AIEEE Solved Exam Paper Mathematics 2005

Sample papers



AIEEE 2005


1. A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?

(a) 3.0 cm                    (b) 2.0 cm                    (c) 1.5 cm                    (d) 1.0 cm

2. Out of the following pairs, which one does not have identical dimensions?

(a) Angular momentum and Planck’s constant

(b) Impulse and momentum

(c) Moment of inertia and moment of a force

(d) Work and torque

3.  A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates 2 m/s squire. He reaches the ground with a speed of 3 m/s. At what height, did he bail. Out?

(a) 91 m                       (b) 182 m                     (c) 293 m                     (d) 111 m

4. The upper half of an inclined plane with inclination ø is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by:

(a) 2 sinø                      (b) 2 cosø                    (c) 2 tanø                     (d) tanø

5. A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is:

(a) 40 m/s                     (b) 20 m/s                    (c) 10 m/s                     (d) 10 Ö30 m/s

6. A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 1/3 M and, a body C of mass 2/3 M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards:

(A) Depends on height of breaking                    (b) Does not shift

(c) Body C                                      (d) Body B

7. The moment of inertia of uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is:

(a)  ¼ Mr2 (b) 2/5 Mr2 (c) Mr2 (d) ½ Mr2

8. A particle of mass 0.3 kg is sbjected to a force F=-kx with k=15 N/m. What will be its initial acceleration, if it is released from a point 20 cm away from the origin?

(a) 3 m/s2 (b) 15 m/s2 (c) 5 m/s2 (d) 10 m/s2

9. A 20 cm long capillary tube is dipped in water. The water rises upto 8 cm. If the entire arrangement is put in a freely falling elevator, the length o water column in the capillary tube will be:

(a) 8 cm                       (b) 10 cm                     (c) 4 cm                       (d) 20 cm

10. A mass ‘m’ moves with a velocity ‘u’ and collides inelastically with another identical mass. After collision the 1st mass moves with velocity u/Ö3 in a direction perpendicular to the initial direction of motion. Find the speed of the 2nd mass after collision:

(a) u                             (b) Ö3 u                       (c) 2/Ö3 u                    (d) u /Ö3

11. Average density of the earth:

(a) Does not depend on g                                 (b) Is a complex function g

(c) Is directly proportional of g              (d) Is inversely proportional to g

12. Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped, is: [mk=0.5]

(a) 800 m                     (b) 1000 m                   (c) 100 m                     (d) 400 m

13. Which of the following is incorrect regarding the first law of thermodynamics?

(a) It is not applicable to any cyclic process

(b) It is a restatement of the principle of conservation of energy

(c) It introduces the concept of the internal energy

(d) It introduces the concept of the entropy

14. The change in the value of ‘g’ at a height ‘h’ above the surface of the earth is the same as at a depth ‘d’ below the surface of earth. When both‘d’ and ‘h’ are much smaller than the radius of earth, then, which one of the following is correct?

(a) D=h/2                     (b) d=3h/2                    (c) d=2h                       (d) d=h

15. A gaseous mixture consists of 16g of helium and 16g of oxygen. The ratio Cr/Cu of the mixture is:

(a) 1.59                        (b) 1.62                        (c) 1.4                          (d) 1.54

16. The intensity of gamma radiation from a given source is I. On passing through 36 mm of lead, it is reduced to I/8. The thickness of lead, which will reduce the intensity to I/2 will be:

(a) 6 mm                      (b) 9 mm                      (c) 18 mm                    (d) 12 mm

17. The electrical conductivity of a electromagnetic radiation of wavelength shorter than 2480 nm, is incident on it. The band gap in (eV) for the semiconductor is:

(a) 1.1 eV                    (b) 2.1 eV                    (c) 0.5 eV                    (d) 0.7 eV 18.

A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed ½ m away, the number of electrons emitted by photocathode would:

(a) Decrease by a factor of 4                            (b) Increase by a factor of 4

(C) Decrease by a factor of 2                           (d) Increase by a factor of 2

19. The function sin2 (wt) represents:

(a) A periodic, but not simple harmonic, motion with a period 2p/w

(b) A periodic, but not simple harmonic, motion with a period p/w

(c) A simple harmonic motion with a period 2p/w

(d) A simple harmonic motion with period p/w

20. A fish looking up through the water sees the outside world, contained in a circular horizon, if the refractive index of water is 4/3 and the fish is 12 cm below the water surface, the radius of this circle in cm is:

(A) 36Ö7                      (b) 36/Ö7                     (c) 36Ö5                       (d) 4Ö5

21. Two point white dot are 1mm apart o a black paper. They are viewed by eye o pupil diameter 3 mm. approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500nm]

(a) 5m                          (b) 1 m                         (c) 6 m                         (d) 3 m


22. A thin glass (refractive index 1.5) lens has optical power of -5D in air. Its optical power in a liquid medium with refractive index 1.6 will be:

(a) 1D                         (b) -1D                                   (c) 25D                        (d) -25D

23. If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor:

(a) ½                            (b) 2                             (c) 1/Ö2                        (d) Ö2

24. In a full wave rectifier circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple world be:

(a) 50 Hz                      (b) 25 Hz                     (c) 100 Hz                    (d) 70.7 Hz

25. In a common base amplifier, the phase difference between the input signal voltage and output voltage is :

(a) p/2                                     (b) p                            (c) zero                        (d) p/2

26. A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions per mlliampere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 volt, the resistance in ohms heeded to be connected in series with the coil will be:

(a) 1000                       (b) 100000                   (c) 99995                     (d) 9995

27. A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

(a) Doubled                  (b) Four times               (c) One-fourth              (d) Halved

28. A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is ‘C’, then the resultant capacitance is:

(a) (n-1) C                   (b) (n+1) C                  (c) C                            (d) nC

29. When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2?

(a) 200 Hz                    (b) 202 Hz                   (c) 196 Hz                    (d) 204 Hz

30. The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom o the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would:

(a) First increase and then decrease to the original value

(b) First decrease and then increase to the original value

(c) Remain unchanged

(d) Increase towards a saturation value

31. An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

(a) Zero                        (b) 0.5%                      (c) 5%                          (d) 20% 32.

A coil of inductance 300 mH and resistance 2 W is connected to a source of voltage 2V. The current reaches half of its steady state value in:

(a) 0.05 s                     (b) 0.1 s                       (c) 0.15 s                     (d) 0.3 s 33.

The self inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of:

(a) 4mF                                    (b) 8mF                        (c) 1mF                                    (d) 2mF

34. An energy source will supply a constant current into the load, if its internal resistance is:

(a) Equal to the resistance of the load

(b) Very large as compared to the load resistance

(c) Zero

(d) Non-zero but less than the resistance of he load

35. A circuit has a resistance of 12 ohm and an impendence of 15 ohm. The power factor of the circuit will be:

(a) 0.8                          (b) 0.4                          (c) 1.25                        (d) 0.125

36. The phase difference between the alternating current and emf is p/2. Which of the following cannot be the constituent of the circuit?

(a) C alone                   (b) R, L                                    (c) L, C                        (d) L alone

37. A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then:

(a) Its velocity, will decrease

(b) Its velocity will increase

(c) It will turn towards right of direction of motion

(d) It will turn towards left of direction of motion

38. In a potentiometer experiment the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of 2W , the balancing length becomes 120 cm. The internal resistance of the cell is:

(a) 1W                          (b) 0.5W                      (c) 4W                          (d) 2W

39. The resistance of hot tungsten filament is about 10 times the cold resistance. What will be the resistance of 100 W and 200V lamp, when not in use?

(a) 40W                        (b) 20W                       (c) 400W                      (d) 200W

40. A magnetic needle is kept in a non-uniform magnetic field. It experiences:

(a) A torque but not a force (b) Neither a force nor a torque (c) A force and a torque (d) A force but not a torque

41. Which one of the following types of drugs reduces fever?

(a) Tranquilizer             (b) Antibiotic                (c) Antipyretic              (d) Analgesic

42. Which of the following oxides is amphoteric in character?

(a) SnO2 (b) SiO2 (c) CO2 (d) CaO

43. Which of the following is a polyamide?

(a) Bakelite                   (b) Terylene                  (c) Nylon-66                (d) Teflon

44. Due to the presence of an unpaired electron, free radicals are:

(a) Cations                   (b) Anions                    (c) Chemically inactive  (d) Chemically reactive

45.  In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be:

(a) 200 W                            (b) 100 W                           (c) 500 W                           (d) 1000 W

46. When an unpolarized light of intensity I0 is incident on a polarizing sheet, the intensity of the light which does not get transmitted is:

(a) ½ I0   (b) ¼ I0  (c) zero                        (d) I0

47. One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed u, where I am the width of each tube will be

(a) Blu                         (b) -Blu                        (c) zero                        (d) 2Blu

48. Two point charges +8q and -2q are located at x=0 and x=L respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is :

(a) 2L                           (b) L/4                         (c) 8L                           (d) 4L

49. If a simple harmonic motion is represented by d2x/dt2+ax=0, its time period is:

(a) 2p/a                      (b) 2p/Öa                    (c) 2pa                        (d) 2pÖa

50. If I0 is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

(a) 2I0 (b) 4I0 (c) I0 (d) I0/2 51.

Two concentric coils each of radius equal to 2 cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber /m2 at the centre of the coils will be (m0=4p*10-7Wb/A.m):

(A) 12*10-5 (b) 10-5 (c) 5*10-5 (d) 7*10-5

52. Which one of the following species is diamagnetic in nature?

(a) H2 (b) H+2 (c) H2 (d) He+2

53. If a is the degree of dissociation of Na2SO4, the Vant Hoff’s factor (i) used for calculating the molecular mass is:

(a) 1-2a                       (b) 1+2a                      (c) 1-a                         (d) 1+a

54. For a spontaneous reaction the DG, equilibrium constant (K) and E0 Cell will be respectively:

(A) –ve,>1,-ve             (b) –ve, <1,-ve             (c) +ve, >1,-ve             (d) –ve,>1, +ve

55. An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be:

(a) A3B                        (b) AB3

(c) A2B                        (d) AB

56. The highest electrical conductivity of the following aqueous solution is of:

(a) 0.1 M difluoroacetic acid                             (b) 0.1 M fluoroacetic acid

(c) 0.1 M chloroacitic acid                                (d) 0.1 M acetic acid

57. The oxidation state of Cr in [Cr (NH3)4CL2] + is:

(A) 0                            (b) +1                          (c) +2                           (d) +3

58. Which of the following oxides is amphoteric in character?

(a) SnO2 (b) SiO2 (c) CO2 (d) CaO 59. Hydrogen bomb is based on the principle of:

(a) Artificial radioactivity                                   (b) Nuclear fusion

(c) Natural radioactivity                                    (d) nuclear fission

60. Lattice energy of an ionic compound depends upon:

(a) Charge on the ion and size of the ion            (b) Packing of ions only

(c) Size of the ion only                          (d) Charge on the ion only

61. Consider an endothermic reaction X®Y with the activation energies Eb and Ef for the backward and forward reactions. Respectively. In general:

(a) There is no definite relation between Eb and Ef (b) Eb=Ef (c) Eb>Ef (d) Eb<Ef 62. A reaction involving two different reactants can never be:

(a) Bimolecular reaction                                    (b) Second order reaction (c) First order reaction                          (d) Unimolecular reaction

63. Two solutions of a substance (nonelectroyte) are mixed in the following manner. 480 mL of 1.5 M first solution +520 mL of 1.2 M second solution. What is the molarity of the final mixture?

(a) 2.70M                    (b) 1.344M                  (c) 1.50M                    (d) 1.20M

64. Which one of the following statements is NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

(a) The area under the distribution curve remains the same as under the lower temperature

(b) The distribution becomes broader

(c) The fraction of the molecules with the most probable speed increases

(d) The most probable speed increases

65. During the process of electrolytic refining of copper, some metals present as impurity settle as ‘anode mud’. These are

(a) Fe and Ni                (b) Ag and Au (c) Pb and Zn               (d) Se and Ag 66.

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will:

(a) Be a function of the molecular mass of the substance (b) Remain unchanged (c) Increase two fold (d) Decrease twice

67. Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point?

(a) RbCl                       (b) KCl                        (c) NaCl                       (d) LiCl

68. Heating mixture of Cu2O and Cu2S will give

(a) Cu2SO3 (b) CuO+CuS              (c) Cu+SO3 (d) Cu+SO2

69. The number of hydrogen atom(s) attached to phosphorus atom in hypo phosphorous acid is:

(a) Three                      (b) One                        (c) Two                        (d) Zero

70. What is the conjugate base of OH?

(a) O2- (b) O (c) H2O                        (d) O2

71. Heating an aqueous solution of aluminium chloride to dryness will give:

(a) Al (OH) Cl2 (b) Al2O3 (c) Al2Cl6 (d) AlCl3

72. The correct order of the thermal stability of hydrogen halides (H-X) is:

(a) HI>HCL<HF>HBr                         (b) HCL<HF>HBr<HI (C) HF>HCL>HBr>HI


73. Calomel (Hg2Cl2) on reaction with ammonium hydroxide gives:

(a) HgO                       (b) Hg2O                      (c) NH2-Hg-Hg-Cl       (d) Hg NH2Cl

74. The number and type of bonds between two carbon atoms in calcium carbide are:

(a) Two sigma, two pi                                       (b) Two sigma, one pi (c) One sigma, two pi

(d) one sigma, one pi

75. A xchematic plot of In Keq verus inerse of temperature for a reaction is shown below The reaction must be:

(a)    Highly spontaneous at ordinary temperature (b)    One with negligible enthalpy change (c)    Endothermic

(d)    Exothermic

76. The oxidation state of chromium in the final product formed by the relation between Kl and acidified potassium dichromate solution is:

(a) +3                           (b) +2                          (c) +6                           (d) +4

77. in silicon dioxide:

(a) There are double bonds between silicon and oxygen atoms

(b) Silicon atom is bonded to two oxygen atoms

(c) Each silicon atom is surrounded by two bounded to two silicon atoms

(d) Each silicon atom is surrounded by four oxygen atoms nd each oxygen atom is bonded to two silicon atoms

78. The lanthanide contraction is responsible for the fact that:

(a) Zr and Zn have the same oxidation state       (b) Zr and Hf have about the same radius (c) Zr and Nb have similar oxidation state          (d) Zr and Y have about the same radius

79. The IUPAC name of the coordination compound K3 [Fe (CN) 6] is:

(a) Tripotassium hexacyanoiron (II)                   (b) Potassium hexacyanoiron (II)

(c) Potassium hexacyanoferrate (III)                  (d) Potassium hexacyanoferrate (II)

80. In which of the following arrangements the order is NOT according to the property indicated against it?

(a) Li<Na<K<Rb: Increasing metallic radius (b) I<Br<F<Cl: Increasing electron gain enthalpy (with negative sign)

(c) B<C<N<O: Increasing first ionisation enthalpy (d) Al3+<Mg2+<Na+<F : Increasing ionic size

81. 2-Methylbutane on reacting with bromine in the presence of sunlight gives mainly:

(a) 1-bromo-3-methylbutane                             (b) 2-bromo-3-methylbutane

(c) 2-bromo-2-methylbutane                             (d) 1-bromo-2-methylbutane

82. Of the following sets which one does NOT contain isoeletronic species?

(a) BO3-3, CO2-3, NO3 (b) SO2-3, CO2-3, NO3 (c) CN, N2, C2-2 (d) PO3-4, SO2-4, CLO4

83. The best reagent to convert pent-3-en-ol into pent-3-en-2-one is:

(a) Pyrdinum chloro-chromate (b) Chromic anhydride in glacial acetic acid

(c) Acidic dichromate (d) Acidic permanganate

84. Which of the following compounds shows optical isomerism?

(a) [Co (CN)6]3- (b) [Cr (C2O4)3]3- (c) [ZnCl4]2- (d) [Cu (NH3)4]2+

85. A photon of hard gamma radiation knocks a proton out of 2412Mg nucleus to form:

(a) The isobar of 2311Na (b) The nuclide 2311Na

(c) The isobar of parent nucleus (d) The isotope of parent nucleus

86. Which one of the following cyano of complexes would exhibit the lowest value of paramagnetic behavior?

(a) [Co (CN) 6]3- (b) [Fe (CN) 6]3- (c) [Mn (CN) 6]3- (d) [Cr (CN) 6]3-

87. Reaction of one molecule of HBr with one molecule of 1, 3-butadiene at 400C given predominantly:

(a) 1-Bromo-2-butene under kinetically controlled conditions

(b) 3-bromobutene under thermodynamically controlled conditions

(c) 1-bromo-2butene under thermodynamically controlled conditions

(d) 3-bromobutene under kinetically controlled conditions

88. Tertiary alkyl halides are practically inert to substitution by SN2 mechanism because of:

(a) Steric hindrance                                                       (b) inductive effect

(c) Instability   (d) insolubility

89. among the following acids which has the lowest pKa value?

(a) CH3CH2COOH                                                      (b) (CH3)2CH-COOH

(c) HCOOH                                                                 (d) CH3COOH

90. Of the five isomeric hexanes, the isomer which can give two monochlorinated compounds is:

(a) 2-methylpentane                                                      (b) 2, 2-dimethylbutane

(c) 2, 3-dimethylbutane                                                 (d) n-hexane

91. In both DNA and RNA, heterocyclic base and phosphate ester linkages are at:

(a) C5 and C1 respectively of the sugar molecule

(b) C1 and C5 respectively of the sugar molecule

(c) C2 and C5 respectively of the sugar molecule

(d) C5 and C2 respectively of the sugar molecule

92. Alkyl halides react with dialkyl copper regents to give:

(a) Alkenyl halides                                                        (b) alkanes

(c) Alkyl copper halides                                                (d) alkenes

93. Which types of isomerism is shown by 2, 3-dichlorobutane?

(a) Structural                                                                (b) Geometric

(c) Optical                                                                    (d) Diastereo

94. Which of the following methods is neither meant for the synthesis nor for separation of amines?

(a) Curtius reaction                                                       (b) Wurtz reaction

(c) Hofmann method                                                     (d) Hinsberg method

95. Acid catalyzed hydration of alkenes except ethane leads to the formation of

(a) Mixture of secondary and tertiary alcohols

(b) Mixture of primary and secondary alcohols

(c) Secondary or tertiary alcohol

(d) Primary alcohol

96. Amongst the following the most basic compound is

(a) p-nitro aniline                                                          (b) acetanilide

(c) Aniline                                                                     (d) benzyl amine

97. Which of the following is fully fluorinated polymer?

(a) PVC           (b) Thiokol                   (c) Teflon                     (d) Neoprene

98. Elimination of bromine from 2-bromobutane results in the formation of:

(a) Predominantly 2-butyne                               (b) predominantly 1-butene

(c) Predominantly 2-butene                               (d) equimolar mixture of 1 and 2-butene

99. Equimolar solution in the same solvent have:

(A) Different boiling and different freezing points

(b) Same boiling and same freezing points

(c) Same freezing point but different boiling point

(d) Same boiling point but different freezing point

100. The structure of diborane (B2H6) contains:

(a) Four 2c-2e bonds and four 3c-2c bonds

(b) Two 2c-2e bonds and two 3c-3e bonds

(c) Two 2c-2e bonds and four 3c-2e bonds

(d) Four 2c-2e bonds and two 3c-2e bonds

101. Which of the following statements in relation to the hydrogen atom is correct?

(a) 3s, 3p and 3d orbitals all have the same energy

(b) 3s and 3p orbitals are of lower energy than 3d orbital

(c) 3p orbital is lower in energy than 3d orbital

(d) 3s orbital is lower in energy than 3p orbital

102. Which of following factors may be regarded as the main cause of lanthanide contraction?

(a) Greater shielding of 5d electron by 4f electrons

(b) Poorer shielding of 5d electron by 4f electrons

(c) Effective shielding of one of 4f electrons by another in the subshell

(d) Poor shielding of one of 4f electron by another in the subshell

103. The value of the ‘spin only’ magnetic moment for one of the following configurations is 2.84 BM. The correct one is:

(a) d5 (in strong ligand field)                                          (b) d3 (in weak as well as well as in strong fields)

(c) d4 (in weak ligand field)                                           (d) d4 (in strong ligand field)

104. Reaction of cyclohexanone with dim ethylamine in the presence of catalytic amount of an acid form a compound of water during the reaction is continuously water during the reaction is continuously removed. The compound formed is generally known as:

(a) An amine                 (b) an imine                              (c) an enamine                          (d) a Schiff’s base

105. If the bond dissociation energies of XY, X2 and Y2 (all diatomic molecules) are in the ratio of 1:1:0.5 and DHf for the formation of XY is-200kj mole -1. The bond dissociation energy of X2 will be:

(a) 400 kJ mol-1 (b) 300 kJ mol-1 (c) 200 kJ mol-1 (d) 100 kJ mol -1

106. An amount of solid NH4HS is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm pressure. Ammonium hydrogen sulphide in the flask. When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to 0.84 atm? The decomposition at this temperature is:

(a) 0.11                        (b) 0.17                                    (c) 0.18                                    (d) 0.30

107. An organic compound having molecular mass 60 is found to contain C=20%, H=6.67% and N= 46.67% while rest is oxygen. On heating it gives NH3 along with a solid residue. The solid residues give violet color with alkaline copper sulphate solution. The compound is:


(b) (NH2)2 CO


(d) CH3NCO

108. t1/4 can be taken as the time taken for the concentration of a reactant to drop to ¾ of its initial value. If the rate constant for a first order reaction is K, the t1/4 can be written as:

(a) 0.75/K                    (b) 0.69/K                                (c) 0.29/K                                (d) 0.10/K

109. If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately:


(a) 24.0                        (b) 25.5                                    (c) 20.5                                    (d) 22.0

110. Let R= [(3, 3), (6,6) (9,9), (12,12), (6,12) (3,9), (3,12), (3,6)] be a relation on the set A=[3,6,9,12]. The relation is:

(a) Reflexive and symmetric only                                   (b) an equivalence relation

(C) Reflexive only                                                         (d) reflexive and transitive only

111. If A2 – A + l =0, then the inverse of A is:

(a) l-A                          (b) A-l                                      (c) A                                        (d) A+l

112. If the cube roots of unity are 1, w, w2, then the roots of the equation (c-1)3+8=0 are :

(a) -1, 1+2w, 1+2w2 (b) -1, 1-2w, 1-2w2

(c) -1,-1,-1                              (d) -1,-1+2w,-1-2w2


113. Area of the greatest rectangle that can be inscribed in the ellipse x2/a2+y2/b2=1 is:

(a) A/b                         (b) Öab                                     (c) ab                                       (d) 2ab

114. The differential equation representing the family of curves y2= 2c(x+Öc), where c>0, is a parameter, is of order and degree as follows:

(a) Order 2, degree 2                                       (b) orders 1, degree3

(c) Order 1, degree 1                                       (d) order 1, degree 2

115. If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number:

(a) 602                         (b) 603                                     (c) 600                                     (d) 601

116. If the coefficients of rth, (r+1)th and (r+2)th terms in the binomial expansion of (1+y)m are in A.P., the m and r satisfy the equation :

(a) m2 –m (4r-1) +4r2+2=0                                           (b) m2-m(4r+1)+4r2-2=0

(c) m2-m (4r+1) +4r2+2=0                                           (d) m2-m (4r-1) +4r2-2=0

117. If z1 and z2 are two non-zero complex number such that |z1+z2|=|z1|+|z2|, then arg z1-arg z2 is equal to:

(a) -p/2                        (b) 0                                         (c) -p                                       (d) p/2

118. The value of a for which the sum of the squares of the roots of the equation x2-(a-2) x – a-1=0 assume the least value is:

(a) 2                             (b) 3                                         (c) 0                                         (d) 1

119. If the roots of the equation x2-bx+c=0 be two consecutive integers, then b2-4c equals:

(a) 1                             (b) 2                                         (c) 3                                         (d) -2

120.In a triangle ABC, let ÐC=p/2, if r is the in radius and R is the circumradius of the triangle ABC, then 2(r+R) equals:

(a) c+a                         (b) a+b+c                                 (c) a+b                                     (d) b+c

121. If in a ABC, the altitudes from the vertices A,B,C on opposite sides are in H.P., then sin A, sin B, sin C are in :

(a) H.P.                                                                        (B) Arithmetic-Geometric Progression

(c) A.P.                                                                        (d) G.P.

122. A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched? Interval             Function

(a) (-¥,-4)                                           x3+6x2+6 (b) (-¥.1/3)                                          3x2-2x+1

(c) (2, ¥)                                              2x3-3x3-12x+6 (d) (-¥,¥)                                            x3-3x2+3x+3

123. The line parallel to the x-axis and passing through the intersection of the lines ax+2by+3b=0 and bx-2ay-3a=0, where (a, b) ¹ (0, 0) is:

(a) Above the x-axis at a distance of 2/3 from it

(b) Above the x-axis at a distance of 3/2 from it

(c) Below the x-axis at a distance of 2/3 from it

(d) Below the x-axis at a distance of 3/2 from it

124. The area enclosed between the curve y= loge (x+e) and the coordinate axes is:

(a) 4                             (b) 3                                         (c) 2                                         (d) 1

125. The parabolas y2 =4x and x2 = 4y divide the square region bounded by the lines x=4, y=4 and the coordinate axes. If s1, s2, s3 are respectively the areas of these parts numbered from top to bottom; then s1:s2:s3 is:

(a) 1:1:1                       (b) 2:1:2                                   (c) 1:2:3                                   (d) 1:2:1 126.

If the plane 2ax -3ay+4az +6=0 passes through the midpoint of the line joining the centers of the spheres x2+y2+z2 +6x-8y-2z=13 and x2+y2+z2-10x+4y-2z=8, then a equals :

(a) 2                             (b) -2                                       (c) 1                                         (d) -1

127. If the circles x2+y2+2ax+CY+a=0 and x2+y2 –3ax +dy-1=0 intersect in two distinct points P and Q then the line 5x+by-a=0 passes through P and Q for:

(a) Exactly two values of a (b) Infinitely many value of a (c) No value of a (d) Exactly one value of a

128. A circle touches the x-axis and also touches the circle with centre at (0,3) and radius 2. The locus of the centre of the circle is:

(a) A parabola              (b) a hyperbola                         (c) a circle                                (d) an ellipse

129. An ellipse has OB as semi minor axis, F and F’ its foci and the angle FBF’is a right angle. Then the eccentricity of the ellipse is:

(a) 1/Ö3                        (b) ¼                                        (c) ½                                        (d) 1/Ö2


130. The angle between the lines 2x= 3y =-z and 6x=-y=-4z is:

(a) 300 (b) 450 (c) 900 (d) 00

131. Three houses are available in a locality. Three persons apply for the houses. Each others. The probability that all the three apply for the same house, is:

(a) 7/9                          (b) 8/9                                      (c) 1/9                                      (d) 2/9

132. A random variable X has Poisson distribution with mean 2. Then P(X>1.5) equals:

(a) 3/e2 (b) 1-3/e2 (c) 0                                         (d) 2/e2

133. A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s2 and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then the lizard will catch the insect after:

(a) 24 sec                     (b) 21 sec                                 (c) 1 sec                                   (d) 20 sec

134. The resultant R of two forces acting on a its magnitude is one third of the other force. The ratio of larger force to smaller one is: (a) 3: 2Ö2                     (b) 3: 2                                     (c) 3: Ö2                                   (d) 2:1

135. A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance: (a) H/A-B                    (b) H/2(A+B)                           (c) H/A+B                                (d) 2H/A-B 136. The pane x+2y-z =4 cut the sphere x2+y2+z2-x+z-2=0 in a circle of radius: (a) Ö2                           (b) 2                                         (c) 1                                         (d) 3

137. If the pair of lines ax2+2 (a+b) xy+by2=0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector, then:

(a) 3a2+2ab+3b2=0      (b) 3a2+10ab+3b2=0                (c) 3a2-2ab+3b2=0                   (d) 3a2-10ab+3b2=0

138. A projectile can have the same range ‘R’ for two angles of projection. If ‘t1’ and ‘t2’ be the times of flights in the two cases, then the product of the two times of flights is proportional to:

(a) R2 (b) 1/R2 (c) 1/R                                     (d) R

139. An annular ring with inner and outer radii R1 and R2 is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F1/F2 is:

(a) R2/R1 (b) (R1/R2)2 (c) 1                                         (d) R1/R2

140. The upper half of an inclined plane with inclination f is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by;

(a) 2 sinf                      (b) 2 cosf                                (c) 2 tanf                                 (d) tanf

141. A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates to the rate f/2 to come to rest. If the total distance traveled is 15 S, then:

(a) S=ft                        (b) S=1/6ft2 (c) S=1/2ft2 (d) S=1/4ft2

142. A particle is moving eastwards with a velocity of 5ms-1. In 10 seconds the velocity changes to 5ms-1 northwards. The average acceleration in this time is:

(a) 1/Ö2 ms-2 towards north-east (b) ½ ms-2 towards north (c) Zero (d) ½ ms-2 towards north-west

143. If ‘S’ is stress and ‘Y’ is Young’s modulus of material of wire, the energy stored in the wire per unit volume is:

(a) 2S2Y                       (b) S2/2Y                                 (c) 2Y/S2 (d) S/2Y

144. A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere (you may take G = 6.67*10-11 Nm2/kg2) :

(a) 13.34 *10-10 J         (b) 3.33*10-10 J                        (c) 6.67*10-9 J                         (d) 6.67*10-10 J

145. starting with a sample of pure 66Cu, 7/8 of it decays into Zn in 15 minutes. The corresponding half-life is:

(a) 10 minute                (b) 15 minute                            (c) 5 minute                              (d) 7.5 minute

146. If radius of the 2713 Al nucleus is estimated to be 3.6 Fermi, then the radius of 52125 Te nucleuses be nearly:

(a) 6 Fermi                   (b) 8 Fermi                               (c) 4 Fermi                               (d) 5 Fermi

147. A Young’s double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is:

(a) Hyperbola               (b) Circle                                  (c) Straight                               (d) Parabola

148. Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are R1 and R2 (R2>R1). If the potential difference across the source having internal resistance R2 is Zero, them:

(a) R = R2*(R1+R2) / (  R2-R1)                                      (b) R = R2-R1

(c) R= R1R2 / (R1+R2)                                                   (d) R = R1R2/ (R2-R1)

149. If f is a real-valued differentiable function satisfying |f(x) – f(y)| £(x-y)2, x,yÎ R and f(o) = 0, then f(1) equals :

(a) 1                             (b) 2                                         (c) 0                                         (d) -1

150. Let x1, x2, …., xn be n observations such that åx2i=400 and å xi = 80. Then a possible value of n among the following is:

(a) 12                           (b) 9                                         (c) 18                                       (d) 15

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  1. 74. The number and type of bonds between two carbon atoms in calcium carbide are: (a) Two sigma, two pi (b) Two sigma, one pi (c) One sigma, two pi (d) one sigma, one pi

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