2) e1 (3) e5 (4) e5

15. The range of the function f(x) = x2x2

, x 2 is -

(1) R (2) R {1} (3) R {1} (4) R {2}

20 AIEEE 2002 Paper

16. The sum of the series 13 23 + 33 ........+ 93 is(1) 300 (2) 125 (3) 425 (4) 0

17. If the third term of an A.P. is 7 and its 7th term is 2 more than three times of its 3rd term, then sum of its first20 terms is(1) 228 (2) 74 (3) 740 (4) 1090

18. 10

0dx|xsin|

is equal to

(1) 20 (2) 8 (3) 10 (4) 18

19. In = 4/

0 tann x dx, then

nlim n [In + In + 2] equals-

(1) 21 (2) 1 (3) (4) zero

20. 2

0[x2] dx is equal to -

(1) 2 2 (2) 2 + 2 (3) 2 1 (4) 2 3 + 5

21.

xcos1)xsin1(x2

2

dx is equal to

(1) 4

2 (2) 2 (3) zero (4) 2

22. Which of the following is not a periodic function -(1) sin 2x + cos x (2) cos x (3) tan 4x (4) log cos 2x

23. The domain of definition of the function f (x) =

4xx5log

2

10 is

(1) [1, 4] (2) [1, 0 ] (3) [0, 5] (4) [5, 0]

24. If sin y = x sin (a + y), then dxdy

is -

(1) )ya(sinasin

2 (2) asin)ya(sin2 (3) sin a sin2 (a + y) (4)

asin)ya(sin2

25. If xy = ex y, then dxdy

is-

(1) xlog1x1

(2) xlog1

xlog1 (3) not defined (4) 2)xlog1(

xlog

26. The two curves x3 3xy2 + 2 = 0 and 3x2y y3 2 = 0

(1) cut at right angle (2) touch each other (3) cut an angle 3 (4) cut at an angle 4

21 AIEEE 2002 Paper

27. The function f(x) = cot1 x + x increases in the interval(1) (1, ) (2) (1, ) (3) (, ) (4) (0, )

28. The greatest value of f(x) = (x + 1)1/3 (x 1)1/ 3 on [0, 1] is(1) 1 (2) 2 (3) 3 (4) 1/3

29. Evaluate 2/

0 xcosxsinxsin

dx -

(1) 4 (2) 2

(3) zero (4) 1

30. )1x(xdxn is equal to-

(1) n

1log 1x

xn

n

+ c (2) n1

log nn

x

1x + c (3) log 1x

xn

n

+ c (4) None of these

31. The area bounded by the curve y = 2x x2 and the straight line y = x is given by

(1) 29

sq unit (2) 643

sq unit (3) 635

sq unit (4) None of these

32. The differential equation of all non-vertical lines in a plane is

(1) 22

dxyd

= 0 (2) 22

dyxd

= 0 (3) dxdy

= 0 (4) dydx

= 0

33. Given two vectors are i j and i + 2 j the unit vector coplanar with the two vectors and perpendicular to firstis -

(1) 21

( i + j ) (2) 51

(2 i + j ) (3) 21

( i + k ) (4) None of these

34. The vector k3jxi is rotated through an angle and doubled in magnitude, then it becomesk2j)2x4(i4 . The value of x are

(1)

2,

32 (2)

2,

31 (3)

0,

32 (4) {2, 7}

35. A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7) parallel to the coordinateplanes. The length of a diagonal of the parallelopiped is(1) 7 unit (2) 38 unit (3) 155 unit (4) None of these

36. The equation of the plane containing the line

n

zzm

yylxx 111

is (where a(x x1) + b(y y1) + c(z z1) = 0)

(1) ax1 + by1 + cz1 = 0 (2) al + bm + cn = 0 (3) nc

m

bla

(4) lx1 + my1 + nz1 = 0

22 AIEEE 2002 Paper

37. If A and B are two mutually exclusive events, then(1) P(A) < P( B ) (2) P(A) > P( B ) (3) P(A) < P(B) (4) None of these

38. The probability of India winning a test match against West-Indies is 1/2 assuming independence from match tomatch. The probability that in a match series India's second win occurs at the third test is

(1) 81 (2) 4

1 (3) 21 (4) 3

2

39. The equation of the directirx of the parabola y2 + 4y + 4x + 2 = 0 is

(1) x = 1 (2) x = 1 (3) x = 23 (4) x = 2

3

40. Let Tn denotes the number of triangles with can be formed using the vertices of a regular polygon of n sides. IfTn+1 Tn = 21, then n equals(1) 5 (2) 7 (3) 6 (4) 4

41. In a triangle ABC, 2ca sin

2

CBA is equal to

(1) a2 + b2 c2 (2) c2 + a2 b2 (3) b2 c2 a2 (4) c2 a2 b2

42. xim

x

2

2

3xx3x5x

is equal to

(1) e4 (2) e2 (3) e3 (4) e

43. The incentre of the triangle with vertices (1, 3 ), (0, 0) and (2, 0) is

(1)

23

,1 (2)

31

,

32

(3)

23

,

32

(4)

31

,1

44. If the vectors a ,

b

and c

form the sides BC, CA and AB respectively of a triangle ABC, then-

(1) a

.

b

=

b

.

c

=

c

.

a 0 (2)

a

b

=

b

c

=

c

a

(3) a

.

b

=

b

.

c

=

c

.

a = 0 (4)

a

b +

b

c

+ c

a =

0

45. If is an imaginary cube root of unity, then (1 + 2)7 equals-(1) 128 (2) 128 (3) 128 2 (4) 128 2

46. If i3201i34

1i3i6

= x + iy, then -

(1) x = 3, y = 1 (2) x = 1, y = 3 (3) x = 0, y = 3 (4) x = 0, y = 0

47. If tan = 34

then sin is

(1) 54

notbut54

(2) 54

or54

(3) 54

notbut54

(4) None of these

23 AIEEE 2002 Paper

48. The radius of the circle passing through the foci of the ellipse 9y

16x 22

= 1 and having its centre at (0, 3) is

(1) 4 unit (2) 3 unit (3) 12 unit (4) 27

unit

49. A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both ofthem win a prize. The probability that they will not win a prize in a single trial, is

(1) 251 (2) 25

24 (3) 252 (4) None of these

50. If ( 1) is cubic root of unity, then 1i1i

11i1i11

2

22

equals

(1) 0 (2) 1 (3) i (4)

51. A biased coin with probability p, 0 < p < 1, of heads is tossed until a head appears for the first time. If theprobability that the number of tosses required is even, is 2/5, then p equals

(1) 31 (2) 3

2 (3) 52 (4) 5

3

52. A fair die is tossed eight times. The probabillity that a third six is observed on the eight throw, is

(1) 75

27

65C (2) 8

52

7

65C (3) 6

52

7

65C (4) None of these

53. Let f(2) = 4 and f(2) = 4, then 2x im 2x)x(f2)2(fx

is equal to

(1) 2 (2) 2 (3) 4 (4) 3

54. Three straight lines 2x + 11y 5 = 0, 4x 3y 2 = 0 and 24x + 7y 20 = 0(1) form a triangle(2) are only concurrent(3) are concurrent with one line bisecting the angle between the other two(4) none of these

55. A straight line through the point (2,2) intersects the lines 3 x + y = 0 and 3 x - y = 0 at the points A andB.The equation to the line AB so that the triangle OAB is equilateral is(1) x 2 = 0 (2) y 2 = 0 (3) x + y 4 = 0 (4) none of these

56. The greatest distance of the point P (10, 7) from the circle x2 + y2 4x 2y 20 = 0 is-(1) 10 unit (2) 15 unit (3) 5 unit (4) None of these

57. The equation of the tangent to the circle x2 + y2 + 4x 4y + 4 = 0 which make equal intercepts on thepositive coordinate axes, is-(1) x + y = 2 (2) x + y = 2 2 (3) x + y = 4 (4) x + y = 8

58. The equation of the ellipse whose foci are (2, 0) and eccentricity is 1/2, is

(1) 116y

12x 22

(2) 112y

16x 22

(3) 18y

16x 22

(4) none of these

24 AIEEE 2002 Paper

59. The equation of the chord joining two points (x1, y1) and (x2, y2) on rectangular hyperbola xy = c2 is

(1) )yy(y

)xx(x

2121

= 1 (2) 21 xxx

+

21 yyy

= 1

(3) 21 yy

x

+

21 xx

y

= 1 (4) 21 yy

x

+

21 xx

y

= 1

60. If the vectors jbandkzjyixa,c are such that c,a and b form a right handed system, then c is(1) kxiz (2) 0 (3) jy (4) kxiz

61. The centre of the circle given by )k2j2i(.r = 15 and )k2j(r

= 4 is

(1) (0, 1, 2) (2) (1, 3, 4) (3) (1, 3, 4) (4) None of these

62. If y = sin2 + cosec2, 0, then(1) y = 0 (2) y 2 (3) y 2 (4) y 2

63. The value of 15tan115tan1

2

2

is

(1) 1 (2) 3 (3) 23 (4) 2

64. If sin ( + ) = 1, sin ( ) = 21

then tan(+ 2) tan(2+) is equal to(1) 1 (2) 1 (3) 0 (4) None of these

65. 22

)yx(xy4

sin

is true if

(1) x y 0 (2) x = y, x 0 (3) x = y (4) x 0, y 0

66. The sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y, where x, y > 0, then the triangle is(1) right angled (2) obtuse angled (3) equilateral (4) none of these

67. In a ABC, tan 2A

= 65

, tan 2C

= 52

, then

(1) a, c, b are in AP (2) a, b, c are in AP (3) b, a, c are in AP (4) a, b, c are in GP

68. The equation a sin x + b cos x = c, where

| c| > 22 ba has(1) a unique solution (2) infinite number of solutions(3) no solution (4) None of the above

69. If is a root of 25 cos2 + 5 cos 12 = 0, 2

< < , then sin 2is equal to

(1) 2524 (2) 25

24 (3) 1813 (4) 18

13

25 AIEEE 2002 Paper

70. tan1

41

+ tan1

92

is equal to

(1) 21

cos1

53 (2) 2

1sin1

53 (3) 2

1tan1

53 (4) tan1

21

71.

0n

ne

!nxlog

is equal to

(1) loge x (2) x (3) log

x e (4) None of these

72. 44)1x(

3

3)1x(2)1x(21)1x(

e

......... is equal to

(1) log (x 1) (2) log x (3) x (4) None of these

73. If |x| < 1, then the coefficient of xn in expansion of (1 + x + x2 + x3 +....)2 is(1) n (2) n 1 (3) n + 2 (4) n + 1

74. The coefficient of x5 in (1 + 2x + 3x2 +.....)3/2 is :(1) 21 (2) 25 (3) 26 (4) none of these

75. The number of real roots of 7x72x23 = 9 is(1) 0 (2) 2 (3) 1 (4) 4

26 AIEEE 2002 Paper

ANSWER KEY TO AIEEE 2002 TEST PAPER (MATHEMATICS)1. (2) 2. (1) 3. (2) 4. (1) 5. (2) 6. (4) 7. (4)

8. (1) 9. (1) 10. (4) 11. (3) 12. (2) 13. (2) 14. (3)

15. (2) 16. (3) 17. (3) 18. (1) 19. (2) 20. (4) 21. (2)

22. (2) 23. (1) 24. (2) 25. (4) 26. (1) 27. (3) 28. (2)

29. (1) 30. (1) 31. (1) 32. (1) 33. (1) 34. (1) 35. (1)

36. (2) 37. (1) 38. (2) 39. (4) 40. (2) 41. (2) 42. (1)

43. (4) 44. (2) 45. (4) 46. (4) 47. (2) 48. (1) 49. (2)

50. (1) 51. (1) 52. (2) 53. (3) 54. (3) 55. (2) 56. (2)

57. (2) 58. (2) 59. (1) 60. (1) 61. (2) 62. (4) 63. (3)

64. (1) 65. (2) 66. (2) 67. (2) 68. (3) 69. (2) 70. (4)

71. (2) 72. (3) 73. (4) 74. (4) 75. (2)

Documents

AIEEE 2002 With Answer Key