Physics

1. Ohm’s law is valid when the temperature of the conductor is

(a)  constant

(b)  very high

(c)  very low

(d)  varying

2. According to the Kirchhoff’s law the sum of the products of current and resistance as well as emfs in a closed loop is

(a)  greater than zero

(b)  less than zero

(c)  zero

(d)  determined by the emf.

3. What happens during the charging of acid cell?

(a)  Voltage increases.

(b)  Energy is given out.

(c)  Relative density of electrolyte decreases.

(d)  Cathode becomes chocolate brown.

4. The relative density of the electrolyte of acid accumulator should not be allowed to fall below

(a)  1.80

(b)  1.50

(c)  1.28

(d)  1.18

5. The electric cell is a device that obtains

(a)  electrons

(b)  electric-charge

(c)  electric energy from chemical energy

(d)  electric force

6. What is the nature of graph between temperature and thermo emf?

(a)  Hyperbola

(b)  Straight line

(c)  Parabola

(d)  Some other curve

7. Two bulbs, one of 50 watt and another 25 watt are connected series to the mains. The current flowing through them will be in the ratio

(a)  2 : 1

(b)  1 : 2

(c)  1

(d)  2 : 3

8. Electric current is passed through the following solutions. In which case hydrogen will be liberated at the cathode?

(a)  Sugar

(b)  Sodium hydroxide

(c)  Sulphuric acid

(d)  Copper & Sulphate

9. An electric kettle is rated at 500 w. The time taken to heat 0.5 litre of water from 30℃ to 100℃ in this kettle is

(a)  7.9 minutes

(b)  3.9 minutes

(c)  4.9 minutes

(d)  5.9 minutes

10. The resistance of an ideal voltmeter is

(a)  zero

(b)  high

(c)  infinite

(d)  low

11. Of the following an ideal voltmeter is

(a)  moving coil voltmeter

(b)  voltameter

(c)  an electrometer

(d)  hot wire voltmeter

12. A copper rod moves parallel to the horizontal direction. The induced e.m.f. developed across its ends due to earth’s magnetic field will be maximum at the

(a)  equator

(b)  latitude 30°

(c)  latitude 60°

(d)  poles

13. Dynamo is designed on the principle of

(a)  electromagnetic induction

(b)  self induction

(c)  mutual induction

(d)  None of the above

14. What does a dynamo generate ?

(a)  Electrons

(b)  Charge

(c)  emf

(d)  None of the above

15. A choke coil should have

(a)  high resistance low inductance

(b)  high resistance high inductance

(c)  low resistance high inductance

(d)  low resistance low inductance

16. An AC. series circuit contains 8 ohm of resistance and 6 ohm of inductive reactance.

(a)  14 ohm

(b)  2 ohm

(c)  10 ohm

(d)  14.2 ohm

17. What is the nature of path of an electron when it moves in a transverse electric field?

(a)  Straight line

(b)  Ellipse

(c)  Parabola

(d)  Circle

18. The seconds hand of a clock is 2.0 cm long. Displacement of the tip of the hand in 15 seconds is

(a)  2.0 cm.

(b)  2√2 cm.

(c)  1.0 cm.

(d)  0.5 cm.

19. A bus travels the first one-third distance at a speed of 10 km/hr., the next one-third distance at 20 km/hr. and the last one third distance at 60 km/hr. The average speed of the bus is

(a)  16 km/hr.

(b)  18 km/hr.

(c)  2√2 km/hr.

(d)  √2 km/hr.

20. A shell following a parabolic path explodes somewhere in its flight. The centre of mass of fragments will continue to move in

(a)  vertical direction

(b)  any direction

(c)  horizontal direction

(d)  same parabolic path

21. If the earth would have been of iron of density 8 × 103 kg/m3, then the value of acceleration due to gravity (g) would be

(a)  zero

(b)  equal to g

(c)  less than

(d)  greater than g

22. If the diameter of the earth becomes two times of its present value and its mass remains unchanged, then how would the weight of an object on the surface of the earth be effected?

(a)  It will become half

(b)  It will become one-fourth.

(c)  It will become double.

(d)  It will become four times.

23. The compressibility of water is 4 × 105 per unit at mospheric pressure. The decrease in volume of 10 cm3 of water under a pressure of 100 atmosphere will be

(a)  0.004 cm3

(b)  0.025 cm3

(c)  0.4 cm3

(d)  4 × 105 cm3

24. A wooden cube first floats inside water when a 200 g mass is placed on it. When the mass is removed, the cube is 2 cm above water level. The size of cube is

(a)  5 cm

(b)  10 cm

(c)  15 cm

(d)  20 cm

25. A boat having a length of 3 metres and breadth 2 metres is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is

(a)  60 kg

(b)  62 kg

(c)  72 kg

(d)  28 kg

26. No other thermometer is suitable as a platinum resistance thermometer to measure temperatures in the entire range of

(a)  −50℃ to + 350℃

(b)  −200℃ to + 600℃

(c)  0℃ to 100℃

(d)  100℃ to 1500℃

27. The temperature of the sun is measured with

(a)  platinum thermometer

(b)  gas thermometer

(c)  pyrometer

(d)  vapour pressure thermometer

28. Absolute scale of temperature is reproduced in the laboratory by making use of a

(b)  platinum resistance thermometer

(c)  constant volume helium gas thermometer

(d)  constant pressure ideal gas thermometer

29. 336 g of ice at 0℃ is mixed with 336g of water at – 80℃. The final temperature of

(a)  80℃

(b)  40℃

(c)  60℃

(d)  0℃

30. NTP corresponds to a temperature of

(a)  0 K

(b)  −273 K

(c)  273 K

(d)  None of the above

31. An isochoric process is one which takes place at

(a)  constant internal energy

(b)  constant entropy

(c)  constant volume

(d)  constant pressure

32. If the temperature of black body raised by 5%, the heat energy radiated would increase by

(a)  6%

(b)  20%

(c)  21.51%

(d)  41.61%

33. On a cold morning a metal surface will fell colder to touch than a wooden surface, because metal has

(a)  high specific heat

(b)  low specific heat

(c)  high thermal conductivity

(d)  low thermal conductivity

34. A body of mass 5 gram is executing S.H.M. about a fixed point O with an amplitude of 10 cm. Its maximum velocity is 100 cm/s. Its velocity will be 50 cm/s at a distance (in cm)

(a)  5

(b)  5√2

(c)  5√3

(d)  10√2

35. A tunnel has been dug through centre of the earth and a ball is released in it. It executes S.H.M. with time period

(a)  42 minutes

(b)  1 day

(c)  1 hour

(d)  84.6 minutes

36. A stone is dropped into a lake from a tower 500 metre high. The sound of splash will be heard by the man approximately after

(a)  11.5 sec.

(b)  21 sec.

(c)  10 sec.

(d)  14 sec.

37. In case of the longitudinal mechanical wave in air what is the phase difference between the pressure wave and the displacement wave?

(a)  0°

(b)  45°

(c)  90°

(d)  180°

38. At what temperature the velocity of sound in air is 1.5 times the velocity at 7℃?

(a)  357℃

(b)  476°

(c)  588℃

(d)  819℃

39. To hear a clear echo, the reflecting surface must be at a minimum distance of

(a)  10 m

(b)  16.5 m

(c)  33 m

(d)  66 cm

40. The distance between any two successive compression zones in medium in which a sound wave of 50 cm wave-length is travelling is

(a)  12.5 cm

(b)  25 cm

(c)  37.5 cm

(d)  50 cm

41. When a wave passes from one medium to another, there is change in

(a)  frequency and velocity

(b)  frequency and wavelength

(c)  wavelength and velocity

(d)  frequency, wavelength and velocity

42. A fork gives 5 beats with a 40 cm length of sonometer wire. If the length of the wire is shortened by 1 cm, the number of beats is still the same. he frequency o f the fork is

(a)  385 Hz

(b)  600 Hz

(c)  395 Hz

(d)  400 Hz

43. A pipe closed at one end and open at the other end, resonates with sound waves of frequency 135 Hz and also 165 Hz, but not with any wave of frequency intermediate between these two. Then the frequency of the fundamental note is

(a)  30 Hz

(b)  15 Hz

(c)  60 Hz

(d)  7.5 Hz

44. The penetration of light into the region of geometrical shadow is called

(a)  Polarisation

(b)  Interference

(c)  Diffraction

(d)  Refraction

45. When light is transmitted from air to glass, its

(a)  wave-length increases

(b)  wave-length decreases

(c)  frequency increases

(d)  There occurs no change.

46. Which of the following is not the case with the image formed by a plane mirror?

(a)  It is erect.

(b)  It is virtual.

(c)  It is diminished.

(d)  It is at the same distance as the object.

47. The low, generally negative D.C. voltage applied to the grid is called

(a)  bias

(b)  signal

(c)  cut off voltage

(d)  None of the above

48. When a compact disc is illuminated by a source of white light, coloured lines are observed. This is due to

(a)  dispersion

(b)  diffraction

(c)  interference

(d)  refraction

49. A beam of monochromatic light is refracted from vacuum into a medium of refractive index 1.5. The wavelength of refracted light will be

(a)  dependent on intensity of refracted light

(b)  same

(c)  smaller

(d)  larger

50. A convex lens of focal length 30 cm forms an image of height 2 cm for an object situated at infinity. If a concave lens of focal length 20 cm is placed coaxially at a distance of 26 cm in front of convex lens, then size of final image would be

(a)  1.5 cm

(b)  2 cm

(c)  2.5 cm

(d)  4 cm

51. A form of electromagnetic radiation with wave-lengths intermediate between those of visible light and those of micro-wave is known as

(c)  visible-spectrum

(d)  None of the above

52. The focal length of a lens for red and violet colours are 16.4 cm and 16 cm. What is the dispersive power?

(a)  0.050

(b)  0.025

(c)  0.012

(d)  0.006

53. Which of the following provides warmth in sunlight?

(a)  X-rays

(b)  Ultraviolet rays

(c)  Visible light

(d)  Infrared rays

54. What causes chromatic aberration ?

(a)  None paraxial rays

(b)  Paraxial rays

(c)  Variation of focal length with colour.

(d)  Difference in radii of curvature of the bonding surfaces of the lens

55. Diameter of objective of telescope is large for

(a)  greater magnification

(b)  greater resolution

(c)  greater ease in handling.

(d)  greater magnifying power

56. A person cannot see object clearly beyond 50 cm. The power of the lens to correct the vision is

(a)  +5 diopter

(b)  −0.5 diopter

(c)  −2 diopter

(d)  +2 diopter

57. A large magnet is broken into two pieces so that their lengths are in the ratio 2 : 1. The pole strengths of the two pieces will have ratio

(a)  2 : 1

(b)  1 : 2

(c)  4 : 1

(d)  1 : 1

58. The ratio of magnetic fields due to a small bar magnet at a given distance in the end on position to broad side on position is

(a)  1/4

(b)  1/2

(c)  1

(d)  2

59. When magnetizing field on a bar of steel is increased, its magnetization given on

(a)  decreasing

(b)  increasing

(c)  increasing first and then decreases

(d)  increasing till it becomes constant

60. The hysteresis cycle for the material of a transformer core is

(a)  short and wide

(b)  tall and narrow

(c)  tall and wide

(d)  short and narrow

61. In a cassette player, materials used for coating magnetic tapes are

(a)  cobalt

(b)  CoFe2O4

(c)  NiFe2O4

(d)  Nickel

62. Water is

(a)  diamagnetic

(b)  paramagnetic

(c)  ferromagnetic

(d)  None of these

63. DEBYE is the unit of

(a)  Electric dipole moment

(b)  Electric flux

(c)  Electric potential

(d)  Electric field

64. A hollow metallic sphere qf radius 10 cm is changes such that potential of its surface is 80 volt. The potential at the centre of the sphere would be

(a)  zero

(b)  8 V

(c)  80 V

(d)  800 V

65. When a dielectric material is introduced between the plates of a changed condenser then electric field between the plates

(a)  decreases

(b)  increases

(c)  remains constant

(d)  None of these

66. The electric field between the two spheres of a charges spherical condenser

(a)  is zero

(b)  is constant

(c)  increases with distance from the centre

(d)  decreases with distance from the centre

Chemistry

1. Acetylene reacts with HCN to produce

(a)  CH4

(b)  CH2 = CH.CN

(c)  C2H5CN

(d)  CH3CN

2. Among the following compounds, the strongest acid is

(a)  HC ≡ CH

(b)  C6H6

(c)  C2H6

(d)  CH3OH

3. The product(s) obtained via oxymercuration (HgSO4 + H2SO4) of 1-butyne would give

(a) (b)  CH3CH2CH2CHO

(c)  CH3CH2CHO + HCHO

(d)  CH3CH2COOH + HCOOH

4. Propyne and propene can be distinguished by

(a)  Conc. H2SO4

(b)  Br2 in CCl4

(c)  dil H2SO4

(d)  AgNO3 in ammonia

5. When propyne is treated with HgSO4/H2SO4 product is

(a)  propanol

(b)  propenal

(c)  propanone

(d)  propanoic acid

6. Which of the following will form sodium salt?

(a)  CH3 – CH3

(b)  CH3-C = C-CH3

(c)  CH3-CH2-C ≡ CH

(d)  None of these

7. KMnO4 will oxidize acetylene to

(a)  ethylene glycol

(b)  ethyl alcohol

(c)  oxalic acid

(d)  acetic acid

8. Octane number can be changed by

(a)  isomerisation

(b)  alkylation

(c)  cyclisation

(d)  All of these

9. Anti-Markownikov addition of HBr is not observed in

(a)  Propene

(b)  -Butene

(c)  But-2-ene

(d)  Pent-2-ene

10. 2-hexyne gives trans-2-hexane on treatment with

(a)  Li-NH3/C2H5OH

(b)  Pd/BaSO4

(c)  LiAlH4

(d)  Pt/H2

11. Out of the following compounds, which one will have a zero dipole moment?

(a)  1, 1-dichloroethylene

(b)  cis-1, 2-dichloroethylene

(c)  trans-1, 2-dichloroethylene

(d)  None of these compounds

12. n-propyl bromide on treatment with ethanolic potassium hydroxide produces

(a)  propane

(b)  propene

(c)  propyne

(d)  propanal

13. 1-chlorobutane on reaction with alcoholic potash gives

(a)  1-Butene

(b)  1-Butanol

(c)  2-Butene

(d)  2-Butanol

14. The produce formed on reaction of ethyl alcohol with bleaching powder is

(a)  CH3OH

(b)  CH3-CH2-OH

(c)  CHCl3

(d)  Both (a) and (b)

15. Which of the following has the highest nucleophilicity ?

(a)  F

(b)  OH

(c)  CH3

(d)  NH2

16. Among the following the molecule with highest dipole moment is

(a)  CH3Cl

(b)  CH2Cl2

(c)  CHCl3

(d)  CCl­4

17. When chloroform is boiled with NaOH, it gives

(a)  formic acid

(b)  trihydroxy methene

(c)  acetylene

(d)  sodium formate

18. The colour of CoCl2 . 5NH3, H2O is

(a)  orange yellow

(b)  orange

(c)  green

(d)  pink

19. Which one of the following is an example of non-typical transition elements?

(a)  Li, K, Na

(b)  Be, Al, Pb

(c)  Zn, Cd, Hg

(d)  Ba, Ca, Sr

20. Which of the following does not have valence electron in 3d-subshell?

(a)  Fe(III)

(b)  Mn(II)

(c)  Cr(I)

(d)  P(0)

21. Effective magnetic moment of Sc3+ ion is

(a)  1.73

(b)  0

(c)  5.92

(d)  2.83

22. The pair of compounds having metals in their highest oxidation state is

(a)  MnO2, FeCl3

(b)  [MnO4]CrO2, Cl2

(c)  [Fe(CN)6]3, [Co(CN)3]

(d)  [NICl4]2, [CoCl4]

23. Which one of the following are prepared by electrolytic method ?

I. Mg   II. Sn   III. Sulphur   IV. F2

(a)  I and II

(b)  II and III

(c)  III and IV

(d)  I and IV

24. Refactory materials are used in furnace because they

(a)  posses great structural strength

(b)  can withstand high temperature

(c)  are chemically inert

(d)  do not require replacement

25. An important ore of Magnesium is

(a)  Malachite

(b)  Cassiterite

(c)  Carnallite

(d)  Galena

26. Red hot iron absorbs SO2 giving the products

(a)  FeS + O2

(b)  Fe2O3 + FeS

(c)  FeO + FeS

(d)  FeO + S

27. All ores are minerals, while al minerals are not ores. because

(a)  the metal can’t be extracted economically from al the minerals

(b)  minerals are complex compounds

(c)  the minerals are obtained from mines

(d)  All of these are correct.

28. Which of the following process is used in the extractive metallurgy of magnesium?

(a)  Fused salt electrolysis

(b)  Self-reduction

(c)  Aqueous solution electrolysis

(d)  Thermite reduction

29. The ore which contains copper and iron both is

(a)  cuprite

(b)  chalcocite

(c)  chalcopyrite

(d)  malachite

30. White phosphorus reacts with caustic soda. The products are PH3 and NaH2PO2. This reaction is an example of

(a)  oxidation

(b)  reduction

(c)  oxidation and reduction

(d)  neutralization

31. HBr and HI reduce sulphuric acid, HCl can reduce KMnO4 and HF can reduce

(a)  H2SO4

(b)  KMnO4

(c)  K2Cr2O7

(d)  None of these

32. Chlorine acts as a bleaching agent only in the presence of

(a)  dry air

(b)  moisture

(c)  sunlight

(d)  pure oxygen

33. HNO3 reacts with iodine to give

(a)  HI

(b)  HOI

(c)  HOIO3

(d)  HOIO3

34. When I2 is dissolved in CCl4, the colour that result is

(a)  brown

(b)  violet

(c)  colour less

(d)  bluish green

35. The oxidation number of sulphur in S8, S2F2 . H2S respectively are

(a)  0, +1 and −2

(b)  +2, +1 and −2.

(c)  0, +1, and +2

(d)  −2, +1 and −2

36. Among the following, identify the species with an atom in +6 oxidation state,

(a)  MnO4

(b)  Cr(CN)63

(c)  NiF62

(d)  CrO2Cl2

37. The reaction : 3ClO(aq) → ClO3(aq) + 2Cl(aq) is an example of

(a)  oxidation reaction

(b)  reduction reaction

(c)  disproportionation reaction

(d)  decomposition reaction

38. Oxidation state of Osmium (Os) in OsO4 is

(a)  +7

(b)  +6

(c)  +4

(d)  +8

39. How many isomers of C5H11OH will be primary alcohols?

(a)  5

(b)  4

(c)  2

(d)  3

40. When CO2 is passed through solution of calcium hydroxide, which one of the following compound is precipitated?

(a)  Ca(HCO3)2

(b)  CaO

(c)  CaCO3

(d)  Ca(OH)2

41. Oleum is chemically known as

(a)  H2SO3

(b)  H2SO5

(c)  H2S2O7

(d)  H2S2O8

42. Ferric alum has the composition (NH4)2SO4, Fe2(SO4)3, xH2 The value of x is

(a)  7

(b)  24

(c)  6

(d)  15

43. The IUPAC name of the compound is

(a)  2-ethyl butanamide

(b)  2-methylbutanamide

(c)  1-amino-2-methylpropane

(d)  1-amino-3-methylpropane

44. The compound is known by which of the following names ? (a)  Bicyclo [2, 2, 2] octane

(b)  Bicyclo [2, 2, 1] octane

(c)  Bicyclo [1, 2, 1] octane

(d)  Bicyclo [1, 1, 1] octane

45. IUPAC name of is

(a)  2-cyano, 3-methyl hexane

(b)  3-methyl, 5-cyanohexane

(c)  2, 2-dimethyl-4-cyanopentane

(d)  2-cyano, 3-methyl hexane

46. IUPAC name of the compound is

(a)  4-methylpentane-2-ol

(b)  2-methylpentanol-4

(c)  4, 4-dimethylbutan-2-ol

(d)  4-methylpentan-2-ol

47. Successive alkanes differ by

(a)  > CH2

(b)  -C-H

(c)  -CH3

(d)  C2H4

48. The IUPAC name of n-butyl chloride is

(a)  1-chlorobutane

(b)  n-chlorobutane

(c)  ter-butylchloride

(d)  2-methylbutane

49. How many methyl groups are present in 2, 5-dimethyl-4-ethy name?

(a)  2

(b)  3

(c)  4

(d)  5

50. A fractionation column is used in

(a)  Sublimation

(b)  Distillation

(c)  Fractional distillation

(d)  Chromatography

51. Copper wire test of halogens is known as

(a)  Beilstein’s test

(b)  Liebig’s test

(c)  Fusion test

(d)  None of these

52. Nitrogen is an organic compound can be estimated by

(a)  Kjeldahl’s method only

(b)  Duma’s method only

(c)  Both the methods

(d)  None of these methods

53. The Beilstein test for organic compounds is used to detect

(a)  Nitrogen

(b)  Sulphur

(c)  Carbon

(d)  Halogens

54. The density of air is 0.00130 g/ml. The vapour density of air will be

(a)  0.00065

(b)  0.65

(c)  14.4816

(d)  14.56

55. Which of the following is not a nucleophile?

(a)  CN

(b)  H2O

(c)  BF3

(d)  Carbanion

56. Of the following compounds, the one having linear structure is

(a)  Methane

(b)  Ethylene

(c)  Acetylene

(d)  Water

57. The Cl-C-Cl angle in 1, 1, 2, 2-tetrachloroethene and tetrachloromethane will be about

(a)  120° and 109.5°

(b)  90° and 109.5°

(c)  109.5° and 90°

(d)  109.5° and 120°

58. Which of the following is an electrophile?

(a)  H2O

(b)  NH3

(c)  AlCl3

(d)  C2H5NH3

59. The most common type reaction in aromatic compounds is

(a)  elimination reaction

(c)  electrophilic substitution reaction

(d)  rearrangement reaction

60. Among the following is strongest nucleophile is

(a)  C2H5SH

(b)  CH3COO

(c)  CH3NH2

(d)  NC-CH2

61. Cetane number of diesel fuel increases with the addition of

(a)  Decane

(c)  Pentane

(d)  Methyl napthalene

62. Petroleum is a mixture of

(a)  alkanes

(b)  alkenes

(c)  alkynes

(d)  alkyl halides

63. Ethyl iodide when heated with sodium in dry ether gives pure

(a)  C4H10

(b)  C2H6

(c)  C3H8

(d)  C2H5OH

64. Which one of the following compounds cannot be prepared by Wurtz reaction?

(a)  CH4

(b)  C2H6

(c)  C3H8

(d)  C410

65. Which of the following alkenes will react fastest with H2 under catalytic conditions ?

(a) (b) (c) (d) 66. Which of the following is the most stable?

(a)  1-butene

(b)  2-butene

(c)  1-pentene

(d)  2-pentene

Mathematics

1. A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is

(a)  3/11

(b)  4/11

(c)  2/11

(d)  0

2. Two cards are drawn at random from a pack of 52 cards. The probability of these being queens is

(a)  1/26

(b)  1/2

(c)  1/221

(d)  None of these

3. If (a)  x = f(y)

(b)  f(1) = 3

(c)  y increases with x for x < 1

(d)  f is not a rational function of %

4. If log10 x = y, then log10 3x2 equals

(a) (b) (c) (d) 5. (a)  1/3

(b)  −1/3

(c)  1/5

(d)  −1/6

6. If = 0, [x] = 0

Where [x] denotes the greatest integer ≤ x, then equals

(a)  1

(b)  0

(c)  −1

(d)  None of these

7. If is

(a) (b) (c) (d) 8. (a)  1/2

(b)  2/3

(c)  3

(d)  None of these

9. The maximum value of sin x + cos x =

(a)  1

(b)  2

(c)  √2

(d)  1/√2

10. (a) (b) (c) (d) 11. (a) (b) (c) (d) 12. (a) (b)  log 2

(c)  log 3

(d)  log √3

13. The value of is

(a)  0

(b)  2

(c)  3

(d)  4

14. The area between the curve y = 1 – |x| and X-axis is

(a)  1

(b)  1/2

(c)  2

(d)  1/3

15. The degree of the differential equation is

(a)  1

(b)  2

(c)  3

(d)  4

16. The solution set of the inequaiton 2x + y > 5 is

(a)  half plane that contains the origin

(b)  open half plane not containing the origin

(c)  whole XY-plane except the points lying on the line 2x + y = 5

(d)  None of these

17. The maximum value of the objective function P = 5x + 3y, subject to the constraints x ≥ 0, y ≥ 0 and 5x + 2y ≤ 10 is

(a)  6

(b)  10

(c)  15

(d)  25

18. If A = {2, 4, 5}, B = {7, 8, 9} then n(A × B) =

(a)  6

(b)  9

(c)  3

(d)  0

19. If A & B are sets, then A ∩ (B – A) is

(a)  ϕ

(b)  A

(c)  B

(d)  None of these

20. If a set A has a n elements, then the total number of subsets of A is

(a)  n

(b)  n2

(c)  2n

(d)  2n

21. (a)  a rational number

(b)  an irrational number

(c)  an imaginary number

(d)  None of these

22. If x and y are real positive numbers, then

(a) (b) (c) (d) 23. If then z69 is equal to

(a)  −i

(b)  i

(c)  1

(d)  −1

24. The number is equal to

(a)  i

(b)  −1

(c)  1

(d)  0

25. The value of (a)  2

(b)  −2

(c)  1

(d)  0

26. If P and P’ be perpendicular from the origin upon the straight lines,

x sec θ + y cosec θ = a and x cos θ – y sin θ = a cos 2θ, then the value of the expression 4P2 + P’2 is

(a)  a2

(b)  3a2

(c)  2a2

(d)  4a2

27. The lines x + (a – 1)y + 1 = 0 & 2x + a2y – 1 = 0 are perpendicular if

(a)  |a| = 2

(b)  0 < a < 1

(c)  −1 < a < 0

(d)  a = −1

28. The equation of the line parallel to x-axis bisecting the joint of (1, 4) and (−2, 6) is

(a)  y = 5

(b)  y = 3

(c)  y + 1 = 0

(d)  x = 5

29. The circle x2 + y2 + 4x – 7y + 12 = 0 cuts an intercept on y-axis equal to

(a)  1

(b)  3

(c)  4

(d)  7

30.  The equation of chord of the circle x2 + y2 – 4x = 0 whose midpoint is (1, 0) is

(a)  y = 2

(b)  y = 1

(c)  x = 2

(d)  x = 1

31. The equation of the circle passing through the origin is x2 + y2 – 6x + 3y = 0. The equation of one of its diameter is

(a)  x + 3y = 0

(b)  x + y = 0

(c)  x = y

(d)  3x + y = 0

32. The slope of a chord of the parabola y2 = 4ax, which is normal at one end and which subtends a right angle at the origin is

(a) (b) (c)  ±2

(d)  None of these

33. The eccentric angle of a point on the ellipse whose distances from the centre of the ellipse is 2, is

(a) (b) (c) (d) 34. The number of values of c such that the straight line y = 4x + c touches the curve is

(a)  0

(b)  1

(c)  2

(d)  Infinite

35. If the major axis of an ellipse is thrice the minor axis, then its eccentricity is equal to

(a)  1/3

(b)  1/√3

(c)  1/√2

(d)  2√2/3

36. For m ≠ n, if tan mθ = tan nθ, then the different values of θ are in

(a)  NO particular sequence

(b)  G.P.

(c)  H.P.

(d)  A.P.

37. tan 20° + tan 40° + √3 tan 20° tan 40° is equal to

(a) (b) (c) (d) 38. Let sin x+ sin y = a and cos x + cos y = b then sin(x + y) is equal to

(a) (b) (c) (d) 39. If sin A = sin B, cos A = cos B, then the value of A in terms of B is

(a)  nπ + B

(b)  nπ + (−1)n B

(c)  2nπ + B

(d)  2nπ − B

40. The number of real solutions of is

(a)  zero

(b)  one

(c)  two

(d)  infinite

41. (a)  π

(b)  π/2

(c)  π/3

(d)  π/4

42. The value of is

(a) (b) (c) (d) 43. If sin1 x + sin1 y + sin1 z = π then x4 + y4 + z4 + 4x2y2z2 = k(x2y2 + y2z2 + z2x2) where k = ?

(a)  1

(b)  2

(c)  4

(d)  None of these

44. A triangle ABC is right-angled at B. Then the diameter of the incircle of the triangle is

(a)  2(c + a – b)

(b)  c + a – 2b

(c)  c + a – b

(d)  None of these

45. If the angles of triangle are in the ratio 1 : 2 : 3, he corresponding sides are in the ratio

(a)  2 : 3 : 1

(b)  √3 : 2 : 1

(c)  2 : √3 : 1

(d)  1: √3 : 1

46. The maximum number of real roots of the equation x2n – 1 = 0 is

(a)  2

(b)  3

(c)  n

(d)  2n

47. We are given b, c & sin B such that B is acute and b < c sin B, then

(a)  No triangle is possible

(b)  One triangle is possible

(c)  Two triangles are possible

(d)  A right-angled triangle is possible

48. The expression ax2 + bx + c, a > 0 is positive for all real x only if

(a)  b2 – 4ac = 0

(b)  b2 – 4ac ≠ 0

(c)  b2 – 4ac < 0

(d)  b2 – 4ac > 0

49. If α, β are the roots of quadratic equation x2 + bx – c = 0 then the equation whose roots are b & c is

(a)  x2 + αx – β = 0

(b)  x2 – [(α + β) + αβ] x – αβ (α + β) = 0

(c)  x2 + [(α + β) + αβ] x + αβ (α + β) = 0

(d)  x2 + (αβ + α + β) x – αβ(α + β) = 0

50. If the ratio of the roots of the equation x2 + bx + c = 0 is the ratio of the roots of the equation x2 + qx + r = 0 then

(a)  r2b = qc2

(b)  r2c = qb2

(c)  c2r = q2b

(d)  b2r = q2c

51. The roots of the equation 4x – 3 . 2x + 3 + 128 = 0 are

(a)  1 and 2

(b)  2 and 3

(c)  3 and 4

(d)  4 and 5

52. If ax = bx = cz and a, b, c are in GP. then x, y, z are in

(a)  A.P.

(b)  G.P.

(c)  H.P.

(d)  None of these

53. If , the value of n is

(a)  35

(b)  36

(c)  37

(d)  38

54. If the sum of n terms of the series 23 + 43 + 63 + …….. ∞ is 3528, then n equals

(a)  6

(b)  7

(c)  8

(d)  9

55. The 99th term of the series 2 + 7 + 14 + 23 + 34 + , ……. is

(a)  9999

(b)  9998

(c)  10000

(d)  None of these

56. The letters of the word RANDOM are written in all possible orders and these words are written out as in a dictionary. Then the rank of the word RANDOM is

(a)  614

(b)  615

(c)  613

(d)  616

57. How many numbers of five digits can be formed from the digits 2, 0, 4, 3, 8 when repetition of digits is not allowed ?

(a)  96

(b)  120

(c)  144

(d)  14

58. If the co-efficient of mth, (m + 1)th and (m + 2)th terms in the expansion of (1 + x)n are in A.P. then

(a)  n2 + 4(4m + 1) + 4m2 – 2 = 0

(b)  n2 + n(4m + 1) + 4m2 + 2 = 0

(c)  (n – 2)m2 = n + 2

(d)  (n + 2m)2 = n + 2

59. The middle term in the expansion of is

(a) (b) (c) (d) 60. The value of the determinant is

(a) (b) (c) (d) 61. The inverse of the matrix is

(a)  A

(b)  Aʹ

(c) (d) 62. If A and B are any 2 × 2 matrices, then det(A + B) = 0 implies

(a)  det A + det B = 0

(b)  det A = 0 or det B = 0

(c)  det A = 0 and det B = 0

(d)  None of these

63. Value of a for which are coplanar

(a)  2

(b)  4

(c)  −4

(d)  3

64. If the vector form of the component of is

(a) (b) (c) (d) 65. The point which divides the line joining the points (2, 4, 5) & (3, 5, −4) in the ratio −2 : 3 lies on

(a)  ZOX plane

(b)  XOY plane

(c)  YOZ plane

(d)  None of these

66. If θ is an angle given by where α, β & γ are the angles made by a line with the positive directions of the axes of reference, then the measure of θ is

(a)  π/3

(b)  π/6

(c)  π/2

(d)  π/4

67. Weighted mean is computed by the formula

(a) (b) (c) (d) 68. The mean and S.D. of 1, 2, 3, 4, 5, 6 is

(a) (b) (c) (d) Biology

1. Excess of the white corpuseles in blood is called

(a)  anaemia

(b)  leukaemia

(c)  anoxia

(d)  septicemia

2. Which of the following organs develops first?

(a)  Liver

(b)  Heart

(c)  Notochord

(d)  Kidney

3. Which one of the following diseases is caused by bacteria?

(a)  Chicken pox

(b)  Poliomyelitis

(c)  Influenza

(d)  Tuberculosis

4. Which of the following micro-organisms can use molecular nitrogen as nutrient?

(a)  Methanomonas

(b)  Mucor

(c)  Rhizobium

(d)  All of these

5. A dry fruit is dispersed by

(a)  wind

(b)  Both (A) and (B)

(c)  body surfaces of animals

(d)  None of these

6. The term ‘anaerobic’ means

(a)  with glucose

(b)  with oxygen

(c)  without glucose

(d)  without oxygen

7. Xylem is primarily instrumental for

(a)  conduction of water

(b)  conduction of solute

(c)  mechanical support

(d)  All of these

8. Which of the following absorbs part of the isolation and preserves earth is radiated heat?

(a)  Nitrogen

(b)  Oxygen

(c)  Water vapour

(d)  Carbon dioxide

9. The condition in which there are more than two complete sets of chromosomes is called

(a)  Monoploidy

(b)  Polyploidy

(c)  Aneuploidy

(d)  Polytene

10. The hardest substances in human body is

(a)  chondrin

(b)  dentine

(c)  enamel

(d)  keratin

11. Cell was discovered by

(a)  Robert Hooke

(b)  Leeuwenhock

(c)  Robert Brown

(d)  Dujardin

12. Cell was discovered in the year

(a)  1652

(b)  1656

(c)  1665

(d)  1674

13. Nucleolus was discovered by

(a)  Oken

(b)  Wagner

(c)  Robert Brown

(d)  Frontana

14. Cell theory was proposed by

(a)  Schwann

(b)  Schleiden

(c)  Galeleo

(d)  None them

15. Father of genetics is

(a)  Devries

(b)  Correns

(c)  Mendel

(d)  Tschermuk

16. TMV is a full name of

(a)  Termie Maselte Virus

(b)  Taretic Mosaic Virus

(c)  Taitric Mosaic Virus

(d)  Tobacco Mosaic Virus

17. The hormone insulin which is used in treating diabetes was discovered by

(a)  F. G. Banting

(b)  Louis Pasteur

(c)  J. E. Salk

(d)  J. F. Enders

18. Colour of blood is red due to

(a)  Haemoglobin

(b)  WBC

(c)  Hormone

(d)  Protein

19. Cancer caused by

(a)  Bacteria

(b)  Virus

(c)  Fungles

(d)  Protozoa

20. The main constituent of chlorofil is

(a)  Mg

(b)  Fe

(c)  Zn

(d)  Cu

21. Photosynthesis take place at

(a)  fungy

(b)  stem

(c)  green leaves

(d)  roots

22. Rickets is caused by the deficiency of

(a)  Vitamin A

(b)  Vitamin C

(c)  Vitamin D

(d)  Vitamin B

23. The main respiratory substrate of human is

(a)  glucose

(b)  food

(c)  meat

(d)  milk

24. Example of monosaccharide is

(a)  Fructose

(b)  Maltose

(c)  Lactose

(d)  Glucose

25. Which one of the following is complete flower?

(a)  Chinarose

(b)  Night queen

(c)  Rose

(d)  None of these

26. Raphides is

(a)  Calcium sulphate

(b)  Calcium carbonate

(c)  Calcium oxalate

(d)  None of these

27. Excretory organs of planaria is

(a)  flame cell

(b)  Gills

(c)  green glands

(d)  Liver

28. Example of Beneficial Bacteria is

(a)  Rhizobium

(b)  Basilas subtilis

(c)  Lactobasilus

(d)  None of these

29. Cholera is caused by

(a)  Vibrio cholerae

(b)  Clostridium tetani

(c)  Tuberculosis

(d)  None of these

30. Cotton fibre is obtained from the

(a)  stem

(b)  seed

(c)  Leaf

(d)  Fruit

31. The adult human skeleton consist of

(a)  204 bones

(b)  201 bones

(c)  206 bones

(d)  208 bones

32. Gene the basic unit of heredity, was first synthesized in the laboratory by

(a)  Hargobind Khorana

(b)  Watson and Crick

(c)  Gregor Mendel

(d)  Arthur Kornberg

33. The Central Drug Research Institute of India is located at

(a)  Bengaluru

(b)  Lucknow

(c)  Chennai

(d)  Delhi

34. The acid present in lemons and oranges is

(a)  acetic acid

(b)  hydrochloric acid

(c)  citric acid

(d)  oxalic acid

35. The most abundant source of iron is

(a)  milk

(b)  green vegetables

(c)  eggs

(d)  beans

36. While cooking food, the compounds lost to the maximum extent are

(a)  fats

(b)  carbohydrates

(c)  vitamins.

(d)  proteins

37. Cholesterol is

(a)  type of chlorophyll

(b)  derivative of chloroform

(c)  fatty alcohol found in animal fats

(d)  chromium salt

38. Antibodies is the name given to

(a)  harmful bacteria

(b)  poisonous substances

(c)  viruses that cause infection

(d)  substances formed in the blood that arrest or destroy harmful bacteria attacks

39. Haemoglobin is

(a)  the colouring matter of leaves of plants

(b)  colouring matter of blood

(c)  a compound present in milk

(d)  a compound transmitting signals to the brain

40. Sweat contains

(a)  pure water

(b)  phosphoric acid

(c)  calcium phosphate and water

(d)  water, salt and waste matter

41. The main use of salt in the diet is to

(a)  make the taste of food better

(b)  produce in small amount the hydrochloric acid that is needed to digest food

(c)  ease the process of cooking.

(d)  increase the solubility o f food particles in water

42. Absolute alcohol is prepared by

(a)  Kolbe’s method

(b)  Vacuum distillation

(c)  Azeotropic distillation

(d)  Fractional distillation

43. The chromosome number in a bacterium is

(a)  2

(b)  1

(c)  3

(d)  4

44. In a plant cell, DNA is found in

(a)  chloroplast

(b)  mitochondria

(c)  nucleus

(d)  All of these

45. Blood is formed in the human adult by the

(a)  heart

(b)  spleen

(c)  yellow bone marrow

(d)  red bone marrow

46. Which of the following sugars are components of cane sugar?

(a)  Glucose and fructose

(b)  Glucose and galactose

(c)  Glucose and mannose

(d)  Glucose and ribose

47. Which of the following compounds found in all living organisms are rich in phosphorus?

(a)  Carbohydrates

(b)  Nucleic acids

(c)  Fats

(d)  Proteins

48. The largest part of most human diets is made up of

(a)  proteins

(b)  nucleic acids

(c)  carbohydrates

(d)  lipids

49. The microscope built by

(a)  Galileo

(b)  Newton

(c)  Jan Swammerdam

(d)  Robert Hooke

50. Which of the following propagates through leaf tip?

(a)  Moss

(b)  Marchantia

(c)  Walking ferm

(d)  Sprout leaf plant

51. Which of the following is a living fossil?

(a)  Spirogyra

(b)  Cycas

(c)  Saccharomyces

(d)  Moss

52. Which of the following is not correctly matched ?

(a)  Vitamin B2 – Pellagra

(b)  Vitamin B1 – Beri-Beri

(c)  Vitamin B6 – Loss of appetite

(d)  Vitamin B12– Pernicious anaemia

53. Hormones are chemically

(a)  steroids only

(b)  proteins only

(c)  biogenetic amines only

(d)  proteins, steroids and bio-genetic amines

54. The maximum growth rate occurs in

(a)  Lag phase

(b)  Exponential phase

(c)  Senescent phase

(d)  Stationary phase

55. Maize grain is a/an

(a)  Fruit

(b)  Ovule

(c)  Seed

(d)  Embryo

56. Guttation occurs through

(a)  Periderm

(b)  Hydathodes

(c)  Stomata

(d)  Lenticels

57. Match List-I (Endocrine glands) with List-II (Hormones secreted) and select the correct answer using the code given below the lists:

List-I                      List-II

(b) pituitary            2. Progesterone

(c) Pancreas            3. Growth hormones

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

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

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

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

58. Uricotelism is found in

(b)  mammals and birds

(c)  fishes and fresh water protozoans

(d)  insects, birds and reptiles

59. Man in the life-cycle of plasmodium is

(a)  primary host

(b)  secondary host

(c)  intermediate host

(d)  None of the above

60. External fertilization occurs almost exclusively inhabitats that are

(a)  warm

(b)  moist

(c)  crowded

(d)  tropical

61. Insect-resistant cotton plants have been genetically engineered by inserting a gene from a/an

(a)  Mangrove plant

(b)  Bacterium

(c)  Insect

(d)  Virus

62. Which of the following animals is not a chrodate?

(a)  Shark

(b)  Snake

(c)  Starfish

(d)  Dolphin

63. Which of the following enzymes digest starch?

(a)  Renin

(b)  Ptyalin

(c)  Pepsin

(d)  Trypsin

64. Tadpole of frog breathes by

(a)  lungs

(b)  gills

(c)  skin and lungs

(d)  skin and gills

65. The theory of continuity of germ-plasm was pronounced by

(a)  Lamarck

(b)  Haeckel

(c)  Weismann

(d)  Mendel

66. Cartilaginous fishes do not have

(a)  Operculum

(b)  Scales

(c)  Gill slits

(d)  Pelvic fins

67. Plant hormone cytokinin stimulates

(a)  cell division

(b)  cell elongation

(c)  cell wall thickening

(d)  cell turgidity