Physics

1. A mass attached to a spring oscillates with frequency f1. The spring is cut into two halves and the same mass when attached to one of the halves oscillates with frequency f2. The ratio f1/f2 is equal to

(a)  1

(b)  1/2

(c)  5/4

(d)  none of these

2. Two boxes of identical shape but of different masses are dropped from the same height. The heavier one will reach the ground (assume the presence of air)

(a)  earlier

(b)  later

(c)  simultaneously with the lighter one

(d)  earlier or later depending on air pressure

3. Photoelectrons from a photosensitive surface are obtained by irradiating it with light of 3000 A0. In order to obtain electrons with higher kinetic energy.

(a)  intensity of the radiation should be increased.

(b)  wavelength of the radiation should be increased.

(c)  wavelength of the radiation should be decreased.

(d)  both intensity and wavelength should be increased.

4. According to Kepler’s Law of planetary motion, the squares of the periods of the planets are proportional to

(a)  their mean distance from the Sun

(b)  the square of masses of the planets

(c)  the square of masses of the planets

(d)  the cube of their mean distance from the Sun.

(e)  None of these

5. Benoulli’s principle is based on the principle of conservation of

(a)  mass

(b)  momentum

(c)  annual momentum

(d)  energy

(e)  none of these

6. When a large bubble rises from the bottom of a lake to the surface, its radius doubles. The atmospheric pressure is equal to that of a column of water of height H. The depth of the lake is

(a)  7H

(b)  2H

(c)  4H

(d)  8H

7. A gymnast sits on a rotating stool, with his arms out stretched. Suddenly he lowers his arms. Then

(a)  the angular momentum increases

(b)  the angular momentum decreases

(c)  the moment of inertia decreases

(d)  the angular velocity remains constant

8. In a heat reservoir, when a certain amount of heat is withdrawn, the temperature of the reservoir.

(a)  decreases

(b)  increases

(c)  becomes zero

(d)  remains constant

9. The specific resistance of a wire

(a)  varies with its mass

(b)  varies with its length

(c)  varies with its cross-section

(d)  varies with length and cross-section

(e)  is independent of mass, length and cross-section

10. You are provided with three “60W-220V” bulbs to be used in household supply. To get the maximum light these are to be connected across the supply

(a)  all in parallel

(b)  two in parallel and one in series

(c)  one in parallel and two in series

(d)  all in series

11. A photon and an electron have the same wavelength.

(a)  The photen has grater momentum

(b)  They have the same momentum

(c)  The electron has greater momentum.

(d)  None of the above conclusion can be uniquely drawn.

12. An electric charge e moves with a constant velocity v parallel to the lines of force of a uniform magnetic field B. The force experienced by the charge is

(a)  evB

(b)  e/Bv

(c)  ev/B

(d)  None of these

13. A boat, with a number of bricks on it, floats in the water of a tank. The bricks are then placed into the water of the tank. What will happen to the water level of the tank?

(a)  The level will remain the same.

(b)  The water level will rise.

(c)  The water level will fall.

(d)  Level may rise or fall.

14. You are required to measure a temperature of about 400℃. What type of thermometer do

(a)  A mercury thermometer

(b)  A resistance thermometer

(c)  A gas thermometer

(d)  A wet bulb thermometer

15. Ammonia can be liquefied at ordinary temperature while oxygen cannot be so liquefied, because.

(a)  Ammonia is a compound

(b)  Oxygen is diatomic

(c)  Oxygen has a lower critical temperature

(d)  None of the above

16. Two straight copper wires are suspended vertically such that their bottom ends dip into a through containing mercury. The top ends are then connected to a battery through a resistance. When the current is passing through the circuit, the copper wires will

(a)  attract each other

(b)  repel each other

(c)  remain vertical

(d)  vibrate

17. You have two bulbs of 60 watt each when connected to 250 volts main. One bulb is made of tungsten filament while the filament of the other is made of carbon. If the two bulbs are joined in series and 250 volts are applied to the assembly

(a)  the bulb with tungsten filament will glow brighter

(b)  the bulb with carbon filament will glow brighter

(c)  the bulbs will glow equally

(d)  Inconclusive

18. Musical instruments having strings are accompanied with a hollow enclosure because it

(a)  produces harmonies

(b)  increases amplitude of vibration

(c)  increases frequency of vibration

(d)  produces resonance

19. The specific gravity of sea water is 1.125 and that of ice is 0.9. The fraction of an iceberg that will be seen above the sea level will be

(a)  0.2

(b)  0.15

(c)  0.09

(d)  0.32

20. When several light nuclei fuse together to form a heavier nucleus, the mass of the heavier nucleus formed is ——–the sum of the masses of constituent nuclei.

(a)  equal to

(b)  slightly higher than

(c)  slightly less than

(d)  much higher than

(e)  much less than

21. Five resistances are connected as shown in the figure. The equivalent resistance when measured at points A and C will be

(a)  30 ohm

(b)  3.33 ohm

(c)  12 ohm

(d)  10 ohm

(e)  None of these

22. The needle of a tangent galvanometer produces a deflection of 45° when a current of 10 ampere is passed through it. To produce a deflection of 30°, the current has to be changed to

(a)  5.77 A

(b)  6.33 A

(c)  4.80 A

(d)  3.33 A

23. An ideal monatomic gas is taken round the cycle ABCDA as shown in the figure. The work done during the cycle is

(a)  pV

(b)  2pV

(c)  4pV

(d)  zero

(e)  None of the above

24. Ferromagnetic substance lose their special

(a)  semi-diamagnetic

(b)  diamagnetic

(c)  paramagnetic

(d)  orthomagnetic

(e)  None of the above

25. In a lift, a man feels his real weight when

(a)  the lift is at rest

(b)  the lift moves with an uniform velocity

(c)  the lift moves up with an acceleration

(d)  Both (a) and (b) occur

26. The velocity of escape for a body on the earth depends

(a)  on the mass of the body

(b)  on the square root of the mass of the body

(c)  on the square of the m ass of the body

(d)  not on the mass of the body

27. Which one of the following statements is not true?

(a)  A body possesses energy but has no momentum

(b)  A body possesses momentum but has no energy.

(c)  Two bodies may have the same kinetic energy but different momenta.

(d)  None of the above.

28. An audio-oscillator is tuned to a tuning fork of nominal value 512 Hz. The oscillator is accurately calibrated and when it reads 514 Hz, a beat frequency of 2 Hz is heard. When it reads 510 Hz, another beat frequency of 6 GHz is heard. The actual frequency of the fork is

(a)  518

(b)  516

(c)  512

(d)  510

(e)  None of these

29. A car travels one third of the total distance with velocity 10 km/h. next one-third with 20 km/h and the last one-third with 60 km/h. The average velocity in the whole journey is

(a)  30 km/h

(b)  18 km/h

(c)  37.5 km/h

(d)  None of these

30. A particle is moving in a circular path with a constant speed v. The change in its velocity after it has moved an angle of 120° is

(a)  zero

(b)  2v

(c)  v√2

(d)  v√3

(e)  None of these

31. The kinetic energy of a body is increased 300%. The percentage increase in its momentum is

(a)  300

(b)  200

(c)  150

(d)  100

(e)  None of these

32. The inductance and resistance are denoted by L and R respectively. The dimensional formula of L/R is

(a)  M0L0T

(b)  M0L0T0

(c)  M2L0T0

(d)  MLT2

33. A graph is plotted with the activity of a radioactive sample against the number of atoms present in it at different times. The graph is

(a)  a parabola

(b)  a hyperbola

(c)  a straight line

(d)  None of these

34. The Young’s modulus of a material is equal to that stress which increase the length l of a wire to

(a)

(b)

(c)

(d)

(e)

35. Two vectors  satisfy the condition that  The angle between  is

(a)  0°

(b)  60°

(c)  90°

(d)  120°

(e) None of these

36. An astronaut while orbiting the earth in a circle 200 km above the earth’s surface releases out his spacecraft a packet. The packet will

(b)  fall vertically downward to the earth

(c)  move irregularly to have a final fall to the earth

(d)  do none of the above

37. Ultrasound may be generated by

(a)  Peltier effect

(b)  Doppler effect

(c)  Piezoelectric effect

38. Decibel is

(a)  a musical note

(b)  a musical instrument

(c)  the wavelength of noise

(d)  the itch of a musical sound

(e)  None of the above

39. When light travels from one medium to another separated by a sharp boundary, the characteristic that remains unchanged is

(a)  velocity

(b)  wavelength

(c)  frequency

(d)  amplitude

(e)  None of these

40. Which one of the following statements is wrong ?

(a)  Infrared rays have more heating power than visible rays.

(b)  Infrared rays travel with the same velocity as visible rays.

(c)  Ultraviolet rays have a wavelength longer than infrared rays.

(d)  Infrared rays can be focused by a lens and reflected by a mirror.

41. 1g of steam at 100℃ can melt an amount m of ice at 0℃. The value of m is

(a)  8 g

(b)  8 kg

(c)  6.75 g

(d)  (80/540)g

(e)  None of these

42. N similar conductors, each of resistance R, when connected in parallel give an equivalent

(a)  r/N2

(b)  N2r

(c)  Nr

(d)  r/N

(e)  None of these

43. A current is passed through a closed circuit of two dissimilar metals. It is found that heat is generated in one junction and absorbed at the other. The phenomenon is called

(a)  Joule effect

(b)  Thomson effect

(c)  Seeback effect

(d)  Peltier effect

44. The ratio of the specific charge of a proton to that of an α-particle is

(a)  1 : 2

(b)  4 : 1

(c)  1 : 4

(d)  2 : 1

45. A body is projected at 30° to the horizontal having kinetic energy E. What will be the kinetic energy at the top most point of the trajectory?

(a)  Zero

(b)

(c)

(d)  None of these

46. The unit of nuclear radius is

(a)  Micron

(b)  Angstrom

(c)  Curie

(d)  Fermi

(e)  None of these

47. The molecular weight of heavy water is

(a)  18

(b)  20

(c)  36

(d)  40

(e)  None of these

48. What is the angle between

(a)  0

(b)  π/2

(c)  π

(d)  2π

(e)  None of these

49. Which of the following effects is shown by a.c. ?

(a)  Magnetic effect

(b)  Chemical effect

(c)  Electro-chemical effect

(d)  Heating effect

50. Which of the following pairs are identical in respect to units or dimensions?

(a)  Force and Work

(b)  Pressure and Density

(c)  Momentum and Impulse

(d)  Moment and Impulse

(e)  None of the above

51. Two musical instruments are sounds together the frequencies of sound emitted by them are

n1 and n2(n1 > n2). The heat frequency is

(a)  2(n1 – n2)

(b)

(c)

(d)

(e)  None of these

52. The energy of monochromatic X-rays of wavelength 1 A0 is about

(a)  2 × 1015 J

(b)  2 × 1010 J

(c)  2 × 1017 J

(d)  2 × 1018 J

(e)  None of these

53. A red postage stamp is viewed in green light. It would appear

(a)  black

(b)  orange

(c)  deep yellow

(d)  reddish green

(e)  None of these

54. The device that converts heat to electrical energy is

(a)  electric cell

(b)  steam engine

(c)  thermocouple

(d)  None of these

55. A lorry and a car moving with the same kinetic energy are brought to rest by the application of brakes that provide equal retarding forces. Which of them will come to rest in a shorter distance?

(a)  Lorry

(b)  Car

(c)  Both in equal distance

(d)  Cannot be said unless their masses are known

56. Therminoic emission is a process in which

(a)  photons are emitted

(b)  heat radiation is given off

(c)  light is emitted

(d)  electrons are emitted

(e)  None of the above is true

57. A car accelerates from rest at a constant rate α for sometime after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t, the maximum velocity acquired by the car is given by

(a)

(b)

(c)

(d)

58. A block can slide on a smooth inclined plane of inclination θ kept on the floor of a lift. When the lift is descending with a retardation a, the acceleration of the block relative to the incline is

(a)  (g – a) sin θ

(b)  (g + a) sin θ

(c)  g sin θ

(d)  (g – a)

59. If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass m, raised from the earth’s surface to a height equal to the radius R of the earth is

(a)

(b)  2mgR

(c)  mgR

(d)

60. A laser beam is different from an ordinary beam of light because

(a)  their frequencies are different

(b)  laser beam has greater amplitude than that of ordinary light

(c)  waves in the laser beam are in phase whereas the waves in ordinary light are not

(d)  wavelength of laser is smaller thall that of ordinary light

61. When the cold junction of a thermocouple is at 0℃, the neutral temperature (max emf) is 200℃. When the cold junction is raised to a temperature of 40℃, the neutral temperature

(a)  becomes 220℃

(b)  remains the same

(c)  decreases

(d)  becomes 240℃

62. A proton moving with constant velocity passes through a region of space without any change in its velocity. If E and B represent the electric and magnetic fields respectively, this region of space may have

(a)  E = 0, B = 0

(b)  E = 0, B ≠ 0

(c)  E ≠ 0, B = 0

(d)  E ≠ 0, B ≠ 0

63. Two vectors are acting at a point. If one of them is reversed in direction, their resultant turns through an angle of 90°. This happens due to which one of the following reasons?

(a)  Two vectors are of unequal magnitude.

(b)  Two vectors are of equal magnitude.

(c)  The magnitude of one vector is double the other.

(d)  None of these

64. A siphon works under atmospheric pressure. What will happen to the efficiency of the siphon when the pressure is increased?

(a)  It will work as before

(b)  The efficiency will increase

(c)  The efficiency will decrease.

(d)  Efficiency may decrease or increase depending on other factors.

65. A beaker filled partly with water is placed on one pan of a balance. it is balanced by putting weights on the other p an and in this condition a piece of stone tied to a string is immersed in the water of the beaker such that no part of the stone or thread touches the beaker or the balance. What will happen to the equilibrium condition of the balance ?

(a)  The pan with the beaker will move upwards.

(b)  The pan with beaker will go down.

(c)  The balance will remain in equilibrium as before.

(d)  Information is insufficient for any conclusion..

66. A boy drops a coin outside a train running with a constant velocity. The trajectory of the coin as seen by another boy sitting in a second train moving in the opposite direction is

(a)  a vertical line

(b)  a parabolic curve

(c)  an arc of a circle

(d)  None of these

Chemistry

67. Formaldehyde reacts with ammonia to give

(a)  Formamide

(b)  Methylamine

(c)  Hexamethylene tetramine

(d)  Formalin

(e)  Formic acid

68. In a reversible reaction, a catalyst influences

(a)  only the equilibrium constant of the reaction

(b)  only the backward reaction rate

(c)  only the forward reaction rate

(d)  the rates of both the forward and backward reactions

69. A solution of a weak monobasic acid and one of its salts will have the maximum buffer efficiency when

(a)  the concentrations of acid and salt are equal

(b)  the pH is 7.0

(c)  the pka is equal to the pH of a solution of the salt

(d)  None of the above

70. Oxidation of isopropanol with acidic dichromate solution gives

(a)  acetone

(b)  acetic acid

(c)  acetaldehyde

(d)  None of these

71. Types of valence bonds in the formation of NH4Cl are

(a)  electrovalent only

(b)  covalent only

(c)  electrovalent and covalent

(d)  electrovalent, covalent and coordinate covalent

72. Bragg equation correlates

(a)  lattice spacing in terms of wavelength

(b)  order of reflection against crystal forms

(c)  glancing angle against axial angles

(d)  electron velocity against wavelength

73. Internal energy of an ideal gas at constant temperature

(a)  is independent of pressure

(b)  is independent of volume

(c)  is independent of both pressure and volume

(d)  changes with pressure and volume

74. During an adiabatic process, the entropy of the system

(a)  increases

(b)  decreases

(c)  remains constant

(d)  cannot be predicted

75. The hardness of a sample of water containing 0.001 mole of MgSO4 in a litre of water in ppm is

[Assume ca = 40, c = 12 and O = 16]

(a)  1000

(b)  100

(c)  10

(d)  1

(e)  0.001

76. Which of the following can absorb CO the most?

(a)  P2O5

(b)  NH3

(c)  NaOH

(d)  CuCl2

(e)  NH3 and CuCl2 in solution

77. Which is the most powerful nucleophile among the following?

(a)  HO

(b)  CH3COO

(c)  Cl

(d)  HSO−4

(e)  Br

78. Which of the following products is obtained when Cl2 gas is passed over heated alumina and coke?

(a)  AlCl3

(b)  CHCl3

(c)  COCl­2

(d)  CCl4

(e)  Al4C3 and HCl

79. Sea-weeds are important commercial source of

(a)  Methane

(b)  Ozone

(c)  Bromine

(d)  Iodine

80. Which of the following pairs of reactant generate H2 gas?

(a)  Zn and cold dilute HNO3

(b)  Mg and cold dilute HNO3

(c)  Cu and conc. H2SO4

(d)  Fe and cold dilute HNO3

81. When CH3 – CH2 – CH = CH2 reacts with HBr, the product is

(a)  CH3 – CH2 – CH2 – CH2Br

(b)  Br – CH2 – CH2 – CH2 – CH2Br

(c)

(d)  CH3.CH2.CH3 and CH3Br

82. While aqueous solution of AlCl3 is acidic towards litmus, that of NaCl is not. This is because of

(a)  hydrolysis

(b)  oxidation

(c)  reduction

(d)  oxidation and reduction

(e)  solubility

83. The solubility of iodine in water is greatly increased by

(c)  boiling the solution

(d)  cooling the solution

(e)  boiling, followed by cooling the solution

84. 1 gram of Zn liberates 224 ml of H2 at N. T.P. from 98 grams of H2SO4 and 0.35 gram of Zn is left unreacted. The data determines the equivalent weight of

(a)  Zn

(b)  H2SO4

(c)  Both (a) and (b)

(d)  None of these

85. Acetate ions in solution behave as

(a)  base

(b)  acid

(c)  both acid and base

(d)  None of these

86. Which of the following compound has different equivalent weight in different media?

(a)  Na2CO3

(b)  FeSO4

(c)  KMnO4

(d)  Oxalic acid

87. 50 volumes of hydrogen takes 20 minutes to diffuse out of a vessel. 40 volumes of oxygen will diffuse out from the same vessel under the same condition in

(a)  4 minutes

(b)  8 minutes

(c)  16 minutes

(d)  64 minutes

88. An unbalanced chemical equation is against the law of

(a)  mass action

(b)  definite proportion

(c)  conservation of mass

(d)  gaseous volume

89. Which one of the following law is represented by the statement – “The same elements combined together in the same proportion always given the same compound.”

(a)  Law of constant proportion

(b)  Law of multiple proportion

(c)  Law of reciprocal proportion

(d)  Law of reciprocal proportion

(e)  None of these

90. The chloride of an element contains 77.43% chlorine. The vaopur density of the compound being 68.69, molecular formula of the compound is

(a)  MCl

(b)  MCl2

(c)  MCl3

(d)  MCl4

91. The value of the universal gas constant is

(a)  1.987 litre atmosphere degree1mole1

(b)  0.082 calories degree1 mole1

(c)  8.03197 joule degree1 mole1

(d)  None of these

92. Paamagnetism often found among the transition metals is because of

(a)  the existence of vacant orbitals

(b)  the presence of one or more unpaired electrons in the system

(c)  lower electropositivity

(d)  variable valency

(a)  semi conductor

(b)  rare gas

(d)  metal detecting device

94. In the nuclear reaction 7N14 + 2He148O17 + X, the term X represents

(a)  1H3

(b)  1H1

(c)  2He4

(d)  γ-rays

95. According to Bohr the motion of an electron is restricted in such a manner that its angular momentum is an integral multiple of

(a)

(b)

(c)

(d)

96. Find from the electronic configuration, the element that belongs to the 5th group in the periodic table.

(a)  1S2. 2S2. 2p6 . 3S2 . 3p3

(b)  1S2. 2S2 . 2p6 . 3S2 . 3p5

(c)  1S2 . 2S2 . 2p6. 3S2 . 3p4

(d)  1S2 . 2S2 . 2p6 . 3S2 . 3p6 . 4S1

97.  An atom of chlorine contains in its nucleus

(a)  17 neutrons

(b)  17 protons

(c)  18 neutrons

(d)  17 protons and 18 neutrons

98. Phosphine is produce by the action of while phosphorus on

(a)  HNO3

(b)  H2SO4

(c)  NaOH

(d)  None of these

99. Which of the following contains fluorine ?

(a)  Phloroglucinol

(b)  Fluorene

(c)  Freon

(d)  Phorone

100. A slurry of gypsum in water is treated with ammonia and carbon-dioxide to manufacture

(a)  Ca(OH)2

(b)  (NH4)2 CO3

(c)  (NH4)2 SO4

(d)  None of these

101. When bi-valent thiosulphate ion is convened to bi-valent tetrathionate ion there is

(a)  no exchange of electrons

(b)  liberation of two electrons per thiosulphate ion

(c)  acceptance of two electrons by one thiosulphate ion

(d)  each thiosulphate ion donates one electron

102. Compound, A is quantitatively converted to a compound P which undergoes further conversion to a third compound B. q­1­ calory of heat is evolved in the first reaction and q2­ calory is absorbed in course of the second. Now, the compound B can be reconverted to A directly during which Q calory, heat is absorbed. Then

(a)  Q > q1 + q2

(b)  Q < q1 + q2

(c)  Q – q1 + q2 = 0

(d)  Q = q1 + q2

103. In dilute solution

(a)  vapour pressure of the solution is equal to the mole fraction of the solute

(b)  vapour pressure of the solution is the product of the vapour pressure of the pure solvent and the mole fraction of the solvent

(c)  relative lowering of vapour pressure is proportional to the mole fraction of the solute

(d)  the vapor pressure of the solution is less than that of the pure solvent by an amount equal to the molality of the solute

104. Which of the following metals is used in storage battery ?

(a)  Copper

(c)  Tin

(d)  Nickel

105. Which of the following statements is according to Hess’s law?

(a)  Heat change in a particular reaction is constant.

(b)  Heat change in a particular reaction is independent of the manner in which the reaction takes place.

(c)  Heat change in a particular reaction is the same regardless of the path by which the change occurs.

(d)  None of these

106. Tyndall effect is

(a)  an electro Binetic phenomenon observed in colloidal system

(b)  a magnetic field effect on the transition elements

(c)  an optical property of colloids

(d)  a characteristic property of olifinic compounds

107. Brownian movement is characteristic of

(a)  crystalloids

(b)  colloid

(c)  true solution

(d)  None of these

108. Which of the following pairs of the solutions will cause the same depression [∆T] of the freezing point of the solvents?

(a)  0.01 Molal solutions of naphthalene and anthraune in benzene

(b)  0.05 Molar solution of urea in water and naphthalene in benzene

(c)  0.02 Molar solution of common salt and urea in water

(d)  0.02 Molar solution of cane sugar and 0.04 Molal solution of glucose

109. A solution of KCl has a specific conductivity of 0.01119 mhos cm1. Its equivalent conductivity is

(a)  111.9 units

(b)  0.0001119 units

(c)  11.19 units

(d)  1119 units

110. Nitrobenzene on reduction with Zn dust and ammonium chloride solution gives mainly

(a)  Aniline

(b)  Phenyl hydrazene

(c)  Phenyl hdyroxylamine

(d)  Azobenzene

111. One example of thermoplastic is

(a)  Area-Formaldehyde

(b)  Phenol-Formaldehyde

(c)  Formica

(d)  P.V.C

(e)  None of the above

112. When does a real gas behave almost as an ideal gas?

(a)  When the temperature is low

(b)  When both the temperature and pressure are low

(c)  When both the temperature and pressure are high

(d)  When the temperature is high but pressure is low

(e)  When the temperature is low but pressure is high

113. Atomic weight determination by Dulong-Petit’s law is not applicable for the metal

(a)  Al

(b)  Mg

(c)  Be

(d)  Cu

(e)  Zn

114. Which one of the following sets may be cited as an example to illustrate the law of multiple proportions ?

(a)  NO and K2O

(b)  Al2O3 and Fe2O3

(c)  CO2 and SO2

(d)  CO and CO2

(e)  HCl, HOCl, HClO3

115. The equivalent conductance of a solution of an electrolyte increases as

(a)  dilution increases

(b)  dilution decreases

(c)  temperature decreases

(d)  cell constant increases

(e)  cell constant decreases

116. Which one of the following is a Lewis acid ?

(a)  NaCl

(b)  CaCl2

(c)  AlCl2

(d)  CCl4

(e)  NH4Cl

117. The velocity of any chemical reaction at any instant at a given temperature is dependent on

(a)  states of rectants and products

(b)  molal concentration of reactants and products

(c)  active mass of the reactants and products

(d)  thermal stabilities of each of the reactants

(e)  the states of aggregation of the reactants

118. The nature of a chemical bond of a binary compound is decided approximately from the

(a)  difference of electronegativity between the two elements

(b)  difference of ionization potential of the two elements

(c)  difference in relative position of elements in the periodic table

(d)  the number of outermost electrons in respective atoms

(e)  None of the above

119. Alkali hydrolysis of glycerides of fatty acids is known as

(a)  Saponification

(b)  Esterification

(c)  Isomerism

(d)  Recemisation

(e)  Epimerisation

120. Electrons ejected in β-emission come from

(a)  the orbital electrons of the atom

(b)  the nucleus of the atom

(c)  the proton of the nucleus

(d)  the neutron of the nucleus

(e)  surrounding ionized air

121. Lucas reagent is a mixture of

(a)  Conc. HCl and hydrated ZnCl2

(b)  Conc. HCl and anhydrous ZnCl2

(c)  Conc. HNO and hydrated ZnCl2

(d)  Conc. HNO3 and anhydrous ZnCl2

(e)  Conc. H2SO4 and anhydrous ZnCl2

122. The shape of BeF2 molecule is

(a)  tetrahedral

(b)  angular

(c)  linear

(d)  trigonal

123. If two solutions have the same osmotic pressure, they are said to be

(a)  isomeric

(b)  isotonic

(c)  isobaric

(d)  isomorphic

(e)  Isotropic

124. The group which does not enter directly in the benzene ring is

(a)  (CH3)2 CH −

(b)  −NO2

(c)  −C2H5

(d)  −NH2

(e)  Cl

125. Maximum number of electrons in an orbit with a definite principal quantum number is ultimately decided by

(a)  Uncertainty principle

(b)  Aufbau principle

(c)  Pauli’s exclusion principle

(d)  Soddy’s rule

126. Formaldehyde can be distinguished from acetaldehyde by their reaction with

(a)  Fehlings solution

(b)  Tollens reagent

(c)  NaHSO3

(d)  50% NaOH

(e)  N2H4

127. The middle oil fraction (170 − 230℃) of coal tar serves as a source for

(a)  benzene and toluene

(b)  phenol and napthalene

(c)  napthalene and anthracene

(d)  phenol and anthracene

(e)  benzene and anthracene

128. Bakelite is a polymer of

(a)  urea and formaldehyde

(b)  phenol and formaldehyde

(c)  phenol and formaldehyde

(d)  hexamethylene diamine and acetic acid

(e)  styrene and ethanol

129. In the gaseous reaction system

A2(g) + 2B2(g)         2AB2(g) + Q cal

a high yield of AB2(g) will be obtained at

(a)  high pressure and low temperature

(b)  high pressure and high temperature

(c)  low pressure and low temperature

(d)  low pressure and high temperature

(e)  high pressure and any temperature

130. Phenol is known to b acidic. The p-Nitrophenol should be

(a)  a stronger acid

(b)  a weaker acid

(c)  a neutral compound

(d)  weakly basic

(e)  equally strong as acid as phenol

131. Introduction of an I group in benzene ring may be carried by

(a)  Friedel Craft reaction

(b)  Cannizaro reaction

(c)  Sandmeyer reaction

(d)  Diazo reaction

(e)  Hell- Volhard’s method

132. Which of the following reagents is used in the transformation CH3COCH3 CH3CH2CH2 ?

(a)  Zn-amalgam + HCl

(b)  Sodium ethoxide

(c)  LiAlH4

(d)  H2/Pd

Biology

133. Consider the following

(1)  structural gene

(2)  messenger RNA

(3)  ribosome

(4)  transcription

(5)  translation

Which one of the following is the correct sequence for protein synthesis ?

(a)  1    4        3        2        5

(b)  1    4        2        3        5

(c)  2    1        3        5        4

(d)  3    2        5        4        1

(e)  3    2        1        5        4

134. Which one of the following factors is the most effective in accelerating the rate of breathing in a mammal?

(a)  A lack of oxygen in the alveoli of the lungs

(b)  An excess of carbon-dioxide in the lungs

(c)  A lack of oxygen in the blood

(d)  An excess of carbon-dioxide in the blood

(e)  A lack of oxygen in the tissues

135. In the Embden-Meyerhof Pathways

(a)  glucose breaks down to pyruvate

(b)  glucose breaks down to CO2 and H2O

(c)  pyruvic acid breaks down to Acetyl COH

(d)  pyruvic acid breaks down to CO2 + H2O

(e)  glucose breaks down to succinic acid

136. Why do we dig for fossils and study them?

(a)  To find out new fossils that have not yet been recorded.

(b)  Fossil finding gives occupation for scientists.

(c)  Fossils fill the gaps in evolutionary records of animals

(d)  Fossils throw light an evolution of animals of the past.

(e)  For the sake of curiosity.

137. During muscle contraction which one of the following doesn’t show any change in their length?

(a)  Sarcomere

(b)  Isotropic band

(c)  H-zone

(d)  Anisotropic band

(e)  Cross-bridges

138. Which of the following p arts of the eye is characteristic of birds ?

(a)  Lens

(b)  Retina

(c)  Pecten

(d)  Iris

(e)  Conjuntiva

139. Provitamins are

(a)  organic substances which are used as raw material for synthesis of vitamin in animal body

(b)  substance which have got structural similarity to the vitamins but without similarity in physiological action

(c)  substance which have got structural and chemical similarity but without having any physiological effect

(d)  organic compounds cannot be synthesized by the organism

(e)  vitamin deficiencies leading to obvious pathological changes in tissues and organs

140. Small pieces of autonomous, extrachromosomal, circular DNA found in some bacterial cells is called

(a)  Prokaryote

(b)  Plasmid

(c)  Peroxisome

(d)  Polysome

(e)  Vector

141. Copper containing blood pigment commonly noticed among molluscs is

(a)  Haemerythrin

(b)  Haemoglobin

(c)  Chlorocruorin

(d)  Haemocyanin

(e)  None of these

142. Cretinism is a diseased condition which occurs due to the deficiency of which one of the following hormones ?

(a)  Thyroxin

(b)  Pituitary hormone

(d)  SH and LH

(e)  Corticotrophin

143. Down’s syndrome is caused due to

(a)  Trisomy of 7th chromosome

(b)  Polyploidy of chromosome No. 20

(c)  Monosomy of No. 16 chromosome

(d)  Trisomy of chromosome No. 21

(e)  Trisomy of chromosome No. 11

144. The allantois in chick is the

(a)  protective membrane surrounding the embryo

(b)  embryonic reservoir of metabolic wastes

(c)  embryonic nutritive organ

(d)  embryonic respiratory organ

(e)  embryonic food reservoir

145. In man 2n = 46. In a primary spermatocyte how many chromosomes will be found ?

(a)  23

(b)  46

(c)  92

(d)  22

(e)  69

146. Carnassial teeth are present in

(a)  Bat

(b)  Rat

(c)  Human

(d)  Guineapig

(e)  Dog

147. The most common chlorofluorocarbons (CFCI3) which is used primarily as a propellent is aerosol spray cans and CF2Cl2 which is used as a refrigerant (commonly known as Freon) is now banned because chlorofluorocarbons in the atmosphere destroy large quantities of ozone (O3) by photolytic process. ozone is necessary as

(a)  Ozone screens out most of the damaging  portion of the ultraviolet radiation

(b)  Ozone supplies most of the O2 necessary for plants and animals

(c)  Ozone damages the ultraviolet light necessary for plants and animals

(d)  Ozone retards the growth of microorganisms

(e)  Ozone damages the cellular level

148. The sodium-potassium pump transports

(a)  Na+ and K+ out of the neuron

(b)  Na+ into the neuron and K+ out

(c)  K+ into the neuron and Na+ out

(d)  Na+ and K+ into the neuron

(e)  None of these

149. The membrane of endoplasmic reticulum consists of

(a)  three layers – protein – lipid – protein

(b)  three layers – carbohydrate – protein – lipid

(c)  four layers –  protein – lipid – lipid – protein

(d)  two layers – protein –lipid

(e) two layers – lipid – protein

150. A bacterium differs from a virus in

(a)  presence of nucleic acid in virus

(b)  presence of cell wall in bacterium

(c)  presence of nucleoid in virus

(d)  disease producing ability in virus

(e)  presence of plasma membrane in virus

151. The giraffe has a long neck because according to Darwin

(a)  its ancestors stretched their necks to get food

(b)  the creator designed in that way

(c)  catastrophes eliminated short-necked forms

(d)  ancestral giraffes with slightly longer necks than others

(e)  getting more food the ancestral giraffes gave birth to such

152. Pyrenoid granules are

(a)  protein covered by starch in spyrogyra

(b)  starch covered by protein in spyrogyra

(c)  fat covered by protein in spyrogyra

(d)  starch and protein covered by lipid layer in fungi

(e)  nucleoprotein present in cytoplasm of algae

153. The significance of meiosis is

(a)  duplication of somatic cells

(b)  multiplication of germ cells

(c)  reduction of chromosome numbers to facilitate recombination with other genetic constituent

(d)  duplication of chromosomes and helping in propagation

(e)  growth of the body as well as gonads

154. The phloem is responsible for

(a)  transfer of food prepared in leaves to different parts of body

(b)  transfer of water absorbed by the roots

(c)  transfer food material absorbed by the roots

(d)  transfer of both food and water in plant body

(e)  storage of food in plant body

155. The Nissl’s granules are

(a)  granular substances found in the cardiac muscle acting as stimulating agent

(b)  granular structures found in neurone acting as catalysts during  transmission of impulse

(c)  granular substances found in the epithelial cells and secretory in function

(d)  vesicular structure enclosing different enzymes

(e)  found in glial cells and secretes neurosecretory substances

156. In the Watson and Crick model, DNA molecule is formed by two polydeoxyribonucleotide strand coiling clockwise. The length of a complete cooling is

(a)  3.4° A

(b)  4.5° A

(c)  10° A

(d)  3.2° A

(e)  5.4° A

157. In a Mendelian dihyrbid cross of sweet pea taking seed coat character you got 1000 offsprings with the following ratio of character after crossing pollens of yellow (Y) and round (R) seed coat character with eggs of green (g) and wrinkled (w) seed coat character.

Yellow Round – 250

Yellow Wrinkled – 250

Green Round – 250

Green Wrinkled -250

From the above result you can conclude that this result is due to “

(a)  incomplete dominance

(b)  independent assortment

(c)  segregation

(d)  yellow round plant was hybrid for both yellow and round character

(e)  green wrinkled plant was hybrid for both green and wrinkled character

158. During cell division, the maximum DNA synthesis occurs in phase

(a)  G1

(b)  G2

(c)  S

(d)  P

(E) M

159. A phase of cell division where chromatids gradually coiled, nuclear membrane and nucleolus disappear, and spindle formed, is called

(a)  Synthesis phase

(b)  Metaphase

(c)  Anaphase

(d)  Telophase

(e)  Prophase

160. The chromosome in the salivary gland of Drosophila is a bigger one with different banding patterns. it is called

(a)  lampbrush chromosome

(b)  giant chromosome

(c)  puff chromosome.

(d)  polytene chromosome

(e)  autosome

161. In a flower the thalamus is hollow and cupshaped, and completely fuses with the lower part of the ovary. The ovary is inferior. The stemens, petals and sepals are placed above the pistil. The flower is called

(a)  Hypogynous

(b)  Epigynous

(c)  Perigynous

(d)  Gamosepalous

(e)  Polysepalous

162. During fertilization in gourd one of the sperm nuclei fuses. with

(a)  synergids to form zygote

(b)  antipodal cells to form zygote

(c)  tube nucleus to form zygote

(d)  definitive nucleus to form zygote

(e)  egg to form zygote

163. During protein synthesis,, the polyribosomes are produced by

(a)  tRNA

(b)  mRNA

(c)  rRNA

(d)  DNA

(e)  Informosomes

164. Which of the following plants belong to Labiatae?

(a)  Ocimum

(b)  Gossiplum

(c)  Cinchona

(d)  Coffea

(e)  Cocos

165. Due to transpiration from leaf surface water is drawn upwards. This is termed as

(a)  water current

(b)  transpiration current

(c)  ascent of sap

(d)  guttation

(e)  imbibitional force

166. The prosthetic group of an enzyme is

(a)  non-protein group attached to the protein

(b)  protein portion attached to the non-protein parts

(c)  phosphate group attached to the enzyme

(d)  isomer of non-protein substances

(e)  −COOH group attached with the proteins parts

167. In the light phase of photosynthesis, which one of the following is produced ?

(b)  Phosphoglyceric acid

(c)  Diphosphoglyceric acid

(d)  Ribulose diphosphate

(e)  Diphosphoribital

168. The liver abscess may be formed due to the infection by which one of the following?

(a)  Entamoeba hystolytica

(b)  Giardia intertinalis

(c)  Plasmodium vivax

(d)  Paramoecium caudatum

(e)  Euglena viridis

169. Incomplete, metamorphosis is evident in

(a)  mosquito

(b)  silk moth

(c)  honey bee

(d)  prawn

(e)  cockroach

170. Which one of the following is a major paddy pest?

(a)  Millipede

(b)  Oryctes

(c)  Crab

(d)  Leptocoryza

(e)  Scorpion

171. Which of the followings is capable taking advantages of both aerial and aquatic respiration ?

(a)  Pila

(b)  Pearl Oyster

(c)  Mytilus

(d)  Sepia

(e)  Lamellideus

172. All vertebrates are chordate but all chordates are not vertebrates because

(a)  all vertebrates posses notochord in any of its life stage but many chordates do not have vertebral column

(b)  all chordates posses vertebral column but  some vertebrates may not have notochord

(c)  chordates have gills for respiration but vertebrates have lungs

(d)  vertebrates have closed blood circulation but some chordates lack it

(e)  all vertebrates have post anal tail but lower chrodates lack it

173. In man Ancyclostoma harbour in

(a)  stomach

(b)  intestinal wall

(c)  intestinal lumen

(d)  liver lobule

(e)  lungs

174. One of the main characteristics of reptiles which is present in on other animal is

(a)  Homodont dentition

(b)  Tympanic membrane

(c)  Scales

(d)  Nails

(e)  Neck

175. The transfer of food energy from the source in plants through a series of organisms with repeated eating and being eaten is called

(a)  energy flow

(b)  food chain

(c)  food web

(d)  pyramid of energy

(e)  ecosystem

176. In a pond ecosystem, trophic status of lata fish is

(a)  producer

(b)  primary consumer

(c)  secondary consumer

(d)  decomposer

(e)  detritus feeder

177. The pinnate compound leaves are found in

(a)  Tamarind

(b)  Hingon

(c)  Mango

(d)  None of these

178. Sweet potato is a modified

(a)  shoot as like potato

(c)  tap root

(d)  prop root

(e)  fibrous root

179. The chloroplast usually contains two types of pigments

(a)  chlorophylls and carotnoids

(b)  chlorophylls and xanthophylls.

(c)  xanthophylls and carotene

(d)  lycopene and luteal

(e)  chlorophyll and lycopene

180. Acrosome Cap of sperm head is formed by

(a)  mitochondria

(b)  golgi bodies

(c)  lisosomes

(d)  endoplasmic reticulum

(e)  nucleus

181. A centrosphere is

(a)  drum like body with two open ends

(b)  cytoplasmic portion surrounding the centriole

(c)  nuclear body forming chromosomes

(d)  ciliated structure within centrosome

182. Deoxycytidylic acid is formed by

(a)  phosphoric acid + deoxyribose sugar + cytosine

(b)  phosphoric acid + deoxyribose sugar + guanine

(c)  phosphoric  acid + deoxyribose sugar + adenine

(d)  phosphoric acid + deoxyribose sugar + thymine

(e)  phosphoric acid + eoxyribose sugar + uracil

183. The opening or closure of the stomatal pore during transpiration i entirely dependent

(a)  on the osmotic pressure (turgidity) of the guard cells

(b)  on sunlight

(c)  on the absorption rate and water pressure of the plant

(d)  on the stomatal march

(e)  upon atmospheric temperature

184. In the model of Watson and Crick, DNA molecule is formed by two polydeoxyribonucleotide strands coiling clockwise. In each coiling the number of deoxyribonucleotide is

(a)  twelve

(b)  five

(c)  ten

(d)  fifteen

(e)  twenty

185. Flower is a modified shoot because

(a)  its sepals are green

(b)  its petals are colourful

(c)  nodes and internodes are present

(d)  stem nature of stamens and carpels

(e)  it is produced from buds

186. In angiosperms the process of double fertilization means

(a)  one of the two nuclei of the male gametes fuses with the egg nucleus and another nucleus fuses with the definitive nucleus of embryosac.

(b)  both the nuclei fuses with ovum one after another

(c)  one nucleus fuses with antipodal cells

(d)  only single nucleus travels through the pollen tube and the other is lost

(e)  pollen grains fall on the stigma at first, then nucleus of pollen grain fuses with the nucleus of ovum

187. ‘Phosphorus’ in plant body is the

(a)  tracer element

(b)  macrometabolic element

(c)  micrometabolic element

(d)  derived element

(e)  non-essential element

188. The pearl is the

(a)  secretion of mantle of pearl oyster

(b)  parasitic action on the pearl oyster

(c)  secretion product of shell of pearl oyster

(d)  gland within the foot of pearl oyster

(e)  accumulated product from the sea water in the gills of pearl oyster

189. The leech can suck blood inclot because it can secrete

(a)  sodium citrate

(b)  potassium citrate

(c)  an anticoagulant enzyme

(d)  hirudin

(e)  toxic substance

190. As fowl is not a running bird, it possesses

(a)  well developed wings

(b)  nopygostyle

(c)  feathers without bards

(d)  well developed sternum with midventral keel

(e)  absence of furcula

191. In vertebrates, the neural plate is developed from

(a)  ectodermis

(b)  endodermis

(c)  mesoderm

(d)  ectoderm and mesoderm

(e)  ectoderm and endoderm

192. Which one of the following does not take place during the first nuclear division of meiosis ?

(a)  Pairing of homologous chromosomes

(b)  complete separation of the chromatids of each chromosome

(c)  Crossing over the chromatids

(d)  Reduction of the chromosome number

193. In the life cycle of any sexually reproducing organism, two essential events are nuclear fusion. and meiosis, but the position of these events may vary so that several distinct types of life cycle are possible. Which one of the following life cycles occurs in nature?

(a)  Diploid organism, meiosis, haploid gametes, nuclear fusion, haploid zygote, diploid organism

(b)  Haploid organism, haploid gametes, nuclear fusion, diploid zygote, meiosis, diploid organism

(c)  Diploid organism, haploid gametes, nuclear fusion, diploid zygote, meiosis, diploid organism.

(d)  Haploid organism, meiosis, haploid gametes,  nuclear fusion, diploid zygotes, haploid organism

(e)  Diploid organism, meiosis, haploid organism, nuclear fusion, diploid organism, haploid gametes.

Ans: (a)

194. The ultrastructure of cross-section of a centriole shows

(a)  ten double microtubules

(b)  nine triple microtubules

(c)  five triple microtubules

(d)  four triple microtubules

(e)  six double microtubules

195. Under the influence of luteinizing hormone (LH) from the anterior pituitary, the

(a)  primary follicles of the ovary begin to grow

(b)  follicle cells are converted into a corpus luteum

(c)  corpus luteum is stimulated to begin secreting oestrogen

(d)  uterus changes in preparation for the fertilized ovum

(e)  placenta is formed

196. The mammal that possess small marsupiesm and also lay eggs is

(a)  bat

(b)  kangaroo

(c)  platypus

(d)  ant-eater

(e)  whale

197. The placenta develops in

(a)  pigeon

(b)  guinea-pig

(c)  crocodile

(d)  hen

(e)  lizard

198. Agar, a complex carbohydrate is extracted from

(a)  green algae

(b)  brown algae

(c)  red algae

(d)  blue green algae

(e)  None of the above

199. Moulting in insects will result in the production of a nymphal or larval stage only if a certain hormone is present. This hormone is produced by

(a)  supra-oesophageal ganglion

(b)  sub-oesophageal ganglion

(c)  prothoracic gland

(d)  corpus allatum

(e)  ventral nerve cord

200. The leaves of Mimosa pudica droop down when they are touched. This movement is called

(a)  seismonasty

(b)  nyctinasty

(c)  photonasty

(d)  epinasty

(e)  chemonasty

Mathematics

1. The mean of marks of 300 students in an examination is 45. The mean of the top 100 students is 70 while the mean of the last 100 is 25. The mean of the other 100 students is

(a)  29

(b)  38

(c)  40

(d)  47

(e)  50

2. The first of the two samples has 100 items with the man 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation  the standard deviation of the reminder of the group is

(a)  3.2

(b)  3.5

(c)  4

(d)  4.5

(e)  None of these

3. How m any optimal solutions the following problem has ?

Maximize z = 6x1 + 10x2

subject to  3x1 + 5x2 ≤ 10

5x1 + 3x2 ≤ 15

and x1, x2 ≥ 0

(a)  None

(b)  1

(c)  3

(d)  4

(e)  Infinitely many

4.  exists then

(a)  derivative of f(x) with respect to x exists at x = 0

(b)  differential co-efficient f(x) with respect to x exists at the point x

(c)  f(x) is differentiable with respect to x everywhere

(d)  f(x) continuous at x = 0

(e)  f(x) is continuous and differentiable every where

5. The roots of the equation  are

(a)  (−3, −2, 0)

(b)  (1, 3, 6)

(c)  (0, 2, 4)

(d)  (−2, 0, 1)

(e)  None of these

6. Which of the following is NOT necessarily a symmetric matrix ?

(a)  Diagonal matrix

(b)  Identity matrix

(c)  Null matrix

(d)  Orthogonal matrix

(e)  Transpose of diagonal matrix

7. The value of  is

(a)  0

(b)  1

(c)  2

(d)  1/2

(e)  None of these

8. The area in the first quadrant bounded by the curves y2 = 4x and (x – 4)2 + y2 = 16 is

(a)

(b)

(c)  28/3

(d)  64/3

(e)  None of these

9. The solution of the differential equation is

(a)  2x + 3y = tan1(cex)

(b)

(c)

(d)

(e)  None of these

10. (1, 2, 3) and (3, 0, 5) are two points on a sphere whose centre lies on the straight line  Then the radius of the sphere is

(a)

(b)

(c)

(d)

(e)

11. If the letters of the word RANDOM be arranged in a row at random, the probability that there are exactly two letters between A and O is

(a)  1/2

(b)  1/3

(c)  1/4

(d)  1/5

(e)  None of these

12. The probability of a man hitting a target is 2/7. In order that the probability of hitting the target at least is greater than 3/4, he must fire at least n times where n is equal to

(a)  5

(b)  6

(c)  7

(d)  8

(e)  none of these

13. If nP5 is equal to 20 nP3, then n is equal to

(a)  8

(b)  9

(c)  10

(d)  1

(e)  6

14. The most general value of θ which satisfies  is

(a)

(b)

(c)

(d)  120°

(e)  None of these

15.  is equal to

(a)

(b)

(c)

(d)

(e)

16. The function of f : A → B, where  and A = {x : x ∈ R, −1 ≤x ≤ x} defined by f(x) sin x is

(a)  one – one an onto

(b)  one – one and into

(c)  many – one and onto

(d)  many – one and into

(e)  Into

17. Differential coefficient of a sin1 x with respect to sin1 x is

(a)  asin1 x

(b)  asin1 x loge a

(c)  asin1 x loga e

(d)

(e)  None of these

18. nCr + n – 1Cr + …..xrCr is equal to

(a)  n+1Cr

(b)  n+1Cr+1

(c)  n+2Cr

(d)  2n

(e)  None of these

19. If  then cos 80° cos 40° cos 20° is

(a)  1/2

(b)  −1/8

(c)

(d)

20. If f : R → R is defined by f(x) = x2 + 1, x ≥ 0, then which of the following is true?

(a)  f1(17) = 4

(b)  f1(17) = −4

(c)  f1(+3) = 0

(d)  f1 (0) = 0

(e)  f1(1) = −1

21. The two circles x2 + y2 + ax – by + c = 0 and x2 + y2 + bx + ay – c = 0

(a)  cannot cut orthogonally

(b)  cut orthogonally whatever values, a, b, c may have

(c)  touch one another

(d)  can cut orthogonally only if c = 0

22. The value of the indefinite integral  is

(a)

(b)

(c)

(d)

23. The two straight line represented by the equation 4x2 – 12xy + 9y2 + 12x – 18y + 10 = 0

(a)  are perpendicular to each other

(b)  make an angle 45° to one another

(c)  are parallel

(d)  make an angle 60° to one another

24. The slope of a curve at any point (x, y) is 2x – 3. The curves passes through (3, 2). The area bounded by the curve, the x-axis and x = 2 and x = 4 is

(a)  4 sq. units

(b)

(c)

(d)  None of these

25. If a variable line makes on the x-axis and y-axis intercepts a and b such that 1/a + 1/b = 1/3. Then the line must p ass through the point

(a)  (3, 0)

(b)  (0, 3)

(c)  (3, 3)

(d)  (a, b)

26. The circles (x – 1)2 + λ(x + 1)2 + (1 + λ)y2 = 0 and (x – 1)2 + μ(x + 1)2 + (1 + μ)y2 = 0 will cut orthogonally if

(a)  λ = 0, μ ≠ 0

(b)  μ = 0, λ ≠ 0

(c)  μ  + λ = 0

(d)  λ – μ = 0

27. The rank of the matrix  is

(a)  3

(b)  2

(c)  1

(d)  0

28. A square matrix A of the order n × n has how many minors of order 1?

(a)  n

(b)  n2

(c)  n(n2 – 1)

(d)  n!

(e)

29. The degree of the polynomial in t represented by the determinant of the matrix  is

(a)  2

(b)  3

(c)  4

(d)  6

(e)  None of these

30. Find the determinant of the matrix X such that

(a)  10/9

(b)  2

(c)  18

(d)  10

(e)  None of these

31. Value of k for which the following three equations are consistent is

4x + 5y – 9 = 0

11x – 4y – k = 0

x + 2y – 3 = 0

(a)  6

(b)  7

(c)  3

(d)  4

(e)  None of these

32. Given 2x + y + z = 1, x – 2y – 3z = 1 and 3x + 2y + 4z = 5, value of y is given by

(a)

(b)

(c)

(d)

33. Consider the following problems :

Maximise      z = 3x1 + 4x2

Subject to      x1 – x2 ≥ 0

−x1 + 3x2 ≤ 3

and x1, x2 ≥ 0. The optimum solution in this case

(a)  is the point of intersection of the lines x1 =  x2 and 3x2 – x1 = 3

(b)  does not exist

(c)  is x1 = x2 = 0

(d)  is unbounded

34. cos 80° + cos 40° is equal to

(a)  cos 20°

(b)  cos 120°

(c)  1/2

(d)  √3/2

35. If in a triangle, cos 3A + cos 3B + cos 3C = 1 then one angle

(a)  must be 90°

(b)  must be 120°

(c)  must be 45°

(d)  cannot be said.

36. Distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to the line 3x – 4y + 8 = 0 is

(a)  5

(b)  7.5

(c)  6/5

(d)  1

37. If the equation ax2 + by2 + 2hxy = 0 represent pair of straight lines passing through the origin then the two straight lines will be perpendicular if

(a)  a = b

(b)  a + b = 0

(c)  a + b = h

(d)  They can never be perpendicular to each other

38. Consider the circle x2 + y2 – 4x – 6y – 12 = 0 and the straight line 3x + 4y + 7 = 0. Which of the following is true ?

(a)  The line cuts the circle in two different points.

(b)  The line touches the circle at a point.

(c)  The line and the circle have no common points.

(d)  The line passes through the centre of the circle.

39.

(a)

(b)

(c)  −sin x

(d)  N one of these

40. Probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, probability that he will miss at least one test is

(a)  2/5

(b)  4/5

(c)  9/25

(d)  16/25

41. The number of words that can be formed with 15 consonant and 2 vowels out of 21 consonants and 5 vowels is

(a)  785

(b)  43584

(c)  542640

(d)  101080

(e)  None of these

42. There are 25 books in a cupboard, namely 13 books of Physics, 4 books of Chemistry, 3 volumes of Mathematics and 5 books of Statistics. Then, the number of possible ways in which some or all of these books may be taken out is

(a)  1679

(b)  1800

(c)  3204

(d)  5400

(e)  None of these

43. If cot1 x + cot1 y + cot1 z = π/2 then

(a)  xyz = x + y + z

(b)  xy + yz + xz = 1

(c)  xy + yz + xz = x + y + z

(d)  xyz = 1

(e)  None of these

44. The greatest distance from the origin of coordinates to the point z for which   is

(a)

(b)

(c)

(d)

(e)

45. The equation to the circle which touches the axis of x at a directed distance + 10 from the origin and cuts off an intercept 4√11 from the axis of y is given by

(a)  x2 + y2 – 10x ± 24y + 100 = 0

(b)  x2 + y2 – 20x ± 24y + 100 = 0

(c)  x2 + y2 + 10x ± 24y + 100 = 0

(d)  x2 + y2 + 200x ± 24y + 100 = 0

(e)  None of these

46. The equations of the tangent and normal to a circle at the point (2, 3) are x + y = 5 and y – x = 1 respectively. Then the equation of the circle is given by

(a)  x2 + y2 – 2x + 4y – 21 = 0

(b)  x2 + y2 – 2x – 4y + 3 = 0

(c)  x2 + y2 + 2x – 4y – 5 = 0

(d)  x2 + y2 + 2x + 4y – 29 = 0

(e)  None of these

47. Let a set W = {0, 2, 5, 9, 11} and let a function f : W → R(where R is the set of real numbers) be defined such that f(x) = x2 – x – 2. Then the range of f is

(a)  {–2, 0, 18, 70, 108}

(b)  {–2, 0, 18, 70, 100}

(c)  {–2, 0, 18, 70, 121}

(d)  {–2, 0, 18, 70, 144}

(e)  None of these

48. The function  for x > 0 is

(a)  monotonically increasing

(b)  monotonically decreasing

(c)  partly increasing and partly decreasing

(d)  a straight line

(e)  None of these

49. 1 is the value of

(a)

(b)

(c)

(d)

(e)

50. If x = a(θ – sin θ), y = a(1 + cos θ), then

(a)  cot θ

(b)  −cot θ

(c)  cot (1/2) θ

(d)  −cot(1/2) θ

(e)  tan θ + cot θ

51. A function f(x) is defined as follows :

Then the function is discontinuous at

(a)  x = 0

(b)  x = −4/5

(c)  x = 4/5

(d)  x = 16/5

(e)  None of these

52. The value of   for 0 is

(a)

(b)

(c)

(d)

(e)

53. The maximum value of x1/x is

(a)  ee

(b)  e

(c)  1/ee

(d)  e1

(e)  None of these

54. The value of integral  is given by

(a)

(b)

(c)

(d)

55. The differential equation of all circles touching the y-axis at the origin is given by

(a)  (x2 – y2)dy – 2xy  dx = 0

(b)  (x2 – y2)dx – 2xy  dy = 0

(c)  (x2 + y2)dy – 2xy  dx = 0

(d)  (y2 – x2)dy – 2xy  dx = 0

(e)  (y2 – x2)dy – 2xy  dy = 0

56. A curve satisfies the different equation  and passes through the point (3, 2). The equation of the curve is given by

(a)

(b)

(c)

(d)

(e)  None of these

57. Area of the segment of the curve y = (1 – x) (x – 4) cut off by the x-axis is

(a)

(b)  5

(c)

(d)

(e)  None of these

58.  then the values of x, y and z are respectively

(a)  –1, 2 and –3

(b)  –1, –2 and –3

(c)  –1, 3 and –3

(d)  –1, –4 and –3

(e)  none of these

59. The co-ordinates of two vertives of a triangle are (2, 3) and (1, 4). Then the equation to the locus of the third vertex if the area of the triangle is 5 square units is given by

(a)  x + y + 5 = 0, x + y + 15 = 0

(b)  x + y + 5 = 0, x + y – 10 = 10

(c)  x + y + 5 = 0, x + y – 15 = 0

(d)  x + y + 5 = 0, x + y – 5 = 0

(e)  None of these

60. The cosine of the angle between the vectors 4i + 3j + 5k and –i + 2j – 3k is

(a)

(b)

(c)

(d)

61. Let  Then [AB]1 is equal to

(a)

(b)

(c)

(d)

(e)  None of these

62. The following linear equations

2x + 3y – 17 = 0

x – 2y + k = 0

3x + y – 1 = 0

are consistent if k has the value of

(a)  –15

(b)  4

(c)  16

(d)  –16

(e)  None of these

63. The matrix  is

I : Singular

II : Non-Singular

III : Idempotent i.e. A2 = A

(a)  Only I is true

(b)  Only II is true

(c)  Both I and III are true

(d)  Both II and III are true

(e)  None of these

64. Given a matrix

It can be uniquely represented as the sum of symmetric and a skew symmetric matrix which are respectively

(a)

(b)

(c)

(d)

65. a = i + 2j + 3k, b = −i + j – k and c = i + 4j + 6k are three vectors. Then the vector d which is both perpendicular to a and b and satisfies the relation d.c = 25 is

(a)  (25, 10, 15)

(b)  (25, –10, 15)

(c)  (–25, –10, 15)

(d)  (–25, –10, –15)

(e)  None of these

66. Let A and B be two events. Then P(A ∩ B) = P(A) P(B) indicates that A and B are two

(a)  exhaustive events

(b)  mutually exclusive events

(c)  independent events

(d)  mutually exhaustive and independent

(e)  None of these

67. The probability of getting a total of 10 points with 4 dice is

(a)  0.723

(b)  0.5

(c)  0.127

(d)  0.061

(e)  None of these