Aieee Home Practice Test 1 2012

7/30/2019 Aieee Home Practice Test 1 2012

1/11

Vidyam andir Classes 1

Aggarw al Corporat e He ights, 3rd Floor, Plot No . A - 7, N eta ji Subha sh Place,

Pitam Pura, Delhi - 110034 Phone: 011-45221190-93. Fax : 25222953

AIEEE Hom e Practice Test - 1 / 20 12

TIM E : 3 .00 Hrs M .M . : 360

Read t he fo llow ing Instructions very care fully before you proceed.

The paper cont ains a tot al of 90 question s

Section - I : Physics, Section - II : Chem istry & Section - III : M ath em atics.

Each que stion carries 4 M arks.1 w ill awarded for every w rong answ er (Negative M arking).

For answe ring a q uestion an AN SW ER SHEET is provided separately.

Please follow th e directions in th e question p aper. Please darken t he ent ire circle that correspoyour answ er for each qu estion . Use only HB pencil to m ark answ er, and erase pencil marks comto m ake a change.

Do not scribble anyt hing on th e answ er sheet.

Please Fill your Roll Nu m ber & Persona l Inform ation Properly in the space provided in t he AN SW ER SH

W rong w ay of filling Right w ay of fillingA B C D A B C D A B C D

Please fill the follow ing inform ation

N A M E

ROLL N U M BER

Invigilato rs Signa tu re


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2 Vidyam and ir Classes

SECTION - I (Chem istry) 30 4 = 121. A mixture of aluminium and zinc weighing 1.67 g was completely dissolved in acid and evolved 1.69 litre of H2 at NTP.

The weight of aluminium at the original mixture is :(A) 2.24 g (B) 1.24 g (C) 6.8 g (D) 4.2 g

2. Which combination is best explained by the coordinate covalent bond ?(A) 2H H O (B) Cl + Cl (C) 2

1Mg O

2(D) H2 + I2

3. If a is the initial concentration of the reactant, the half life period of the reaction of nth order is proportional to :(A) n 1a (B) an (C) 1 na (D) an + 1

4. In the sequence of following nuclear reactions.n238 218

92 84X Y Z L M

The value of n will be :(A) 3 (B) 4 (C) 5 (D) 6

5. Borax structure contains :(A) two BO4 groups and two BO3 groups (B) four BO4 groups only(C) four BO3 groups only (D) three BO4 and one BO3 groups

6. In an isobaric process the ratio of heat supplied to the system d and work done by the system (dW) for diatomic gas is(A) 1 : 1 (B) 7 : 2 (C) 7 : 5 (D) 5 : 7

7. The azeotropic mixture of water (b. pt.100 C) and HCl (b.pt.85 C) boils at108.5 C. When this mixture is distilled it is

possible to obtain :(A) pure HCl (B) pure water(C) pure water as well as HCl (D) neither HCl nor H2O in their pure states

8. The solubility of AgCl will be minimum in a sample of water containing :(A) AgNO3 (B) pure water (C) CaCl2 (D) Na

9. 38 6 4NHC H O X Y

The compound X is :(A) o-xylene (B) phthalic acid (C) phthalic anhydride (D) salicyclic acid

10. Which shows the least dipole moment ?(A) CHCl3 (B) CH3CH2OH (C) CH3COCH3 (D) CCl4

11. Which of the following is most stable ?(A) Na3N (B) Li3N (C) K3N (D) Rb3N

12. The compound reacts with MeMgI to give A and with Me2CuLi to give B. What are A and B

(A) (B) (C) (D)

O

ClO

Me

O

MeMe

Me

MeCl

OMgIMe

Cl

OMgIMe O

Me Me

OMgIMe

Cl

OLiMe


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13. For a gas in equilibrium with a liquid, the ratio of the concentration of the gas in the solution phase to that in thphase is constant at constant temperature only if molecules undergo :(A) ionization (B) dissociation (C) isolation (D) reaction with solvent

14. Number of optical isomers of lactic acid are :(A) 1 (B) 2 (C) 3 (D) 4

15. Which of the following reactions would convert 2-butanol into deuterated compound3 2 3CH CH C H CH|D

?

(A) (B)

(C) (D)

16. In a cubic closed packed structure of mixed oxides, the lattice a made up of oxide ions, one eighth of tevoids are occupied by divalent ions (A2+), while one half of the octahedral voids are occupied by trivalent (B3+). What is the formula of the oxide ?(A) A3B2O4 (B) A2B2O4 (C) AB2O5 (D) AB2O4

17. Which of the following represents the correct sets of the four quantum numbers of a 4d electron ?

(A) 4, 2, 1, 0 (B) 14, 2, 1,2

(C) 14, 3,2,2

(D) 14, 3, 2,2

18. Reddish-brown (chocolate) ppt. are formed with(A) 2 46Cu and Fe(CN) (B) 2 24Ba and SO (C) 2Pb and I (D) None

19. 3 2 2 2NOClCH .CH .CH , NH A . Here A is :

(A) CH3CH2CH2Cl (B) CH3CH2CH2OH

(C) 3 2 2CH CH C HNH

|OH

(D) 3 2 2CH CH CH NH Cl

20. Action of concentrated nitric acid (HNO3) on metallic tin produces :

(A) stannic nitrate (B) stannous nitrite(C) meta stannic acid (D) stannous nitrate

21. When phenolic ether is heated with HI it yields :

(A) alkyl halide + aryl halide + water (B)

(C) alcohol + aryl halide (D) None of these

alkyl halide +

OH

OH H2SO4 heat

1. BD3 /THF2. H2O2, NOOH

OH H2SO4 heat

D2 /Pt

OH PBr3 1. Mg, diethyl ether2. D2O

OH PBr3 NaOD, D2O


4/11


22. Consider gaseous equilibrium of

2 2H (g) I (g) 2 HI (g) In the following graphs, the three gases are at equilibrium in a container. At some time t, extra I2 is added. Which of following sets will respond to this situation ?

(A) (B)

(C) (D)

23. What is the product of the following series of reactions ?

(A) (B) (C) (D)

24. Cu+ ion is not stable in aqueous solution because of disproportionation reaction.E value for disproportionation of Cu+ is(given, 2 2Cu / Cu Cu / CuE 0.15, E 0.34V ) :(A) + 0.38 V (B) 0.38V (C) + 0.49 V (D) 0.49V

25. When AgNO3 is added to a solution of 3 5 3Co(NH ) Cl, the precipitate of AgCl shows two ionizable chloride ions. Tmeans :(A) two chlorine atoms satisfy primary valency and one secondary valency(B) one chlorine atom satisfies primary as well secondary valency

(C) three chlorine atoms satisfy primary valency(D) three chlorine atoms satisfy secondary valency

26. The order of activity of the various o- and p-direction is :(A) 3 3O OH OCOCH COCH (B) 3 3OH O OCOCH COCH (C) 3 3OH O COCH OCOCH (D) 3 3O COCH OCOCH OH

27. In the extraction of silver from argentite ore the ore is treated with dilute solution as NaCN in water in the presewhereby the following reaction takes place

2 2 2 4Ag X 4NaCN 2Y 2Na Ag(CN) Na XO

X and Y in this reaction are represented by :(A) Cl and S (B) S and O2 (C) O and O2 (D) O and S

28. Ortho and para hydrogen differ in :(A) nuclear charge (B) nuclear reaction(C) electron spin (D) proton spin

PHII2

H2

t

PHII2

H2

t

PHI

I2 H2

t

PHI

I2

H2

t

ClO = C CH3

ClCOOCH3

ClHO CH CH3

ClCH2CN

ClNH2

NaNO2, HClH2O, 0 C

CuCN 1. CH3MgBr2. H2O, H+


5/11


6/11


38. A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a cinstant of time, the stone is at its lowest position and has a speedu. The magnitude of the change in its velocity as reaches a position where the string is horizontal is :

(A) 2 2u gL (B) 2gL (C) 2u gL (D) 22 u gL 39. Find the ratio of lengths of an iron rod and aluminium rod for which the difference in the lengths of rod is indep

temperature. 5 5iron Al1 2 10 and 2 4 10. / C . / C

(A) 1 : 2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1

40. Which of the following in electricity is analogous to momentummv in dynamics ?(A) IV (B) IL (C) QL (D) IQ

41. A paper, with two marks having separationd , is held normal to the line of sight of an observer at a distance of 50m.The diameter of the eye-lens of the observer is 2mm. Which of the following is the least value of d , so that the marks canbe seen as separate ? The mean wavelength of visible light may be taken as 5000

(A) 1.25m (B) 12.5cm (C) 1.25cm (D) 2.5mm

42. A metal rod of resistance20 is fixed along a diameter of a conducting ring of radius0 1. m and lies on x-y plane. Thereis a magnetic field 50 B T k . The ring rotates with an angular velocity 120 rads about its axis. An externalresistance of 10 is connected across the centre of the ring and rim. The current through external resistance is :

(A)12

A (B)13

A (C)14

A (D) None of these

43. What is the binding energy per nucleon of 126C nucleus ?

Given : mass of C 12

(mc) = 12.000u mass of proton (m p) = 1.0078u mass of neutron (mn) = 1.0087u and 1amu = 931.4 MeV (A) 5.26 MeV (B) 10.11 MeV (C) 15.65 MeV (D) 7.68 MeV

44. A and B are two identically spherical charged bodies which repel each other with forceF , kept at a finite distance. A thirduncharged sphere of the same size is brought in contact with sphere B and removed. It is then kept at mid point of A and B.Find the magnitude of force onC .(A) F /2 (B) F /8 (C) F (D) Zero

45. A particle is projected with initial velocityu at an angle above the horizontal, then variation of torque and angumomentum with time will be :

(A) (B) (C) (D)

46. Pick out the correct statements.I. Susceptibility of a diamagnetic substance is high and negative.II. In paramagnetic substance, the intrinsic magnetic moment is not zero.III. When a paramagnetic substance is heated, it becomes ferromagnetic.IV. Spin exchange interaction is present in the absence of external magnetic field.(A) I and II (B) III and IV (C) II and III (D) II and IV

, LL

t

, L L

t

, L L

t

, L L

t


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46. Two short magnets of equal dipole moments M are fastened perpendicularly at their centres (figure). The magnitude omagnetic field at a distanced from the centre on the bisector of the right angle is :

(A) 0 34 M

d

(B) 0 32

4 M

d

(C) 0

32 2

4 M

d

(D) 0

32

4 M

d

48. A raw egg and a hard boiled egg are made to spin on a table with the same angular speed about the same axis. Tthe time taken by the two to stop is :(A) = 1 (B) < 1 (C) > 1 (D) None of these

49. A signal emitted by an antenna from a certain point can be received at another point of the surface in the form of:(A) Sky wave (B) Grounded wave(C) Sea wave (D) Both (A) and (B)

50. A battery is connected between two points A and B on the circumference of a uniform conducting ring of radiusr andresistance R. One of the arcs AB of the ring subtends an angle at the centre. The value of the magnetic induction at tcentre due to the current in the ring is :(A) proportional to 2 180 (B) inversely proportional tor (C) zero, only if 180 (D) zero for all values of

51. Figure shows two rays A and B being reflected by a mirror and going as A and B . The mirror :(A) is plane(B) is convex

(C) is concave(D) may be any spherical mirror

52. In a meter bridge experiment, null point is obtained at 20cm from one end of the wire when resistance X is balancedagainst another resistanceY . If X < Y , then where will be the new position of the null point from the same end, idecides to balance a resistance of 4 X againstY ?(A) 50 cm (B) 80cm (C) 40 cm (D) 5 cm

53. In a photoelectric experiment anode potential is plotted against plate current :(A) A and B will have different intensities while B andC will have different

frequencies(B) B and C will have different intensities while A and C will havedifferent frequencies

(C) A and B will have different intensities while A and C will have equalfrequencies

(D) A and B will have equal intensities while B and C will have differentfrequencies

54. The atmospheric temperature is below0 C and its value is , then ice starts forming on the surface of lake. Find the timin which thickness of ice formed getsh m . Let us considerK is the thermal conductivity of ice, is the density of ice. L f is

the latent heat of fusion :(A)

2

2 f L h

K

(B)

2 f L h

K

(C)

2

2 f L h

K (D) None of these

AB

C BA

V

I

N

S

S

N

45


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55. Water flows in a stream line manner through a capillary tube of radius a, the pressure difference beingP and the rate flowQ. If the radiusa reduced toa /2 and the pressure is increased to 2P , the rate of flow becomes :(A) 4Q (B) Q (C) Q/ 2 (D) Q /8

56. An electric bulb is at a vertical distance of h over the centre of a circular table of radius R as shown in figure. By whatfactor the intensity of illumination at the centreO is greater than that at the edge of the table ?

(A) 3 22

21 /

R

h

(B) 3 22

21 /

R

h

(C) 2

21R

h

(D) 2

21R

h

57. The bob of a simple pendulum executes simple harmonic motion in water with a periodt , while the period of oscillation of

the bob ist 0 in air. Neglecting frictional force of water and given that the density of the bob is 34

10003

kg / m . What

relationship betweent and t 0 is true ?(A) t = t 0 (B) t = t 0 /2 (C) t = 2t 0 (D) t = 4t 0

58. Which one of the following curves represents the variation of impedance ( z) with frequency f in series LCR circuit

(A) (B) (C) (D)

59. What is the plate current in a diode value under the space charge limited operation, when the plate potential is 6V ? In a

diode valve, the plate current is 320 mA, when the plate potential is 240V :(A) 30 mA (B) 20mA (C) 40 mA (D) 10mA

60. A long conducting wire AH is moved over a conducting triangular wireCDE with aconstant velocity v in a uniform magnetic field B directed into the paper. Resistance perunit length of each wire is . Then :(A) a constant clockwise induced current will flow in closed loop(B) an increasing clockwise induced current will flow in the closed loop(C) a decreasing anticlockwise induced current will flow in the closed loop(D) a constant anticlockwise induced current will flow in the closed loop

SECTION - III (M athe m atics) 30 4 = 12

61. If , , are the cube roots of p ( p < 0), then for any x, y and z ; x y z

x y z

equals to :

(A) 1

1 32

i (B) 1 1 32 i (C) 1 1 32

i (D) None of these

62. If 20 1 21 n nn x C C x C x . . . C x , then the value of 0

r sr s n

r s C C is :

(A) 2 2nn . (B) 2nn . (C) 2 22 nn . (D) None of these

Z

f

Z

f

Z

f

Z

f

A

B

F G H

v

C E

D


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63. For 0

n

m x

sin xm, n I , Lim

sinxis equal to :

(A) 1 (B) 1 (C) n / m (D) None of these

64.

2

21

1log x

log x

dx is equal to :

(A) 2 1 x

c x

(B) 2 1

xc

log x (C) 21

x xec

x (D)

2 1log x

clog x

65. The equation 22 2

3 54 4 2

log x log x x has :

(A) At least one real solution (B) Exactly three real solutions(C) Exactly one irrational solution (D) All of these

66.Given a, g are the roots of the equation

2

4 1 0 Ax x and b, d are the roots of the equation2

6 1 0 Bx x . If a, b,g, d are in H.P., then the values of A and B are respectively :(A) 3, 5 (B) 8, 5 (C) 5, 8 (D) 3, 8

67. If A and B are two independent events such that 215P A B and 16

P A B , thenP( B) is :

(A) 1/5 (B) 1/6 (C) 2/5 (D) 5/6

68. The difference of the tangents of the angles which the lines 2 2 2 2 22 0 x sec sin xy tan y sin make withthe x-axis, is :

(A) 2tan (B) 2 (C) 2cot (D) 2sin

69. If 12 z i tan

, then polar form of the complex number z is :

(A) 1 cos i sincos

(B) 1 cos i sincos

(C) 1 2 2cos i sincos

(D) None of these

70. If the tangent at a point acos , b sin on the ellipse2 2

2 2 1 x y

a b meets the auxiliary circle in two points, the chor

joining them subtends a right angle at the centre, then the eccentricity of the ellipse is given by :

(A) 1 2

21/

cos (B) 21 sin (C)

1 221 sin (D) 21 cos 71. Consider a circle with its centre lying on the focus of the parabola y2 = 2 px such that it touches the directrix of the

parabola. Then a point of intersection of the circle and the parabola is :

(A) 2 p

, p

or2 p

, p

(B) 2 2 p p

,

(C) 2 p

, p

(D) 2 2 p p

,


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72. The greatest and the least values of 3 31 1sin x cos x are respectively :

(A) 2 2

, (B)

3 3

8 8 ,

(C) 3 37

32 8 ,

(D) None of these

73. In a ABC , if 11 01

a b

c a

b c

, then 2 2 2sin A sin B sin C is equal to :

(A) 9/4 (B) 4/9 (C) 1 (D) 3 3

74. A particle begins to move from a distance a towards a fixed centre, which repels it with retardation x . If its initialvelocity is a then its equation of motion is :

(A) t x ae (B) t x ae (C) t x a e (D) t x a e

75. The centre of the circle passing through (0, 0) and (1, 0) and touching the circle2 2 9 x y is :

(A) 1 12 2 , (B)

122 ,

(C)

3 12 2 , (D)

1 32 2 ,

76. 32 7 1n n is divisible by (for alln N ) :(A) 64 (B) 36 (C) 49 (D) None of these

77. The function 1 x

f x x tan x

has :

(A) one point of minimum in the interval02 ,

(B) one point of maximum in the interval02

,

(C) no point of maximum, no point of minimum in the interval02 ,

(D) two points of maxima in the interval02 ,

78. Let f ( x) = (1 +b2) x2 + 2bx + 1 and letm (b) be the minimum value of f ( x). Asb varies, the range of m(b) is :

(A) [0, 1] (B) 102 ,

(C) 1 12 ,

(D) (0, 1]

79. A rectangular hyperbola whose centre isC is cut by any circle of radiusr in four pointsP , Q, R and S . Then

2 2 2 2CP CQ CR CS is equal to :(A) 2r (B) 22r (C) 23r (D) 24r

80. 2sin x . log cos x dx is equal to :

(A) 212cos x log cos x k

(B) 2cos x . log cos x k

(C) 212cos x log cos x k

(D) None of these

81. The angle between the lines whose direction cosines are given by the equations2 2 2 0 0l m n , l m n is :

(A) 6 (B)

4 (C)

3 (D)

2


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82. For any integern the integral 2 3

02 1cos xe cos n x dx

has the value :

(A) (B) 1 (C) 0 (D) None of these

83. The equation of the circle having the lines2 2 3 6 0 x xy y y as its normal and having size just sufficient to

contain the circle 4 3 0 x x y y is :(A) 2 2 3 6 40 0 x y x y (B) 2 2 6 3 45 0 x y x y

(C) 2 2 8 4 20 0 x y x y (D) 2 2 4 8 20 0 x y x y

84. Area of the rhombus enclosed by the lines 0 ax by c is :

(A) 12

ab sq. unit (B) 21

2cab

sq. unit (C) 22c

absq. unit (D) None of these

85. If from each of the three boxes containing3 white and1 black,2 white and2 black,1 white and3 black balls, one ball isdrawn at random, then the probability that two white and one black ball will be drawn is:

(A) 1332

(B) 14

(C) 132

(D) 316

86. From a point on the ground, the angles of elevation of a bird flying with a constant speed in a horizontal directio

intervals of time are , , and . Then 2 2cot cot is equal to :

(A) 2 23 cot cot (B) 2 2cot cot (C) 2 23 cot cot (D) 2 2cot cot

87. Let the unit vectorsa and b be perpendicular to each other and the unit vectorc be inclined at an angle to botha and b . If c xa yb z a b , then :(A) 2 x cos , y sin , z cos (B) 2 x sin , y cos , z cos

(C) 2 2 x y cos , z cos (D) 2 2 x y cos , z cos

88. If x y y x y

, then its solution is :

(A) 2 22 y xy x c (B) 2 22 y xy x c (C) 2 22 y xy x c (D) 2 22 y xy x c

89. The value of 2 2

1 10 0sin x cos xsin t dt cos t dt is :

(A) (B) 2 (C)

4 (D) 1

90. The value1 7 5 3

12

1

x 3x 7x x I cos x dx

cos x

is:

(A) /2 (B) 0 (C) 2 (D)

* * * * Vidyam andir w ishes you the very best for AIEEE - 2012 * * * *

Aieee Home Practice Test 1 2012

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