Aieee-2012 Study Material

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EXTRA PREPARATORY MATERIAL FOR AIEEE PHYSICS

Reynolds Number Re: ev dR

where density:

v : velocity of flow. d : diameter of pipe

visocity of the liquid:

* Re < 1000, the flow is stream line or laminar * 1000 < Re < 2000, the flow is unsteady

* Re > 2000, the flow is turbulent.

Free forced and damped oscillations and Resonance:

Free oscillations: When a system is displaced from its equilibrium position and released, it oscillates with its natural frequency , and the oscillations are called free oscillations. Damped Oscillation: All free oscillations are eventually die out because of the presence of the damping (resistive) forces, and these oscillations are called damped oscillations. Forced Oscillations: If an external agent maintains the oscillations, these are called forced or driven oscillations In general damping forces is proportion to velocity and suppose an external force F(t) of amplitude F0 that varies periodically with time is applied to damped oscillator is represented as 0 dF F cos t where d is

called driven frequency then equation of motion is given as 0 dma kx bv F cos t

or 2

02 dd x dxm b kx F cos t

dtdt .

The oscillator initially oscillates with its natural frequency , when we apply the external periodic force, the oscillations with the natural frequency die out, and then the body oscillates with the angular frequency of the

external periodic force. Solution to above equation is given as dx A cos t

Where

0 01 22 2 2 2 2 0

and/d

d d

F vA tanxm b

where v0 and x0 are velocity and displacement of the particle at time t = 0, which is the moment when we apply the periodic force. Resonance: The phenomenon of increase in amplitude when the driving frequency is close to the natural frequency of the oscillator is called resonance. Drift velocity: When potential difference is applied across the conductor electrons move with an average velocity which is independent of time, although electrons are accelerated. This is the phenomenon of drift and the velocity vd is called the drift velocity.

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dI n e Av …(1) I : current in the wire

n : no. density of electrons A : area of cross-section of the wire vd : drift velocity

also de Evm

…(2) E : electric field

m : mass of e s e : electronic charge : relaxation time.

From equation (1) and (2) we have current density 2I neJ E

A m and comparing it with microscopic from

of ohm’ Law i.e. J E , we have (where : conductivity)

2ne

m

Mobility : An important quantity is the mobility is defined as the magnitude of the drift velocity per unit

electric field.

d

dv e E& vE m

em

Colour Codes of resistance: The resistors have a set of coaxial colourd rings on them whose significance is listed in table. Colour Number Multiplier Tolerance (%) Black 0 1 Brown 1 101 Red 2 102 Orange 3 103 Yellow 4 104 Green 5 105 Blue 6 106 Violet 7 107 Gray 8 108 White 9 109

Gold 110 5

Silver 210 10 Nocolour 20 Note: the order of the first letter of the colours can be learned as

has0 1 2 3 4 5 6 7 8 9

of reat ritain a ery ood ifeB B R O Y G B V G W

The first two bands from the end indicate the first two significant figures of the resistance in ohms. The Third band indicates the decimal multiplier. The Last band stands for tolerance or possible variation in percentage.

First band 2nd band Third band

Last band

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Cyclotron: The working of the cyclotron is based on the fact that the time period of revolution of circular motion of a changed particle inside the magnetic field is independent of the radius of the circular motion

1 2 andm mvT Rf qB qB

and R is increased as velocity is increased by an oscillating electric field between the two

Dees, which has same oscillating frequency as the frequency of revolution of the charge particle.

Definition of Ampere: The ampere is the value of that steady current which, when maintained in each of the two very long, straight, parallel conductors of negligible cross-section, and placed one meter about in vacuum, would produce on

each of these conductors a force equal to 72 10 Newton’s per meter of length

Current sensitivity of the galvanometer: is defined as the deflection per unit length.

N ABI K N : no. of turns

A : area of coil B : magnetic field strength K : torque constant of spring

Bar magnet as an equivalent solenoid:

03

24

mBr

m is magnetic moment of the bar, 2m i a .

When a magnetic needle of magnetic moment m and moment of inertia I is allowed to oscillate in magnetic field B,

then time period of its oscillation is given as 2 ITmB

Sharpness of resonance: It is also called the quality factor Q of the circuit.

0 0

0

12

LQR CR

Where 0 : resonance frequency and Δ is difference in two angular frequencies at which the amplitude of current is

1 2/ times the amplitude of current at resonance.

EM waves: Direction of propagation of em waves is along E B .

* speed of light in vacuum 0 0

1C

* speed of light in medium whose electric permittivity is E and magnetic permeability is 1v

* If total energy transferred to a surface in time t is U, then magnitude of the total momentum delivered to this

surface (for complete absorption) is UPC

.

The microscope:

* Simple microscope: linear magnification 1 ; 25Dm D cmf

f : focal length.

angular magnification when image formed at infinity Dmf

* Compound microscope: 00

ee

L Dm m mf f

a B i

2

r

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* Telescope: 0

e

fmf

if length of the telescope is f0 + fe

* Diffraction is the phenomenon of bending of light round the sharp corners and spreading into the regions of the geometrical shadow is called diffraction.

* Diffraction from a slit

(i) Angular position of the nth secondary minimum nn

(ii) Distance of the nth secondary maximum from the centre of the screen nnDx

(iii) Angular positions of the nth secondary maximum 2 1

2nn

n

(iv) Distance of the nth secondary maximum from the centre of the screen 2 1

2nn D

x

(v) Width of a secondary maximum or minimum D

(vi) Width of the central maximum 02D

* The phenomenon due to which vibrations of light are restricted in a particular plane is called polarization. * Brewster’s Law states that when light is incident at polarizing angle, the reflected and refracted rays are

perpendicular to each other Mathematically ptan i

* Law Malus states that when a completely plane polarized light beam is incident on an analyzer the intensity of the emergent light varies as the square of the cosine of the angle between the plane of transmission of the analyzer and the polarizes

Mathematically 20I I cos

* Doppler shift.

(A) Δ vv vc

(B) Δ vc

*. A semiconductor is perfect insulator at 0 K. *. Te energy band formed by a series of level containing valence electrons is called valence band and the lowest

unfilled energy band formed just above the valence band is called conduction band. The energy gap between valence band and conduction band is called forbidden energy gap.

*. In intrinsic or pure semiconductors b en n .

*. the process of adding impurity atoms (heptavalent or trivalent) to a pure semiconductor so as to increase conductivity in controlled manner is doping.

*. In extrinsic semiconductor if en is the electron density and bn in the hole density the material will be n-type

if e bn n . The material will be p-type if b en n .

*. In metals, valence band and conduction band overlap therefore, energy gap, 0gE . In semiconductors

1gE eV and insulators have 6gE eV .

*. In n-type semiconductor, conductivity n e en e

In p-type semiconductor conductivity p b bn e

In intrinsic semiconductor conductivity int rinsic b b e en e n e

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*. A p-n junction or a diode may be assumed ideal diode. It may be assumed to act like an ON switch when forward biased and like an OFF switch when reverse biased. That is, diode shows full conduction (r = 0) when forward biased and no conduction ( r ) when reverse biased.

*. Zener diode is a highly doped p-n diode which is not damaged by high reverse current. It is always used in reverse bias in breakdown voltage region and is chiefly used as voltage regulator.

*. For a sufficiently high reverse bias voltage the reverse current increases. This voltage is called zener voltage or breakdown voltage or avalanche voltage.

*. A transistor is a combination of two p-n junctions joined in series. A junction transistor is known as bipolar junction transistor (BJT)

Transistor are of two type (i) n-p-n and (ii) p-n-p transistor *. A transistor has three regions (i) An emitter (ii) A base (iii) A collector *. *.

*. and1 1e c bi i i

*. Use the relations in order to simplify logical expressions. (i) A + A = A its dual A . A = A

(ii) 1A A its dual = 0A. A

(iii) A + 1 = A its dual A . 1 = A (iv) A + AB = A + B its dual A (A + B) = A

(v) A AB A B its dual A A B AB

(vi) ;A B A.B A . B A B

(vii) 1 1 1 0 0A A

1.0 = 0.1 : 1 = 1 * NAND and NOR gates are universal gates. NOT gate is unipolar. All other gates are bipolar. * A single which has only two levels of voltage are called digital signals. The two levels of a digital singal are

represented as 0 and 1. * The OR gate (i) Its Booleans expenssion is Y = A + B. The truth table of OR gate is given below

Current gain 1ci

e

iAi

Voltage gain 1 1Vi

RAr

Power gain 2 1

11p

RAr

No phase shift between input and output

In common base (CB) Amplifier

FBh

Current gain 1 1r

p

iAi

Voltage gain 1 1Vi

RAr

Power gain 1

11p

RAr

Phase shift = 180º or rad

In common base (CE) Amplifier

FBh

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A B Y 0 0 0 0 1 1 1 0 1 1 1 1

(ii) The AND gate

Its Boolean expression is Y = A . B. The truth table of AND gate is given below A B Y 0 0 0 0 1 0 1 0 0 1 1 1

(iii) The NOT gate

Its Boolean expression is Y A . The truth table of NOT gate is given below

A Y 0 1 1 0

1. A potential difference V is applied to a copper wire of length and thickness d. If V is doubled, the drift velocity

(A) is doubled (B) is halved (C) remains same (D) becomes zero

2. In a region 1910 -particle and 1910 protons move to the left, while 1910 electrons move to the right per second. The current is

(A) 3.2 towards left (B) 3.2 A towards right (C) 6.4 towards left (D) 6.4 A towards right

3. Every atom makes one free electron in copper. If 1 A current is flowing in the wire of copper having 1 mm

diameter, then the drift velocity (approx.) will be (density of copper = 3 39 10 kg m and atomic weight of

copper = 63)

(A) 10 1. mms (B) 10 2. mms (C) 10 3. mms (D) 10 2. cms

4. A charge of 22 10 C move at 30 revolutions per second in a circle of diameter 80cm. The current linked

with the circuit is : (A) 0.02 A (B) 20 A (C) 0.60 A (D) 60 A

5. The electron hydrogen atom is considered to be revolving round a proton in circular orbit of radius 2 2/ me

with velocity 2e / , where 2h / . The current is :

(A) 2 5

24 me

(B) 2 2

34 me

(C) 2 2 2

34 m e

(D)

2 5

34 me

6. Assume that each atom of copper contributes one free electron. What is the average drift velocity of

conduction electron in a copper wire of cross-sectional area 7 210 m , carrying a current of 1.5 A? (Given

density of copper = 3 39 10 kgm ; atomic mass of copper = 63.5 ; Avogadro’s number = 236 023 10. per

gram atom)

(A) 2 11 1 10. ms (B) 3 11 1 10. ms (C) 2 12 2 10. ms (D) 3 12 2 10. ms

7. A current through a wire depends on time t is I = 10 + 4t. The charge crossing through the section of the wire in to s is:

(A) 50 C (B) 300 C (C) 400 C (D) 4 C

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8. In the above question if potential difference is applied, the drift velocity at temperature T is :

(A) Inversely proportional to T (B) proportional to T (C) zero (D) finite but independent of T

9. Two wires of the same material but different diameters carry the same current i. If the ratio of their diameters is 2 : 1 then the corresponding ratio of their mean drift velocity will be :

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

10. A straight conductor of uniform cross – section caries a current i. If s is the specific charge of an electron, the momentum of all the free electrons per unit length of the conductor, due to their drift velocity only is:

(A) is (B) i / s (C) i / s (D) 2i / s

11. The amount of charge Q passed in time t through a cross – section of a wire is 25 3 1Q t t . The value of

current at time t = 5 s is : (A) 9A (B) 49A (C) 53A (D) None of these

12. In a neon gas discharge tube Ne ions moving through a cross – section of the tube each second to the right is 182 9 10. , while 181 2 10. electrons move towards left in the same time ; the electronic charge being

191 6 10. C , the net electric current is :

(A) 0.27 A to the right (B) 0.66 A to the right (C) 0.66 A to the left (D) zero

13. The speed at which the current travels, in a conductor, is nearly

(A) 4 13 10 ms (B) 5 13 10 ms (C) 6 14 10 ms (D) 8 13 10 ms

14. If the electronic charge is 191 6 10. C , then the number of electrons passing through a section of wire per

second, when the wire carries a current of 2 A is :

(A) 171 25 10. (B) 171 6 10. (C) 191 25 10. (D) 191 6 10.

15. Constant current is flowing through a liner conductor of non-uniform area of cross-section. The charge flowing per second through the area of conductor at any cross-section is

(A) proportional to the area of cross – section (B) inversely proportional to the area of cross – section (C) independent of the area of cross – section (D) dependent on the length of conductor

16. A metallic block has no potential difference applied across it, then the mean velocity of free electrons at absolute temperature T is :

(A) Proportional to T (B) proportional to T (C) zero (D) finite but independent of T

17. A metallic resistor is connected across a battery. If the number of collisions of the free electrons with the lattice is some how decreased in the resistor (for example by cooling it), the current will.

(A) remains constant (B) increase (C) decrease (D) become zero

18. Current flows through a metallic conductor whose area of cross – section increases in the direction of the current. If we move in this direction.

(A) the carrier density will change (B) the current will change (C) The drift velocity will decrease (D) The drift velocity will increase

19. A steady current is set up in a metallic wire of non-uniform cross – section. How is the rate of flow of electrons (R) related to the area of cross – section (A) ?

(A) 1R A (B) R A (C) 2R A (D) R is independent of A

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20. A capacitor of 10 F has a potential difference of 40V across it. If it is discharged in 0.2 s, the average current

during discharge is : (A) 2mA (B) 4mA (C) 1mA (D) 0.5 mA

21. There is a current of 0.21 A in a copper wire whose area of cross – section is 6 210 m . If the number of free

electrons per m3 is 288 4 10. , then find the drift velocity, ( 191 6 10e . C )

(A) 5 12 10 ms (B) 5 11 56 10. ms (C) 5 11 10 ms (D) 5 10 64 10. ms

22. The current density (number of free electrons per m3) in metallic conductor is of the order of (A) 1022 (B) 1024 (C) 1026 (D) 1028

23. The steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities constant along the length of the conductor is/are.

(A) Current, electric field and drift velocity (B) drift speed only (C) current and drift speed (D) current only

24. Which of the following characteristics of electron determines the current in a conductor ? (A) Thermal velocity alone (B) Drift velocity alone (C) Both thermal velocity and drift velocity (D) None the above

25. A potential difference of V is applied at the ends of a copper wire of length l and diameter d. On doubiling only d the drift velocity

(A) becomes two times (B) become half (C) does not change (D) becomes one-fourth

26. In the circuit shown figure potential difference between X and Y will be : (A) zero

(B) 20V (C) 60 V

(D) 120 V 27. The area of cross – section of three magnets of same length are A, 2 A and 6A respectively. The ratio of their

magnetic moments will be : (A) 6 : 2 : 1 (B) 1 : 2 : 6 (C) 2 : 6 : 1 (D) 1 : 1 : 1

28. A bar magnet of length 3 cm has a point A and B along axis at a distance of 24 cm and 48 cm on the opposite ends. Ratio of magnetic fields at these points will be :

(A) 8 (B) 3

(C) 4 (D) 1 2 2/

29. Two magnets of equal magnetic moments M each are placed as shown in figure. The resultant magnetic moment is :

(A) M

(B) 3 M

(C) 2M (D) 2M /

30. A short bar magnet placed with its axis at 30 , with a uniform external magnetic field of 0.25T experiences a

torque of 24 5 10. N m . Magnetic moment of the magnet is :

(A) 10 36. J T (B) 10 72. J T (C) 10 18. JT (D) Zero

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

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

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32. A short bar magnet with the north pole facing north forms a neutral point at P in the horizontal plane. If the magnet is rotated by 90 in the horizontal plane, the net magnetic induction at P is (Horizontal component of earth’s magnetic field = BH)

(A) zero (B) 2BH (C) 52 HB (D) 5 HB

33. The earth’s magnetic induction at a certain point is 1 27 10 Wbm . This is to be annulled by the magnetic

induction at the centre of a circular conducting loop of radius 15 cm. The required current in the loop is : (A) 0.56 A (B) 5.6 A (C) 0.28 A (D) 2.8 A

34. At a certain place, horizontal component is 3 times the vertical component. The angle of dip at this place is (A) zero (B) 3/ (C) 6/ (D) None of these

35. The angle of dip at a certain place where the horizontal and vertical components of the earth’s magnetic field ae equal is : (A) 30 (B) 90 (C) 60 (D) 45

36. A magnet is placed on a paper in a horizontal plane for locating neutral points. A dip needle placed at the neutral point will be horizontal at the

(A) magnetic poles (B) magnetic equator (C) latitude angle 45 (D) latitude angle of 60

37. A dip needle which is free to move in a vertical plane perpendicular to magnetic meridian will remain (A) horizontal (B) vertical (C) neither horizontal nor vertical (D) inclined

38. The variation of the intensity of magnetization (I) with respect to the magnetizing field (H) in a diamagnetic substance is described by the graph in figure.

(A) OD (B) OC (C) OB (D) OA

39. The space inside a toroid is filled with tungsten shoes susceptibility is 56 8 10. . The percentage increase in

the magnetic field will be : (A) 0.0068 % (B) 0 0068. % (C) 0 68. % (D) None of these

40. Liquid oxygen remain suspended between two poles of magnet become it is : (A) diamagnetic (B) paramagnetic (C) ferromagnetic (D) antiferromagnetic

41. The time period of a thin bar magnet in earth’s magnetic field is T. If the magnet is cut into four equal parts perpendicular to its length, the time period of each part in the same field will be :

(A) T/2 (B) T/4 (C) 2T (D) 2T

42. A magnet freely suspended in a vibration magnetometer makes 40 oscillations per minute at a place A and 20

oscillations per minute at a plane B. If the horizontal component of earth’s magnetic field at 636 10 T , then

its value at B is

(A) 636 10 T (B) 69 10 T (C) 6144 10 T (D) 6228 10 T

43. A magnet performs 10 oscillations per minute in a horizontal plane at a plane where the angle of dip is 45 and the total intensity is 0.707 CGS units. The number of oscillations per minute at a place where dip angle 60 and total intensity is 0.5 CGS units will be :

(A) 5 (B) 7 (C) 9 (D) 11

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44. The magnetic needle of a tangent galvanometer is deflected at an angle 30 due to a magnet. The horizontal

component of earth’s magnetic field 40 34 10. T is along the plane of the coil. The magnetic intensity is :

(A) 41 96 10. T (B) 41 96 10. T (C) 51 96 10. T (D) 51 96 10. T

45. A bar magnet is oscillating in the Earth’s magnetic field with a period T. What happens to its period of motion if its mass is quadrupled?

(A) Motion remains SHM with time period = T/2 (B) Motion remains SHM and period remains nearly constant (C) Motion remains SHM with time period = T/2 (D) Motion remains SHM with time period = 4T

46. The correct 1-H curve for a paramagnetic material is represented by, figure. (A) (B) (C) (D) 47. Two bar magnets of the same mass, same length and breadth but having magnetic moments M and 3M are

joined together pole for pole and suspended by a string. The time period of assembly in a magnetic field of strength H is 3s. If now the polarity of one of the magnets is reversed and the combination is again made to oscillation in the same field, the time of oscillation is :

(A) 3s (B) 3 3s (C) 3 3/ s (D) 6s

48. The variation of magnetic susceptibility ( ) with temperature for a diamagnetic substance is best represented

by figure.

(A) (B) (C) (D) 49. An inductor of 10mH shows 50 mH when operated with a core made of ferrite. The susceptibility of ferrite is : (A) 5 (B) 4 (C) 3 (D) None of these

50. A uniform magnetic field parallel to the plane paper existed in space initially directed from left to right. When a bar of soft iron is placed in the field parallel to it, the lines of force passing through it will be represented by figure.

(A) (B)

(C) (D)

51. The relative permeability of a substance X is slightly less than unity and that of substance Y is slightly more than unity, then

(A) X is paramagnetic and Y is ferromagnetic (B) X is diamagnetic and Y is ferromagnetic (C) X and Y both are paramagnetic (D) X is diamagnetic and Y is paramagnetic

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52. The magnetizing field required to be applied in opposite direction to reduce residual magnetism to zero is called

(A) coercivity (B) retentivity (C) hysteresis (D) None of these

53. The magnifying power of a telescope is 9. When it is adjusted for parallel rays, the distance between the objective and the eye – piece is found to be 20 cm . The focal lengths of the lenses are

(A) 18 cm, 2 cm (B) 11 cm, 9cm (C) 10 cm, 10 cm (D) 15 cm, 5 cm

54. In compound microscope, magnifying power is 95 and the distance of object from objective lens is 13 8

cm.

.

The focal length of objective lens is 14

cm . What is the magnification of eye piece?

(A) 5 (B) 10 (C) 100 (D) 200

55. The focal length of the objective and eyelenses of a microscope are 1.6 cm and 2.5 cm respectively. The distance between the two lenses is 21.7 cm. If the final image is formed at infinity, the distance between the object and the objective lens :

(A) 1.8 cm (B) 1.70 cm (C) 1.65 cm (D) 1.75 cm

56. Two points separated by a distance of 0.1 mm, can just be inspected on a microscope when light of wavelength 6000Å is used. If the light of wavelength 4800Å is used, the limit of resolution is :

(A) 0.8 mm (B) 0.08 mm (C) 0.1 mm (D) 0.04 mm

57. The diameter of moon is 33 5 10. km . The focal length of the objective and eye-piece are 4m and 10cm

respectively. The diameter of the image of the moon will be approximately (A) 2 (B) 21 (C) 40 (D) 50

58. With diaphragm of the camera lens set at 2f / , the correct exposure time is 1/100s. Then with diaphragm set

f/8, the correct exposure time is : (A) 1/100s (B) 1/400s (C) 1/200s (D) 16/100s

59. An objective is viewed through a compound microscope and appears in focus when it is 5mm away from the objective lens. When a sheet of transparent material 3 mm thick is place between the objective and the microscope, the objective lens has to be moved 1 mm to bring the object back into the focus. The refractive index of the transparent material is :

(A) 1.5 (B) 1.6 (C) 1.8 (D) 2.0

60. A hypermetropic person having near point at a distance of 0.75m puts on spectacles of power 2.5 D. The near point now is at

(A) 0.75 m (B) 0.83 m (C) 0.26 cm (D) 0.26 m 61. An astronomical telescope has a converging eye-piece of focal length 5cm and objective of focal length 80 cm.

When the final image is formed at the least distance of distinct vision (25 cm), the separation between the two lenses is :

(A) 75.0 cm (B) 80.0 cm (C) 84.2 cm (D) 85.0cm

62. The focal length of objective and eye lens of an astronomical telescope are respectively 2m and 5 cm. Final image is formed at (1) least distance of distinct vision (2) infinity. Magnifying powers in two cases will be :

(A) 48 40 (B) 40 48 (C) 40 48 (D) 48 40

63. A man’s near point is 0.5 m and far point is 3m. Power spectacle lenses repaired for (i) reading purposes (ii) seeing distance objects, respectively. (A) 2 and 3D D (B) 2 and 3D D (C) 2 and 0 33D . D (D) 2 and 0 33D . D

64. A hypermetropic person has to use a lens of power +5D to normalize his vision. The near point of the

hypermetropic eye is (A) 1 m (B) 1.5 m (C) 0.5 m (D) 0.66 m

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65. A compound microscope has an objective and eye-piece as thin lenses of focal length 1 cm and 5 cm respectively. The distance between the objective and the eye-piece is 20 cm. The distance at which the objective must be placed infront of the objective if the final image is located at 25 cm from the eye-piece, is numerically.

(A) 95 6/ cm (B) 5 cm (C) 95 89/ cm (D) 25 6/ cm

66. The focal length of the objective and the eye-piece of a microscope are 4 mm respectively. If the final image is formed at infinity and the length of the tube 16cm, then the magnifying power of microscope will be :

(A) 337 5. (B) 3 75. (C) 3 375. (D) 33 75.

67. A simple microscope consists of a concave lens of power 10D and a convex lens of power 20D in contact. If the image is formed at infinity, then the magnifying power CD = 25cm is :

(A) 2.5 (B) 3.5 (C) 2.0 (D) 3.0

68. The magnifying power of an astronomical telescope is 10 and the focal length of its eye-piece is 20 cm. The focal length of its objective will be :

(A) 200 cm (B) 2 cm (C) 0.5 cm (D) 20 5 10. cm

69. A parallel beam of light of wavelength 3141.59 Å is incident on a small aperture. After passing through the aperture, the beam is no longer parallel but diverges at 1 to the incident direction. What is the diameter of the aperture?

(A) 180 m (B) 18 m (C) 1.8 m (D) 0.18 m

70. To observe diffraction, the size of an aperture (A) Should be of the same order as wavelength should be much larger than the wavelength (B) should be much larger than the wavelength (C) have no relation to wavelength (D) should be exactly 2/

71. Air has refractive index 1.003. The thickness of air column, which will have one more wave length of yellow light ( 6000 Å ) then in the same thickness of vacuum is :

(A) 2 mm (B) 2 cm (C) 2 m (D) 2 km

72. The distance between the first and the sixth minima in the diffraction pattern of a single slit is 0.5 mm. The screen is 0.5m away from the slit. If the wavelength of light used is 5000 Å , then the slit width will be :

(A) 5 mm (B) 2.5 mm (C) 1.25 cm (D) 1.0 mm

73. Plane microwave are incident on a long lit having width of 5 cm. The wavelength of the microwave if the first minimum is formed at 30 is :

(A) 2.5 cm (B) 2 cm (C) 25 cm (D) 2 mm

74. A plane wave of wavelength 6250Å is incident normally on a slit of width 22 10 cm . The width of the

principal maximum on a screen distance 50 cm will be :

(A) 3312 5 10. cm (B) 4312 5 10. cm (C) 312 cm (D) 5312 5 10. cm

75. The main difference between the phenomena of interference and diffraction is that (A) diffraction is caused by reflected wave from a source whereas interference is caused due to refraction

of wave from a source. (B) diffraction is due to interaction of waves derived from the same source, whereas interference is that

bending of light from the same wavefornt (C) diffraction is due to interaction of light from wavefront, whereas the interference is the interaction of

two waves derived from the same source. (D) diffraction is due to interaction light from the same wavefront whereas interference is the interaction

of wave from two isolated sources.

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76. Light of wavelength 6000 Å is incident on a single slit. The first minimum of the diffraction pattern is

obtained at 4 mm from the centre. The screen is at a distance of 2m from the slit. The slit width will be : (A) 0.3mm (B) 0.2mm (C) 0.15 mm (D) 0.1 mm

77. The Fraunholder ‘diffraction’ pattern of a single slit is formed in the focal plane of a lens of focal length 1 m. The width of slit is 0.3mm. If third minimum is formed at a distance of 5 mm from central maximum, then wavelength of light will be :

(A) 5000 Å (B) 2500 Å (C) 7500 Å (D) 8500 Å

78. What should be refractive index of a transparent medium to be invisible in vacuum? (A) 1 (B) < 1 (C) > 1 (D) None of these

79. A slit 5 cm wide is irradiated normally with microwaves of wavelength 1.0 cm. Then the angular spread of the central maximum on either side of incident light is nearly

(A) 1/5 rad (B) 4 rad (C) 5 rad (D) 6 rad

80. Which of the following phenomena is not to common to sound and light waves? (A) Interference (B) Diffraction (C) Coherence (D) Polarisation

81. A beam of ordinary unpolarised light passes through a tourmaline crystal C1 and then it passes through another tourmaline crystal C2, which is oriented such that its principal plane is parallel to that of C2. The intensity of emergent light is I0. Now C2 is rotated by 60 about the ray. The emergent ray will have an intensity.

(A) 2I0 (B) I0/2 (C) I0/4 (D) 0I 2/

82. A ray of light strikes a glass plate at an angle of 60 . If the reflected an refracted rays are perpendicular to each other, the index of refraction of glass is

(A) 12

(B) 32

(C) 32

(D) 1 732.

83. An unpolarised beam of intensity 2a2 passes through a thin Polaroid. Assuming zero absorption in the Polaroid, the intensity of emergent plane polarized light is :

(A) 22a (B) 2a (C) 22a (D) 2

2a

84. 80 g of impure sugar when dissolved in a liter of water gives an optical rotation of 9 9. , when placed in a tube of length 20cm. If the specific rotation of sugar is 66 , then concentration of sugar solution will be :

(A) 180 gL (B) 175 gL (C) 165 gL (D) 150gL

85. If for a calcite crystal ando e are the refractive indices of the crystal for O-ray and E-ray respectively, then

along the optic axis of the crystal (A) o e (B) e o (C) e o (D) None of these

86. anda m are the wavelength of a beam of light in air and medium respectively. If is the polarizing single,

the correct relation between anda m is :

(A) 2a m tan (B) 2

m a tan

(C) a m cot (D) m a cot

87. Ordinary light incident on a glass slab at the polarizing angle, suffers a deviation of 22 . The value of the angle of refraction in glass in this case is :

(A) 56 (B) 68 (C) 34 (D) 22

88. At what angle should an unpolarised beam be incident on a crystal of 3 , so that reflected beam is

polarized? (A) 45 (B) 60 (C) 90 (D) 0

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89. An n-type semiconductor is (A) negatively charged

(B) positively charged (C) neutral

(D) negatively or positively charged depending upon the amount of impurity

90. The correct relation between en and hn in an intrinsic semiconductor at ordinary temperature is

(A) e hn n (B) e hn n (C) e hn n (D) 0e hn n

91. The resistivity of a semiconductor at room temperature is in between ?

(A) 2 510 to 10 Ωcm (B) 2 610 to 10 Ω cm

(C) 610 108 Ωto cm (D) 10 1210 to 10 Ω cm

92. The ratio of electron and hole current in a semiconductor is 7/4 and the ratio of drift velocities of electrons and holes is 5/4, then ratio of concentration of electrons and hole will be :

(A) 5/7 (B) 7/5 (C) 25/49 (D) 49/25

93. p-type semiconductors are (A) positively charged (B) produced when boron is added as an impurity

(C) produced when phosphorus is added as an impurity to silicon (D) produced when carbon is added as an impurity to germanium

94. A piece of copper and other of germanium are cooled from the room temperature to 80 K, then (A) resistance of each will increase (B) resistance of each will decrease (C) the resistance of copper will increase, while that of germanium will decrease (D) the resistance of copper will decrease, while that of germanium will increase

95. A donor impurity results in the (A) production of n-semiconductor (B) production of p-semiconductor (C) increase of resistance of the semiconductor (D) energy bands just above the filled valency band

96. Electrical conductivity of a semiconductor (A) increases with the rise in its temperature (B) decrease with the rise in its temperature (C) does not change with the rise in its temperature (D) first increase and then decreases with the rise in its temperature

97. An n-type and a p-type silicon semiconductor can be obtained by doping pure silicon with (A) sodium and magnesium (B) phosphorus and boron respectively (C) boron and phosphorus respectively (D) indium and sodium respectively

98. A silicon specimen is made into a p-type semiconductor by doping, on an average, one indium atom per 75 10 silicon atoms. If the number density of atoms in the silicon specimen in 285 10 atoms 3m , then

the number of acceptor atoms in silicon per cubic centimeter will be :

(A) 30 32 5 10 atoms. cm (B) 35 32 5 10 atoms. cm

(C) 13 31 0 10 atoms. cm (D) 15 31 0 10 atoms. cm

99. The typical ionization energy of a donar in silicon is (A) 10.0 eV (B) 1.0 eV (C) 0.1 eV (D) 0.0001 eV

100. The energy gap of silicon is 1.14 eV. The maximum wavelength at which silicon starts energy absorption, will

be 34 8 16 62 10 3 10h . Js c ms

(A) 10 888 Å. (B) 108 88 Å. (C) 1088 8 Å. (D) 10888Å

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101. A sinusolul voltage of peak value 200 volt is connected to a diode and resistor R in the circuit figure, so that halfwave rectification occurs. If the forward resistance of the diode is negligible compared to R, the RMS voltage (in volt) across R is approximately.

(A) 200 (B) 100

(C) 2002

(D) 280

102. In a junction diode, the direction diffusion current is : (A) from -region to p-region

(B) from p-region to -region (C) from -region to p-region if the junction is forward baised and vice if it is reverse baised. (D) from p-region to - region if the junction is forward baised and vice versa if it is reversed biased

103. The correct curve between potential (V) and distance (d) near p n junction is :

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

104. If the forward voltage in a semiconductor diode is changed from 0.5V to 0.7 V, then the forward current changes by 1.0 mA. The forward resistance of diode junction will be :

(A) 100 Ω (B) 120 Ω (C) 200 Ω (D) 240 Ω

105. The value of ripple for full wave rectifier is : (A) 40 6%. (B) 48 2%. (C) 81 2 %. (D) 121%

106. The average value of output direct current in a half wave rectifier is : (A) 0I / B) 0 2I / (C) 0 2I / (D) 02I /

107. For a junction diode the ratio of forward current ( pI ) and reverse current ( rI ) is :

[ eI = electronic charge, V = voltage applied across junction

K = Boltzmann constant T = temperature in Kelvin]

(A) V / kTe (B) v / kTe (C) 1eV / kTe (D) 1V / KTe

108. The value of current in the following diagram will be (A) zero

(B) 210 A (C) 10A (D) 0 025. A

109. In case of a p-n junction diode at high value of reverse bises, the current rises sharply. The value of reverse bias is known as :

(A) cut-off voltage (B) zener voltage (C) inverse voltage (D) critical voltage

110. In a p-n junction diode (A) the current in the reverse biased condition is generally very small (B) The current in the reverse biased condition is small but the forward biased current is independent of

the bias voltage (C) The reverse biased current is strongly dependent on the applied bias voltage (D) The forward biased current is very small in comparison to reverse biased current

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111. p-n junction is said to be forward biased, when (A) the positive pole of the battery is joined to the p-semiconductor and negative pole to the

n-semiconductor (B) the positive pole of the battery is joined to the n-semiconductor and negative pole to the

n-semiconductor and p-semiconductor (C) the positive pole of the battery is connected to n-semiconductor and p-semiconductor (D) a mechanical force is applied in the forward direction

112. The reverse bias in a junction diode is changed from 8 V to 13 V then the value of the current changes from 40 A to 60 A . The resistance of junction diode will be :

(A) 52 10 Ω (B) 52 5 10 Ω. (C) 53 10 Ω (D) 54 10 Ω

113. Consider the junction diode is ideal. The value of current in the figure is :

(A) zero (B) 210 A

(C) 110 A (C) 310 A

114. If the two ends p and n of a p-n diode junction are joined by a wire (A) there will not be a steady current in the circuit (B) there will be a steady current from n-side to p-side (C) there will be a steady current from p-side to n-side (D) there will not be a current depending upon the resistance of the connecting wire.

115. Current gain in common emitter configuration is more than 1 because (A) c bI I (B) c eI I (C) c eI I (D) c bI I

116. Current gain in common base configuration is less than 1 because (A) e bI I (B) b eI I (C) c eI I (D) e cI I

117. Three amplifier stages each with a gain of 10 are cascaded. The overall gain is : (A) 10 (B) 30 (C) 1000 (D) 100

118. A transistor has 40 . A change in base current of 100 A , produces change in collector current.

(A) 40 100 A (B) 100 40 A (C) 100 40 A (D) 100 40 A

119. Current gain AC common emitter mode of transistor is

(A) ΔΔ

CAC C

S

I VI

= constant (B) BAC C

C

I VI

= constant

(C) ΔΔ

CAC C

E

I VI

= constant (D) ΔΔ

EAC C

C

I VI

= constant

120. Current gain of a transistor in common base mode is 0.95. Its value in common emitter mode is :

(A) 0.95 (B) 1.5 (C) 19 (D) 119

121. The current gain of a transistor in a common emitter configuration is 40. If the emitter current is 8.2 mA, then base current is :

(A) 0.02 mA (B) 0.2 mA (C) 2.0 mA (D) 0.4mA

122. In a common emitter transistor amplifier 060 5000ΩR and internal resistance of a transistor if

500 Ω . The voltage amplification of amplifier will be :

(A) 500 (B) 460 (C) 600 (D) 560

123. In a n-p-n transistor 1010 electrons enter the emitter in 610 s . 4% of the electrons are lost in base. The current transfer ratio will be :

(A) 0.98 (B) 0.97 (C) 0.96 (D) 0.94

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124. A transistor has a base current of 1 mA and emitter current 90 mA. The collector current will be : (A) 90mA (B) 1 mA (C) 89 mA (D) 91mA

125. In a common base transistor circuit, the current gain is 0.98. On Changing emitter current by 5.00 mA , the change in collector current is :

(A) 0.196 mA (B) 2.45mA (C) 4.9mA (D) 5.1mA

126. The equivalent decimal number of binary number (11001.001)2 is : (A) 19.100 (B) 19.050 (C) 25.250 (D) 25.125

127. What is the value of A . A in Boolean algebra?

(A) zero (B) 1 (one) (C) A (D)

128. What is the output Y of the gate circuit shown in figure ?

(A) A . B (B) A .B

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

129. Which gate is represented by the symbolic diagram given here? (A) AND gate (B) NAND gate (C) OR gate (D) NOR gate 130. What is the name of the gate obtained by the combination shown in figure? (A) NAND (B) NOR (C) NOT (D) XOR 131. The following configuration of gate is equivalent to figure. (A) NAND

(B) XOR (C) OR (D) None of these

132. When A is the internal stage gain of an amplifier and is the feedback ratio, then the amplifier becomes as

oscillator if (A) is negative and magnitude of 2A /

(B) is negative and magnitude 1 / A

(C) is negative and magnitude of A

(D) is positive and magnitude of 1 / A

133. For the given combination of gates, if the logic states of inputs A, B C are as follows A = B = C = 0 and A = B = 1, C = 0, then the logic states of output D are

(A) 0, 0 (B) 0, 1 (C) 1, 0 (C) 1, 1

134. The circuit shown in the figure contains two diodes each with a forward resistance of 50Ω and with infinite backward resistance. If the battery is 6 V, the current through the 100Ω resistance (in ampere) is :

(A) Zero (B) 0.02

(C) 0.03 (D) 0.036

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135. A full wave rectifier circuit along with the input and output are shown in the figure, the contribution from the diode I is (are)

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

136. The combination of ‘NAND’ gates shown here under figure, are equivalent to

(A) an OR gate and an AND gate respectively (B) An AND gate and a NOT gate respectively (C) An AND gate and an OR gate respectively (D) An OR gate and a NOT gate respectively 137. In p-n junction, the barrier potential offers resistance to (A) free electrons in n-region and holes in p-region

(B) free electrons in p-region and holes in n – region (C) Only free electron in n-region (D) only holes in p-region

138. In the case of forward biasing of p-n junction, which one of the following figures correctly depicts the direction of flow of carriers?

(A) (B)

(C) (D) 139. In an intrinsic semiconductor, the Fermi level is (A) nearer to valency band than conduction band (B) equidistance from conduction band and valency band (C) nearer to conduction band than valency band (D) bisecting the conduction band

140. In a common base amplifier circuit, calculate the change in the base current if that in the emitter current is 2 mA and 0 98.

(A) 0.04 mA (B) 1.96 mA (C) 0.98 mA (D) 2mA

141. Platinum and silicon are heated upto 250 C and after that cooled. In the process of cooling (A) resistance of platinum will increase and that of silicon will decrease

(B) resistance of both will increase (C) resistance of platinum will decrease and that of silicon will increase (D) resistance of both will decrease 142. Doping of a semiconductor (with small traces of impurity atoms) generally changes the resistivity as follows (A) does not alter

(B) increase (C) decreases (D) may increases or depending on the dopant

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143. A semiconductor device is connected in a series circuit with a battery and a resistance. A current is found to pass through the circuit. If the polarity of the battery is reversed, the current drops almost to zero. The device may be:

(A) a p – type semiconductor (B) an n-type semiconductor (C) decreases (D) an intrinsic semiconductor

144. The correct relation between the two current gains and in a transistor is :

(A) 1

(B) 1

(C) 1

(D) 1

145. The diode used in the circuit shown in the figure has a constant voltage drop of 0.5 V at all currents and a maximum power rating of 100 mW. What should be the value of the resistor R, connected in series with the diode for obtaining maximum current?

(A) 1 5Ω. (B) 5 Ω (C) 6 67 Ω. (D) 200 Ω

146. In p-type semiconductors, conduction is due to (A) greater number of holes and less number of electrons (B) Only electrons (C) Only holes (D) greater number of electrons and less number of holes.

147. In the a common emitter amplifer, using output resistance of 5000Ω and input resistance of 2000Ω , if the peak value of input singal voltage is 10mV and 50 , then peak value of output voltage is :

(A) 65 10 V (B) 612 50 10. V (C) 125 V (D) 125.0 V

148. What is the output of the combination of the gates shown in the figure?

(A) A A. B (B) A B A . B

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

149. If a zener diode (Vz = 5V and Iz = 10 mA) is connected in series with a resistance and 20 V is applied across the combination, then the maximum resistance one can use without spoiling zener action is

(A) 20 Ωk (B) 15 Ωk (C) 10 Ωk (D) 1 5 Ω. k

150. If the output of a logic gate is 0 when all its inputs are at logic 1, then the gate is either. (A) NAND or Ex-NOR (B) NOR or OR (C) Ex-OR or NOR (D) AND or NOR

151. The circuit shown in the figure contains two diodes each with a forward resistance of 30Ω and with infinite backward resistance. If the battery is 3V, the current through the 50Ω resistance (in ampere) is :

(A) zero (B) 0.01 (C) 0.02 (D) 0.03

152. In the network shown, the current flowing through the battery of negligible internal resistance is (A) 0.10 A

(B) 0.15 A (C) 0.20 A (D) 0.30 A

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153. The output Y of the logic circuit shown in figure is best represented as

(A) A B . C (B) A B . C

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

154. A p-n junction (D) shown in the figure can act as a rectifier. An alternating current source (V) is connected in the circuit. The current (I) in the resistor (R) can be shown by

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

155. In the circuit as shown in figure, A and B represent two inputs and C represents the (A) OR gate

(B) NOR gate (C) AND gate (D) NAND gate

156. A working transistor with its three legs marked P, Q and R is tested using a multimeter. No. conduction is found between P and Q. By connecting the common (negative terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following is true for the transistor?

(A) It is an n-p-n transistor with R as collector (B) It is n-p-n transistor with R as base (C) It is p-n-p transistor with R as collector (D) It is p-n-p transistor with R as emitter

157. Carbon, silicon and germanium have four valence electron each. At room temperature, which one of the following statements is most appropriate?

(A) The number of free electrons for conduction is significant only in Si and Ge but small in C. (B) The number of free conduction electrons is negligibly small in Si and Ge (C) The number of free conduction electrons is negligibly small in all the three (D) The number of free electrons for conduction is significant in all the three

158. In common base mode of transistor, the collector current is 5.488 Ma for an emitter current of 5.60mA. The value of the base current amplification factor ( ) will be

(A) 48 (B) 49 (C) 50 (D) 51

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CHEMISTRY

Theory for Purification of Compounds

Estimation of ‘C’ & ‘H’

2mass of CO12of 10044 mass of organic compound

% C

2mass of H O2of 10018 mass of organic compound

% H

Estimation of ‘N’

(a) DUMA’s method:

2vol. of N evolved @STP28% of N = × ×10022,400 mass of organiccompound

(b) KJELDAHL’s method:

2 42 4

Molarity of H SO vol. of NaOH% of N = 1.4 × × 2 vol. of H SO -mass of organic compound 2

Estimation of Halogen’s

35 5 wt. of AgClof 100143 5 wt. of compound

.% Cl.

80 wt. of AgBrof 100188 wt. of compound

% Br

127 wt. of AgIof 100235 wt. of compound

% I

Estimation of Sulphur

4wt. of BaSO32of 100233 wt. of organic compound

% S

Estimation of Phosphorus

2 2 7wt. of Mg P O formed62% of P = × × 100222 wt. of compound

Estimation of Oxygen % of oxygen = 100 sum of % of all other elements.

Environmental Chemistry

1. Which of the following is the hottest region of the atmosphere? (A) Mesosphere (B) Stratosphere

(C) Thermosphere (D) Troposphere

2. Radioactive pollutions in caused by (A) solid pollutants (B) liquid pollutants

(C) gaseous pollutants (D) None of these

3. The biotic and abiotic components that are affected adversely from harmful substances are called (A) target (B) receptor (C) atmosphere (D) Both (A) and (B)

4. Which of the following is a biodegradable pollutant? (A) Plastic (B) Sewage (C) Asbestos (D) Mercury

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5. A secondary pollutant is. (A) CO (B) CO2 (C) PAN (D) Aerosol

6. Pneumoconiosis is caused by in halation of (A) coal dust (B) silica dust (C) cotton fibre dust (D) asbestos dust

7. White lung cancer is caused by (A) asbestos (B) silica (C) paper (D) textiles

8. Chlorofluorocarbons (CFCs) are widely used by earth conditioners, refrigerators etc because of being.

(A) highly reactive (B) flammable (C) non reactive (D) All of these

9. Which of the following is a viable particulate? (A) Algae (B) Smoke (C) Mist (D) Fumes

10. Photochemical smog is caused by (A) CO (B) CO2 (C) O3 (D) NO2

11. ‘Los Angeles’ smog is (A) sulphurous smog (B) photochemical smog

(C) industrial smog (D) All of these

12. Which of the following is not a green house gas? (A) CO2 (B) Water vapour (C) CH4 (D) O2

13. What BOD5 represent? (A) Biological ozone depletion in five days

(B) Dissolved oxygen left after five days (C) Dissolved oxygen consumed in five days (D) Micro-organisms killed by ozone in sewage treatment plants in five hours

14. Drained sewage has BOD (A) more than that of water (B) less than that of water

(C) equal to that of water (D) None of these

15. Phosphate pollution is caused by (A) weathering of phosphate rocks only (B) agricultural fertilizers only

(C) phosphate rocks and sewage (D) sewage and agricultural fertilizers

16. Minamata disease is due to pollution of (A) organic waste into drinking water (B) oil spill in water (C) industrial waste mercury into fishing water (D) arsenic into the atmosphere

17. For a healthy aquatic life, the amount of dissolved oxygen in a water body must be equal to (A) 5 ppm (B) 4 ppm (C) 3 ppm (D) 2 ppm

18. Which one of the following is not an application of green chemistry? (A) Replacement of CFCs by CO2 as blowing agent in the manufacture of polystyrene foam

sheets (B) Reacting methylamine and phosgene to produce methyl isocyanate

(C) Replacement of organotins by ‘sea-nine’ as anti fouling compound in sea marines (D) Catalytic dehydrogenation of the diethanol amine without using cyanide and formaldehyde

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19. The greatest affinity for hameoglobin is shown by (A) NO (B) CO (C) O2 (D) CO2

20. When rain is accompanied by a thunderstorm, the collected rain water will have a pH value (A) uninfluenced by occurrence of thunderstorm (B) which depends on the amount of dust in air

(C) slightly lower than that of rain without thunderstorm (D) slightly higher than that when the thunderstorm is not there

21. The instrument used for measuring soil salinity is. (A) photometer (B) voltameter (C) conductivitymeter (D) calorimeter

22. Statement-1: Photochemical smog is produced by nitrogen oxides. Statement-2: Vehicular pollution is a major source of nitrogen oxides. (A) Statement-1 is True, Statement-2 is True and Statement-2 is a correct for Statement-1 (B) Statement-1 is True, Statement-2 is True and Statement-2 is NOT correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

23. Which of the following is responsible for depletion of the ozone layer in the upper strata of the atmosphere?

(A) Polyhalogens (B) Ferrocenes (C) Fullerenes (D) Freons

24. Pick p the correct statement (A) CO which is major pollutant resulting from the combustion of fuels in automobiles plays a

major role in photochemical smog (B) Classical smog has an oxidizing character while the photochemical smog is reducing in

character (C) Photochemical smog occurs in day time whereas the classical smog occurs in early morning

hours (D) During formation of smog the level of ozone in the atmosphere goes down

25. In Antarctica ozone depletion is due to the formation of following compound (A) acrolein (B) peroxyacetyl nitrate

(C) SO2 and SO3 (D) chlorine nitrate Purification of Organic Compounds

26. A mixture of camphor and benzoic acid can be easily separated by (A) sublimation (B) extraction with solvent (C) fractional crystallisation (D) chemical method

27. Chromatography technique is used for the separation of (A) small samples of mixture (B) plant pigments

(C) dyestuff (D) All of the above

28. Fractional distillation is useful in distillation of (A) petroleum (B) coal-tar (C) crude alcohol (D) All of these

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29. Steam distillation is based on the fact that vaporization of organic liquid takes place at (A) Lower temperature than is boiling point (B) higher temperature than its boiling point

(C) its boiling point (D) water and organic liquid both undergo distillation

30. Nitrogen containing organic compound when fused with sodium forms (A) sodium azide (B) sodium cyanide

(C) sodamide (D) sodium cyanate

31. In Lassaigne’s test, the organic compound is fused with a piece of sodium metal in order to (A) increased the ionization of the compound (B) decrease the melting point of the compound (C) increase the reactivity of the compound (D) convert the covalent compound into a mixture of ionic compounds

32. Copper wire test of halogens is known as (A) Liebig’s test (B) Lassaigne’s test (C) Fusion test (D) Beilstein’s test

33. Sodium nitroprusside when added to an alkaline solution of sulphide ions produces a colouration (A) red (B) brown (C) blue (D) purple

34. Duma’s method involes the determination of nitrogen content in the organic compound in the form of

(A) NH3 (B) N2 (C) NaCN (D) (NH4)2SO4

35. In estimation of nitrogen by Dumma’s method 1.18 g of an organic compound gave 224 mL of N2 at STP. The percentage of nitrogen in the compound is.

(A) 20.0 (B) 11.8 (C) 47.7 (D) 23.7

36. In Kjeldahl’s method for the estimation of nitrogen, the formula used to

(A) 1.4 VW% of NN

(B) 1.4 VN% of NW

(C) VNW% of N1.8

(D) 1.4WN% of NV

37. In the estimation of sulphur in an organic compound, fuming nitric acid is used to convert sulphur into

(A) SO2 (B) H2S (C) H2SO3 (D) H2SO4

38. In Carius method of 0.099 g organic compound gave 0.287 g AgCl. The percentage of chlorine in the compound will be

(A) 28.6 (B) 71.7 (C) 35.4 (D) 64.2

39. 0.4 g of a silver salt of a monobasic organic acid gave 0.26 g pure silver on ignition. The molecular weight of the acid is (atomic weight of silver = 108)

(A) 58 (B) 37 (C) 89 (D) 105

40. The silver salt of a monobasic acid on ignition gave 60% of Ag. The molecular weight of the acid is (A) 37 (B) 57 (C) 73 (D) 88

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41. Which of the organic compounds will give red colour in Lassaigne test?

(A) NaCNS (B) 2 2

S||

NH C NH

(C) 2 2NH CO NH (D) None of these

42. The Lassaigne’s extract is boiled with dil HNO3 before testing for halogens because (A) AgCN is soluble in HNO3

(B) silver halides are soluble in HNO3 (C) Na2S and NaCN are decomposed by HNO3

(D) Ag2S is soluble in HNO3

43. Which of the following elements can’t be detected by direct tests? (A) N (B) O (C) S (D) Br

*44. Which of the following common reactions occur during Duma’s method and Liebig’s method?

(A) 2C 2CuO 2Cu CO (B) 2N CuO N Oxides of Nitrogen

(C) 22H CuO Cu H O (D) 2 4 3 3 4 3Na PO 3HNO H PO 3NaNO

*45. Kjeldahl’s method can’t be used for estimation of nitrogen in (A) pyridine (B) C6H5NO2 (C) C6H5NHCOCH3 (D) 6 5 6 5C H N N C H

46. Naphthalene can be easily purified by (A) sublimation (B) crystallisation (C) distillation (D) vaporisation

47. Air contains 20% O2 by volume. How much volume of air will be required for 100 cc of acetylene? (A) 500 cc (B) 1064 cc (C) 212.8 cc (D) 1250 cc

48. A compound contains 69.5% oxygen and 30.5% nitrogen and its molecular weight is 92 formula of the compound is.

(A) N2O (B) NO2 (C) N2O4 (D) N2O5

49. A mixture of o-nitrophenol and p-nitrophenol can be separated by (A) fractional crystallization (B) sublimation (C) chemical separation (D) steam distillation

50. How much of sulphur is present in an organic compound, if 0.53 g of the compound gave 1.158 g of BaSO4 on analysis?

(A) 10% (B) 15% (C) 20% (D) 30%

BIO-MOLECULES & POLYMERS

51. The two forms of D-glucopyranose obtained from the solution of D-glucose are called (A) isomer (B) anomer (C) epimer (D) enantiomer

52. If D glucopyranose is reacted with acetic anhydride at 373 K, the major product is the isomer of the pentaacetate. It is attributed to.

(A) isomerisation of D int o D -glucose at 373 K (B) opening of glucopyranose ring

(C) Both the statements are correct (D) None of the statement is correct

Vidyamandir Classes

VMC 26 AIEEE-2012

53. Glucose molecules reacts with X number of molecules of phenylhydrazine to yield osazone. The value of X is.

(A) three (B) two (C) one (D) four

54. An optically active compound A, gave an 25D 30 , while a mixture of A and its enantiomer B

gave 25D 15 . The ratio of A to B in the mixture is.

(A) 1 : 3 (B) 3 : 1 (C) 1 : 2 (D) 2 : 1

55. Which enzyme is present in saliva? (A) Urease (B) Maltase (C) Lactase (D) Amylase

56. Which of the nitrogen of histidine is first protonated? (A) (B) (C) Both (A) and (B) (D) None of these

57. In an electric field, if an amino acid migrates towards cathode, the pH of the solution is said to be (A) less than pI (B) more than pI (C) equal to pI (D) 7

58. Vitamin B6 is known as (A) pyridoxin (B) thiamine (C) tocopherol (D) riboflavin

59. The deficiency of vitamin B1 causes (A) beri-bezi (B) dermatitis (C) scurvy (D) rickets

60. A DNA nucleotide chain has AGCTTCGA sequence. The nucleotide sequence of other chain would be

(A) TCGAAGCT (B) GCTAAGCT (C) TAGCATAT (D) GATCCTAG

61. DNA temple sequence of CTGATAGC is transcribed over m-RNA as. (A) GUCTUTCG (B) GACUAUCG

(C) GAUTATUG (D) UACTATUC

62. The vector for genetic code is called (A) messenger RNA (B) transfer RNA

(C) ribosomal RNA (D) viral DNA

63. The only vitamin with metal atom in it (A) vitamin A (B) vitamin K

(C) vitamin B12 (D) vitamin E

64. The reason for double helical structure of DNA is operation of (A) van der Waals’ forces (B) dipole-dipole interaction

(C) hydrogen bonding (D) electrostatic attractions

65. The chemical name of vitamin C is. (A) nicotinic acid (B) folic acid

(C) tartaric acid (D) ascorbic acid

66. The two functional groups present in a typical carbohydrate are. (A) OH and COOH (B) CHO and COOH (C) (D) OH and CHO

N

NH

N H3|

CH CHCOO2

C O and OH

Vidyamandir Classes

VMC 27 AIEEE-2012

67. Stachyose is (A) monosaccharide (B) disaccharide

(C) trisaccharide (D) tetrasaccharide

68. Which of the following is heterocyclic amino acid? (A) Glycine (B) Alanine (C) Phenylalanine (D) Tryptophane

69. Which of the following indicates open chain structures of glucose? (A) Penta-acetyl derivative of glucose (B) Cyanohydrin formation with HCN

(C) Reaction with Fehling solution (D) Reaction with Tollen’s reagent

70. Which of the following type of forces are present in Nylon-6, 6? (A) van der Waals’ forces of attraction (B) Hydrogen bonding

(C) Three dimensional network of bonds (D) Metallic bonding

71. Low density polythene is prepared by (A) free radical polymerisation (B) cationic polymerisation (C) anionic polymerisation (D) Ziegler-Natta polymerisation

72. Vulcanised rubber resists (A) wear and tear due to friction (B) high temperature

(C) action of heat (D) cryogenic temperature

73. Caprolactum is used to prepare which of the following polymer? (A) Nylon-6, 6 (B) Malamina (C) Nylon-6 (D) PMMA

74. Caprolactum is obtained from (A) cyclohexane (B) hexane (C) adipic acid (D) adipic acid and hexamethylene diamine

75. Arrange the following monomers in order of decreasing ability to undergo cationic polymerization I. 2 6 5 2NO C H CH CH

II. 2 6 5 3CH CH C H CH

III. 2 6 5 3CH CH C H OCH (A) I > II > III (B) III > II > I (C) II > I > III (D) I > III > II

*76. Which of the following fibers are made of polyamides? (A) Wool (B) Natural rubber (C) Artificial silk (D) Butyl rubber

77. Bakelite is a (A) natural polymer (B) addition polymer

(C) condensation polymer (D) homopolymer

78. Bakelite is obtained polymer phenol by reacting with (A) 2 2CH OH (B) CH3CHO (C) CH3COCH3 (D) HCHO

79. Which of the following is currently used as a true cord? (A) Polyethylene (B) Polypropylene (C) Bakelite (D) Nylon-6

80. Nylon threads are made of (A) polyvinyl polymer (B) polyester polymer

(C) polyamide polymer (D) polyethylene polymer

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VMC 28 AIEEE-2012

Chemical in Everyday Life

81. Penicillin is a/an (A) hormone (B) antibiotic (C) antipyretic (D) anagesic

82. One of the most known antiseptic, dettol is a mixture of terpineol and (A) bithional (B) chloroxylenol (C) o-cresol (D) serotonin

83. The correct structure of the drug paracetamol is.

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

84. Which of the following is not used as an antacid? (A) Magnesium hydroxide (B) Sodium carbonate

(C) Sodium bicarbonate (D) Aluminium phosphate

85. Which of the following drugs is an analgesic? (A) Sulphuaguanidine (B) Paludrin

(C) Analgin (D) Iodex

86. Oral contraceptive drugs contain (A) mestranol (B) Norethindrone (C) Both (A) and (B) (D) None of these

87. An antibiotic effective in treatment of pneumonia, bronchitis etc, is. (A) pencillin (B) patalin (C) chloromycetin (D) tetracycline

88. Match list I with list II and select the correct answer using the codes given below the lists

List-I List-II I. II. III. IV.

Iodoform Methyl salicylate Diethyl ether Hexachlorocyclohexane

A. B. C. D. E.

Anaesthetic Antiseptic Insecticide Detergent Pain balm

Codes (A) I-B, II-E, III-C, IV-D (B) I-D, II-B, III-A, IV-C

(C) I-B, II-E, III-A, IV-C (D) I-C, II-A, III-D, IV-B

89. Trade name of aspartame is. (A) Alitame (B) Saccharin (C) Sucralose (D) Nutra Sweet

90. Choose the correct statement. (A) Saccharin is 650 times sweeter than sugar (B) Aspartame is 550 times sweeter than sugar (C) Sucralose is 160 times sweeter than sugar (D) Alitame is 2000 times sweeter than sugar

91. Which of the following is a germicide also? (A) Cationic detergent (B) Anionic detergent

(C) Non-ionic detergent (D) None of the above

OH

CONH2

OH

NHCOCH3

Cl

CONH2

Cl

COCH3

Vidyamandir Classes

VMC 29 AIEEE-2012

92. Which of the following represents a synthetic detergent? (A) 15 31C H COOK (B) 3 2 6CH CH COONa

(C) (D) All of the above

93. Detergents obtained from LAB are biodegradable. LAB stands for. (A) laboratory tested raw material (B) low anionic balance

(C) linear alkyl benzene (D) None of the above

94. An antibiotic contains nitro group attached to aromatic nucleus in its structure. It is (A) pencillin (B) streptomycin

(C) tetracyclin (D) chloramphenicol

95. Aspartame is one of the good artificial sweeteners whose use is limited to cold foods and soft drinks because.

(A) it has very low boiling point (B) it gets dissociated at cooking temperature (C) it is sweetener at low temperature only (D) it is insoluble at higher temperatures

96. Morphine on alkylation and acetylation gives respectively. (A) heroin, codeine (B) heroin, meperidine (C) codeine, heroin (D) meperidine, heroin

97. Which set has different class of compounds? (A) Tranquillizers : equanil, heroin, valium (B) Antiseptic : bithional, dettol, boric acid

(C) Analgesics : naproxen, morphine, aspirin (D) Bacericidal : Pencillin, aminoglycosides, ofloxacin

*98. Which of the following drugs are used for the treatment of tuberculosis? (A) PAS (B) INH (C) Streptomycin (D) Chloromycetin

For Q-99-100

In the following set of questions, a Statement-1 is given and corresponding Statement-2 is given below it. Mark the correct answer as:

(A) Statement-I is True, Statement-II is True and Statement-II is a correct for Statement-I (B) Statement-I is True, Statement-II is True and Statement-2 is NOT correct explanation for Statement-I (C) Statement-I is True, Statement-II is False (D) Statement-I is False, Statement-II is True

99. Statement-I: Paracetamol is popular antipyretics Satement-II: it is used to bring down the body temperature during fever.

100. Statement-I: Tertiary butyl hydroquinone is an antioxidant. Statement-II: Antioxidants inhibit free radical reactions.

101. Match the chemicals in Column-I with their uses in Column-II. Column-I Column-II

(I) Sodium perborate (p) Disinfectant (II) Chlorine (q) Antiseptic (III) Bithional (r) Milk bleaching (IV) Potassium strearate (s) Soap

(A) I : p, II : q, III :r, IV : s (B) I : q, II : r, III : s, IV : p (C) I : r, II : p, III : q, IV : s (D) I : s, II : p, III : q, IV : r

C12H25 SO3Na

Vidyamandir Classes

VMC 30 AIEEE-2012

102. Bithional is added to soap as an additive to function as a/an. (A) softner (B) hardener (C) dryer (D) antiseptic

103. The drug used to bring down fever are known as. (A) analgesic (B) antibiotic (C) antipyretic (D) sulpha drugs

104. Which of the following is not an antibiotic? (A) Penicillin (B) Oxytocin (C) Ofloxacin (D) Tetracycline

105. Chloramphenicol is. (A) narrow spectrum antibiotic (B) broad spectrum analgesic

(C) broad spectrum antibiotic (D) broad spectrum antibacterial

Vidyamandir Classes

VMC 31 AIEEE-2012

MATHEMATICS

1. cA B A is equal to :

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

2. A B C is equal to :

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

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

3. The group of beautiful girls is : (A) a null set (B) a finite set (C) a singleton set (D) not a set

4. If A B , then A B is equal to

(A) A B B A (B) A B

(C) B A (D) None of these

5. If A = {1, 2, 3] and B = {3, 4}, then A B A B is :

(A) {3, 3} (B) {(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4)} (C) {(1, 3), (2, 3), (3, 3)} (D) {(1, 3), (2, 3), (3, 3), (4, 3)}

6. If A = {5, 6, 7} and B = {1, 2, 3, 4}, the number of elements in set A B B is equal to : (A) 36 (B) 48 (C) 16 (D) None of these

7. In a battle 70% of the combatants lost one eye, 80% an ear, 75% an arm, 85% a leg, x% lost all the four limbs. The minimum value of x is :

(A) 10 (B) 12 (C) 15 (D) None of these

8. In a city 20 per cent of the population travels by car, 50 per cent travels by bus and 10 per cent travels by both car and bus. Then persons travelling by car or bus is :

(A) 80 per cent (B) 40 per cent (C) 60 per cent (D) 70 per cent

9. R is a relation over the set of real numbers and it is given by 0nm . Then R is : (A) symmetric and transitive (B) reflexive and symmetric (C) a partial order relation (D) an equivalence relation

10. Let R = {(1, 3), (2, 2), (3, 2)} and S = {(2, 1), (3, 2), (2, 3)} be two relations on set A = {1, 2, 3}. Then RoS is equal to :

(A) {(1, 3), (2, 2), (3, 2), (2, 1), (2, 3)} (B) {(3, 2), (1, 3)} (C) {(2, 3), (3, 2), (2, 2)} (D) {(2, 3), (3, 2)}

11. Let N denotes the set of all natural numbers and R be the relation on N N defined by (a, b) R(c, d) if ad (b + c) = bc (a + d), then R is :

(A) symmetric only (B) reflexive only (C) transitive only (D) an equivalence relation

12. Let L be the set of all straight lines in the Euclidean plane. Two lines l1 and l2 are said to be related by the relation R, iff l1 is parallel to l2. Then the relation R is :

(A) reflexive (B) symmetric (C) transitive (D) equivalence

13. A class has 175 students. The following data shows the number of students obtaining one or more subjects, Mathematics 100, Physics 70, Chemistry 40, Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone ?

(A) 35 (B) 48 (C) 60 (D) 22

Vidyamandir Classes

VMC 32 AIEEE-2012

14. Consider the following statements : I. The product of two even or odd function is an even function. II. The products of an even function and an odd function is an odd function. III. Every function can be expressed as the sum of an even and an odd function. Which of the statements given above is(are) correct ? (A) Only I (B) Only II (C) Only III (D) All I, II and III

15. N is the set of natural numbers. The relation R is defined on N N as follows : a, b R c, d a d b c is :

(A) reflexive (B) symmetric (C) transitive (D) all of these

16. If 1 2

2 1A

and 31

B , AX B

, then X is equal to :

(A) [0, 7] (B) 5173

(B) 1 5 73

(D) 57

17. If 1 11 1

A

, then A100 is equal to :

(A) 2100 A (B) 299 A (C) 100 A (D) 299 A

18. For the matrix 1 1 01 2 12 1 0

A

, which of the following is correct ?

(A) 3 23 0A A I (B) 3 23 0A A I (C) 3 22 0A A I (D) 3 2 0A A I

19. For non-singular square matrices A, B and C of same order, 11AB C is equal to :

(A) 1 1A BC (B) 1 1 1C B A (C) 1 1CB A (D) 1 1C BA

20. If A and B are square matrices of size n n such that 2 2A B A B A B , then which of the following

will be always true ? (A) AB = BA (B) either of A or B is a zero matrix (C) either of A or B is an identity matrix (D) A = B

21. Let 1

2

3

1 1 22 0 13 2 1

xX x , A

x

and 314

B

. If AX = B, then X is equal to :

(A) 123

(B) 12

3

(C) 123

(D) 1

23

22. If matrix 3 2 41 2 10 1 1

A

and 1 1A adj Ak

, then k is :

(A) 7 (B) 7 (C) 1/7 (D) 11

23. If 3 45 7

A

, then A . (adj A) is equal to :

(A) A (B) | A | (C) | A | I (D) None of these

Vidyamandir Classes

VMC 33 AIEEE-2012

24. If 1 2 11 1 2

2 1 1A

, then det [adj (adj A)] is equal to :

(A) 124 (B) 134 (C) 144 (D) None of these

25. If D = diagonal [d1, d2, d3, . . . . , dn], where 0id

1 2 3i , , , . . . ., n , then 1D is equal to :

(A) O (B) In

(C) diagonal 1 1 11 2 nd , d , . . . , d (D) None of these

26. If 3 2 1 2 1 1

0 11 2 3 2

/ /P , A

/ /

and TQ PAP , then 2005TP Q P is :

(A) 1 20050 1

(B) 1 2005

2005 1

(C) 1 0

2005 1

(D) 1 00 1

27. ‘A’ is any square matrix, then TTdet A A is equal to :

(A) 0 (B) 1 (C) can be 0 or a perfect square (D) cannot be determined

28. A square matrix P satisfies 2P I P , where I is the identity matrix. If 5 8nP I P , then n is equal to : (A) 4 (B) 5 (C) 6 (D) 7

29. If ijA a is a 4 4 matrix and ijc is the co-factor of the element ija in A , then the expression

11 11 12 12 13 13 14 14a c a c a c a c is equal to :

(A) 0 (B) 1 (C) 1 (D) | A |

30. The value of for which the system of equations 1x y z 2 4x y z

24 10x y z

is consistent, are given by : (A) 1 2, (B) 1 2, (C) 1, 2 (D) None of these

31. If P(n) is a statement n N such that, if P(k) is true, P(k + 1) is true for k N , then P(n) is true :

(A) for all n (B) for all n > 1 (C) for all n > 2 (D) nothing can be said

32. If P(n) is a statement such that P(3) is true. Assuming P(k) is true 1P k is true for all 3k , then P(n)

is true : (A) for all n (B) for 3n (C) for 4n (D) None of these

33. If : 3 !,nP n n n N , then P(n) is true :

(A) for 6n (B) for 7n (C) for 3n (D) for all n

34. Let P(n) : n2 + n + 1 is an even integer. If P(k) is assumed true P(k + 1) is true. Therefore P(n) is true : (A) for n > 1 (B) for all n N (C) for n > 2 (D) None of these

35. The greatest positive integer, which divides (n + 2) (n + 3) (n + 4) (n + 5) (n + 6) for all n N , is :

(A) 4 (B) 120 (C) 240 (D) 24

Vidyamandir Classes

VMC 34 AIEEE-2012

36. The smallest positive integer n for which 1!2

nnn

holds, is :

(A) 1 (B) 2 (C) 3 (D) 4

37. If m, n are any two odd positive integer with n < m, then the largest positive integers which divides all the

numbers of the type 2 2m n is : (A) 4 (B) 6 (C) 8 (D) 9

38. 1 1 1n n nx x n n is divisible by 2x for :

(A) n > 1 (B) n > 2 (C) all n N (D) None of these

39. 2 1 3 12 4 3n n is divisible by for all n N :

(A) 2 (B) 9 (C) 3 (D) 11

40. The inequality 1! 2nn is true for : (A) n > 2 (B) n N (C) n > 3 (D) None of these

41. In a triangle ABC, a = 5, b = 7 and 34

sin A , then the number of possible triangles are :

(A) 1 (B) 0 (C) 2 (D) infinite

42. In ABC , 2 22 2 2 2A B B Acot cot a sin b sin

is equal to :

(A) cot C (B) c cot C (C) 2Ccot (D)

2Cccot

43. In 2 222 2C AABC, a sin c sin

is equal to :

(A) a b c (B) c a b (C) b c a (D) a + b + c

44. In ABC , if 12 2 2A Ctan tan , then a, b, c are in :

(A) AP (B) GP (C) HP (D) None of these

45. In a triangle ABC, 2sin Bcos AsinC

, then the triangle is :

(A) equilateral (B) isosceles (C) right angled (D) None of these

46. In triangle ABC, if 45 75A , B , then 2a c is equal to :

(A) 0 (B) 1 (C) b (D) 2b

47. In a triangle ABC, 3 3 3a cos B C b cos C A c cos A B is equal to :

(A) abc (B) 3 abc (C) a + b + c (D) None of these

48. If the area of a triangle ABC is , then 22 2a sin B b sin A is equal to : (A) 3 (B) 2 (C) (D)

49. If 2 2 2a , b , c are in AP, then which of the following are also in AP ?

(A) sin A, sin B, sin C (B) tan A, tan B, tan C (C) cot A, cot B, cot C (D) None of these

50. In ABC, a cos A b cos B c cos C is equal to :

(A) 4 R sin A sin B sin C (B) 3R sin A sin B sin C (C) sin A sin B sin C (D) 4R cos A cos B cos C

Vidyamandir Classes

VMC 35 AIEEE-2012

51. If in a triangle PQR, sin P, sin Q, sin R are in AP, then : (A) the altitude are in AP (B) the altitude are in HP (C) the medians are in GP (D) the medians are in AP

52. In triangle ABC, b ca is equal to :

(A) 1

212

cos B C

sin A

(B)

12

12

sin B C

cos A

(C)

12

12

cos B C

sin A

(D)

12

12

cos B C

cos A

53. In triangle ABC, (b + c) cos A + (c + a) cos B + (a + b) cos C is : (A) 0 (B) 1 (C) a + b + c (D) 2 (a + b + c)

54. In triangle ABC, if cos A cos B cos Ca b c

, then the triangle is :

(A) right angled (B) obtuse angled (C) equilateral (D) isosceles

55. In ABC , if 2 2 22 2 2A B Csin , sin , sin be in HP, then a, b, c will be in :

(A) AP (B) GP (C) HP (D) None of these

56. In ABC , if sin A : sin C = :sin A B sin B C , then :

(A) a, b, c are in AP (B) a2, b2, c2 are in AP (C) a2, b2, c2 are in GP (D) None of these

57. The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the sides of the triangle are :

(A) 1, 2, 3 (B) 2, 3, 4 (C) 3, 4, 5 (D) 4, 5, 6

58. In a ABC , among the following which one is true ?

(A) 2 2A B Cb c cos a sin

(B)

2 2B C Ab c cos a sin

(C) 2 2

B C Ab c cos a cos

(D) 2 2A B Cb c cos a sin

59. If in a triangle ABC, CD is the angle bisector of the angle ACB, then CD is equal to :

(A) 2 2a b Ccos

ab (B)

2a b Ccosab (C) 2

2ab Ccos

a b (D) None of these

60. In a triangle ABC, if D s middle point of BC and AD is perpendicular to AC, then cos B is equal to :

(A) 2ba

(B) ba

(C) 2 2b cca (D)

2 2c aca

61. Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is :

(A) 48 (B) 82 (C) 50 (D) 80

62. The mean of the values of 1, 2, 3, . . . . ., n with respectively frequencies x, 2x, 3x, . . . . , nx is :

(A) 2n (B) 1 2 1

3n (C) 1 2 1

6n (D)

2n

63. The mean of n items is X . If the first term is increased by 1, second by 2 and so on, then the new mean is:

(A) X n (B) 2nX (C) 1

2nX

(D) None of these

Vidyamandir Classes

VMC 36 AIEEE-2012

64. The AM of the series 1, 2, 4, 8, 16, . . . . , 2n is :

(A) 2 1n

n (B)

12 11

n

n

(C) 2 1n

n (D) 2 1

1

n

n

65. In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls :

(A) 73 (B) 65 (C) 68 (D) 74

66. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set :

(A) is increased by 2 (B) is decreased by 2 (C) is two times the original median (D) remains the same as that of the original set

67. If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately: (A) 24.0 (B) 25.5 (C) 20.5 (D) 22.0

68. Let x1, x2, . . . . . , xn be n observations such that 2 400ix and 80ix . Then a possible value of n among

the following is : (A) 12 (B) 9 (C) 18 (D) 15

69. In a series of 2n observations, half of them equal a and remaining half equal a . If the standard deviation of the observations is 2, then | a | equal to :

(A) 1n

(B) 2 (C) 2 (D) 2n

70. In a class of 100 students, the average amount of pocket money is Rs.35 per student. If the average is Rs.25 for girls and Rs.50 per boys, then the number of girls in the class is :

(A) 20 (B) 40 (C) 60 (D) 80

71. The AM of n observations is M. If the sum of 4n observation is a, then the mean of remaining four

observations is :

(A) 4

nM a (B) 2

nM a (C) 2

nM a (D) nM + a

72. If 1X and 2X are the means of two distributions, such that 1 2X X and X is the mean of the combined

distribution, then :

(A) 1X X (B) 2X X (C) 1 22

X XX (D) 1 2X X X

73. The first of two samples has 100 items with mean 15 and SD = 3. If the whole group has 250 items with mean

15.6 and 13 44SD . the SD of the second group is : (A) 5 (B) 4 (C) 6 (D) 3.52

74. The marks of some students were listed out of 75. The SD of marks was found to be 9. Subsequently the marks were raised to a maximum of 100 and variance of new marks was calculated. The new variance is :

(A) 144 (B) 122 (C) 81 (D) None of these

75. Suppose a population A has 100 observations 101, 102, . . . . . , 200 and another population B has 100 observations 151, 152, . . . . ., 250. If VA and VB represent the variances of the two population respectively, then VA/VB is :

(A) 9/4 (B) 4/9 (C) 2/3 (D) 1

76. If p = He is intelligent, q = He is strong. Then, symbolic form of statement “It is wrong that he intelligent or strong,” is :

(A) ~ p ~ q (B) ~ p q (C) ~ p q (D) p ~ q

Vidyamandir Classes

VMC 37 AIEEE-2012

77. The switching function for the following network is :

(A) p q r t

(B) p q r t

(C) p r q t

(D) None of these

78. If p and q are two statements, then ~ p q ~ q p is :

(A) tautology (B) contradiction (C) neither tautology nor contradiction (D) either tautology nor contradiction

79. A compound sentence formed by two simple statements p and q using connective ‘and’ is called (A) conjunction (B) disjunction (C) implication (D) None of these

80. If statements p and r are false and q is true, then truth value of ~ p q r r is a :

(A) tautology (B) contradiction (C) neither tautology nor contradiction (D) both tautology and contradiction

81. Let p and q be two statements. Then, p q is false, if :

(A) p is false and q is true (B) Both p and q are false (C) Both p and q are true (D) None of these

82. Let p q r p q p r . Then, this law is known as :

(A) Commutative law (B) Associative law (C) De-Morgan’s law (D) Distributive law

83. The switching function for switching network is :

(A) x y y z z x (B) x y z x y z

(C) x y y z z x (D) None of these

84. Switching function of the network is :

(A) a b c a b c (B) a b c a b c

(C) a b c a b c (D) None of these

85. The statement p ~ p is :

(A) Tautology (B) Contradiction (C) Neither a tautology nor a contradiction (D) None of these

86. If p q r is false, then truth values of p, q, r are respectively :

(A) F, T, T (B) T, T, F (C) T, F, F (D) F, F, F

Vidyamandir Classes

VMC 38 AIEEE-2012

87. If p ~ p q is false, the truth values of p and q are respectively :

(A) F, T (B) F, F (C) T, T (D) T, F

88. H : Set of holidays. S : Set of Sundays. U : Set of day’s Then, the Venn diagram of statement, “Every Sunday implies holidays” is :

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

89. If p : A man is happy. q : A man is rich. Then, the statement, “If a man is not happy, then he is not rich” is written as : (A) ~ p ~ q (B) ~ q p (C) ~ q ~ p (D) q ~ p

90. If p : Ram is smart. q : Ram is intelligent. Then, the symbolic form Ram is smart and intelligent, is :

(A) p q (B) p q (C) p ~ q (D) p ~ q

Vidyamandir Classes

VMC 39 AIEEE-2012

Answers

PHYSICS:

1 2 3 4 5 6 7 8 9 10

A C A C D B B A D C

11 12 13 14 15 16 17 18 19 20

C B D C C C B C A A

21 22 23 24 25 26 27 28 29 30

B D D B C D B A A A

31 32 33 34 35 36 37 38 39 40

D D B C D B B B A B

41 42 43 44 45 46 47 48 49 50

B B B C C C B D B B

51 52 53 54 55 56 57 58 59 60

D A A A D B B D A D

61 62 63 64 65 66 67 68 69 70

C A C A C A A A B A

71 72 73 74 75 76 77 78 79 80

A B A A C A A A A D

81 82 83 84 85 86 87 88 89 90

C D B B A D C B C C

91 92 93 94 95 96 97 98 99 100

B B B D A A B D C D

101 102 103 104 105 106 107 108 109 110

C B A C B A D B B A

111 112 113 114 115 116 117 118 119 120

A B B C D C C A A C

121 122 123 124 125 126 127 128 129 130

B C C C C D A B D A

131 132 133 134 135 136 137 138 139 140

B D D B C A A D B A

141 142 143 144 145 146 147 148 149 150

B C C C B A C A D A

151 152 153 154 155 156 157 158

C B D B A B A B

Vidyamandir Classes

VMC 40 AIEEE-2012

CHEMISTRY:

1 2 3 4 5 6 7 8 9 10

C D D B C D B C A D

11 12 13 14 15 16 17 18 19 20

B D C A D C A B A C

21 22 23 24 25 26 27 28 29 30

C B D D A D D D A B

31 32 33 34 35 36 37 38 39 40

D D D B D B D B A C

41 42 43 44 45 46 47 48 49 50

B C B AB ABD A D C D D

51 52 53 54 55 56 57 58 59 60

B A A B D B A A A A

61 62 63 64 65 66 67 68 69 70

B B C C D C D D A B

71 72 73 74 75 76 77 78 79 80

A A C A B ABD C D D C

81 82 83 84 85 86 87 88 89 90

B B B B C C C C D D

91 92 93 94 95 96 97 98 99 100

A C C D B C A ABC A A

101 102 103 104 105

C D C B C

MATHEMATICS:

1 2 3 4 5 6 7 8 9 10

D A B C D B A C D C

11 12 13 14 15 16 17 18 19 20

D D C D D B B B D A

21 22 23 24 25 26 27 28 29 30

D D C C C A C C D C

31 32 33 34 35 36 37 38 39 40

D B B D B B C C D C

41 42 43 44 45 46 47 48 49 50

B D B D B D B C C A

51 52 53 54 55 56 57 58 59 60

B A C C C B D D D C

Vidyamandir Classes

VMC 41 AIEEE-2012

61 62 63 64 65 66 67 68 69 70

C B D B B D A C C C

71 72 73 74 75 76 77 78 79 80

A D B A D C B C A B

81 82 83 84 85 86 87 88 89 90

B D A A A C D C A A