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ENVIRONMENTAL CHEMISTRY, & CHEMISTRY IN EVERYDAY LIFE, DEFINITE & INDEFINITE

INTEGRALS & AREA UNDER THE CURVE & DIFFERENTIAL EQUATIONS

1. When a circular coil of radius 1m and 100 turns is rotated in a horizontal uniform magnetic field, the peak value of emf induced is 100V. The coil is unwound and then rewound into a circular coil of radius 2m. If it is rotated now, with the same speed , under similar conditions , the new peak value of emf developed is a) 50 V b) 25V c) 100 V d) 150V e) 200 V

2. A copper disc of radius 0.1 m is rotated about its centre with 20 rev s-1 in a uniform magnetic field 0.1 T with its plane perpendicular to the field. The emf induced across the radius of the disc is

a) π

V20

b) π

V20

c) 20πm V d) 10πm V e) 2πm V 3. The magnitude of the earth`s magnetic field at a

place is B0 and the angle of dip is δ. A horizontal conductor of length l lying magnetic North South moves Eastwards with a velocity v, the emf induced across the conductor is a) Zero b) B0lvsin δ c) B0 sin δ d) Bolv cos δ e) B0vsin δ/l

4. A short solenoid of length 4cm, radius 2cm and 100 turns is placed inside and on the axis of a long solenoid of length 80cm and 1500 turns. A current of 3 A flows through the short solenoid. The mutual inductance of two solenoids is a) 2.96 ×10-4H b) 5.3 ×10-5H c) 3.52×1 10-3 H d) 8.3 ×110-5 H e) 2.96×1 10-3 H

5. The core of a transformer is laminated to reduce a) flux leakage b) output power c) hysteresis d) eddy current e) none of these

6. A transformer has an efficiency of 80%. It is connected to a power input of 5 kW at 200 V. If the secondary voltage is 250V,the primary and secondary currents are respectively a) 25A , 20A b) 20A , 16A c) 25A , 16A d) 40A , 16A e) 40A,16A

7. If E=100 sin (100t) volt and I =100 sin

1003

tπ +

mA are the instantaneous values of

voltage and current are respectively a) 70.7V,70.7mA b) 70.7V,707A c) 141.4V,141.4mA d) 141.4V,141.4A e) 100V,100 mA

8. The impedance of a R-C circuit is Z1 for frequency f

and Z2 for frequency 2f. Then , 1

2

Z

Zis

a) between 1 and 2 b) 2

c) between1

2 and 1 d)

1

2 e) 4

9. In an L-C-R series AC circuit the voltage across L,Cand R is 10V each. If the inductor is short circuited , the voltage across the capacitor would become

a) 10V b) 20

2V c) 20 2V d) 10

2V e) 20V

10. The resonance frequency of the tank circuit of an

oscillator when L= 2

10

πmH and C=0.04 µF are

connected in parallel is a) 250 kHz b) 25 kHz c) 2.5 kHz d) 25 MHz e) 2.5 kHz

11. An alternating voltage e=200 sin 100 t is applied to a series combination R= 30Ω and an inductor of 400mH . The power factor of the circuit is a) 0.01 b) 0.2 c) 0.05 d) 0.042 e) 0.6

12. When a DC voltage of 200V is applied to a coil of

self-inductance 2 3

π H, a current of 1A flows

through it. But by replacing DC source with AC source of 200V, current in the coil is reduced to 0.5A.Then the frequency of AC supply is a) 100Hz b) 75 Hz c) 60Hz d) 30Hz e) 50Hz

13. In an L-R circuit ,the value of L is 0.4 π

H and the

value of R is 30. If in the circuit , an alternating emf of 200V at 50 cycle is connected, the impedance of the circuit and current will be a) 11.4 Ω, 17.5 b) 30.7Ω,6.5 A c) 40.4 Ω , 5A d) 50 Ω ,4A e) 35 Ω , 6.5

14. The electric field of an electromagnetic wave travelling through vacuum is given by the equation. E=E0 sin(kx-ωt) . The quantity that is independent of wavelength is

a) k

ω b) kω c) ω d) k e) k2ω

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15. The electric field of a plane electromagnetic wave varies with time of amplitude 2 Vm-1 propagating along Z- axis . The average energy density of the magnetic field is (in Jm-3) a) 13.29 ×10-12 b) 8.85 ×10-12 c) 17.72× 10-12 d) 4.43 ×10-12 e) 2.22 ×10-12

16. The refractive index and the permeability of a medium are 1.5 and 5× 10-7 Hm -1 respectively. The relative permittivity of the medium is nearly a) 25 b) 15 c) 81 d) 10 e) 6

17. A plane EM wave travels in free space along X-axis. At a particular point in space , the electric field along Y- axis is 9.3 Vm-1 .The magnetic induction is a) 3.1 ×10-8 T b) 3× 10-5 T c) 3 ×10-6 T d) 9.3 ×10-6 T e) 3.1 ×10-7 T

18. A ) The wavelength of microwaves is greater than that of ultraviolet rays. B) The wavelength of infrared rays is lesser than that of ultraviolet rays C) The wavelength of microwaves is lesser than that of infrared rays D) γ–rays has shortest wavelength in the electromagnetic spectrum a) A and B are correct b) B and C are correct c) C and D are correct d) A and C are correct e) A and D are correct

19. A light ray of wavelength 5895Å travelling in vacuum enters a medium of refractive index 1.5 .The speed of light in the medium is a) 3× 108 ms-1 b) 2 × 108 ms-1 c) 1.5 × 108 ms-1 d) 6× 108 ms-1 e) 5× 107 ms-1

20. The focal length of the lens refractive index (µ=1.5) in air is 10cm.If air is replaced by water of µ=4/3, its focal length is a) 20cm b) 30cm c) 40cm d) 25cm e) 35cm

21. A plane electromagnetic wave travelling along the X–direction has a wavelength of 3 mm. The variation in the electric field occurs in the Y-direction with an amplitude 66Vm-1. The equations for the electric and magnetic field as a function of x and t are respectively

a) 1133cos 10y

xE t

c = π× −

7 111.1 10 cos 10z

xB t

c− = × π× −

b) 1133cos 10y

xE t

c = π× −

7 1111 10 cos 2 10y

xB t

c− = × π× −

c) 1133cos 10x

xE t

c = π× −

7 1111 10 cos 10y

xB t

c− = × π× −

d) 1166cos 2 10y

xE t

c = π× −

7 112.2 10 cos 2 10z

xB t

c− = × π× −

e) 1166 cos 10y

xE t

c = π× −

7 112.2 10 cos 10z

xB t

c− = × π× −

22. Two plane –concave lenses (1 and 2 ) of glass of refractive index 1.5 have radii of curvature 25 cm and 20cm.They are placed in contact with their curved surfaces towards each other and the space between them is filled with liquid of refractive index 4/3.Then , the combination is

a) convex of focal length 70cm b) concave of focal length 70cm c) concave of focal length 66.6cm d) convex of focal length 66.6cm e) concave of focal length 72.5 cm

23. If the angle of minimum deviation is of 600 for an equilateral prism, then the refractive index of the material of the prism is a ) 1.41 b) 1.5 c) 1.6 d) 1.33 e) 1.73

24. If the ratio of amount of scattering of two light waves is 1:4 , the ratio of their wavelength is

a) 1:2 b) 2 :1 c) 1:√2 d) 1:1 e) 2:1 25. Identify the mismatch in the following

a) Myopia – Concave lens b) For rear view – Concave mirror c) Hypermetopia – Convex lens d) Astigmatism – Cylindrical lens e) Reflecting telescope – Convex mirror

26. Magnification at least distance of distinct vision, of a simple microscope having its focal length 5cm is a) 2 b) 4 c) 5 d) 6 e) 7

27. A narrow slit of width 2mm is illuminated by monochromatic light of wavelength 500nm. The distance between the first minima on either side on a screen at a distance of 1 m is a) 5mm b) 0.5 mm c) 2.5mm d) 10mm e) 2.5 mm

28. Light of wavelength 6000 Å falls on a single slit of width 0.1mm. The second minimum will be formed for the angle of diffraction of a) 0.08 rad b) 0.06 rad c) 0.12rad d) 0.15 rad e) 0.012 rad

29. Two beams of light of intensity I1 and I2 interfere to give an interference pattern. If the ratio of maximum intensity to that of minimum intensity is

25

9, then 1

2

I

Iis

a) 5/3 b) 4 c) 81/625 d) 16 e) 2 30. If the polarizing angle of a piece of glass for green

light is 54.740 , then the angle of minimum deviation for an equilateral prism made of same glass is (Given, tan 54.740=1.414) a) 450 b) 54.740 c) 600 d) 900 e) 300

31. The flux linked with a circuit is given by ϕ=t3+3t-7. The graph between time (x-axis ) and induced emf(y-axis) will be a a ) straight line through the origin b) straight line with positive intercept c) straight line with negative intercept d) parabola through the origin e) parabola not through the origin

32. A square coil of side 25cm having 1000 turns is rotated with an uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is e = 200 sin 100πt. The magnetic induction is a) 0.50T b) 0.02T c) 10-3 T d) 0.1T e) 0.01T

33. If E0 is the peak emf, I0 is the peak current and ϕ is the phase difference between them, then the average power dissipation in the circuit is

a) 0 0

1

2E I b) 0 0

2

E I

c) 0 0

1sin

2E I φ d) 0 0

1cos

2E I φ

e) 0 0

1tan

2E I φ

34. A resistor 30Ω , inductor of reactance 10 Ω and capacitor of reactance 10 Ω are connected in series to an AC voltage source e=300√2 sin(ωt) . The current in the circuit is a) 10√ 2 A b) 10A c) 30√11A d) 30/√11A e) 5A

35. For the L-C-R circuit shown in the figure, what is the resonance frequency and the amplitude of the current at the resonating frequency ?

a) 2500 rads-1 and 5√2A b) 2500 rads-1 and 5A

c) 2500 rads-1 and 5

2A

d) 250 rads-1 and 5√2A e) 25 rads-1 and 5√2A

36. The dielectric constant of air is 1.006. The speed of electromagnetic wave travelling in air is a×108ms-1, where , a is about a) 3 b) 3.88 c) 2.5 d) 3.2 e) 2.8

37. In an electromagnetic wave, direction of propagation is in the direction of a) E. b) B c) E×B d) None of these e) B×E

38. A square wire of side 1 cm is placed perpendicular to the principle axis of a concave mirror of focal length 15cm at a distance of 20cm.The area enclosed by the image of the wire is a) 4 cm2 b) 6 cm2 c) 2 cm2 d) 8 cm2 e) 9 cm2

39. The wavelength of red light from He-Ne laser is 633 nm in air but 474 nm in the aqueous humor inside the eye ball. Then , the speed of red light through the aqueous humor is a) 3 ×108 ms-1 b) 1.34 ×108 ms-1 c) 2.25 ×108 ms-1 d) 2.5 ×108 ms-1 e) 2.75× 108ms-1

40. The refractive index of water is 4/3 and that of glass is 5/3 what will be critical angle for the ray of light entering water from the glass ?

a) 1 4sin

5−

b) 1 5sin

4−

c) 1 1sin

2−

d) 1 2sin

1−

e) None of these 41. In the following reaction

The major product is

e) None of these

42. Decreasing order of reactivity in Williamson’s ether synthesis of the following is: I. Me3CCH2Br II. CH3CH2CH2Br III. CH2 = CHCH2Cl IV. CH3CH2CH2Cl a) III > II > IV > I b) I > II > IV > III c) II > III > IV > I d) I > III > II > IV e) II > IV > III > I

43. Identify the product of the reaction

PhC ≡ CMe 2

3H O ,Hg+ +

→ ? a) PhCH2CH2CHO b) PhCOCH2CH3 c) PhCH2COCH3 d) PhCOCOMe e) PhCOCH2CH2CH3

44. Positive carbylamine test is shown by a) N, N – dimethylaniline b) Triethylamine c) N – methylaniline d) p – methylbenzylamine e) dimethylamine

45. Which of the following exists as zwitter ion? a) p – aminophenol b) salicylic acid c) sulphanilic acid d) ethanolamine e) All of these

46. In the diazotisation of aniline with sodium nitrite and hydrochloric acid, the excess of hydrochloric acid is used primarily to a) suppress the concentration of free amine b) suppress the hydrolysis to phenol c) ensure a stochiometric amount of nitrous acid d) neutralise the base liberated e) None of these

47. Among the alkenes which one produces tertiary butyl alcohol on acid hydration? a) CH3CH2CH = CH2 b) CH3CH = CHCH3 c) (CH3)2C = CH2 d) CH3CH = CH2

e) CH3CH = CHCH2CH3 48. Which of the esters shown, after reduction with

LiAlH 4 and aqueous work up, will yield two molecules of only a single alcohol? a) C6H5COOC6H5 b) CH3CH2COOCH2CH3 c) C6H5COOCH2C6H5 d) CH3COOCH3 e) CH3COOCH2CH2CH3

49. Among the following four compounds (i) phenol (ii) methyl phenol (iii) meta- nitrophenol (iv)para – nitrophenol The acidity order is a) (iv) > (iii) > (i) > (ii) b) (iii) > (iv) > (i) > (ii) c) (i) > (iv) > (iii) > (ii) d) (ii) > (i) > (iii) > (iv) e) (iv) > (i) > (iii) >(ii)

50. Which of the following will not be soluble in sodium bicarbonate? a) 2,4,6 – Trinitrophenol b) Benzoic acid c) o – Nitrophenol d) Benzenesulphonic acid e) None of these

51. The major product (s) of the following reaction is (are)

a) P b) Q c) R d) S e) None of these

52. The sweetest artificial sweetening agent among the following is a) aspartame b) sucrolose c) alitame d) sucrose e) Neotame

53. Air pollution causing photochemical oxidants production include a) carbon monoxide,sulphur dioxide b) Nitrous oxide, nitric acid fumes,nitric oxide c) Ozone,peroxyacetyl nitrate,aldehydes d) Oxygen,chlorine,fuming nitric acid.

54. Identify the product Y in the following reaction sequence

a) Pentane b) Cyclobutane c) Cyclopentane d) Cyclopentanone e) Butane

55. Arrange the following compounds in increasing order of their reactivity in nucleophilic addition reactions. Ethanal (I), Propanal (II), Propanone (III), Butanone (IV) a) III <II < I < IV b) II < I < III < IV c) IV < III < II < I d) I < II < III < IV e) IV < II < III < I

56. Oxidation of acetaldehyde with selenium dioxide produces a) Ethanoic acid b) Methanoic acid c) Glyoxal d) Oxalic acid e) Butanoic acid

57. Bromination of PhCOMe in acetic acid medium produces mainly

58. Aldol condensation does not occur between a) two different aldehydes b) two different ketones c) an aldehyde and a ketone d) an aldehyde and an ester e) an aldehyde and lactone

59. The compound formed as a result of oxidation of ethylbenzene by alkaline KMnO4 is: a) benzyl alcohol b) benzophenone c) acetophenone d) benzoic acid e) None of these

60. The correct acidity order of the following is

a) (III) > (IV) > (II) > (I) b) (IV) > (III) > (I) > (II) c) (III) > (II) > (I) > (IV) d) (II) > (III) > (IV) > (I) e) (I) > (IV) > (II) > (III)

61. Among the given compounds, the most susceptible to nucleophilic attack at the carbonyl group is a) CH3COCl b) CH3COOCH3 c) CH3CONH2 d) CH3COOCOCH3 e) CH3CHO

62. Which of the following compounds will not undergo Friedel – Crafts reaction easily? a) Nitrobenzene b) Toluene c) Cumene d) Xylene e) None of these

63. Identify the major product of the following reaction:

64. The strongest base in aqueous solution among the

following amines is a) N , N - diethylethanamine b) N – ethylethanamine c) N - methylmethanamine d) ethanamine e) phenylmethanamine

65. Anilinium hydrogen sulphate on heating with sulphuric acid at 453 – 473 K produces a) benzenesulphonic acid b) anthranilic acid c) aniline d) m – aminobenzenesulphonic acid e) sulphanilic acid

66. Which of the following statements about primary amines is ‘False’? a) Alkylamines are stronger bases than ammonia b) Alkylamines are stronger bases than aryl amines c) Alkylamines react with nitrous acid to produce alcohols d) Arylamines react with nitrous acid to produce phenols e) Aryl amines react with HNO2 to form diazonium salts.

67. Ribose and 2- deoxyribose can be differentiated by a) Fehling’s solution b) Tollen’s reagent c) Barfoed’s reagent d) Osazone formation e) Molisch’s test

68. Methyl α - D(+) – glucoside and methyl β -D(+)-

glucoside are a) epimers b) anomers c) enantiomers d) conformers e) None of these

69. The monomers of buna – S- rubber are a) vinyl chloride and sulphur b) butadiene c) styrene and butadiene d) isoprene and butadiene e) Phenol and formaldehyde

70. In the reaction the products are

71. The catalyst used for olefin polymerization is

a) Ziegler – Natta catalyst b) Wilkinson catalyst c) Raney nickel catalyst d) Merrified resin e) Platinum catalyst

72. The class of drugs used for the treatment of stress is a) analgesics b) antiseptic c) antihistamine d) tranquillizers e) Anesthetic

73. The organic detergent that is used in hair conditioners is a) sodium dodecylbenzene sulphonate b) sodium lauryl sulphate c) tetramethylammonium chloride d) sodium stearyl sulphate e) cetyltrimethylammonium bromide

74. Which of the following statements are not correct? (i) F- ion concentration above 2 ppm causes brown mottling in teeth. (ii) Excessive F- (over 10 ppm) causes harmful effect to bones and teeth (iii) Excessive lead in drinking water causes disease methemoglobinemia (iv) Deficiency of sulphate in drinking water causes laxative effect. a) (ii) and (iv) b) (ii) and (iii) c) (ii), (iii) and (iv) d) (iii) and (iv)

75. Column I Column II Distinguish By A) Methanol and ethanol (p) Lucas reagent B) Phenol and cyclohexanol (q) sodium metal C) n- Butyl alcohol and tert (r) Iodoform test butyl alcohol D) Methanol and diethyl ether (s) Ferric chloride a) A – q, B – s, C– p, D – r b) A – s, B – p, C– q, D – r c) A – p, B – q, C– r, D – s d) A – r, B – s, C– p, D – q

76. Which of the following alcohols gives the best yield of dialkyl ether on being heated with a trace of sulphuric acid? a) 2- pentanol b) cyclopentanol c) 2- methyl -2-butanol d) 2- propanol e) 1- pentanol

77. In the following sequence of reactions, what is D?

a) Primary amine b) An amide c) Phenyl isocyanate d) Chain lengthened hydrocarbon

78. Cellulose upon acetylation with excess acetic anhydride /H2SO4 (catalytic) gives cellulose triacetate whose structure is

79. Among cellulose, poly (vinyl chloride), nylon and

natural rubber, the polymer in which the intermolecular force of attraction is weakest is a) Nylon b) poly (vinyl chloride) c) Cellulose d) natural rubber

80. Under column – I, a list of gases that are known to have a greenhouse effect’ is given. Relate them to their main source selecting from the list given under column – II Column – I Column – II A Nitrous oxide from

car exhausts 1 Secondary pollutant

B Chlorofluorocarbons (CFCs)

2 Combustion of fossil fuels , wood , etc

C Methane 3 Denitrification D Ozone (O3) 4 Refrigerators,

aerosol, sprays E Carbon dioxide 5 Cattle, rice fields,

toilets a) A – 3 , B – 4 , C – 5 , D – 1 , E – 2 b) A – 5 , B – 1 , C – 3 , D – 4 , E – 2 c) A – 4 , B – 5 , C – 1 , D – 2 , E – 3 d) A – 1 , B – 3 , C – 4 , D – 5 , E – 2

81. 1 cosx+∫ dx is equal to

a) 2 sin 2

xC +

b) 2 sin

2

xC

+

c) 1 sin2 2

xC

+

d) 2sin

2 2

xC

+

e) 2 2 sin2

xC

+

82. If I 1 = 1 1 22sin sin 1 ,x dx and I x dx− −= −∫ ∫

then a) I1 = I2

b) I2 = 12I

π

c) I1 + I2 = 2

x Cπ +

d) I1 + I2 = 2

π

e) None of these

83. If 2

1 ( ) ,

1

d df x then

dx x dx=

+f(x 3) is equal

to

a) 3

3

1

x

x+ b)

2

6

3

1

x

x+

c) ( )

5

26

6

1

x

x

−

+ d)

5

6

6

1

x

x

−+

e) tan -1 x

84. If u = - f ′′ (θ) sin θ + f ′ (θ) cos θ and v = f ′′ (θ) cos θ + f ′ (θ) sin θ, then

1/22 2du dv

d dθ θ +

∫ d θ is equal to

a) f (θ) - f ′ (θ) + C b) f (θ) + f ′′ (θ) + C c) f ′ (θ) + f ′′ (θ) + C d) f ′ (θ) - f ′′ (θ) + C e) f (θ) + f ′ (θ) + C

85. 4

2 4 2 1/2

1

( 1)

xdx

x x x

−+ +∫ is equal to

a) 4 2 1x x

Cx

+ + +

b) 2

4 2 1

xC

x x+

+ +

c) x (x4 + x2 + 1)3/2 + C

d) 4 3 1x x

Cx

+ + +

e) 4 2 1x x C+ + +

86. 2

(1 )

sin ( )

x

x

x e dx

xe

+∫ dx is equal to

a) – cot (ex) + C b) tan (xex) + C c) tan (ex) + C d) cot (xex) + C e) – cot (xex) + C

87. 2(1 )

xxedx

x+∫ is equal to

a) 1

xeC

x

− ++

b) 1

xeC

x+

+ c)

1

xxeC

x+

+∫

d) 1

xxeC

x

− ++

e) ( )2

1

xeC

x+

+

88. ( )sin 2cos sinxe x x x dx isequal to+∫

a) ex cos x + C b) ex sinx + C c) ex sin2 x + c d) ex sin2 x + c e) ex (cos x + sinx) + C

89. 4 6

9 4

x x

x x

e e

e e

−

−

+−∫ dx is equal to

a) 23 35log | 9 4 |

2 35xx e C+ − +

b) 23 36log | 9 4 |

2 36xx e C+ − +

c) 23 35log | 9 4 |

2 36xx e C− + − +

d) 25 35log | 9 4 |

2 36xx e C− + − +

e) 25 35log | 9 4 |

2 66xx e C+ − +

90. 2

cos sin

cos

x x x

x x x

++∫ dx is equal to

a) sin

log1 cos

xC

x+

+ b)

sinlog

cos

xC

x x+

+

c) 2sin

logcos

xC

x x+

+ d)

sinlog

cos

x xC

x x+

+

e) logcos

xC

x x+

+

91. 1

(log )ex ex∫

dx is equal to

a) loge (1 – loge x) + C b) loge (loge ex –1) + C c) loge (loge x –1) + C d) loge (loge x + x) + C e) loge (1 + loge x) + C

92. 1tan ,1

xIf dx A x B x C

x−= + +

+∫ then

a) A = 1, B = 1 b) A = 1, B = 2 c) A = 2, B = 2 d) A = 2, B = - 2 e) A = - 2, B = - 2

93. If f (x) = tan x – tan3 x + tan 5 x - … ∞

with 0 < x < 4

π then

/4

0( )f x dx is equal to

π

∫

a) 1 b) 0 c) 1

4

d)1

2 e) -

1

4

94. The value of 1 (1 )

e

e

dt

t t− +∫ is

a) 0 b) log 1

e

e +

c) log 1

1 e +

d) log (1+e) e) 1

95. ( )3 31

1( )x x x xe e e e− −

−+ −∫ dx is equal to

a) 2

22

ee− b) e2 – 2e

c) 2 (e2 – e) d) 2e-2 – 2e e) 0

96. If 0 0

(2 ) ( ) ,a a

f a x dx m and f x dx n− = =∫ ∫ then

2

0 ( )

af x dx∫ is equal to

a) 2m + n b) m + 2n c) m – n d) n – m e) m + n

97. If /2

0 0(sin ) (sin ) ,x f x dx A f x dx

π π=∫ ∫ then A

is equal to

a) 0 b) π c) 4

π d) 2 π e) 3 π

98. If/2 6

0

5sin ,

32x dx then the value

π π=∫ of

6 6(sin cos )x x dxπ

π−+∫ is

a) 5 π / 8 b) 5π / 16 c) 5π / 2 d) 5 π / 4 e) 5π / 32

99. 2 2

0[ ]x dx∫ is equal to

a) 2 - 2 b) 2 + 2

c) 2 - 1 d) 2 3− − e) none of thse 100. If f (x) = x – [x], for every real x, where [x] is

the greatest integer less than or equal to x. Then

, 1

1( )f x

−∫ dx is equal to

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

2

101. The value of sin/2

sin cos0

2

2 2

x

x xdx

π

+∫ is

a) 2 b) π c) 4

π d) 2π e)

2

π

102. The area in the first quadrant between x2 + y2 = π2 and y = sin x is

a) 3 8

4

π − b)

3

4

π

c) 3 16

4

π − d)

3 8

4

π − e)

3

2

π

103. Area (in sq units) bounded by the curves y = ex , y = e – x and the straight line x = 1 is

a) e + 1

e b) e +

12

e+ c) e +

1

e-2

d) e - 1

e+2 e) e -

1

e

104. The area (in sq units) of the region bounded by the curves y2 = 4ax and x2 = 4ay, a > 0 is

a) 16 2

3

a b) 14

2

3

a

c) 132

3

a d) 16a2 e) None of these

105. The area (in sq units) of the plane region bounded by the curve x = y2 – 2 and the line y = - x is

a) 13

3 b)

2

5 c)

9

2

d) 5

2 e)

13

2

106. The given figure shows a ∆ AOB and the parabola y = x2 . The ratio of the area of the ∆ AOB to the area of the region AOB of the parabola y = x2 is equal to

a) 3

5 b)

3

4 c)

7

8 d)

5

6 e)

2

3

107. The area bounded by y = |sin x|, X – axis and the lines |x| = π is a) 2 sq units b) 3 sq units c) 4 sq units d) 5 sq units e) None of these

108. The area bounded by y = sin – 1 x, x = 1

2and X

– axis is

a) 1

12

+

sq units

b) 1

12

−

sq units

c) 4 2

π sq units

d)1

14 2 2

π + −

sq units

e) none of these 109. The area bounded by the parabola y2 = 8x and its

latusrectum is a) 16/3 sq units b) 32/3 sq units c) 8/3 sq units d) 64/3 sq units e) 4/3 sq units

110. The family of curves y = ea sin x, where a is an arbitrary constant is represented by the differential equation

a) log y = tan x dy

dx

b) y log y = tan xdy

dx

c) y log y = sin x dy

dx

d) log y = cos xdy

dx

e) y log y = cos xdy

dx

111. The order and degree of the differential equation 3/4 1/32 2

21

dy d y

dx dx

+ =

are

a) (2,4) b) (2,3) c) (6,4) d) (6,9) e) (2,12)

112. The differential equation representing the family of curves y = xecx (c is a constant) is

a) dy

dx= 1 log

y y

x x −

b)dy

dx= log 1

y y

x x +

c) dy

dx= 1 log

y y

x x +

d) dy

dx+1 = log

y y

x x

e) dy

dx = 1 log

x y

y x +

113. The order and degree of the differential equation

sin ( ) cos ( )x dx dy x dx dy+ = − are a) (1,2) b) (2,2) c) (1,1) d) (2,1) e) (0,1)

114. The general solution of the differential equation

( 2 )y x xdye e e x

dx−= + + is

a) e-y = ex – e – x + x2 + C b) e-y = e- x – ex - x2 + C c) e – y = - e – x – ex – x2 + C d) ey = e – x + ex + x2 + C e) ey = e – x + ex + C

115. The solution of cos ydy

dx = ex + sin y + x2 e siny is

a) ex – e – sin y + 3

3

xC=

b) e-x - e –sin y + 3

3

xC=

c) ex + e – sin y + 3

3

xC=

d) ex – e sin y - 3

3

xC=

e) ex – e sin y +3

3

xC=

116. The solution of dy

dx = 1 + y + y2 + x + xy + xy2

is

a) 1 22 1tan

3

yx x C− + = + +

b) 1 24 14 tan 3(2 )

3

yx x C− + = + +

c) 1 23 13 tan 4(1 )

3

yx x C− + = + + +

d) 1 22 1tan 4(2 )

3

yx x C− + = + +

e) 1 22 14 tan 3(2 )

3

yx x C− + = + +

117. The solution of e dy/dx = (x + 1), y (0) = 3 is a) y = x log x – x + 2 b) y = (x + 1) log |x + 1| - x + 3 c) y = (x + 1) log |x + 1| + x + 3 d) y = x log x + x + 3 e) y = - (x + 1) log | x + 1| + x + 3

118. An integrating factor of the differential equation

(1 + x2) dy

dx + xy = x is

a) 21

x

x+ b) 21

log(1 )2

x+ c) 21 x+

d) x e) 2

1

1 x+

119. The integrating factor of the different equation (y log y) dx = (log y – x ) dy is

a) 1

log y b) log (log y)

c) 1 + log y d) 1

log(log )y e) log y

120. The solution of the differential equation dy

dx =

2

1

x y+ is

a) y = – x2 – 2x – 2 + Cex b) y = x2 +2x +2 – Cex c) x = – y2 – 2y +2 – Cey d) x = – y2 – 2y –2 + Cey e) x = y2 + 2y +2 – Cey

KKEERRAALLAA MMOODDEELL EENNTTRRAANNCCEE EEXXAAMM

RREEPPEEAATTEERRSS –– EENNGGIINNEEEERRIINNGG ((MMOODDUULLEE –– II)) EELLEECCTTRROOMMAAGGNNEETTIICC IINNDDUUCCTTIIOONN,, AALLTTEERRNNAATTIINNGG CCUURRRREENNTT, ELECTOMAGNETIC WAVES ,RAY

OPTICS& OPTICAL INSTRUMENTS ,WAVE OPTICS ,ALCOHOLS, PHENOLS &

ETHERS,ALDEHYDES,KETONES & CABOXYLIC ACIDS, AMINES, BIMOLECUELS, POLYMERS,

ENVIRONMENTAL CHEMISTRY, & CHEMISTRY IN EVERYDAY LIFE, DEFINITE & INDEFINITE

INTEGRALS & AREA UNDER THE CURVE & DIFFERENTIAL EQUATIONS

AANNSSWWEERR KKEEYY VVEERRSSIIOONN CCOODDEE –– AA

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

E C B A D C A A D B E E D A B

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

E A E B C D D E B B D A E D E

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

E E D B B A C E C A A C B D C

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

A C C A C B C C C C C D D D A

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

A A D B E D D B C D A D E D D

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

E C A D A E C B B D E B C C E

91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

E D C D E E B D E A C A C A C

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

B C D B B A C C B C E B C E B

AANNSSWWEERR KKEEYY VVEERRSSIIOONN CCOODDEE –– BB

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

B A D A A B E D A B E A E B B

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

D D D D E C C D E E D B A C C

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

E B A E E C A E E B D A D E D

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

C A D C B C A B B D A D B C A

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

C A D C D C C C C C D A E D C

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

A D E D A B D B C E C E B E E

91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

C C C C B A C C B E C B E C E

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

D D E D A A A B B D B C B E C

2288..0022..1199

First No: Version code: A Second No: Version code: B1. 20

2. 21

3. 1

4. 2

5. 3

6. 22

AANNSSWWEERRSS AANNDD SSOOLLUUTTII

Second No: Version code: B

7. 4

8. 5

9. 23

10. 6

11. 24

IIOONNSS

12. 7

13. 8

14. 9

15. 10

16. 11

17. 12

18. 13

19. 14

20. 30

21. 16

22. 17

23. 31

24. 15

26. 18

27. 33

28. 34

29. 19

30. 38

31. 25

32. 39

33. 26

34. 40

35. 27

36. 28

37. 29

38. 35

39. 36

40. 37

41. 80

42. 64

44. 65

46. 52

47. 66

48. 51

49. 60

50. 67

51. 53

55. 49

56. 70 oxidation of acetaldehyde with SeOglyoxal

57. 74 Under acidic conditions, reaction stops at the monobromination stage. Thus, option (d) is correct.

58. 41

60. 62

61. 42

62. 72

63. 48

64. 58

66. 45

oxidation of acetaldehyde with SeO2 gives

Under acidic conditions, reaction stops at the monobromination stage. Thus, option (d) is

67. 57

68. 54

70. 43

76. 78 1o Alcohols on treatment with a trace of Hgive best yields of dialkyl ethers. i.e. 1pentanol.

77. 46

78. 56 Cellulof one glucose unit and Cthree free OH groups at 2, 3 and 6 positions, therefore, OAc groups appear at Cpositions. Thus, option (a) is correct

79. 79 Natural rubberforces of attraction.

Alcohols on treatment with a trace of H2SOgive best yields of dialkyl ethers. i.e. 1- pentanol.

Cellulose has β- glycosidic linkages between Cof one glucose unit and C4 of the other. It has three free OH groups at 2, 3 and 6 positions, therefore, OAc groups appear at C2, C3 and Cpositions. Thus, option (a) is correct

Natural rubber has the weakest intermolecular forces of attraction.

SO4

glycosidic linkages between C1 of the other. It has

three free OH groups at 2, 3 and 6 positions, and C6

has the weakest intermolecular

81. 89

82. 101

83. 81

84. 102

85. 82

86. 103

87. 83

88. 104

89. 84

90. 105

91. 85

92. 106

93. 86

94. 107

95. 87

96. 108

97. 88

98. 109

99. 90

100. 110

101. 91

102. 111

103. 92

104. 112

105. 93

106. 113

107. 94

108. 115

109. 95

110. 116

111. 96

112. 117

113. 97

114. 118

115. 98

116. 119

117. 99

118. 120

120. 114