Aieee-2012 Study Material

Vidyamandir Classes

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EXTRA PREPARATORY MATERIAL FOR AIEEE PHYSICS Reynolds Number Re: Re 

 vd 

 : density

where

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 F  F0 cos d t where d is called driven frequency then equation of motion is given as ma   kx  bv  F0 cos d t or

m

d 2x 2

 b

dx  kx  F0 cos d t . dt

dt 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 x  A cos d t    Where A 

F0

m  2

2



 d2  d2 b2

1/ 2



and tan  

v0 d x0

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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1

AIEEE-2012

Vidyamandir Classes I  n e Avd

…(1)

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

also vd 

eE  m

…(2)

E : electric field m : mass of e  s e : electronic charge  : relaxation time.

I ne2   E and comparing it with microscopic from A m of ohm’ Law i.e. J   E , we have (where  : conductivity) From equation (1) and (2) we have current density J 

ne2  m Mobility  : An important quantity is the mobility  is defined as the magnitude of the drift velocity per unit

 

electric field.



 vd  E

& vd 

eE  m

e  m



Colour Codes of resistance: First band

2nd band

Third band Last band

The resistors have a set of coaxial colourd rings on them whose significance is listed in table. Colour Black Brown Red Orange Yellow Green Blue Violet Gray White

Number 0 1 2 3 4 5 6 7 8 9

Multiplier 1 101 102 103 104 105 106 107 108 109

101

Gold

10

Silver Nocolour Note:

2

Tolerance (%)

5 10 20

the order of the first letter of the colours can be learned as B B ROY G B V G W of reat ritain has a ery ood ife 0 1 2 3 4 5 6 7 8 9

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.

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AIEEE-2012

Vidyamandir Classes 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 m mv T   and R  and R is increased as velocity is increased by an oscillating electric field between the two f qB qB 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 2  107 Newton’s per meter of length Current sensitivity of the galvanometer: is defined as the deflection per unit length.

 N AB  I K

N : no. of turns A : area of coil B : magnetic field strength K : torque constant of spring

Bar magnet as an equivalent solenoid:

2 a

i

B

B

0 2m 4 r 3

r m is magnetic moment of the bar, m  i  a 2 . 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 T  2

I mB

Sharpness of resonance: It is also called the quality factor Q of the circuit.   L 1 Q 0  0  2 R 0CR 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 .

1 0 0

*

speed of light in vacuum C 

*

speed of light in medium whose electric permittivity is E and magnetic permeability  is v 

1 

*

If total energy transferred to a surface in time t is U, then magnitude of the total momentum delivered to this U surface (for complete absorption) is P  . C The microscope: D * Simple microscope: linear magnification m  1  ; D  25 cm f f : focal length. D angular magnification when image formed at infinity m  f *

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 L D Compound microscope: m  m0 me       f0   fe 

3

AIEEE-2012

Vidyamandir Classes f0 if length of the telescope is f0 + fe fe

*

Telescope: m 

*

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 n (i) Angular position of the nth secondary minimum  n   nD (ii) Distance of the nth secondary maximum from the centre of the screen xn  

*

* *

*

Angular positions of the nth secondary maximum  n 

(iv)

Distance of the nth secondary maximum from the centre of the screen xn 

*. *. *.

 2n  1 D

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

I  I 0 cos 2 

Doppler shift.

v v c v (B) Δ    c 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 nb  ne . (A)

*. *.

2n

2 D (v) Width of a secondary maximum or minimum    2D (vi) Width of the central maximum 0   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   tan i p

Mathematically *

 2n  1 

(iii)

Δv  

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 ne is the electron density and nb in the hole density the material will be n-type if ne  nb . The material will be p-type if nb  ne .

*.

In metals, valence band and conduction band overlap therefore, energy gap, E g  0 . In semiconductors

E g  1eV and insulators have E g  6eV . *.

In n-type semiconductor, conductivity  n  ne e e In p-type semiconductor conductivity  p  nb b e In intrinsic semiconductor conductivity  int rinsic  nb eb  ne ee

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4

AIEEE-2012

Vidyamandir Classes *.

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 ic Current gain Ai     1 ie

*. *.

*. *.

Voltage gain AV   

R1 1 ri

In common base (CB) Amplifier   hFB

R1 1 r1

Power gain Ap   2

No phase shift between input and output *. Current gain A1   

ir 1 ip

Voltage gain AV   

Power gain Ap  

R1 1 ri

In common base (CE) Amplifier   hFB

R1 1 r1

Phase shift = 180º or  rad

  and   1 1 

*.

ie  ic  ib   

*.

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

A  A  1 its dual = A. A  0

(iii) (iv)

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

(v)

A  AB  A  B its dual A A  B  AB

(vi) (vii) * * *

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



A  B  A.B ; A . B  A  B A  A111 0  0

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

5

AIEEE-2012

Vidyamandir Classes A 0 0 1 1

B 0 1 0 1

Y 0 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 0 1

Y 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 1019  -particle and 1019 protons move to the left, while 1019 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 = 9  103 kg m 3 and atomic weight of copper = 63) (A)

4.

0.1 mms 1

0.2 mms 1

(C)

0.3 mms 1

(D)

0.2cms 1

A charge of 2  102 C move at 30 revolutions per second in a circle of diameter 80cm. The current linked with the circuit is : (A) 0.02 A

5.

(B)

(B)

20 A

(C)

0.60 A

(D)

60 A

The electron hydrogen atom is considered to be revolving round a proton in circular orbit of radius  2 / me2 with velocity e 2 /  , where   h / 2 . The current is : (A)

6.

4 2 me5 2

(B)

4 2 me2

(C)

3

4 2 m 2 e2 3

(D)

4 2 me5 3

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 107 m 2 , carrying a current of 1.5 A? (Given density of copper = 9  103 kgm 3 ; atomic mass of copper = 63.5 ; Avogadro’s number = 6.023  1023 per gram atom) (A)

7.

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1.1  102 ms 1

(B)

1.1  103 ms 1

(C)

2.2 102 ms 1

(D)

2.2  103 ms 1

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) 4C

6

AIEEE-2012

Vidyamandir Classes 8.

In the above question if potential difference is applied, the drift velocity at temperature T is : (A) (C)

Inversely proportional to T zero

(B) (D)

proportional to T 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)

11.

is

(B)

i/s

(C)

 i / s 2

(D)

The amount of charge Q passed in time t through a cross – section of a wire is Q  5t 2  3t  1 . The value of current at time t = 5 s is : (A) 9A (B)

12.

i/s

49A

(C)

53A

(D)

None of these

In a neon gas discharge tube Ne  ions moving through a cross – section of the tube each second to the right is

2.9  1018 , while 1.2  1018 electrons move towards left in the same time ; the electronic charge being 1.6  1019 C , the net electric current is : (A) (C) 13.

(B) (D)

0.66 A to the right zero

The speed at which the current travels, in a conductor, is nearly (A)

14.

0.27 A to the right 0.66 A to the left

3  104 ms 1

(B)

3  105 ms 1

(C)

4  106 ms 1

3  108 ms 1

(D)

If the electronic charge is 1.6  1019 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)

1.25  1017

(B)

1.6  1017

(C)

1.25  1019

1.6  1019

(D)

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) (C)

Proportional to T zero

(B) (D)

proportional to T 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)

VMC

R  A1

(B)

RA

(C)

7

R  A2

(D)

R is independent of A

AIEEE-2012

Vidyamandir Classes 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

21.

(B)

4mA

(C)

1mA

(D) 6

0.5 mA 2

There is a current of 0.21 A in a copper wire whose area of cross – section is 10 m . If the number of free electrons per m3 is 8.4 1028 , then find the drift velocity, ( e  1.6  1019 C ) (A)

2  105 ms 1

(B)

1.56  105 ms 1 (C)

1 105 ms 1

(D)

0.64  105 ms 1

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 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

27.

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)

29.

30.

4

(D)

1/ 2 2

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

3M

(C) (D)

2M M /2

A short bar magnet placed with its axis at 30 , with a uniform external magnetic field of 0.25T experiences a torque of 4.5  102 N  m . Magnetic moment of the magnet is : (A)

31.

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0.36 J T 1

(B)

0.72 J T 1

(C)

0.18 JT 1

(D)

Zero

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

8

AIEEE-2012

Vidyamandir Classes 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)

33.

zero

(B)

2BH

(C)

5 BH 2

(D)

5 BH

The earth’s magnetic induction at a certain point is 7  101Wbm 2 . 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 (A)

zero

(B)

3 times the vertical component. The angle of dip at this place is

 /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 6.8  105 . The percentage increase in the magnetic field will be : (A) 0.0068 % (B)

40.

41.

(C)

0.68%

(D)

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

None of these

antiferromagnetic

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)

42.

0.0068%

T/2

(B)

T/4

(C)

2T

(D)

2T

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 36  106 T , then its value at B is (A)

43.

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36  106 T

(B)

9  106 T

(C)

144  106 T

(D)

228  106 T

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

9

AIEEE-2012

Vidyamandir Classes 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 0.34  104 T is along the plane of the coil. The magnetic intensity is : (A)

1.96  104 T

(B)

1.96  104 T

(C)

1.96  105 T

(D)

1.96  105 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.

47.

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

48.

3s

(B)

(C)

3 3s

3 / 3s

(D)

6s

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

49. 50.

51.

VMC

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

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

10

AIEEE-2012

Vidyamandir Classes 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 The focal length of objective lens is (A)

5

(B)

1 cm . What is the magnification of eye piece? 4 10 (C) 100 (D)

1 cm . 3.8

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 3.5  103 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 40 (A) (B) (C) 2 21

58.

(D)

50

With diaphragm of the camera lens set at f / 2 , 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) (B) (C) (D) 48  40 40 48 40  48 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 D and  3D (B)  2 D and  3D (C) 2 D and  0.33D (D)

64.

VMC

2 D and  0.33D

A hypermetropic person has to use a lens of power +5D to normalize his vision. The near point of the hypermetropic eye is (A) 1m (B) 1.5 m (C) 0.5 m (D) 0.66 m

11

AIEEE-2012

Vidyamandir Classes 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) (B) (C) (D) 95 / 6 cm 5 cm 95 / 89 cm 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)

0.5  102 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) (C) 1.8 m (D) 0.18 m 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)

72.

2 mm

(B)

2 cm

(C)

2m

(D)

2 km

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 2  102 cm . The width of the principal maximum on a screen distance 50 cm will be : (A)

75.

VMC

312.5  103 cm (B)

312.5  104 cm (C)

312 cm

(D)

312.5  105 cm

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.

12

AIEEE-2012

Vidyamandir Classes 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)

78.

5000 Å

(B)

(C)

2500 Å

7500 Å

(D)

What should be refractive index of a transparent medium to be invisible in vacuum? (A) 1 (B) 1 (D)

8500 Å

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)

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)

82.

84.

85.

2I0

(B)

1 2

(B)

(C)

I0/4

(D)

I0 / 2

3 2

(C)

3 2

(D)

1.732

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 :

a2 2 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)

2a 2

(B)

a2

(C)

2a 2

(D)

(A)

80 gL1

(B)

75 gL1

(C)

65 gL1

(D)

50gL1

If for a calcite crystal o and e are the refractive indices of the crystal for O-ray and E-ray respectively, then along the optic axis of the crystal (A) (B) o  e

86.

I0/2

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)

83.

Polarisation

e  o

(C)

e  o

(D)

None of these

a and m are the wavelength of a beam of light in air and medium respectively. If  is the polarizing single, the correct relation between a  m and  is : (A)

a  m tan 2 

(B)

m  a tan 2 

(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 : 56 68 34 (A) (B) (C) (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

VMC

(B)

60

(C)

13

90

(D)

0

AIEEE-2012

Vidyamandir Classes 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 ne and nh in an intrinsic semiconductor at ordinary temperature is (A)

91.

ne  nh

(B)

ne  nh

(C)

ne  nh

(D)

ne  nh  0

The resistivity of a semiconductor at room temperature is in between ? (A)

102 to 105 Ωcm

(B)

102 to 106 Ω cm

(C)

106 to 108 Ω cm

(D)

1010 to 1012 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) (C) increase of resistance of the semiconductor (D)

production of p-semiconductor 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

5  107 silicon atoms. If the number density of atoms in the silicon specimen in 5  1028 atoms m 3 , then the number of acceptor atoms in silicon per cubic centimeter will be :

99. 100.

(A)

2.5  1030 atoms cm 3

(B)

2.5  1035 atoms cm 3

(C)

1.0  1013 atoms cm 3

(D)

1.0  1015 atoms cm 3

The typical ionization energy of a donar in silicon is (A) 10.0 eV (B) 1.0 eV (C)

(D)

0.0001 eV

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



be h  6.62  1034 Js  c  3  108 ms 1 (A)

VMC

0.1 eV

10.888 Å

(B)



108.88 Å

(C)

14

1088.8 Å

(D)

10888Å

AIEEE-2012

Vidyamandir Classes 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) 100 200 (C) (D) 280 2

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) (B) (C) (D) 100 Ω 120 Ω 200 Ω 240 Ω

105.

The value of ripple for full wave rectifier is : (A) 40.6% (B) 48.2%

106.

107.

81.2 %

(D)

121%

The average value of output direct current in a half wave rectifier is : I0 /  I0 / 2  I0 / 2 (A) B) (C)

(D)

2I 0 / 

For a junction diode the ratio of forward current ( I p ) and reverse current ( I r ) is : [ I e = electronic charge,

V = voltage applied across junction

K = Boltzmann constant

T = temperature in Kelvin]

(A) 108.

(C)

e

V / kT

(B)

e v / kT

(C)

e

 eV / kT



1

(D)

e

V / KT



1

The value of current in the following diagram will be (A) zero (B) (C) (D)

102 A 10A 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

VMC

15

AIEEE-2012

Vidyamandir Classes 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)

113.

2  105 Ω

(B)

2.5  105 Ω

(C)

3  105 Ω

(D)

4  105 Ω

Consider the junction diode is ideal. The value of current in the figure is : (A)

zero

(B)

102 A

(C)

101 A

(C)

103 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) Ic  Ib (B) Ic  Ie (C) Ic  Ie

(D)

Ic  Ib

Current gain in common base configuration is less than 1 because (A) Ie  Ib (B) Ib  Ie (C) Ic  Ie

(D)

Ie  Ic

116.

117. 118.

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

A transistor has   40 . A change in base current of 100  A , produces change in collector current. (A)

119.

100

40  100  A

(B)

100  40 A

(C)

100  40  A

(D)

100  40  A

Current gain  AC common emitter mode of transistor is (A)

 ΔI   AC   C   VC = constant  ΔI S 

(B)

 I   AC   B   VC = constant   IC 

 ΔI   ΔI   AC   C   VC = constant (D)  AC   E   VC = constant Δ I  E  ΔI C  Current gain of a transistor in common base mode is 0.95. Its value in common emitter mode is : (C)

120.

(A)

0.95

(B)

1.5

(C)

19

(D)

19 1

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   60 R0  5000Ω and internal resistance of a transistor if 500 Ω . The voltage amplification of amplifier will be :

(A) 123.

VMC

500

(B)

460

(C)

600

(D)

560

In a n-p-n transistor 1010 electrons enter the emitter in 106 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

16

AIEEE-2012

Vidyamandir Classes 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

127.

25.125

(D)



What is the value of A . A in Boolean algebra? (A)

128.

(D)

zero

(B)

1 (one)

(C)

A

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   A / 2 (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

VMC

17

AIEEE-2012

Vidyamandir Classes 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

VMC

18

AIEEE-2012

Vidyamandir Classes 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)

145.

 

 1

(B)

 

 1 

(C)

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? 1.5Ω (A) (B) (C) 5Ω

 

 1 

6.67 Ω

1  

(D)

 

(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)

148.

5  106V

(B)

12.50  106V

(C)

125 V

(D)

125.0 V

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) 20kΩ (B) (C) 10kΩ (D) 15k Ω 1.5 kΩ

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

VMC

19

AIEEE-2012

Vidyamandir Classes 153.

The output Y of the logic circuit shown in figure is best represented as (A)

A  B .C A  B .C

(C)

154.

(B)

A  B .C

(D)

A  B .C

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)

VMC

48

(B)

49

(C)

20

50

(D)

51

AIEEE-2012

Vidyamandir Classes CHEMISTRY Theory for Purification of Compounds  Estimation of ‘C’ & ‘H’ mass of CO 2 12 % of C    100 44 mass of organic compound % of H 

mass of H 2 O 2   100 18 mass of organic compound

 Estimation of ‘N’ (a)

(b)

DUMA’s method: vol. of N 2 evolved @STP 28 % of N = × ×100 22, 400 mass of organic compound KJELDAHL’s method: % of N = 1.4 ×

Molarity of H 2SO 4 vol. of NaOH   × 2  vol. of H 2SO 4  mass of organic compound 2  

 Estimation of Halogen’s 35.5 wt. of AgCl % of Cl    100 143.5 wt. of compound % of Br  % of I 

80 wt. of AgBr   100 188 wt. of compound

127 wt. of AgI   100 235 wt. of compound

 Estimation of Sulphur wt. of BaSO 4 32 % of S    100 233 wt. of organic compound  Estimation of Phosphorus 62 wt. of Mg 2 P2 O7 formed % of P = × × 100 222 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 (C) gaseous pollutants

(B) (D)

liquid pollutants 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)

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21

Asbestos

(D)

Mercury AIEEE-2012

Vidyamandir Classes 5. 6. 7.

A secondary pollutant is. (A) CO (B)

CO2

(C)

PAN

(D)

Pneumoconiosis is caused by in halation of (A) coal dust (B) silica dust

(C)

cotton fibre dust (D)

asbestos dust

White lung cancer is caused by (A) asbestos (B) silica

(C)

paper

textiles

(D)

Aerosol

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

Photochemical smog is caused by (A) CO (B) CO2

(C)

O3

(D)

NO2

‘Los Angeles’ smog is (A) sulphurous smog (C) industrial smog

(B) (D)

photochemical smog All of these

10. 11.

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 (C) equal to that of water

(B) (D)

less than that of water None of these

Phosphate pollution is caused by (A) weathering of phosphate rocks only (C) phosphate rocks and sewage

(B) (D)

agricultural fertilizers only sewage and agricultural fertilizers

15.

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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22

AIEEE-2012

Vidyamandir Classes 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) (C) conductivitymeter (D)

22.

voltameter calorimeter

Statement-1: Photochemical smog is produced by nitrogen oxides. Statement-2: Vehicular pollution is a major source of nitrogen oxides. (A) (B) (C) (D)

Statement-1 is True, Statement-2 is True and Statement-2 is a correct for Statement-1 Statement-1 is True, Statement-2 is True and Statement-2 is NOT correct explanation for Statement-1 Statement-1 is True, Statement-2 is False 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) (C) crude alcohol (D)

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23

coal-tar All of these AIEEE-2012

Vidyamandir Classes 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 (C) Fusion test

(B) (D)

Lassaigne’s test 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 1.4 VW 1.4 VN (A) % of N  (B) % of N  N W VNW 1.4WN (C) (D) % of N  % of N  1.8 V

37.

In the estimation of sulphur in an organic compound, fuming nitric acid is used to convert sulphur into (A) SO2 (B) H2 S (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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24

AIEEE-2012

Vidyamandir Classes 41.

Which of the organic compounds will give red colour in Lassaigne test? S (A) NaCNS (B) || NH 2  C  NH 2 (C)

NH 2  CO  NH 2

(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

*44.

(D)

Br

Which of the following common reactions occur during Duma’s method and Liebig’s method? (A)

C  2CuO   2Cu  CO 2



(B)

N  CuO   N 2  Oxides of Nitrogen



(C)

2H  CuO   Cu  H 2 O



(D)

Na 2 PO 4  3HNO3   H3 PO 4  3NaNO3



*45.

Kjeldahl’s method can’t be used for estimation of nitrogen in (A) pyridine (B) C6H5NO2 (C) C6H5NHCOCH3 (D) C6 H 5  N  N  C6 H 5

46.

Naphthalene can be easily purified by (A) sublimation (C) distillation

(B) (D)

crystallisation 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) N2 O (B) NO2 (C) N2 O4 (D) N2 O5

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.

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(A)

isomerisation of   D int o   D -glucose at 373 K

(B) (C) (D)

opening of glucopyranose ring Both the statements are correct None of the statement is correct 25

AIEEE-2012

Vidyamandir Classes 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   25  30 , while a mixture of A and its enantiomer B D gave   25   15 . The ratio of A to B in the mixture is. D (A)

55. 56.

1:3

(B)

3:1

Which enzyme is present in saliva? (A) Urease (B) Maltase

(C)

1:2

(D)

2:1

(C)

Lactase

(D)

Amylase



(C)

None of these

Both (A) and (B)

(D)

 N H3 | CH 2 CHCOO 

 N

Which of the nitrogen of histidine is first protonated? (A)  (B)

 N H

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)

59.

thiamine

The deficiency of vitamin B1 causes (A) beri-bezi (B)

(C)

dermatitis

tocopherol (C)

(D)

scurvy

riboflavin (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 (C) ribosomal RNA

(B) (D)

transfer RNA viral DNA

The only vitamin with metal atom in it (A) vitamin A (C) vitamin B12

(B) (D)

vitamin K vitamin E

63.

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 (C) tartaric acid

66.

folic acid ascorbic acid

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

VMC

(B) (D)

C  O and  OH

(D)

26

OH and  CHO

AIEEE-2012

Vidyamandir Classes 67.

68.

Stachyose is (A) monosaccharide (C) trisaccharide

(B) (D)

Which of the following is heterocyclic amino acid? (A) Glycine (B) Alanine (C)

disaccharide tetrasaccharide 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 (C) anionic polymerisation

(B) (D)

cationic polymerisation Ziegler-Natta polymerisation

Vulcanised rubber resists (A) wear and tear due to friction (C) action of heat

(B) (D)

high temperature cryogenic temperature

72.

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 (C) adipic acid

75.

*76. 77.

78.

(B) (D)

hexane adipic acid and hexamethylene diamine

Arrange the following monomers in order of decreasing ability to undergo cationic polymerization I. NO 2 C6 H5  CH  CH 2 II.

CH 2  CH  C6 H5CH 3

III.

CH 2  CH  C6 H5OCH3

(A)

I > II > III

(B)

III > II > I

(C)

II > I > III

Which of the following fibers are made of polyamides? (A) Wool (B) Natural rubber (C) Artificial silk Bakelite is a (A) natural polymer (C) condensation polymer

(B) (D)

I > III > II

(D)

Butyl rubber

addition polymer homopolymer

Bakelite is obtained polymer phenol by reacting with (A)

 CH 2OH 2

(B)

CH3CHO

(C)

CH3COCH3

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 (C) polyamide polymer

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(D)

(B) (D) 27

(D)

HCHO

polyester polymer polyethylene polymer AIEEE-2012

Vidyamandir Classes Chemical in Everyday Life 81. 82. 83.

Penicillin is a/an (A) hormone

(B)

87. 88.

(B)

(C)

(D)

serotonin Cl

(D) COCH3

Which of the following is not used as an antacid? (A) Magnesium hydroxide (B) (C) Sodium bicarbonate (D)

Sodium carbonate Aluminium phosphate

Which of the following drugs is an analgesic? (A) Sulphuaguanidine (C) Analgin

(B) (D)

Paludrin Iodex

Oral contraceptive drugs contain (A) mestranol (C) Both (A) and (B)

(B) (D)

Norethindrone None of these

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

tetracycline

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

Codes (A) I-B, II-E, III-C, IV-D (C) I-B, II-E, III-A, IV-C Trade name of aspartame is. (A) Alitame (B)

Saccharin

A. B. C. D. E.

I-D, II-B, III-A, IV-C I-C, II-A, III-D, IV-B

(C)

Sucralose

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 (C) Non-ionic detergent

(B) (D) 28

List-II Anaesthetic Antiseptic Insecticide Detergent Pain balm

(B) (D)

90.

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anagesic

CONH2

NHCOCH3

List-I I. Iodoform II. Methyl salicylate III. Diethyl ether IV. Hexachlorocyclohexane

89.

(D)

Cl

OH

CONH2

86.

antipyretic

The correct structure of the drug paracetamol is.

(A)

85.

(C)

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

84.

antibiotic

(D)

Nutra Sweet

Anionic detergent None of the above AIEEE-2012

Vidyamandir Classes 92.

Which of the following represents a synthetic detergent? (A)

C15 H31COOK

(C)

C12H25

SO3Na

(B)

CH3  CH 2 6 COONa

(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. (I) (II) (III) (IV)

(A) (C) VMC

Column-I Sodium perborate Chlorine Bithional Potassium strearate

(p) (q) (r) (s)

I : p, II : q, III :r, IV : s I : r, II : p, III : q, IV : s

Column-II Disinfectant Antiseptic Milk bleaching Soap

(B) (D) 29

I : q, II : r, III : s, IV : p I : s, II : p, III : q, IV : r AIEEE-2012

Vidyamandir Classes 102. 103. 104. 105.

VMC

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

(D)

antiseptic

The drug used to bring down fever are known as. (A) analgesic (B) antibiotic (C)

antipyretic

(D)

sulpha drugs

Which of the following is not an antibiotic? (A) Penicillin (B) Oxytocin

(C)

Ofloxacin

(D)

Tetracycline

Chloramphenicol is. (A) narrow spectrum antibiotic (C) broad spectrum antibiotic

(B) (D)

broad spectrum analgesic broad spectrum antibacterial

30

AIEEE-2012

Vidyamandir Classes MATHEMATICS 1.

 A  B c  A (A)

2.

(C)

4.

5.

B

(B)

A B

(C)

A B

(D)

(B)

 A  B   A  C 

(D)

None of these

(C)

a singleton set

A B

A   B  C  is equal to :

(A)

3.

is equal to :

 A  B   A  C   A  B  C

The group of beautiful girls is : (A) a null set (B)

a finite set

(D)

not a set

If A  B , then A  B is equal to (A)

 A  B    B  A

(B)

A B

(C)

B A

(D)

None of these

If A = {1, 2, 3] and B = {3, 4}, then  A  B    A  B  is : (A) (C)

{3, 3} {(1, 3), (2, 3), (3, 3)}

(B) (D)

{(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4)} {(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 nm  0 . 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

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31

AIEEE-2012

Vidyamandir Classes 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) 15.

(A)

18.

(B)

symmetric

[0, 7]

(B)

1 5   3 7 

A3  3 A2  I  0 (B)

23.

VMC

all of these

(B)

1 5 7  3

(D)

5 7   

(C)

100 A

(D)

299 A

A3  2 A2  I  0 (D)



For non-singular square matrices A, B and C of same order, AB 1C

A1BC 1

(B)

C 1B 1 A1

(C)



1

A3  A2  I  0

is equal to :

CB 1 A1

(D)

C 1BA1

If A and B are square matrices of size n  n such that A2  B 2   A  B  A  B  , then which of the following (B) (D)

either of A or B is a zero matrix A=B

 x1  1 1 2  3     Let X   x2  , A   2 0 1  and B  1  . If AX = B, then X is equal to :  x3   3 2 1   4   1  2     3

(D)

 1 2    3 

3 2 4  1 If matrix A  1 2 1 and A1  adj A , then k is : k 0 1 1  (A) 7 (B) (C) 7

1/7

(D)

11

3 4  If A    , then A . (adj A) is equal to : 5 7  (A) A (B) |A|

|A|I

(D)

None of these

(A)

22.

(D)

A3  3 A2  I  0 (C)

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

21.

transitive

(C)

1 1 0 For the matrix A  1 2 1  , which of the following is correct ?  2 1 0 

(A) 20.

reflexive

 a  d  b  c is :

1 1 100 If A    , then A is equal to : 1 1 (A) 2100 A (B) 299 A

(A) 19.

All I, II and III

 1 2   3 If A    and B  1 , AX  B , then X is equal to : 2  1     (A)

17.

(D)

N is the set of natural numbers. The relation R is defined on N  N as follows :

 a, b  R  c, d 

16.

Only III

1  2    3 

(B)

 1  2     3 

(C)

(C)

32

AIEEE-2012

Vidyamandir Classes

24.

25.

 1 2 1 If A   1 1 2  , then det [adj (adj A)] is equal to :  2 1 1  (A) 124 (B) 134 (C)

144

(D)

None of these

(D)

1 0  0 1   

If D = diagonal [d1, d2, d3, . . . . , dn], where di  0  i  1, 2 , 3, . . . ., n , then D 1 is equal to :

26.

(A)

O

(C)

diagonal d11 , d 21 , . . . , d n1

 3/2 If P    1 / 2 (A)

27.





In

(D)

None of these

1 / 2  1 1 T T 2005 P is : , A   and Q  PAP , then P Q 0 1 3 / 2  

1 2005 0 1  

2005  1  2005 1  

(B)



‘A’ is any square matrix, then det A  AT (A) (C)

(B)

T



0  1  2005 1   

(C)

is equal to :

0 can be 0 or a perfect square

(B) (D)

1 cannot be determined

28.

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

29.

If A   aij  is a 4  4 matrix and cij is the co-factor of the element aij in

A , then the expression

a11c11  a12 c12  a13c13  a14c14 is equal to : (A) 30.

0

(B)

1

(C)

1

(D)

|A|

(C)

1, 2

(D)

None of these

The value of  for which the system of equations x  y  z 1 x  2 y  4z  

x  4 y  10 z   2 is consistent, are given by : (A) (B) 1,  2 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)

32.

for all n (B)

for all n > 1

(C)

for all n > 2

(D)

nothing can be said

If P(n) is a statement such that P(3) is true. Assuming P(k) is true  P  k  1 is true for all k  3 , then P(n) is true : (A) for all n (B)

33.

1, 2

for n  3

(C)

for n  4

(D)

None of these

If P  n  : 3n  n!, n  N , then P(n) is true : (A)

for n  6

(B)

for n  7

(C)

for n  3

(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)

VMC

4

(B)

120

(C)

33

240

(D)

24

AIEEE-2012

Vidyamandir Classes n

36.

 n 1  The smallest positive integer n for which n !    holds, is :  2 

(A) 37.

1

(B)



41.

49.

(C)

all n  N

(D)

None of these

2

(B)

9

(C)

3

(D)

11

(C)

n>3

(D)

None of these

1

(B)

0

3 , then the number of possible triangles are : 4 (C) 2 (D) infinite

(B)

cot C

c cot C

(C)

cot

C 2

(D)

c cot

(B)

abc

AP

c a b

(C)

bca

(D)

a+b+c

A C 1 tan  , then a, b, c are in : 2 2 2 (B) GP

(C)

HP

(D)

None of these

equilateral

right angled

(D)

None of these

(D)

2b

(D)

None of these

(D)



sin B , then the triangle is : 2 sin C (B) isosceles (C)

0

(B)

1

(C)

b

abc

(B)

3 abc

(C)

a+b+c

If the area of a triangle ABC is  , then a  sin 2 B  b2 sin 2 A is equal to : (A) (B) (C) 2  3

C 2

If a 2 , b 2 , c 2 are in AP, then which of the following are also in AP ? sin A, sin B, sin C cot A, cot B, cot C

(B) (D)

tan A, tan B, tan C None of these

(B) (D)

3R sin A sin B sin C 4R cos A cos B cos C

In ABC , a cos A  b cos B  c cos C is equal to : (A) (C)

VMC

n>2

In a triangle ABC, a 3 cos  B  C   b3 cos  C  A   c 3cos  A  B  is equal to :

(A) (C) 50.

9

In triangle ABC, if A  45, B  75 , then a  c 2 is equal to :

(A) 48.

(D)

2

(B)

In a triangle ABC, cos A 

(A) 47.

n>1

In ABC , if tan

(A) 46.

8

C A  In ABC, 2  a sin2  c sin2  is equal to : 2 2 

(A) 45.

4

A B  B A  In ABC ,  cot  cot   a sin 2  b sin 2  is equal to : 2 2 2 2   

(A) 44.

(C)



In a triangle ABC, a = 5, b = 7 and sin A 

(A)

43.

6

The inequality n!  2n 1 is true for : (A) n>2 (B) nN

(A) 42.

(D)

2  42n  1  33n  1 is divisible by for all n  N : (A)

40.

3

x x n 1  n n 1   n  n  1 is divisible by  x    for :

(A) 39.

(C)

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 m2  n2 is : (A) 4 (B)

38.

2

4 R sin A sin B sin C sin A sin B sin C

34

AIEEE-2012

Vidyamandir Classes 51.

52.

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

bc is equal to : a

1 B C 2 1 sin A 2

cos (A)

53.

54.

(B)

1 B  C 2 1 sin A 2

cos (C)

cos A cos B cos C , then the triangle is :   a b c right angled (B) obtuse angled (C) equilateral

1 B  C 2 1 cos A 2

cos (D)

(D)

2 (a + b + c)

(D)

isosceles

(D)

None of these

In triangle ABC, if

In ABC , if sin2 (A)

56.

1 B C 2 1 cos A 2

sin

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

(A) 55.

the altitude are in HP the medians are in AP

AP

A B C , sin2 , sin 2 be in HP, then a, b, c will be in : 2 2 2 (B) GP (C) HP

In ABC , if sin A : sin C = sin  A  B  : sin  B  C  , then : (A) (C)

a, b, c are in AP a2, b2, c2 are in GP

(B) (D)

a2, b2, c2 are in AP 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  BC   a sin   2  2 

(B)

 b  c  cos 

B C  A  a cos 2  2

(D)

 b  c  cos

(A)

 b  c  cos

(C)

 b  c  cos  

59.

60.

BC  A  a sin  2  2  A  B C   a sin   2  2 

If in a triangle ABC, CD is the angle bisector of the angle ACB, then CD is equal to : ab C ab C 2ab C (A) (B) (C) (D) cos cos cos 2ab 2 ab 2 ab 2

None of these

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

2b a

(B)



b a

(C)

b2  c 2 ca

(D)

c2  a2 ca

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)

63.

(B)

1  2n  1 3

(C)

1  2n  1 6

(D)

n 2

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)

VMC

n 2

X n

(B)

X

n 2

(C)

35

X

n 1 2

(D)

None of these

AIEEE-2012

Vidyamandir Classes 64.

The AM of the series 1, 2, 4, 8, 16, . . . . , 2n is : (A)

2n  1 n

(B)

2n  1  1 n 1

(C)

2n  1 n

(D)

2n  1 n 1

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  xi2  400 and  xi  80 . 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)

1 n

2

(B)

(C)

2

(D)

2 n

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  n  4  observation is a, then the mean of remaining four observations is : (A)

72.

nM  a 4

(B)

nM  a 2

(C)

nM  a 2

(D)

nM + a

If X1 and X 2 are the means of two distributions, such that X1  X 2 and X is the mean of the combined distribution, then : (A)

73.

X  X1

(B)

X  X2

(C)

X 

X1  X 2 2

(D)

X1  X  X 2

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 SD  13.44 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)

VMC

~ p~q

(B)

~  p  q

(C)

36

~  p  q

(D)

p~q

AIEEE-2012

Vidyamandir Classes 77.

The switching function for the following network is :

(B)

 p  q  r  t  p  q  r  t

(C)

prqt

(D)

None of these

(A)

78.

If p and q are two statements, then ~  p  q   ~  q  p  is : (A) (C)

tautology neither tautology nor contradiction

(B) (D)

contradiction 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) (C)

81.

(C)

(C)

Commutative law De-Morgan’s law

(B) (D)

Associative law Distributive law

 x  y    y  z    z  x  x  y    y  z    z  x

(B)

 x  y  z    x  y   z 

(D)

None of these

 a  b   c   a  b  c  a  b   c   a  b  c

(B)

 a  b   c   a  b  c

(D)

None of these

Tautology Neither a tautology nor a contradiction

(B) (D)

Contradiction None of these

If p   q  r  is false, then truth values of p, q, r are respectively : (A)

VMC

Both p and q are false None of these

The statement p  ~ p is : (A) (C)

86.

(B) (D)

Switching function of the network is :

(A)

85.

p is false and q is true Both p and q are true

The switching function for switching network is :

(A)

84.

contradiction both tautology and contradiction

Let p   q  r    p  q    p  r  . Then, this law is known as : (A) (C)

83.

(B) (D)

Let p and q be two statements. Then, p  q is false, if : (A) (C)

82.

tautology neither tautology nor contradiction

F, T, T

(B)

T, T, F

(C)

37

T, F, F

(D)

F, F, F

AIEEE-2012

Vidyamandir Classes 87.

If p   ~ p  q  is false, the truth values of p and q are respectively : (A)

88.

F, T

90.

(C)

T, T

(D)

T, F

(B)

(C)

(D)

q ~ p

(D)

 p ~ q 

(D)

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 If

p : Ram is smart. q : Ram is intelligent. Then, the symbolic form Ram is smart and intelligent, is : (A)

VMC

F, F

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) 89.

(B)

 p  q

(B)

 p  q

(C)

38

 p ~ q 

AIEEE-2012

Vidyamandir Classes

Answers PHYSICS:

VMC

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

39

AIEEE-2012

Vidyamandir Classes 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:

VMC

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

40

AIEEE-2012

Vidyamandir Classes

VMC

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

41

AIEEE-2012