aieee 2011 fst iii qns

7/28/2019 Aieee 2011 Fst III Qns

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1. If z1 and z2 are two nonzero complex

numbers such that z1 z

2= z

1 z

2,

then arg z1 arg z2 is equal to

(1) 0 (2)

2(3)

2(4)

2. If the roots of the quadratic equation

x2 +px +q =0 are tan 30 and tan 15respectively, then the value of

5 + q p is

(1) 0 (2) 5 (3) 6 (4) 3

3. The trigonometric equation

sin 1 x =2 sin 1a, has a solution for

(1) all real values of a

(2) a < 12

(3) a 1

2

(4)1

2< a 2 (4) 2 < r < 8

5. The number of integral terms in the

expansion of 3 8

5

256

is(1) 33 (2) 34 (3) 35 (4 ) 32

6. If f(x) =sin x, g(x) =x2, h(x) = logex and

F(x) = (h g f) (x), then F(x) is

(1) 2 cosec 2 x

(2) 2 cosec 2 x

(3) 2x cot x2

(4) 2 cot x2 4 x2 cosec2 x2

7. The number of values of k for which the

equation x3 3x + k = 0 has two

different roots lying in the interval (0, 1)are

(1) 0 (2) 2

(3) 3 (4) infinitely many

Brilliant Tutorials Pvt. Ltd. AIEEE/FST 3/MPC/Obj/Qns - 2

PA RT A : M A THEM A TIC S

SPAC E FO R RO UG H WO RK


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8. Direction ratios of normal to the planewhich passes through the points (1, 0, 0)

and (0, 1, 0) which makesangle

4with

x + y = 3 are

(1) 1, 1, 2 (2) 2,1,1

(3)1, 1, 2 (4)1, 2,1

Questions 9 to 14 are Assertion-Reason type

questions. Select the correct choice from thefollowing options:

(1) Statement 1 is true, statement 2 is true,

statement 2 is no t a correct explanation

for statement 1.

(2) Statement 1 is true, statement 2 is false.

(3) Statement 1 is false, statement 2 is true.

(4) Statement 1 is true, statement 2 is true,

statement 2 is a correct explanation forstatement 1.

9 . Sta t e m e n t 1 : If the roots of x2 +px +q =0

are both greater than 1,

then the roots of x2 px +

q =0 are both less than 1

Sta tem ent 2 : If is a root of f(x) =0, then is a root of f( x) = 0.

1 0. Sta te m e n t 1: The number of termsin the

expansion of

(a + b + c + d)5 is 56.

Sta tem ent 2 : The number of non-

negative integral solutionsof x + y + z + t = 5 is 56.

1 1. Sta te m e n t 1: If cosec2 = 4xyx y

2,

then x = y.

Sta tem ent 2 : cosec21.

1 2. Sta te m e n t 1: The solution of the

differential equationdy

dx=

x

y, y(5) = 3 is the

entire hyperbolax2 y2 = 16.

Sta tem ent 2 : y(5) = 3 no part of the

curve lies above the X-

axis.


SPACE FOR ROUGH WORK


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20. If

a b c a2

b c a b2

c a b c2

= 0, then the line

ax + by + c = 0 passes through

(1) (1, 1) (2) ( 1, 1)

(3) (0, 1) (4) (1, 1)

21. 10 different letters of the alphabet are

given. Words with 5 letters are formedwith these given letters. The number ofwords which have at least one letterrepeated is

(1) 59720 (2) 79260

(3) 69760 (4) None of these

22. The point of intersection of the lines

x5

3=

y7

1=

z2

1and

x3

36=

y3

2 =

z6

4is

(1) (2, 10, 4) (2) 21,5

3,10

3

(3) (5, 7, 2) (4) ( 3, 3, 6)

23. If the mean of n observations

12, 22 , 32 , ... , n2 is46n

11, then n =

(1) 11 (2) 12 (3) 23 (4 ) 22

24. If f() = tan

2(1 + sec ) (1 + sec 2)

(1 +sec 4) (1 + sec 8) (1 +sec 16),

then f

64=

(1) 1 (2) 12

(3) 1

4(4)

1

16

25. If in a G.P. tp +q =m a nd tp q =n, then

tp =

(1) mn (2) mn

(3) m

n(4)

n

m

26. If z22i = 1, then the minimum

value of z =

(1) 2 21 (2) 2 2

(3) 2 21 (4) 2 22




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27. If the normal to the rectangularhyperbola xy = c2 at the point ct ,

c

t

meets the curve again at ct ,c

t,

then

(1) t3t = 1 (2) t3t = 1

(3) tt = 1 (4) tt = 1

28. The number of divisors of 1029, 847, 122

are in

(1) G.P. (2) H.P. (3) A.P. (4) A.G.P.

29. xe x dx =

(1) 2 xe x4 xe x

(2) 2x4 x4 e x

(3) 2x4 x4 e x

(4) 4 x e x

30. The compound statement (p q) is

logically equivalent to

(1) p q (2) p q

(3) p q (4) p q




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31. The Youngs modulus of steel is

2 1011 N/m2. The interatomic distance

of the particles in steel is 2.8. If a stress

of 109 N/m2 is applied, then the change

in interatomic distance will be (in )

(1) 7 10 3 (2) 14 10 3

(3) 21 10 3 (4) 28 10 3

32. The resistivity of metals (where

temperature T is in C)

(1) always varies as T5

(2) is independent of temperature

(3) increases linearly with room tempe-

rature and above

(4) attains a constant value (nonzero)

as temperature tends to absolute

zero

33. If the earth suddenly contracts to half its

radius, then the length of the day willbe

(1) 24 hours only

(2) 12 hours

(3) 6 hours

(4) 48 hours

34. A transformer has an efficiency of 80%.

It is connected to a power output of 4 kW and 100 V. if the secondaryvoltage is 240 V, then the secondarycurrent is

(1) 4.6 A (2) 40 A

(3) 4.3 A (4) 13.3 A

35. An Amplitude-Modulated radio receiver

is to be used forspeech (500 Hz) and formusic (5 kHz). The minimum possiblebandwidths of the RF amplifier (Br) and

AF amplifier (Ba) are respec tively

(1) 10 kHz and 0.5 kHz

(2) 5 kHz and 1 kHz

(3) 10 kHz and 4.5 kHz

(4) 5.5 Hz and 500 Hz



PART B : PHYSIC S


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36. In the photomultiplier tube (PMT), foreach electron incident, six leave the

dynode. These six are acc elerated to a

second dynode, so produc ing 36

electrons, which are all acc elerated to

the third dynode, and so on.

The electron emitted from the tenth

dynode are collected and constitute a

current of 7.2 nA. The incident light has

a wavelength of 365 nm. At this

wavelength one in three of the incident

photons ejects an electron from the

photocathode. The power of incident

light is of the order of 610 610

7

(1) 10 12

W (2) 1 W

(3) 10 15 W (4) 10 3 W

37. Hydrogen atom does no t emit X-rays

because

(1) its energy levels are too close to

each other

(2) its energy levels are too far apart

(3) it is too small in size

(4) it has a single elec tron

38. What is work done in enlarging the size

of soap bubble from 2 cm to 4 cm

diameter?

(Given: surface tension of soap solution

is 2 10 2 N/m)

(1) 24 10 6 J

(2) 12 10 6 J

(3) 48 10 6 J

(4) 4 10 2 J




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39. A rectangular loop of coil rotates in amagnetic field. The induced voltage

will be maximum at

(1) 0 and 180

(2) all through 360

(3) 180 and 360

(4) 90 and 270

40. Given two statements:

(A ) Magnetic flux through a closed

surface is zero

(R) Gauss law applies in case of

elec tric flux only

(1) Both A and R are true and R is

correc t reason for A

(2) Both A and R are true but R is no t

correc t reason for A

(3) A is true but R is false

(4) A is false but R is true

41. An LC resonant c irc uit c ontains a

c apac itor 400 pF and an induc tor

100 H. It is set to oscillations (by coupling

to an antenna). The wavelength of the

radia ted elec tromagnetic wave is

(1) 176 m (2) 377 m

(3) 5298 (4) 400 nm

42. Given two statements:

Sta tem ent 1 : Narrower the open organ

pipe, higher will be the

pitch.

Sta tem ent 2 : The frequency of open

organ pipe depends on its

radius.

(1) Both statements statement 1 andstatement 2 are true and statement 2

is reason for statement 1

(2) Both statement 1 and statement 2

are true but statement 2 is no t

reason for statement 1

(3) Statement 1 is true but statement 2

is false

(4) Statement 1 is false but statement 2

is true

43. Three point charges q, q and 2q are

located at (0, a, a), (0, a, a) and

(0, 0, a) respectively. The net dipole

moment of this charge distribution is

(1) 4aq k (2) 2qa k

(3) 4qa i (4) 2qa j




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44. Which one of the following disinteg-ration series of the heavy elements will

give 209 Bi as a stable nucleus?

(1) Thorium series

(2) Neptunium series

(3) Uranium series

(4) Actinium series

45. The ratio of the rise in temperature of a

gas when compressed adiabatically to

that when compressed isothermally to

the same extent

(1) is more than 1

(2) is less than 1

(3) is equal to 1

(4) depends on the gas

46. Monochromatic energy density (U)

(i.e., perunit volume) of the radiation of

a blackbody is proportional to (where

is wavelength)

(1) T4

(2) 5

(3)

5

2 (4) T

5

4

Da ta for que stions 47 and 48

Two blocks A and B of masses 2 kg and

4 kg are placed one overthe other as shown.

A time-varying horizonta l force F = 2t is

applied on upper block (Here t is in second

and F is in Newton).

The coefficient of friction between A and

B is =1

2and the horizontal surface over

which B is placed is smooth (g = 10 m/s2)

47. The maximum ac celeration of B can be

(1) 1.5 m/s2 (2) 2.5 m/s2

(3) 10 m/s2 (4) 3.5 m/s2




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48. Given two following statementsstatement 1 and statement 2 about the

graphs between acc elerations aA and

aB versus t.

Sta tem ent 1 : For t 7.5 s, aA versus t or

aB

versus t graph is a

straight line passing through

origin and of slope1

3

Sta tem ent 2 : For t 7.5 s, aA versust is astraight line parallel to t-

axis but aB

versus t is a line

of slope1

3and intercept 2


are true

(2) Only statement 1 is true

(3) Only statement 2 is true


are false

49. By capturing an electron Mn25

54

transforms into Cr24

54releasing

(1) a neutrino (2) an antineutrino

(3) an -particle (4) a positron

50. The diameter of aperture of a plano-

convex lens is 6 cm and its maximum

thickness is 3 mm. The velocity of light in

the material of lens is 2 108 m/s. The

focal length of lens is

(1) 15 cm (2) 6 cm

(3) 30 cm (4) 37.5 cm

51. In Youngs experiment, the third bright

band for wavelength of light (source A)

6000 coincides with the fourth brightband for another source B in the same

arrangement. The wavelength of the

source B is

(1) 6289 (2) 4500

(3) 2250 (4) 6000

52. Two simple pendula of length L and 16 L

are in phase at the mean position at a

certa in instant. If T is the period of

shorter pendulum, then the minimumtime after which they will be again in

phase is

(1) T

3(2)

2T

3

(3)3T

2(4)

4T

3




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53. Identify the function F generated by thelogic network shown below.

(1) F = (X + Y) Z

(2) F = Z Y YX

(3) F =ZY Y X

(4) F = XYZ

54. Which one of the following is no t a

correct statement about semicon-

duc tors?

(1) The electrons and holes have

different mobilities in a semicon-

ductor.

(2) In an n-type semiconductor, the

fermilevel lies closer to theconduction band edge.

(3) Silicon is a direct band gap semi-

conductor.

(4) Silicon has diamond crystal

structure.

55. Given below is the performance of twolearners A and B.

Whic h one of the following c an be

deduced from the graph?

(1) The learning task was difficult

(2) The learning task was easy

(3) B learned faster than A throughout

the task

(4) A learned faster than B throughout

the task

56. A partic le is pro jected from point A

towards a building of height h as shown

at an angle of 60 with horizontal. It

strikes the roof of build ing at B at as

angle of 30 with the horizontal. The

speed of projection is




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(1) gh (2) 2gh (3) 3gh (4) 2 gh

57. The random error in the arithmetic

mean of 100 observations is x. Then, the

random error in the arithmetic mean of

400 observations will be

(1) 4x (2) 1

4x (3) 2x (4)

x

2

Da ta for que stions 58 , 59 and 60

A uniform circular lamina with centre at O

mass m and radius a is free to rotate about a

tangent AB at P which is fixed horizontally. The

lamina is initially held at rest with its plane

horizontal and then released.

58. The angular velocity of the laminawhen it has turned through an angle of

30 will be

(1) g

a(2)

g

3a

(3) 2g

5a(4) 2

g

a

59. The linear speed v of the centre O of

the lamina when the plane becomesvertical is

(1) 2ga (2) 22ga

5

(3) 3ga (4) ga

60. If a perfectly inelastic peg located at

distance a vertically below P stops the

lamina bringing it to instantaneous rest,

then the impulsive reaction at themoment of impact is

(1) m 2ga (2) zero

(3) m 1.6ga (4) mga




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67. X;

The X in the reaction is

(1) phenyl acetate

(2) acetophenone

(3) benzoic acid

(4) benzophenone

68. 0.66 g of a metal was deposited when

a current of 2 amperes is passed

through a metal ion solution for 100

seconds. The electrochemical equivalent

of the cell is

(1) 3.3 10 3 (2) 3.3 10 4

(3) 0.033 (4) 3.3

69. The maximum amount of BaSO4

precipitated on mixing BaCl2

0.5 M with

H2

SO4

I M will corresponds to

(1) 0.5 M (2) 1.0 M

(3) 1.5 M (4) 2.0 M

70. When 3,3-dimethyl-2-butanol is heated

with H2SO

4, the product obtained is

(1) cis and trans isomers of2, 3 dimethyl-2-butene

(2) 3, 3-dimethyl-1-butene

(3) 2, 3-dimenthyl-2-butene

(4) 2, 3-dimethyl-1-butene

71. Reaction between acetone and chloro-

form in the presence of a strong base

will be

(1) chloral

(2) 2-chloro propene

(3) 2-3-dichloro propene

(4) chloretone

72. When phenol is treated with CHCl3

and

NaOH and acidification the product

formed is

(1) salicylaldehyde

(2) salicylic ac id

(3) benzoic acid

(4) benzaldehyde




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73. Which of the following spec ies haslowest ionisation potential?

(1) O (2) O2

(3)O2

(4)O

2

74. The free energy change for a reversible

reaction a t equilibrium is

(1) zero (2) small positive

(3) small negative (4) large positive

75. On the basis of Le-Chatelliers principle,

the condition that is unfavourable for

the formation of SO3

is

2SO2(g)

+ O2(g)

2SO3(g)

;

H = 42 kcal

(1) low pressure

(2) high pressure

(3) high temperature

(4) high concentration of SO2

76. The rate constant for the reaction2N

2O

5(g) 4NO2(g) + O2(g)

is 3.0 10 5 sec 1. If the rate is

2.4 10 5 mol lit 1 sec 1, then the

concentration of N2O5 in mol lit 1 is

(1) 1.4 (2) 1.2 (3) 0.04 (4 ) 0.8

77. Variable valency is a characteristic of

(1) halogens

(2) transition elements

(3) alkali metals

(4) noble gases

78. Hydrogen behaves as an oxidising

agent in its reaction with

(1) chlorine (2) nitrogen

(3) sodium (4) sulphur

79. The process for the manufac turing of

Na2CO3 is

(1) van-Arkel proc ess

(2) Nelsons process

(3) Solvays process

(4) Down process




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80. Which of the following oxides is mostalkaline in nature ?

(1) B2O

3 (2) Al

2O

3

(3)In2O

3 (4) Tl

2O

81. When alumina is heated with carbon in

the atmosphere of nitrogen then the

products formed are

(1) Al + CO2 (2) Al + CO

(3) Al + CO + N2 (4) AlN + CO

82. Which is anhydride of orthophosphoric

ac id ?

(1) P4O10 (2) P2O5

(3) P4O

6 (4) P

2O

3

83. Bromine water reacts with SO2 to form

(1) H2O and HBr

(2) H2SO4 + HBr

(3) HBr + S

(4) S and H2BrO4

84. Which of the following ion disproportio-

nates in aquous solution?

(1) Cu3+ (2) Fe3+

(3) Cu+ (4) Cu2+

85. The IUPAC name of 4-isopropyl-m-xylene is

(1) 4-isopropyl-m-xylene

(2) 1-isopropyl-2, 4-dimethyl benzene



86. Ethyl ester X; X is

(1)

(2)

(3)

(4)




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87. .

The product B is

(1) propene (2) propyne

(3) propanone (4) propanal

88. Which one of the following compounds

can undergo Cannizzaros reaction?

(1) (CH3)2 CHCHO (2) CH3CH2CHO

(3) C6H

5CHO (4) HCHO

89.

; The product B is

(1) phenol

(2) chlorobenzene

(3) o-cresol

(4) meta-chloroaniline

90.

;

C - in the reaction is

(1) butyric ac id

(2) butanol

(3) butanal

(4) n-butane




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READ THE FOLLOWING INSTRUCTIONS CAREFULLY


1. The candidates should fill in the required particulars on the Test Booklet and Answer Sheet(Side-1) with Blue/Black Ball Point Pen.

2. For writing/marking particulars on Side-2 of the Answer Sheet, use Blue/Black Ball PointPen only.

3. The candidates should not write their Roll Numbers anywhere else (except in the specifiedspace) on the Test Booklet/Answer Sheet.

4. For each incorrect response, one-fourth of the total marks allotted to the question would bededucted from the total score. No deduction from the total score, however, will be made ifno response is indicated for an item in the Answer Sheet.

5. Handle the Test Booklet and Answer Sheet with care, as under no circumstances (exceptfor discrepancy in Test Booklet Code and Answer Sheet Code) will another set be provided.

6. The candidates are not allowed to do any rough work or writing work on the Answer Sheet.All calculations/writing work are to be done in the space provided for this purpose in the TestBooklet itself, marked Space for Rough Work.

7. On completion of the test, the candidates must hand over the Answer Sheet to theInvigilator on duty in the Room/Hall. However, the candidates are allowed to take awaythis Test Booklet with them.

8. Each candidate must show on demand his/her Admit Card to the Invigilator.

9. No candidate, without special permission of the Superintendent or Invigilator, should leavehis/her seat.

10. The candidates should not leave the Examination Hall without handing over their AnswerSheet to the Invigilator on duty and sign the Attendance Sheet again. Cases where acandidate has not signed the Attendance Sheet a second time will be deemed not to havehanded over the Answer Sheet and dealt with as an unfair means case. The candidatesare also required to put their left hand THUMB impression in the space provided inthe Attendance Sheet.

11. Use of Electronic/Manual Calculator and any Electronic Item like mobile phone etc., isprohibited.

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14. Candidates are not allowed to carry any textual material, printed or written, bits ofpapers, pager, mobile phone, electronic device or any other material except the AdmitCard inside the examination hall/room.

aieee 2011 fst iii qns

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