2010 O.A.U.T Question with Answer

Physics

 

1. Two thin lenses of focal lengths 20 cm and −30 cm are placed in contact with each other. The combination has a focal length

(a)  −10 cm

(b)  50 cm

(c)  60 cm

(d)  10 cm

Answer: (c)

2. A film projector magnifies a 100 cm2 film strip on a screen. If the linear magnification is 4, the area of the magnified film on the screen is

(a)  1600 cm2

(b)  400 cm2

(c)  800 cm2

(d)  200 cm2

Answer: (a)

3. The objective of a small telescope has focal length of 120 cm and diameter 5 cm. The focal length of the eye piece is 2 cm. The magnifying power of the telescope for distant object is

(a)  12

(b)  24

(c)  60

(d)  300

Answer: (c)

4. If a bar magnet of magnetic moment 80 unit be cut into two halves of equal lengths, the magnetic moment of the each half of the will be

(a)  80 unit

(b)  40 unit

(c)  60 unit

(d)  20 unit

Answer: (a)

5. A device which converts electrical energy into mechanical energy is

(a)  dynamo

(b)  induction coil

(c)  electric motor

(d)  generator

Answer: (c)

6. The magnetic field at a distance d from a short bar magnet in longitudinal and transverse positions are in the ratio

(a)  1 : 1

(b)  1 : 2

(c)  2 : 1

(d)  3 : 1

Answer: (c)

7. Soft iron is used to manufacture electromagnets because their

(a)  magnetic saturation limit it high and retentivity and coercive force are small

(b)  retentivity is high

(c)  coercive force is high

(d)  area of hysteresis curve is large

Answer: (b)

8. A dip needle in a plane perpendicular to magnetic meridian will remain

(a)  vertical

(b)  horizontal

(c)  in any direction

(d)  at angle of dip to the horizontal

Answer: (d)

9. A sensitive magnetic instrument can be shielded very effectively from outside fields by placing it inside a box of

(a)  teak wood

(b)  plastic material

(c)  soft iron of high permeability

(d)  a metal of high conductivity

Answer: (c)

10. Which one of the following is the unit of electric charge?

(a)  coulomb

(b)  newton

(c)  volt

(d)  coulomb/volt

Answer: (a)

11. An electric field can deflect

(a)  X-rays

(b)  neutrons

(c)  α-particles

(d)  γ-rays

Answer: (c)

12. Of the following groups which one contains good conductors of electricity?

(a)  Iron nickel and cobalt

(b)  Copper, silver sand aluminium

(c)  Mica, distilled water and ceramics

(d)  Diamond, ebonite and wood

Answer: (b)

13. Unit electric field in volt/m is equal to

(a)  1 N/C

(b)  3 × 1010 N/C

(c)  107 N/C

(d)  1010 N/C

Answer: (a)

14. The canal rays are

(a)  a steam of electrons

(b)  a stream of positively charged particles

(c)  light rays

(d)  a stream of uncharged particles

Answer: (b)

15. According to classical theory Rutherford atom was

(a)  stable

(b)  unstable

(c)  semistable

(d)  metastable

Answer: (b)

16. The ratio of the energies of the hydrogen atom in its first to second excited states is

(a)  1/4

(b)  4/9

(c)  9/4

(d)  4

Answer: (a)

17. X-rays were discovered by

(a)  Becquerel

(b)  Roentgen

(c)  Marie Curie

(d)  Von Laue

Answer: (b)

18. Two radiations containing photons of energy twice and five times the work functions of a metal are incident successfully on the metal sur3face. The rates of the maximum velocities of the emitted electrons in the two cases will be

(a)  1 : 3

(b)  1 : 4

(c)  1 : 2

(d)  1 : 1

Answer: (c)

19. If R be the Rydberg constant for hydrogen, the wave number of the first line in the Lyman series is

(a)  R/2

(b)  2R

(c)  R/4

(d)  3R/4

Answer: (d)

20. An electric kettle has two heating elements. One brings at to boil in 10 minutes and other in 15 minutes. If the two heating filaments be connected in parallel, the water in the kettle will boil in

(a)  6 min.

(b)  8 min.

(c)  25 min.

(d)  5 min.

Answer: (a)

21. Radio waves and visible light in vacuum have

(a)  different velocity and different wavelength

(b)  same velocity and same wavelength

(c)  same wavelength but different velocity

(d)  same velocity but different wavelength

Answer: (a)

22. Sound source is moving towards a stationary listener with 1/10th of the speed of sound. The ratio of apparent o real frequency is

(a) 

(b) 

(c) 

(d) 

Answer: (a)

23. The diffraction effects are easier to notice in the case of sound waves than in the case of light waves because

(a)  sound waves are of longer wavelength

(b)  sound waves are mechanical waves

(c)  sound is perceived by the car

(d)  sound waves are longitudinal

Answer: (d)

24. An example of diamagnetic substance is

(a)  nickel

(b)  aluminium

(c)  copper

(d)  iron

Answer: (d)

25. Device used to measure very high temperature is

(a)  calorimeter

(b)  bolometer

(c)  thermometer

(d)  pyrometer

Answer: (d)

26. The number of degrees of freedom for molecules of a monoatomic gas is

(a)  6

(b)  5

(c)  3

(d)  4

Answer: (c)

27. Percentage of the original number of atoms in a radioactive sample remaining at the end of one mean life is

(a)  37

(b)  63

(c)  60

(d)  50

Answer: (a)

28. Choke used to limit high frequency A.C. has

(a)  iron core

(b)  air core

(c)  a diamagnetic core

(d)  a paramagnetic core

Answer: (c)

29. Kirchoff’s voltage law is based on the law of conservation of

(a)  energy

(b)  mass

(c)  charge

(d)  momentum

Answer: (a)

30. When a proton in a radioactive nucleus becomes a neutron the emitted particle is

(a)  positron

(b)  electron

(c)  π-meson

(d)  neutrino

Answer: (b)

31. An electric bulb marked 40 W, 220 V, is used in a circuit of supply voltage 100 V. Its power now is

(a)  100 W

(b)  40 W

(c)  10 W

(d)  20 W

Answer: (c)

32. Phenomenon of diffraction of light was discovered by

(a)  Fresnel

(b)  Grimaldi

(c)  Huygens

(d)  Newton

Answer: (c)

33. In a longitudinal stationary wave produced in a gas, pressure changes are maximum

(a)  at the nodes

(b)  at the antinodes

(c)  at all points

(d)  None of the above

Answer: (b)

34. The unit of power is

(a)  kilowatt

(b)  kilowatt-hour

(c)  dyne

(d)  joule

Answer: (a)

35. The surface tension of a liquid is 70 dyne/cm. It may be expressed in MKS system as

(a)  7 × 102 N/m

(b)  7 × 102 N/m

(c)  7 × 103 N/m

(d)  70 N/m

Answer: (a)

36. A cube has numerically equal volume and surface area. The volume of such cube is

(a)  216 units

(b)  1000 units

(c)  2000 units

(d)  3000 units

Answer: (a)

37. Identify the vector quantity

(a)  Time

(b)  Work

(c)  Heat

(d)  Angular momentum

Answer: (d)

38. A river is flowing from west to east at a speed of 5 m/min. A man on the south bank of the river, capable of swimming at 10m/min. in still water, wants to swim across the river in shortest time. he should swim in a direction

(a)  due north

(b)  30° west of north

(c)  30° east of north

(d)  60° east of north

Answer: (b)

39. A pendulum is suspended from five of a train moving with acceleration a. The inclination θ to the vertical is given by

(a)  0°

(b)  tan1 (a/g)

(c)  tan1 (g/a)

(d)  sin1 (a/g)

Answer: (b)

40. A bomb of mass 9 kg explodes into two pieces of mass 3 kg and 6 kg. The velocity of the mass of 3 kg is 16 m/sec. The kinetic energy of mass 6 kg is

(a)  96 J

(b)  192 J

(c)  384 J

(d)  768 J

Answer: (b)

41. The acceleration of body which is performing uniform circular motion is

(a)  v2r

(b)  v2/r

(c)  v/r

(d)  vr

Answer: (b)

42. The M.I. of a circular ring with mass M and radius R about an axis passing through its centre and perpendicular to its plane is

(a) 

(b) 

(c) 

(d) 

Answer: (b)

43. The value of Universal Gravitational Constant G in MKS system of units is

(a)  6.66 × 103

(b)  6.66 × 106

(c)  6.66 × 1011

(d)  6.66 × 105

Answer: (c)

44. The temperature of a block of iron is 140℉. Its temperature on the Celsius scale is

(a)  108°

(b)  32°

(c)  60°

(d)  140°

Answer: (c)

45. A Celsius is a unit

(a)  of electric potential difference

(b)  of trigonometric angle

(c)  equivalent to degree kelvin

(d)  equivalent to degree centigrade

Answer: (d)

46. When water is heated from 0℃ to 10℃, its volume

(a)  increases

(b)  decreases

(c)  does not change

(d)  first decreases and then increases

Answer: (d)

47. The amount of heat required to raise the temperature of 1 kg of water by 1℃ is called

(a)  kilocarloric

(b)  Calorie

(c)  B. Th. U.

(d)  Calorie/℃

Answer: (a)

48. 1 g of ice is mixed with 1 g of steam. After thermal equilibrium, the temperature of the mixture is

(a)  0℃

(b)  100℃

(c)  55℃

(d)  80℃

Answer: (b)

49. Melting point of ice is

(a)  increases with increasing pressure

(b)  decreases with increasing pressure

(c)  is independent of pressure

(d)  is proportional to pressure

Answer: (b)

50. Some quantity of tap water is place in an open pan and allowed to evaporate. After sometime the temperature of the water

(a)  decreases slightly

(b)  increases slightly

(c)  remains the same

(d)  increases considerably

Answer: (a)

51. A jar has a mixture of hydrogen and oxygen gases in the ratio 1 : 5. The ratio of mean kinetic energies of hydrogen and oxygen molecules is

(a)  1 : 16

(b)  1 : 4

(c)  1 : 5

(d)  1 : 1

Answer: (c)

52. If the pressure in a closed vessel be reduced by drawing some gas, the mean free path of the molecules

(a)  decreases

(b)  increases

(c)  remains unchanged

(d)  first increases and then decreases

Answer: (b)

53. Avagadro’s number is the number of molecules present in

(a)  one litre of the gas at NTP

(b)  22.4 litre of the gas at NTP

(c)  22.4 ml of the gas at NTP

(d)  44.8 litre of the gas at NTP

Answer: (b)

54. A cold cake bottle is left open on the pan of a balance and its weight observed from time to time. The weight

(a)  increases

(b)  decreases

(c)  increases, reaches a maximum and then starts decreasing

(d)  remains stationary

Answer: (c)

55. A sound wave has frequency 500 Hz and velocity 350 m/ sec. What is the distance between the two particle having phase difference of 60°?

(a)  0.7 cm

(b)  12.0 cm

(c)  70 cm

(d)  120 cm

Answer: (b)

56. The velocity of sound in air at 4 atmosphere and at 1 atmosphere pressure would be

(a)  1 : 1

(b)  4 : 1

(c)  1 : 4

(d)  3 : 1

Answer: (d)

57. The wavelength of sound from a tuning fork of frequency 330 Hz is nearly

(a)  100 cm

(b)  10 cm

(c)  1 cm

(d)  330 cm

Answer: (b)

58. The intensity of a sound gets reduced by 20% on passing through a slab. The reduction in intensity of passage through two consecutive slab is

(a)  40%

(b)  36%

(c)  30%

(d)  60%

Answer: (b)

59. A light bulb is placed between two plane mirrors inclined at an angle of 60°

(a)  6

(b)  2

(c)  5

(d)  4

Answer: (a)

60. A plane mirror is approaching you at 10 cm/sec. You can see your image in it. At what speed will your image approach you?

(a)  10 cm/sec

(b)  5 cm/sec

(c)  20 cm/sec

(d)  15 cm/sec

Answer: (c)

61. A bird flying high up in the air does not cast shadow on the ground because

(a)  size of the bird is smaller than sun

(b)  layers of atmosphere are dense

(c)  the light rays are not falling on it

(d)  None of these

Answer: (a)

62. The image formed by a convex mirror of focal length 30 cm is a quarter of the size of the object. Then the distance of the object from the mirror is

(a)  30 cm

(b)  90 cm

(c)  120 cm

(d)  60 cm

Answer: (b)

63. A diminished virtual image can be obtained only in a

(a)  plane mirror

(b)  concave mirror

(c)  convex mirror

(d)  parabolic mirror

Answer: (c)

64. The refractive index of a given piece of transparent quartz is greatest for

(a)  red light

(b)  violet light

(c)  green light

(d)  yellow light

Answer: (a)

65. A cut diamond sparkles because of its

(a)  hardness

(b)  high of light by the diamond

(c)  emission of light by the diamond

(d)  absorption of light by the diamond

Answer: (d)

66. A lens behaves as converging lens in air and as a diverging lens in water. The refractive index of materials is

(a)  equal to unity

(b)  equal to 1.33

(c)  between unity and 1.33

(d)  greater than 1.33

Answer: (c)

Chemistry

 

1. When ethyl hydrogen sulphate is heated at 140℃ with excess of alcohol, the product formed is

(a)  ethane

(b)  ethylene

(c)  diethyl ether

(d)  diethyl sulphate

Answer: (c)

2. Which of the following oxides of nitrogen is not a common air pollutant?

(a)  N2O

(b)  NO

(c)  NO2

(d)  N2O5

Answer: (c)

3. Man made chemical responsible for the depletion of ozone layer is

(a)  ethylene

(b)  acetylene

(c)  teflon

(d)  CFC

Answer: (d)

4. Aspirin is a/an

(a)  antibiotic

(b)  antipyretic

(c)  antiseptic

(d)  pyretic

Answer: (b)

5. SLV-3 uses propellants

(a)  solid

(b)  liquid

(c)  solid-liquid

(d)  biliquid

Answer: (c)

6. Rutherford’s scattering experiment is related to the size of the

(a)  nucleus

(b)  atom

(c)  electron

(d)  neutron

Answer: (a)

7. Electromagnetic radiation with maximum wavelength is

(a)  ultraviolet

(b)  radiowave

(c)  X-ray

(d)  infrared

Answer: (b)

8. The lightest particle is

(a)  electron

(b)  proton

(c)  neutron

(d)  None of these

Answer: (a)

9. Oleum is

(a)  castor oil

(b)  oil of vitriol

(c)  fuming H2SO4

(d)  None of these

Answer: (c)

10. Which one is known as oleum?

(a)  H2SO3

(b)  H2SO4

(c)  H2S2O8

(d)  H2S2O7

Answer: (d)

11. Peroxo acid of sulphur is

(a)  H2SO3

(b)  H2SO5

(c)  H2S2O7

(d)  None of these

Answer: (b)

12. The element which liberates O2 from water is

(a)  P

(b)  Na

(c)  F

(d)  I

Answer: (c)

13. Freon is

(a)  CCl2F2

(b)  CF4

(c)  CClF3

(d)  None of these

Answer: (a)

14. Chlorine gas dried over

(a)  CaO

(b)  NaOH

(c)  KOH

(d)  Conc. H2SO4

Answer: (d)

15. P. and M.P. of inert gases are

(a)  high

(b)  low

(c)  very high

(d)  very low

Answer: (d)

16. Percentage of Ar in air is about

(a)  1%

(b)  2%

(c)  3%

(d)  4%

Answer: (a)

17. Which of the following fluorides of xenon is impossible?

(a)  XeF2

(b)  XeF3

(c)  XeF4

(d)  XeF6

Answer: (a)

18. An isomer of ethanol is

(a)  methanol

(b)  diethyl ether

(c)  acetone

(d)  dimethyl ether

Answer: (d)

19. How many chain isomer can be obtained from the alkane C6H14 ?

(a)  4

(b)  5

(c)  6

(d)  7

Answer: (b)

20. The compound C4H10O can show

(a)  metamerism

(b)  functional isomerism

(c)  positional isomerism

(d)  All types

Answer: (d)

21. One Faraday of electricity will liberate one gram atom of the metal from a solution of

(a)  AuCl3

(b)  BaCl2

(c)  CuSO4

(d)  NaCl

Answer: (d)

22. Law of electrolysis was given by

(a)  Lamark

(b)  Ostwald

(c)  Faraday

(d)  Arrhenius

Answer: (c)

23. Al galvanic cells do not contain

(a)  a cathode

(b)  an anode

(c)  ions

(d)  a porous plate

Answer: (d)

24. The rate of reaction of substances is proportional to their

(a)  stability

(b)  molecular weight

(c)  equivalent weight

(d)  active mass

Answer: (d)

25. The law of mass action was enunciated by

(a)  Guldberg and Waage

(b)  Bodenstein

(c)  Berthelot

(d)  Graham

Answer: (a)

26. In which of the following gaseous equilibria Kp is less than Kc ?

(a)  N2SO4 ⇌ 2NO2

(b)  2HI ⇌ H2 + I2

(c)  2SO2 + O2 ⇌ 2SO3

(d)  N2 + O2 ⇌ 2NO

Answer: (c)

27. The pH of a 0.005 molar aqueous solution of sulphuric acid is approximately

(a)  0.005

(b)  2

(c)  1

(d)  0.01

Answer: (b)

28. Concentration of hydrogen ion in water is

(a)  8

(b)  1 × 107

(c)  7

(d)  1

Answer: (b)

29. The pH of normal KOH is

(a)  1

(b)  0

(c)  14

(d)  7

Answer: (c)

30. How many primary amines are possible for the formula C4H11N?

(a)  1

(b)  2

(c)  3

(d)  4

Answer: (d)

31. Which alkane would have only the primary and tertiary carbon ?

(a)  Pentane

(b)  2-Methylbutane

(c)  2, 2-Dimethylpropane

(d)  2, 2-Dimethylbutane

Answer: (d)

32. How many oxygen atoms are present in 0.5 mole of sulphur dioxide ?

(a)  6.02 × 1023

(b)  3.01 × 1023

(c)  9.03 × 1023

(d)  12.04 × 1023

Answer: (a)

33. Volume occupied by 4g CO2 is

(a)  2.24 litres

(b)  22.4 litres

(c)  224 litres

(d)  None of these

Answer: (a)

34. Which of the following sub-shell is not possible ?

(a)  2d

(b)  4f

(c)  6p

(d)  3s

Answer: (a)

35. Maximum electron in a d-orbital are

(a)  2

(b)  10

(c)  6

(d)  14

Answer: (b)

36. Number of elements present in 5th period is

(a)  8

(b)  18

(c)  32

(d)  24

Answer: (b)

37. Element with highest electron affinity is

(a)  F

(b)  Cl

(c)  Br

(d)  I

Answer: (a)

38. Which of the following has zero dipole moment?

(a)  CHCl3

(b)  CHCl2

(c)  CH2Cl

(d)  CCl4

Answer: (d)

39. Which of the following has the smallest bond angle ?

(a)  NH3

(b)  BeF2

(c)  H2O

(d)  CH4

Answer: (c)

40. The density of neon will be highest at

(a)  S.T.P.

(b)  0℃, 2 atm

(c)  273℃, 1 atm

(d)  273℃, 2 atm

Answer: (c)

41. The pressure at which one mole of a gas at 0℃ occupies a volume of al litre is

(a)  2.24 atm

(b)  4.48 atm

(c)  11.2 atm

(d)  22.4 atm

Answer: (d)

42. Which of the following is not a colloidal system ?

(a)  Milk

(b)  Blood

(c)  Ice Cream

(d)  urea dissolved in water

Answer: (d)

43. Which of the following substances is not used for preparing lyophilic sols?

(a)  Starch

(b)  Gum

(c)  Gelatin

(d)  Metal sulphide

Answer: (d)

44. Order of reaction is decided by

(a)  molecularity

(b)  Pressure

(c)  Temperature

(d)  mechanism of reaction as well as relative concentration of reactants

Answer: (d)

45. Rate constant depends on

(a)  temperature

(b)  time

(c)  initial concentration

(d)  None of these

Answer: (a)

46. Which one is used as an air purifier in spacecraft?

(a)  Quick lime

(b)  Slacked lime

(c)  Potassium superoxide

(d)  Anhydrous CaCl2

Answer: (c)

47. Melting point is lowest for

(a)  Be

(b)  Mg

(c)  Ca

(d)  Sr

Answer: (a)

48. Sea weeds are important source of

(a)  Fluorine

(b)  Chlorine

(c)  Bromine

(d)  Iodine

Answer: (d)

49. Which one of the following halogens exhibit only one oxidation state in its compounds?

(a)  Bromine

(b)  Chlorine

(c)  Fluorine

(d)  Iodine

Answer: (c)

50. Transition elements

(a)  do not act as catalysts

(b)  have low melting point

(c)  exhibit variable valency

(d)  exhibit inert pair effect

Answer: (c)

51. Percentage of silver in Germanium silver is

(a)  0%

(b)  1%

(c)  5%

(d)  None of these

Answer: (a)

52. The alloy of steel that is used for making automobile parts and utensils is

(a)  Stainless steel

(b)  Nickel steel

(c)  Tungsten steel

(d)  Chromium steel

Answer: (d)

53. Galvanization of iron denotes coating with

(a)  Al

(b)  Sn

(c)  Cd

(d)  Zn

Answer: (d)

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

(a)  MnO4

(b)  Cr(CN)3/6

(c)  NiF2/6

(d)  CrO2Cl2

Answer: (d)

55. For decolourisation of 1 mole of KMnO4, the moles of H2O2 required is

(a)  1/2

(b)  3/2

(c)  5/2

(d)  7/2

Answer: (c)

56. The metal which forms a bicarbonate is

(a)  Zn

(b)  Sr

(c)  Na

(d)  Al

Answer: (c)

57. The by-product of Solvay ammonia process is

(a)  Carbon dioxide

(b)  Ammonia

(c)  Calcium chloride

(d)  Calcium carbonate

Answer: (c)

58. The easiest and the quickest way to purify camphor is by

(a)  sublimation

(b)  distillation

(c)  chromatography

(d)  differential extraction

Answer: (a)

59. Dumas method involves the determination of nitrogen content in the organic compound in the form of

(a)  NH3

(b)  N2

(c)  NaCN

(d)  (NH4)2SO4

Answer: (c)

60. The isomers of a substance must have same

(a)  chemical properties

(b)  structural formula

(c)  molecular formula

(d)  functional groups

Answer: (c)

61. Bond length is shortest in

(a)  methane

(b)  ethane

(c)  ethylene

(d)  acetylene

Answer: (d)

62. LPG mainly contains

(a)  methane

(b)  butane

(c)  ethane

(d)  ethyne

Answer: (b)

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

(a)  CH4

(b)  C2H6

(c)  C3H8

(d)  C4H10

Answer: (a)

64. When chloroform is boiled with NaOH, it gives

(a)  formic acid

(b)  trihydroxy methane

(c)  acetylene

(d)  sodium formate

Answer: (d)

65. Allyl Chloride on dehydrochlorination gives

(a)  propadiene

(b)  propylene

(c)  allyl alcohol

(d)  acetone

Answer: (b)

66. Ann alcohol produced in the manufacture of soap is

(a)  butanol

(b)  glycerol

(c)  ethanol

(d)  ethylene glycol

Answer: (b)

Mathematics

1. is discontinuous when

(a)  x > 3

(b)  x < −3

(c)  −3 < x < 3

(d)  None of these

Answer (c)

2. is discontinuous at x = ?

(a)  0

(b)  1

(c)  −1

(d)  Both (b) and (c)

Answer (d)

3.  is equal to

(a)

(b) 

(c) 

(d) 

Answer (c)

4. If   is

(a)  2

(b) 

(c)  

(d)  None of these

Answer (a)

5. If y = a cos x + b sin x then  is equal to

(a)  y

(b)  −y

(c)  aby

(d)  None of these

Answer (c)

6. The probability of a sure event is

(a)  1

(b)  2

(c)  1/2

(d)  unlimited

Answer (b)

7. If y = aex + be−x then  is

(a)  y

(b)  −y

(c)  aby

(d)  None of these

Answer (a)

8. If y = cot x, then  is

(a)  −cosec2 x

(b)  2cosec2x cot x

(c)  cosec2x cot x

(d)  None of these

Answer (b)

9. If y = log x2, then the value of  is

(a) 

(b) 

(c) 

(d) 

Answer (b)

10. If  is

(a)  −cosec2x

(b)  −cosec x cot x

(c)  cos2 x

(d)  None of these

Answer (b)

11. 

(a) 

(b)  2 sin x cos x +c

(c) 

(d)  None of these

Answer (c)

12. 

(a) 

(b) 

(c) 

(d) 

Answer (b)

13.  is equal to

(a)  cot x – tan x + c

(b)  tan x – cot x + c

(c)  tan x + cot x + c

(d)  None of these

Answer (d)

14.  is equal to

(a)  2 tan x + c

(b) 

(c)  sec x – x + c

(d)  tan x – x + c

Answer (d)

15. The value of  is

(a)  π/2

(b)  −π/2

(c)  0

(d)  None of these

Answer (d)

16. The value of  is

(a)  2

(b)  1/2

(c)  3/2

(d)  None of these

Answer (c)

17. 

(a)  0

(b) 1

(c)  2

(d)  None of these

Answer (b)

18.  is equal to

(a) 

(b) 

(c) 

(d) 

Answer (c)

19. If n(A) = 3 and n(B) = 6 and A ⊆ B, then the number of elements in A ∪ B is equal to

(a)  3

(b)  9

(c)  6

(d)  None of these

Answer (c)

20. A relation R on a set A is called an equivalence relation if

(a)  it is reflexive

(b)  it is symmetric

(c)  it is transitive

(d)  it is reflexive, symmetric and transitive

Answer (d)

21. The number log2 7 is

(a)  an integer

(b)  a rational number

(c)  an irrational number

(d)  a prime number

Answer (c)

22. 

(a)  a rational number

(b)  an irrational number

(c)  an imaginary number

(d)  None of these

Answer (a)

23. The sum of the series  is

(a)  log 2

(b)  e1

(c)  √e

(d)  None of these

Answer (a)

24. An approximate value of log 3 correct to one place of decimal is

(a)  0.5

(b)  1.2

(c)  1.1

(d)  1.0

Answer (c)

25. Which of the following is not a measure of central tendency?

(a)  Mean

(b)  Median

(c)  Mode

(d)  Range

Answer (d)

26. The mean of first n natural numbers is

(a) 

(b)  n(n + 1)

(c) 

(d)  (n + 1)

Answer (c)

27. If the mode of a data is 18 and the mean is 24, then median is

(a)  18

(b)  24

(c)  22

(d)  21

Answer (c)

28. 49n + 16n – 1 is divisible by

(a)  3

(b)  64

(c)  19

(d)  29

Answer (b)

29. The value of 13C2 + 13C3 + …….+ 13C13 is

(a)  213 – 13

(b)  213 – 14

(c)  an odd number ≠ 213 – 12

(d)  an even number of ≠ 213 – 14

Answer (b)

30. The 4th term in the expansion of  is

(for x > 0)

(a)  independent of x

(b)  positive

(c)  negative

(d)  the only middle term

Answer (a)

31. Angle between vectors  is

(a) 

(b) 

(c) 

(d) 

Answer (d)

32. The area of the parallelogram of which  are adjacent is

(a)  2

(b)  1/2

(c)  1

(d)  √2

Answer (c)

33. The unit vector perpendicular to vectors  forming a right-handed system is

(a)

(b)

(c)  

(d) 

Answer (a)

34. The value of n, when nP2 = 20 is

(a)  3

(b)  4

(c)  6

(d)  5

Answer (d)

35. If 2 + i√5is a root of a quadratic equation then the other root is

(a)

(b) 

(c) 

(d) 

Answer (c)

36. If 3 − √7 is a root of a quadratic equation then the other root of it is

(a)  3 + √7

(b)  √3 + 7

(c)  √7 – 3

(d)  None of these

Answer (a)

37. If the roots of the equation x2 – ax + b = 0 are reciprocal to each other then

(a)  b = 0

(b)  b = 1

(c)  b = a

(d)  None of these

Answer (b)

38. If sum of the two roots of a quadratic equation is 8 and product of the two roots is 9 then the quadratic equation is

(a)  x2 – 8x + 9 = 0

(b)  x2 + 8x + 9 = 0

(c)  x2 + 9x + 8 = 0

(d)  None of these

Answer (a)

39. If x + iy = 0 then

(a)  x = 0, y = 1

(b)  x = y = 0

(c)  x = y = 1

(d)  None of these

Answer (b)

40. The value of  is

(a)  −1

(b)  +1

(c)  i

(d)  −i

Answer (b)

41. The value of  where  is

(a)  2i

(b)  0

(c)  √2

(d)  None of these

Answer (c)

42. The complex conjugate of 2 + 5i is

(a)  2 – 5i

(b)  5 + 2i

(c)  5 – 2i

(d)  None of these

Answer (a)

43. If tan x tan 3x = 1 then tan x is

(a)  1

(b) 

(c) 

(d)  None of these

Answer (d)

44. Given that,  and θ lies in the 4th quadrant, then the value of cos θ is

(a) 

(b) 

(c) 

(d) 

Answer (c)

45. The number of solutions of the equation  lying between 0 to 2π is

(a)  1

(b)  2

(c)  3

(d)  4

Answer (c)

46. If sin θ = 1, the value of θ (0 ≤ θ < 360°) is

(a)  270°

(b)  180°

(c)  0°

(d)  90°

Answer (d)

47. The point (−3, 6) lies in the

(a)  1st quadrant

(b)  2nd quadrant

(c)  3rd quadrant

(d)  4th quadrant

Answer (b)

48. Which one is polar co-ordinate?

(a)  (2, 3)

(b)  (3, π/3)

(c)  (5, 9)

(d)  None of these

Answer (b)

49. The cartesian co-ordinates of the point whose polar co-ordinates are (3, π/6), are

(a) 

(b) 

(c) 

(d) 

Answer (b)

50. The distance between two points (3, 5) and (8, 10) is

(a)  2√5

(b)  5

(c)  5√2

(d)  None of these

Answer (c)

51. The slop of the line 2x + 3y – 5 is

(a)  2/3

(b)  −2/3

(c)  3/2

(d)  None of these

Answer (b)

52. The equation of the line parallel to X-axis and at a distance of 5 units from it is

(a)  x = 5

(b)  x + y = 5

(c)  y = 5

(d)  None of these

Answer (c)

53. The angle made by the straight line y = −x with the positive direction of X-axis is

(a)  −45°

(b)  45°

(c)  135°

(d)  None of these

Answer (c)

54. The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 is

(a)  3/2

(b)  3/10

(c)  6

(d)  None of these

Answer (b)

55. The equation of the circle whose centre is (0, 0) and radius is 5, is

(a)  x2  + y2 = 25

(b)  (x – 5)2 + (y – 5)2 = 52

(c)  x2 + (y – 5)2 = 52

(d)  None of these

Answer (a)

56. The equation k(x2 + y2 – 2x – 2y – 1) = 0 where k ≠ 0 represents

(a)  a circle

(b)  a parabola

(c)  an ellipse

(d)  a pair of straight lines

Answer (a)

57. The latus rectum of the parabola y2 = −48x is

(a)  −48

(b)  −12

(c)  48

(d)  12

Answer (b)

58. The length of the radius of the circle x2 + y2 + 4x – 7y – t = 0 is 9/2, then value of t is

(a)  8

(b)  4

(c)  2

(d)  None of these

Answer (c)

59. The co-ordinates of the locus of the parabola y2 = 2ax which passes through the point of intersection of the straight lines  are

(a)  (3, 10)

(b)

(c)  (10, 3)

(d)  None of these

Answer (b)

60. The length of the latus rectum of the parabola y2 = 25x is

(a)  6

(b)  25

(c)  25/2

(d)  None of these

Answer (b)

61. The value of |x| when x = −3, is

(a)  −3

(b)  3

(c)  ±3

(d)  None of these

Answer (b)

62. √3 is a

(a)  rational number

(b)  irrational number

(c)  real number

(d)  None of these

Answer (b)

63. If f(x) = loge x and g(x) = ex, then g{f(x)} is

(a)  ex

(b)  loge x

(c)  x

(d)  None of these

Answer (c)

64. If f(x) = |x| – 2x, then the value of f(−4) is

(a)  4

(b)  −12

(c)  12

(d)  None of these

Answer (c)

65. If  then  is

(a)  1

(b)  −1

(c)  1/2

(d)  None of these

Answer (a)

66. 

(a)  2

(b)  1/2

(c)  1

(d)  None of these

Answer (b)

67. 

(a)  1/2

(b)  2

(c)  0

(d)  None of these

Answer (b)

68. The value of  is

(a)  loge 2/loge 3

(b)  loge(2/3)

(c)  loge(3/2)

(d)  None of these

Answer (b)

Biology

1. Which one of the following is not a fish

(a)  Lung fish

(b)  Whale

(c)  Saw fish

(d)  Dog fish

Answer (a)

2. Phylloclade is a modification of

(a)  root

(b)  stem

(c)  leaf

(d)  None of these

Answer (b)

3. Prickles in rose are

(a)  modified leaves

(b)  accessory buds

(c)  exogenous in origin

(d)  endogenous in origin

Answer (d)

4. As a tree grows older, which increases rapidly in thickness ?

(a)  its heart wood

(b)  its sap wood

(c)  its cortex

(d)  Phloem

Answer (a)

5. Annual rings are distinct in plants growing in

(a)  Tropics

(b)  Artic zones

(c)  Grass land

(d)  Temperate

Answer (a)

6. Winter sleep is known as

(a)  Hibernation

(b)  Aestivation

(c)  Nocturnal

(d)  None of these

Answer (b)

7. The efferent process of neuron is known as

(a)  Axon

(b)  Dendrite

(c)  Cyton

(d)  Neurofibrillae

Answer (b)

8. Cilia are formed by

(a)  Dictyosome

(b)  Centrioles

(c)  Peroxisome

(d)  Lysosome

Answer (b)

9. Who proved that plant cells are totipotent?

(a)  Steward

(b)  Haberlandt

(c)  Muir

(d)  Maheshwari

Answer (b)

10. The two strands of DNA are held together by

(a)  Nitrogen

(b)  Carbon

(c)  Oxygen

(d)  Hydrogen

Answer (d)

11. The smallest RNA is

(a)  m-RNA

(b)  t-RNA     

(c)  r-RNA

(d)  Chromosomal RNA

Answer (c)

12. In mitosis, nuclear envelop and nucleolus disappear during

(a)  Prophase

(b)  Interphase

(c)  Metaphase

(d)  Telophase

Answer (a)

13. Colchicine influences

(a)  DNA replication

(b)  organization of spindle

(c)  chromosome condensation

(d)  chromosome division

Answer (a)

14. Gurad cells differ from epidermal cells in having

(a)  mitochondria

(b)  vacuoles

(c)  cell wall  

(d)  chloroplast

Answer (d)

15. Plasmolysis occurs due to

(a)  Absorption

(b)  Osmosis

(c)  Endosmosis

(d)  Exosmosis

Answer (c)

16. Die-back disease of citrus is caused by

(a)  B

(b)  Mn

(c)  Cu

(d)  Zn

Answer (c)

17. Lack of which element has made some plants insectivorous?

(a)  Iron

(b)  Sodium

(c)  Nitrogen

(d)  Magnesium

Answer (b)

18. Chloroplast fix

(a)  O2

(b)  H2

(c)  CO2

(d)  N2

Answer (b)

19. Carbon-dioxide acceptor in C3 plants is

(a)  PEP

(b)  PGA

(c)  RMP

(d)  RuBP

Answer (b)

20. Fermentation is performed by

(a)  all microorganisms

(b)  some fungi & some bacteria

(c)  all bacteria

(d)  all fungi

Answer (c)

21. Total ATP produced during EMP pathway is

(a)  6

(b)  7

(c)  24

(d)  36

Answer (a)

22. Hormone responsible for apical dominance is

(a)  IAA

(b)  GA

(c)  ABA

(d)  Florigen

Answer (d)

23. Movement of auxin is

(a)  Acropetal

(b)  Basipetal

(c)  Centripetal

(d)  Both (b) & (c)

Answer (a)

24. The first permanent teeth develops at the age of

(a)  3 years

(b)  5 years

(c)  4 years

(d)  6 years

Answer (a)

25. Vermiform appendix is a part of

(a)  Intestine

(b)  Liver

(c)  Stomach

(d)  Rectum

Answer (b)

26. Percentage of O2 present in inhaled air in man is about

(a)  21%

(b)  1%

(c)  78%

(d)  43%

Answer (b)

27. Blood contains CO2 in which of the following forms?

(a)  NaHCO3

(b)  Carbonic acid

(c)  Hb-CO2

(d)  Hb-CO2 and CO

Answer (d)

28. Chordae tendineae in the heart are found in

(a)  ventricle

(b)  left auricle

(c)  right auricle

(d)  None of these

Answer (b)

29. Human spleen

(a)  controls pulse rate

(b)  secretes hormones

(c)  regulates heart beat     

(d)  controls blood volume

Answer (a)

30. Mark the odd one

(a)  Ammonotelism

(b)  Micturition

(c)  Ureotelism

(d)  Uricotelism

Answer (b)

31. Which one of the following are not filtered in the glomerulus?

(a)  Urea

(b)  Blood cells

(c)  Water

(d)  Glucose

Answer (d)

32. In human body, the number of bones is

(a)  106

(b)  426

(c)  306

(d)  None of these

Answer (d)

33. The tissue with highest total glycogen content is

(a)  kidney

(b)  Muscle

(c)  Liver

(d)  Nerve

Answer (c)

34. Iris is a part of

(a)  sclerotic

(b)  choroid

(c)  choroid and retina

(d)  sclerotic & choroid

Answer (b)

35. Which one of the following called false fruit ?

(a)  Apple

(b)  Mango

(c)  Orange

(d)  Guava

Answer (c)

36. How many cells does a pollen grain have ?

(a)  One

(b)  Two

(c)  Three

(d)  Four

Answer (d)

37. How many spermatozoa are produced from five secondary spermatocytes ?

(a)  2

(b)  3

(c)  8

(d)  10

Answer (b)

38. The spermatogonia of an animal contains 32 chromosomes. What will be the number of spermatids chromosomes in it?

(a)  16

(b)  18

(c)  20

(d)  22

Answer (a)

39. How many chromosomes are present in the nucleus of a human sperm?

(a)  21

(b)  22

(c)  23

(d)  24

Answer (a)

40. What percentage of sperms are there in an ejaculate vigorous motility, for normal fertility?

(a)  40% of the sperms

(b)  50% of  the sperms

(c)  30% of the sperms

(d)  10% of the sperms

Answer (b)

41. How many eggs do you think were released by the ovary of a female dog which gave birth of 6 puppies ?

(a)  5

(b)  6

(c)  7

(d)  12

Answer (d)

42. How many eggs are released by a human ovary in a month ?

(a)  One egg

(b)  Two eggs

(c)  Three eggs

(d)  Four eggs

Answer (a)

43. Humans are

(a)  oviparous

(b)  viviparous

(c)  ovoviviparous

(d)  None of these

Answer (a)

44. STDS are also called

(a)  Venereal diseases (VDS)

(b)  Reproductive tract infections (RTI)

(c)  Both (a) and (b)

(d)  Medical termination of pregnancy

Answer (a)

45. A body has blood group AB. What is true of the inheritance of this blood group in his case?

(a)  His parents should be one with O group and the other with B group

(b)  His parents should be one with O group and the other with A group

(c)  Both his parents should be with B group

(d)  His parents should e with A group and mother with B group

Answer (d)

46. Mention the age group where STDS are reported to be very high occurrence

(a)  10-12 years

(b)  12-14 years

(c)  15-24 years

(d)  20-24 years

Answer (d)

47. How many types of gametes are produced by an individual with genotype Aa Bb?

(a)  4

(b)  5

(c)  6

(d)  7

Answer (b)

48. How many different phenotypes are formed in the 16-squares in a Punnet square as a result of dihybrid cross?

(a)  2

(b)  4

(c)  6

(d)  8

Answer (b)

49. The egg of an animal contains 10 chromosomes, of which one is X-chromosome. How many autosomes would be there in the karyotype of this animal?

(a)  2 pairs

(b)  3 pairs

(c)  9 pairs

(d)  18 pairs

Answer (a)

50. How many autosomes are found in a single mature human sperm?

(a)  22

(b)  24

(c)  26

(d)  28

Answer (b)

51. Which of the following changes is the cause for sickle cell anaemia ?

(a)  Glutamic acid to valine

(b)  Glutamic acid to methionine

(c)  Glutamic acid to alanine

(d)  Glutamic acid to tyrosine

Answer (c)

52. Which one of the following disorders appears more in human males than in females ?

(a)  Phenylketonuria

(b)  Sickle-cell anaemia

(c)  Red-green colour blindness

(d)  Albinism

Answer (a)

53. Down’s syndrome is caused due to

(a)  Monosomy of 21st chromosome

(b)  Trisomy of 21st chromosome

(c)  an extra Y-chromosome in male

(d)  an extra X-chromosome in female

Answer (d)

54. A hemophilic man marries a normal homozygous woman. What is the probability that their daughter will be hemophilic?

(a)  100%

(b)  75%

(c)  50%

(d)  0%

Answer (d)

55. If a double standed DNA has 20 percent of cytosine, calculate the percentage of adenine in that DNA.

(a)  30%

(b)  35%

(c)  40%

(d)  60%

Answer (a)

56. The complementary strand of a DNA synthesized on a template of DNA with the codons TAGCATACT is

(a)  ATCGTATGA

(b)  AUCGGATTGA

(c)  ATGGUATGA

(d)  ATCGTATCA

Answer (c)

57. How many base pairs are present in one full turn of DNA helix ?

(a)  5

(b)  10

(c)  15

(d)  20

Answer (b)

58. What is the length of the pitch of the helix ?

(a)  3.4 nm

(b)  4.3 nm

(c)  34 nm

(d)  43 nm

Answer (b)

59. What is the distance between two base pairs in a strand of DNA ?

(a)  3.4 nm

(b)  0.34 nm

(c)  0.04 nm

(d)  0.24 nm

Answer (a)

60. What is approximate length of DNA in a typical mammalian cell ?

(a)  2.2 m

(b)  2.4 m

(c)  2.8 m

(d)  3.0 m

Answer (b)

61. The smallest unit of classification is

(a)  Family

(b)  Order

(c)  Genus

(d)  Species

Answer (c)

62. The largest herbarium of the world is located at

(a)  Geneva

(b)  Berlin

(c)  New York

(d)  Kew

Answer (d)

63. Red tides are produced by

(a)  Red algae

(b)  Dinoflagellates

(c)  Diatoms

(d)  Phaeophyceae

Answer (d)

64. The cell wall of diatoms is formed of

(a)  cellulose

(b)  pectin

(c)  cellulose and silica

(d)  cellulose and chitin

Answer (a)

65. Venter is the part of

(a)  Sporogonium

(b)  Sporangium

(c)  Antheridium

(d)  Archegonium

Answer (b)

66. Which of the following is least likely to occur along the sea coast ?

(a)  Green algae

(b)  Brown algae

(c)  Red algae

(d)  Mosses

Answer (d)

67. Continued secretion of milk is maintained by

(a)  Aldsterone

(b)  Progesterone

(c)  Oestrogen

(d)  Prolactin

Answer (a)

68. Macropus is

(a)  Prototherian

(b)  Marsupian

(c)  Eutherian

(d)  Amphibian

Answer (a)