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EXTRA PREPARATORY MATERIAL FOR AIEEE
PHYSICS
Reynolds Number Re: e v d R where :density v : velocity of flow. d : diameter of pipevisocity 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
F cos
0
dt
where
dis called driven frequency then equation of motion is given asma kx bv F cos0 dt or 2 0 2 d d x dx m b kx F cos 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 asx
A cos
dt
Where
0 0 1 2 2 2 2 2 2 0 and / d d d F v A tan x m 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.
d
I n e A v …(1) I : current in the wire n : no. density of electrons
A : area of cross-section of the wire vd : drift velocity also vd e E m …(2) E : electric field m : mass of e s e : electronic charge
: relaxation time. From equation (1) and (2) we have current density2
I ne
J E
A m
and comparing it with microscopic from of ohm’ Law i.e. J E, we have (where
: conductivity)2
ne m
Mobility
: An important quantity is the mobility
is defined as the magnitude of the drift velocity per unit electric field.
d d v e E & v E m
e m 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
10
1 5 Silver10
2 10 Nocolour 20Note: the order of the first letter of the colours can be learned as has
0 1 2 3 4 of 5 reat 6ritain a 7ery 8ood 9 ife
B 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 2
nd band
Third band
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 and m mv T R f 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 2107 Newton’s per meter of length
Current sensitivity of the galvanometer: is defined as the deflection per unit length. N A B
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:
0 3 2 4 m B 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.
0 0 0 1 2 L Q R 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 1 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 surface (for complete absorption) isP U
C
.
The microscope:
* Simple microscope: linear magnification m 1 D ; D 25cm f
f : focal length. angular magnification when image formed at infinity m D
f * Compound microscope: 0 0 e e L D m m m f f a B i
2
r* Telescope: 0
e
f m
f
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 n n
(ii) Distance of the nth secondary maximum from the centre of the screen xn nD
(iii) Angular positions of the nth secondary maximum
2 1
2 n n n (iv) Distance of the nth secondary maximum from the centre of the screen
2 1
2 n n D x (v) Width of a secondary maximum or minimum D
(vi) Width of the central maximum 0 2D
* 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 ip
* 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 I I cos0 2 * Doppler shift. (A) Δv vv c (B) Δ v 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.
*. 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 n is the electron density and e n in the hole density the material will be n-type b 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 1
g
E eV and insulators have Eg 6eV. *. In n-type semiconductor, conductivity
n ne ee
In p-type semiconductor conductivity
p nb be
In intrinsic semiconductor conductivity
int rinsic n eb b n ee e
*. 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
*. *. *. and 1 1 e c b i i i
*. Use the relations in order to simplify logical expressions. (i) A + A = A its dual A . A = A
(ii) A A1 its dual = A. A 0
(iii) A + 1 = A its dual A . 1 = A
(iv) A + AB = A + B its dual A (A + B) = A (v) AABAB its dual A A
B
AB (vi) AB A.B A . B; A B(vii) A A11100 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 i c 1 e i A i Voltage gain V 1 1 i R A r Power gain 2 1 1 1 p R A r
No phase shift between input and output In common base (CB) Amplifier FB h Current gain 1 r 1 p i A i Voltage gain V 1 1 i R A r Power gain 1 1 1 p R A r
Phase shift = 180º or rad
In common base (CE) Amplifier
FB
h
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 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 = 910 kg m3 3 and atomic weight of copper = 63)
(A) 0 1. mms1 (B) 0 2. mms1 (C) 0 3. mms1 (D) 0 2. cms1
4. A charge of 2102C 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/ me2 with velocity e / , where 2 h /2. The current is :
(A) 2 5 2 4 me (B) 2 2 3 4 me (C) 2 2 2 3 4 m e (D) 2 5 3 4 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 107m2, carrying a current of 1.5 A? (Given density of copper = 910 kgm3 3 ; atomic mass of copper = 63.5 ; Avogadro’s number = 6 023. 1023 per gram atom)
(A) 1 1. 102ms1 (B) 1 1. 103ms1 (C) 2 2 10. 2ms1 (D) 2 2. 103ms1 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:
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)
i / s
211. The amount of charge Q passed in time t through a cross – section of a wire is Q5t2 3t . The value of 1 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 18
2 9 10. , while 1 2. 1018 electrons move towards left in the same time ; the electronic charge being 19
1 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) 3104ms1 (B) 310 ms5 1 (C) 410 ms6 1 (D) 310 ms8 1
14. If the electronic charge is 1 6. 1019C, 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 (D) 1 6. 1019
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) ?
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 106m2. If the number of free electrons per m3 is 8 4 10. 28, then find the drift velocity, (e1 6. 1019C)
(A) 210 ms5 1 (B) 1 56. 105ms1 (C) 1 10 ms 5 1 (D) 0 64. 105ms1 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) M /2
30. 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. 102Nm. Magnetic moment of the magnet is :
(A) 0 36. J T1 (B) 0 72. J T1 (C) 0 18. JT1 (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
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)
5
2 BH (D) 5BH
33. The earth’s magnetic induction at a certain point is 710 Wbm1 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 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 6 8. 105. 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 36 10 T 6 , then its value at B is
(A) 3610 T6 (B) 910 T6 (C) 14410 T6 (D) 22810 T6
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 :
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. 104T is along the plane of the coil. The magnetic intensity is : (A) 1 96. 104T (B) 1 96. 104T (C) 1 96. 105T (D) 1 96. 105T
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/ 3s (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
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 1
3 8. cm.
The focal length of objective lens is 1
4cm. 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 6000 Å is used. If the light of wavelength 4800 Å 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. 103km. 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 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) 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) 2Dand3D (B) 2Dand3D (C) 2Dand0 33. D(D) 2Dand0 33. 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
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) 0 5. 102cm
69. A parallel beam of light of wavelength 3141.59Å 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) 18m (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 6250 Å is incident normally on a slit of width 2102cm. The width of the principal maximum on a screen distance 50 cm will be :
(A) 312 5. 103cm (B) 312 5. 104cm (C) 312 cm (D) 312 5. 105cm 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.
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) I0/ 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) 1 2 (B) 3 2 (C) 3 2 (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) 2a 2 (B) a 2 (C) 2a 2 (D)
2
2
a
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) 80 gL1 (B) 75 gL1 (C) 65 gL1 (D) 50gL1
85. If for a calcite crystal o ande 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. a andm 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 tan2 (B) m a tan2 (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?
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 n and e n in an intrinsic semiconductor at ordinary temperature is h (A) ne nh (B) ne nh (C) ne nh (D) ne nh 0 91. The resistivity of a semiconductor at room temperature is in between ?
(A) 102to 105Ωcm (B) 10 to 10 Ω cm 2 6
(C) 106to108 Ωcm (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) 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 7
5 10 silicon atoms. If the number density of atoms in the silicon specimen in 51028 atoms m3, then the number of acceptor atoms in silicon per cubic centimeter will be :
(A) 2 5. 1030 atomscm3 (B) 2 5. 1035 atomscm3
(C) 1 0. 1013 atomscm3 (D) 1 0. 1015 atomscm3
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
h6 62. 1034 Js c 3108ms1
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) 200
2 (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 pnjunction 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) I /0 B) I /0 2 (C) I /0 2 (D) 2I /0 107. For a junction diode the ratio of forward current (Ip) and reverse current (I ) is : r
[I = electronic charge, e V = voltage applied across junction K = Boltzmann constant T = temperature in Kelvin]
(A) eV / kT (B) ev / kT (C)
eeV / kT 1
(D)
eV / KT 1
108. The value of current in the following diagram will be
(A) zero
(B) 102A (C) 10 A (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
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) 210 Ω5 (B) 2 5. 10 Ω5 (C) 310 Ω5 (D) 4 10 Ω 5
113. Consider the junction diode is ideal. The value of current in the figure is :
(A) zero (B) 102A
(C) 101A (C) 103A
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
116. Current gain in common base configuration is less than 1 because
(A) Ie Ib (B) Ib Ie (C) Ic Ie (D) Ie Ic 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) 40100 A (B)
10040 A
(C) 10040A (D) 10040A 119. Current gain AC common emitter mode of transistor is(A) Δ Δ C AC C S I V I = constant (B) AC B C C I V I = constant (C) Δ Δ C AC C E I V I = constant (D) Δ Δ E AC C C I V I = 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)
19 1121. 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 60R0 5000Ω 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 1010electrons enter the emitter in 106s. 4% of the electrons are lost in base. The current transfer ratio will be :
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 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
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
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) 510 V6 (B) 12 50. 106V (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)
AB . 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
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) AB .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
CHEMISTRY
Theory for Purification of Compounds
Estimation of ‘C’ & ‘H’
2
mass of CO
12
of
100
44
mass of organic compound
%
C
2
mass of H O
2
of
100
18
mass of organic compound
%
H
Estimation of ‘N’
(a)
DUMA’s method:
2
vol. of N evolved @STP
28
% of N =
×
×100
22, 400
mass of organic compound
(b)
KJELDAHL’s method:
2 4
2 4
