Career
Career
Career
Subject
Page No.
Alternating Current 01
Transformer 09
D.C Machine 20
3-phase induction motor 31
Single Phase motors 37
Alternators 44
Parallel Operations 47
Synchronous Motor 50
Electric Power Generation 23
Steam Power Station Hydro-Electric. 59
Power Transmission 62
Power Systems Analysis 72
Power System Protection 79
Illumination 92
High Voltage 97
Electronics 111(a)
Cathode Ray tube 118
Digital Elements and Circuits 120
Computers in Power System. 124
Multiple Choice Questions 130
PREFACE
There are two modes of examination. One, the written and the other
oral. Written examinations are usually the tests of one’s memory. To test the
Depth of knowledge and understanding oral and viva-voce are the best way.
That is why in engineering institution equal weight is given to written and oral
Examination.
Keeping this in view, I have prepared a manual which covers almost all
the topics of Electrical Engineering including computer, Emphasis have been
Made to fulfill the needs of undergraduate students and the engineers who are in
search of jobs.
If red after studying the subject, will help to have a very clear picture of
the subject.
I am very much thankful to Almighty Allah, the Creator, who has given us the power to
understand, wisdom and ability to read and write.
I am also thankful to Mr. Aamir Hanif and Syed Waqas Hussain Shah
to help me in the preparation of manual.
Thanks also for Mr. Muhammad Ali for designing the title page.
AUTHOR.
1
ALTERNATING CURRENT
Q: What is Hz?
A: It is unit of frequency i.e. the cycles/second is called Hz.
2
Q: What is wave length?
A: It is linear distance traveled by a wave during one cycle.
Q: What is velocity of propagation?
A: It is the velocity with which a wave travels. In an electric circuit it is
Given by:
V = 1/√LC
Where V is the velocity of propagation
L is the inductance of the path through which wave is traveling
C is capacitance of the path
Q: Describe relation between wave length, frequency and velocity of
Propagation?
A: f =λ v
Where λ is wave length.
Q: What is the supply frequency in Pakistan?
A: It is 50 Hz.
3
Q: How rms value is related to average value?
A: I ave = 0.637 I max
Q: What is an instantaneous value?
A: It is the value of alternating quantity at any time during a cycle.
Q: What is resistance?
A: It is opposition to the flow of D.C.
Q: What is impedance?
A: It is the total opposition to the flow of electrical alternating current.
Q: What is inductance?
A: It is the property of an a.c circuit due to which an opposing emf is produced in
the same circuit. This opposing emf opposes the flow of current in that circuit.
Q: What is susceptance?
A: It is reciprocal of reactance and is denoted by ‘b’.
Q: What is conductance?
A: It is reciprocal of resistance and is denoted by ‘G’.
Q: What is an admittance?
A: It is reciprocal of impedance and is denoted by ‘Y’
Where c is capacitance.
Q: How line voltage and phase voltage are related in star connection?
A: Vp = VL/√3
7
Q: How line voltage and phase voltage are related in delta connection?
A: Vp = VL
Q: How line current and phase current are related in star connection?
A: IL = I p
Q: How line current and phase current are related in delta connection?
A: Ip = IL/ √3
Q: Name the parameter of circuit which stores energy in the from of electric
Field?
A: Capacitance.
8
Q: What is the relation between frequency and inductive/ capacitive
Reactance?
A: Inductive reactance is directly proportional to frequency while capacitive
Reactance is inversely proportional to frequency.
9
TRANSFORMER
Q: What is transformer?
A: Transformer is a device which transforms electrical energy from one
Circuit to another through a magnetic link with a rise / fail in current/
Voltage.
10
Q: Name the two components of no-load current?
A: These are:
Magnetizing component.
Iron loss component.
Q: Does the flux in the core changes due to change in the load?
A: Flux at all loads remains constant except a very small change from no- load
to full-load.
Q: What is a core?
A: It is made of silicon steel laminations and provides an easy path to the flow
of flux, windings are also wound on it.
11
Q: What are the types of core?
A: Usually these are core type and shell type. Core type is usually used in
distribution and power transformers while shell type is used in small
transformers.
Q: What is the relation between limb and yoke cross sectional areas?
A: If grain oriented steel is used limb area is equal to yoke area,
otherwise yoke area is grater depending upon the ‘KVA’ of transformer.
12
Q: How cores are cooled?
A: Axial and radial ducts are made.
13
Q: How efficiency is measured?
A: By performing no-load test and short circuit tests.
Q: What is an auto-transformer?
A: It consists of one winding only, part of which is used as primary and part is used
as secondary. Its primary and secondary are coupled electrically as well as
magnetically.
14
Q: Why efficiency of an auto-transformer is higher than an ordinary transformer?
A: Since it carries only one winding and for same k V A output an auto
transformer requires relatively small iron as compared to ordinary two
winding transformers. So we see that copper losses as well as iron losses
would be less and efficiency would be higher.
15
Q: How regulation of a transformer is found out?
A: By performing short circuit and no load test.
A: Because
t is not possible to load high rating machines I the laboratory
Consumes high energy
t is inaccurate.
1+0 Where first figure gives the no. of rows of tubes on front
1+1 and back and second figure give no. of rows on sides of the
16
2+0 tank etc. e.g (2+1) mean two rows on front and back an 1 row
2+1 on sides.
17
Q: What is the best iron/copper ratio?
A: The best ratio is between 3 & 5.
Q: What do you understand about the lifting lugs, jacking lugs and lashing
lugs?
A: Lifting lug s are used to lift. The jacking lugs are used to change the
direction and lashing lugs are used during transpiration for securing the
transformer.
18
19
Q: What is meant by parallel operation of transformers?
A: When the demand increase from the capacity of a transformer another
transformers may be connected in parallel to supply the excess demand.
Q: What are the conditions for the parallel operation of 3-phase transformers?
A:
Transformation ration should be same.
Phase sequence should be same.
Phase notation must be same.
Q: For performing shout circuit test which winding should be short circuit?
A: Low voltage winding.
Q: Why the losses occurring during short circuit test are considered to copper
losses only?
A: Because a reduced voltage about 10% of normal voltage is applied hence only
10% of flux flows and iron losses occur but are negligibly small.
20
D.C MACHINES
STATOR:-
It carries the field magnetic and remains stationary. It also provides low
reluctance path for the flux.
POLE:-
These are electromagnets which produce flux.
COMMUTATOR:-
It converts a.c. into d.c. It also acts a means of taking/giving supply to
the rotating armature winding.
YOKE:
Outer part of the machine which protects the machine from external
damage or which acts as a protecting covering for the whole machine.
WINDINGS:
These are the conductors which out the magnetic flux and a voltage is
induced in them.
21
INTERLOPOES;-
These are small poles between the main poles and are used to facilitate
commutation.
COPENSATING WINDINGS;-
The armature field has two components i.e. demagnetizing and cross-
magnetizing which weakens and distort the main field. The compensating
windings are used to compensate for these in large machines.
STATOR/YOKE:-
It is usually made of cast steel.
ARMATURE WINDINGS;
These are made of copper. Theses are usually of two types.
i. Wave windings used for low current high voltage machines.
ii. Lap windings used for huge current and low voltage machine.
INDTERPOLES;
They have two parts i.e. windings which are made made of copper wire and
pole which is made of silicon steel.
COMPENSATING WINDINGS:-
These are usually made of copper wire/ strip.
CARBON BRUSHES;-
These are fixed on commentator which revolves with armature. These are used
for the collection of current generated in armature windings.
COMMUTATOR:-
It is made of copper segments separated by mica insulation. The copper
segments are usually equal to number of coils in simplex windings.
22
ARMATURE WINDINGS.
Q: How windings are classified?
A: These are
i. Lap winding
ii. Wave winding
iii. Foreleg winding which combination is of lap an wave winding. The lap and
Wave windings are further subdivided as simplex, duplex-etc.
Q: Why wave windings are called series windings and lap windings are called
Parallel windings?
A: Because in wave windings there are only two parallel paths irrespective of No.
of poles and in lap windings no of parallel is equal to no. of poles.
Q: Why equalizer rings are needed in lap winding not in wave winding?
A: Each parallel path in lap winding is under the influence of one pair of poles,
And so if a machine consists of multiple pairs of poles then dissimilarities
occurs, due to which unequal voltages may b e induced in the paths and a
circulating current may flow. In wave winding each path is under the influence
of all poles, so voltages are induced in each path. Equalizers in lap windings are
used to remove this dissimilarity.
Q: What is relation between no. of conductors and no. of coils in d.c. windings?
A: no. of conductors = 2 x no. of coils.
23
Q: What is magnetic neutral axis (MNA) and geometrical neutral axis (GNA)?
A: A line perpendicular to resultant magnetic field is called MNA and a line
Perpendicular to main field only is GNA.
Q: Is it possible to use copper/gun metal are hard metal brushes then carbon?
A: NO, because copper/gun metal are hard materials an will spoil the surface of
Commutator, (Magnetic field and a armature reaction.)
Q: In a d.c generator running at no load what is the relation between MMA and
GNA?
A: They coincide.
24
Q: What is the relation between GNA and MNA in loaded generators?
A: The position of MNA shifts and makes an angle with GNA.
PRINCIPAL OF WORKING.
25
Q: How the direction of induced e.m.f is known?
A: Iris gin by Fleming’s right hand rule
PNZ
A: E
60a
26
Q: What is an O.C.C?
A: It is the open circuit characteristics; it is also called as magnetic characteristics.
Q: What is saturation?
A; It is the property of magnetic material that flux becomes constant at certain
value of current i.e. no further flux produces.
27
Q: How iron and friction / windage losses can be measured?
A: By performing no load test.
Q: What is techo-generator?
A: It is small permanent magnet generator whose generated voltage is directly
proportional to the speed.
28
D.C. MOTORS.
A: I = V – Eb
R
Q: Comment on the statement that a generator tries to run back as motor and motor
tries to run back as generator?
A: In case o generator when armature windings are rotated in magnetic field a
current is produced in them. Now these current carrying conductor in the
presence of magnetic field experience a force and tries to run back as motor and
vice versa.
29
Q: What are the types of d.c motors?
A: These are:
i. Series motors
ii. Shunt motors.
iii. Compound motor; The compound motors are further classified as cumulative
compound and differential compound.
Are called the characteristics of motor and speed/ torque characteristics are
called speed characteristics and Armature current / torque characteristics are
allied torque characteristics.
The speed and torque characteristics and relation between torque and armature
current is called torque characteristics.
30
31
Q: What is a starter?
A: It is tapped resistor.
Q: Why three phase squirrel cage induction motor in very widely used?
A: Because of very simple and rigid construction, it requires no maintenance.
Usually no fault develops in the rotor.
32
Q: Why is it not possible for the rotor to run at synchronous speed?
A: Because if rotor catches synchronous speed the relative motion will become
zero and no induction will take place.
Q: What is slip?
A: It is N S – N R
NS
Where N S is Synchronous Speed,
N R is rotor speed.
It is expressed as percentage slip
A: It is NS-0 =1
NS
Q: What is frequency of voltage induced in the rotor?
A: It is fr = sfs
fr is frequency of induced voltage in the rotor.
fs is synchronous / supply frequency.
‘s’ is slip.
33
Q: What is the relation between rotor reactance at any slip and rotor reactance at
standstill?
A; Xr = SXs
Q: What is the relation between voltage induced at standstill and voltage induced
under running condition?
A: If Es the voltage induced at stand still then Es = sEr.
KV2 Rr
A: T=
(Rr) 2+ (Xr) 2
34
35
Q: Why starters are required for starting three phase induction motor?
A: Since it draws a large amount of current at starting.
Q: Name a few methods of starting?
A:
i. Auto-Transformer are starting?
ii. Start-Delta Stater.
iii. Resistors may be used.
Q: Why applying variable voltage method is not preferred for the speed control of
3-phase induction motor?
A; The torque of 3-phase induction motor is proportional to the square of voltage
and hence if voltages are halved, the torque will reduce to 1/4.
36
Q: Compare slip ring induction motor with squirrel cage induction motor as regard
starting and efficiency?
A: Slip ring motor is better.
Q: Name the parameters which are to suppose to start the design of induction
motor?
A: Power factor and efficiency.
On starting, currents are induced in upper bar being close to magnetic field and
having smaller self inductance and there by improves the starting torque under
running conditions the rotor frequency falls and more currents flows in the
lower case and hence the efficiency is improved due to flow resistance of lower
cage.
37
SINGLE PHASE MOTORS
Q: In a single phase resistance start induction motor how the starting windings
produce rotation?
A: The starting winding is highly resistive and the main winding is inductive so the
phase difference between the two current becomes nearly 90 0and hence the
motor start as two phase motor.
Q: What will happen if the centrifugal switch fails to open the starting windings?
A: Excessive heat will produce due to high resistance of starting winding due to
which stator temperature will rise and eventually both winding will burn.
Q: What is the difference between split phase and split phase capacitor start motor?
A: In split phase capacitor start motor, a capacitor is added in series with the
starting winding.
Q: What are the advantages of adding capacitor in split phase capacitor start
motor?
A: Starting torque which is very low in split phase motor is improved.
Q: Is there any relation between the capacitance’s of two capacitors used in two
value capacitor motor?
A: Starting capacitor has about 10-15 times high capacity than the value of running
capacitor.
40
Q: Why shaded pole single phase induction motor dos not need any special starting
techniques like capacitor and auxiliary winding etc.?
A: Because it is inherently self started motor. The construction of the poles is such
that they give a sweep to the magnetic flux and motor starts rotating.
41
Q: How speed of shaded pole motor is controlled?
A: By applying reduce voltage.
Q: What is reluctance principle?
A It states that, where air gap is small. the self inductance in the field winding is
great. causing the current i the field winding to lag the flux which
produced it. conversely. where the air gap is great self inductance is
reduced. and the current is more nearly in phase with the flux. The mutual air
gap flux is delayed. therefore, producing a sweeping effect similar to that
produced in the shaded pole motor.
42
Q: Is it possible to operate d.c series motor on A.C supply without
modifications?
A: For small sizes operation, it is quite satisfactory, but at large sizes above a few
h.p. operates poorly on alternating current. There is a great deal of sparking
at the brushes and the efficiently and power factor are low. Several
modification are necessary to improve its operation on a.c.
Q: Explain why d.c shunt motor will not work on a.c satisfactorily?
A: A very little starting and running torques are produced since torque is
T = k Ф f la cos θ:
Where angle θ is nearly 90”.
Q: Why a single phase series motor is preferred for traction service rather than
the induction or synchronous motor?
A:
i) They operate on high p.f of about 0.95
ii) Their efficiency is very high.
iii) Speed regulation is very easy.
Q: In case of resistance start and capacitor start single phase induction motor
the starting winding is cut off when the machine attains 70% speed How is it
accomplished?
43
Q: Can you give an example of permanent capacitor motor?
A: Ceiling fan or table fan.
44
ALTERNATORS
Q: What is an alternator?
A: An alternator is a machine which converts mechanical energy into electrical
energy and generate A.C
Q: What is a turbo-alternator?
A: A steam driven generator is called turbo-alternator. It is usually cylindrical rotor
type.
45
Q: What is difference between an alternator and a D.C generator?
A: In principle there is no difference. if commutator is removed from D.C
generator it becomes alternator.
Vn1 V f l
Voltage regulation x100
V fl
Where Vn1 is voltage at no load.
Vfl is voltage at full load.
46
Q: How the resistance of armature is found?
A: By apply D.C between two phases of star connected winding keeping the third
phase open.
1 Vd .c
x
Rdc 2 1d .c
Q: How the A.C resistance is found from D.C resistance?
A: By multiplying Rdc with 1.6 at 60 Hz and 1.4 at 50 Hz.
Q: What is an exciter?
A: An exciter is a D.C generator to supply D.C voltage to the rotor windings.
47
PARALLEL OPERATION
48
Q: What is a synchronizing current?
A: It is circulating current which circulates between the machines because of small
difference of voltage between the alternators.
Q: What is hunting?
A: It is the tendency of alternators to keep themselves into synchronism.
49
Q: Describe a complete for placing 3-phase alternator in parallel?
A:
i) The alternator is brought up to speed, and its effective line voltages are adjusted
to the bus voltage by means of a voltmeter.
ii) The phase sequence is checked.
iii) The frequency of incoming machine is checked by means of dark lamp method,
the speed of prime-mover is adjusted to give correct frequency.
iv) The alternator is made to take load by increasing the excitation.
v) The bus voltage is adjusted by adjusting the all field rehostates simultaneously.
50
SYNCHRONOUS MOTOR
Q: How it is started?
A: With the help of damper windings.
Q: What is a V-Curve?
A: It is the relation between field current and armature current keeping load
constant.
51
Q: Why these are called V-curves?
A: Because the curvier attains the V-shape.
Q: Name few special types of synchronous motors which do not employ D.C field
excitation?
A:
i. The synchronous induction motor.
ii. Reluctance motor.
iii. Hysteresis motor.
iv. Sub synchronous motor.
52
Q: What is a amortizes windings?.
A: These are the damper windings.
Q: Explain why a synchronous motor will run at synchronous speed or not at all?
A: Because if the motor runs at any other speed, the interlocking will be finished.
53
ELECTICAL POWER GENERATION
54
Q: What is pump storage scheme?
A: A power station containing mix of thermal and hydro generation can lead to use
of pump storage schemes. A pump storage scheme needs the existence of two
natural reservoirs at different levels and reasonably close to each other. At off-
peak periods cheap power can be provided by the most efficient thermal station
to pump water from the lower to the higher reservoir. At times of peak power
the pump motors run as generators and use this water for electricity generation.
Thereby reducing the amount of load which has to be supplied by the less
economic thermal plant on the system. Such facility can reduce the overall cost
generation.
55
Q: How a photocell convert light energy into electrical energy?
A: It is a natural property of a P.N. junction that, if it is exposed to light a voltage
of about 0.5 volts is developed across the junction. Many such junctions can be
connected in parallel to heave large voltage.
It consists of a hollow steel sphere that floats on the surface of water of the sea
and is connected by a road to a platform anchored below the surface because
the submerged platform is much heavier than the sphere, the movement if
sphere set the platform in motion. Such a mechanism may produce power up to
20 MW.
Q: Why a steam turbine at nuclear power station needs a large amount of water?
A: Because it has to handle a large amount of wet low pressure steam.
56
Q: What is the function of a reactor?
A: In a reactor heat is produced by fissioning or splitting of uranium atoms.
57
58
Q: Why good foundation conditions are essential for sitting a nuclear power plant?
A: Because reactor weight about 50,000 tons with of 3.5 tons/sq- in.
59
Q: What is a boiler?
A: It is a device in which steam is produced under pressure.
60
Q: What is intake?
A: Its function is to let the water enter into the penstock under controlled
conditions.
Q: What is penstock?
A: It is a conduit system which direct water from reservoir to turbine.
61
62
POWER TRANSMISSION
Q: What is transmission system?
A: It is a medium through which electrical energy is transferred from generating
stations to load centers.
Q: What are the factors with complicate the calculation of the resistance of line?
A:
i) Skin effect
ii) Stranding
iii) Temp.
63
Q: What is transposition?
A: It is the exchange of the position of the conductors at regular intervals along the
line so that each conductor occupies the original position of every other
conductor over an equal distance.
i) Overhead lines
ii) Underground cables
iii) High voltage d.c transmission.
64
65
66
Q: What is creepage?
A: The path through which leakage current flows.
Q: Name the types of tests which an insulator of an overhead line should pas?
A:
i) Impulse test
ii) One minute power frequency wet test.
iii) Corona free test.
67
Q: Describe a few devices which are used for voltage control of lines?
A:
i) Static capacitors
ii) Synchronous condensers
iii) Saturated reactors
iv) Regulating and tap changing transformers.
68
Q: What are the problems in the use of saturated reactors as voltage control
device?
A: They generate harmonics.
69
70
Q: What is corona?
A: The high voltages at which lines operate produces electric field strength of
sufficient intensity to ionize the air near the phase conductor. This effect is
called corona.
71
Q: What is span?
A: Horizontal distance between two consecutive towers is called span.
Q: What is sag?
A: The vertical distance between the conductor at maid point and the line
joining the two adjacent level supports is known as sag.
72
POWER SYSTEM ANALYSIS
73
Q: What is mismatch?
A: It is the difference between specified value and calculated value.
74
75
Q: Describe the methods of improving steady state and transient state stabilityof
the system?
A:
i) By decreasing the generator reactance.
ii) Using damper windings.
iii) Using fast clearing circuit breaker.
iv) By decreasing transmission lines reactance
v) By earthling the transformers neutral through a low resistance.
76
FAULT ANALYSIS
77
78
79
Q: What is a relay?
A: It is a key component. It receives information from the system and convey it to
circuit breaker by performing one or two switching operations.
80
Q: What are the standard values of voltage and current at which relays operate?
A: These are 120 V and 5 A.
81
Q: What is CT burden?
A: It is the terminating secondary impedance in ohms. Sometimes it is expressed in
volt-amperes at a specified voltage or current and power factor.
Q: What is CT error?
A: The CT error is the percentage of mismatch between the input current ( in
secondary terms) and the output current.
Q: Upon what factor CT error depends?
A:
i. CT current.
ii. Terminating impedance.
82
Q: In a D.C circuit 100 V are applied. Assume that switch in this circuit is opened
at t=0 when the switch contacts are close together say 0.01mn.
What is the voltage gradient?
83
Q: What is an Auto-recloser?
A: It is a circuit breaker which has built in instrument transformers and relay. It
sense the over-current and opens instantaneously or after an intentional time
delay. After a short interval of 20 cycles it recluses. If the fault persists, it again
trips and wait for about 15 seconds, closes again and trip again if the fault
persists. After a third interval of about 45 seconds it again closes for last time. If
the fault persists it opens and locks out.
84
85
Q: How the generators are protected when unbalances exist at the stator terminal?
A: Ann unbalance voltage system can be decomp9ose into symmetrical
components. The positive sequence components produces a revolving field that
revolves in the same direction and with same velocity as rotor so no relative
speed exists and no voltage is induced. However negative sequence quantities
produce a magnetic field in a direction opposite to the rotor with a relative
speed of double the rotor speed. Due to this double frequency, voltage and
current are produced in windings and iron.. Due to which machine is over
heated. To protect machine under condition negative sequence filters are used.
86
Q: How generators are protected against the fault in the system i.e. external fault?
A: Over-current protection is used.
87
Q: What are the consequences of reversal of real power flow i.e. motoring?
A:
i. Turbine blade overheating.
ii. Cavitations with hydraulic turbine.
iii. Back fire and fire hazard with diesel engines.
Q: What are the factors which complicate the feeder protection using over current
relays?
A:
i. Motor-starting current.
ii. Transformer inrush current.
iii. CT error.
iv. D.C offset.
88
Q: What are the basic communication channels used to carry the information in
pilot relaying?
A:
i. Separate electrical circuits, frequently telephone circuits.
ii. Power line carriers.
iii. Microwave.
Q: Why the pilot wire relaying is applied to protected the feeders of les then – 18
Km?
A: Because the open circuit impedance and short circuit impedance of pilots
become equal at a length greater than 48 km and it becomes difficult to
distinguish between external and internal faults.
89
Q: What is the phase relation between CT secondary current for external or through
fault?
A: They are opposite in phase.
Q: Describe the factor s which relation between CT secondary current for internal
fault?
A: They are in phase.
Q: Describe the factors which then to reduce the tripping angles of power line
carrier scheme from 1800?
A:
i. Liner length.
ii. Transformer and other sending equipment.
90
Q: What are the factors which must be considered before applying a fuse for
particular application?
A:
i. Voltage rating.
ii. Continuous current rating.
iii. Time response.
iv. Interrupting-current rating.
91
92
ILLUMINATION
Q: What is illumination?
A: It is also called photometric brightness.
It is a measure of luminous flux reflected from an object and has units of
candela/m2
Q: What is contrast?
A: It is related to the luminance of an object and its immediate background. It is
defined as:
L0 - Lb
C=
Lb
Where L0 = Luminance of object, cd/m2
Lb = Luminance of background, cd/m2
Q: What is reflectance?
A: It is the ratio between luminance and luminance.
93
94
Q: What is ballast?
A: It is an inductor which provides an initial high voltage pulse to initiate the
discharge through a conducting gas or vapour.
95
Q: What is relation between the light emitted by incandescent lamp and HPMV
lamp?
A: HPMV lamp gives 2.5 to 3 time more light.
96
Q: What are the draw backs of sodium vapour lamp due to which these are not
used commonly?
A:
i. They produce an intense single – point light which is best utilized at least three
meters above the work plan:
ii. Their ballast produces a low decibel hum.
iii. They have 5 – 15 minute sup period give full light.
97
HIGH VOLTAGE
Flash over:
Break down between electrodes in a gas or liquid but across a solid surface.
Puncture:
Break down through the volume of a solid dielectric.
98
Q: Enumerate the factors which give rise to induce charge on transmission line as a
result of an indirect stroke?
A: The magnitude of trapped charge depends upon, or is a function of
i. Initial cloud-to-earth voltage gradient.
ii. Closeness of stroke to the line.
Q: Give a brief description of the phenomenon which may occur, when a direct
stroke hits a tower-top?
A: If lighting hits a tower top, some of the current may flow through the shield
wire and remaining current magnitude and rat of rise. The current may flow into
the ground without any harm provided that tower footing resistance is very low.
Otherwise the lightning current will raise the tower top to a high voltage above
ground, causing a flash-over from the tower, over the line insulators to tone or
more phase conductors.
Q: Briefly describe; what happens when a direct stroke hits a line conductor?
A: When lightning hits line directly, the raised voltage at the contact point
propagates in the form of a traveling wave in both the directions and raise the
potential of line to the voltage of downward leader. It may further caused
insulation failure.
99
A: The shadow area for towers having double ground wires is given by
W = D + 4H
Where D = Distance between the ground – wire.
H = Average height of ground – wire.
100
101
Q: Define,
i. Impulse ratio for flash-over
ii. Impulse ratio for puncture.
A:
Impulse ratio for flash-over
t is ratio of impulse flash-over voltage to the peak value of power frequency
flash-over voltage.
ii. impulse ratio for puncture;
it is ratio of impulse puncture voltage to the power frequency voltage.
ή = Emax./Eav:
where ή = Field factor
Emax = Maximum field strength
Eav: = Average field strength
102
Q: To which the current capability of expulsion tube is related and what is its
expression?
Distribution or
Transmission class
103
104
Where p = Pressure in mm of Hg
T = Temperature in K0.
d = Spacing in cm
when p = 760 mm of Hg;
t = 20 C0
6.08
V = 24.22 + x
105
106
Q: Does the insulation strings and the clearances in air very linearly with voltage?
A: The answer is “NO”. At higher transmission voltages. The insulation strings and
clearances in air do not increase linearly with voltage but increase
approximately to V1.6.
107
P 293
d= x
1013 273 + t
108
109
The routine tests comprise one minute power frequency voltage dry withstand
tests.
Q: In what manner the test voltage for impulse & power frequency tests shall be
applied in case of circuit breakers?
A: The test voltage will be applied as follows;
i. With circuit breaker closed.
Between the terminal of each pole in turn and the frame of circuit breaker, the
terminals of all there poles being connected to the frame.
ii. With circuit fully open
a) Between the terminal of all the poles connected together and the frame
of C.B.
b) Between one terminals of each pole and other terminal of the same pole
connected to the frame.
110
111
ELECTRONICS
Q: What is a semi-conductor?
A: A semi conductor is defined as a material whose receptivity is much less than
receptivity of an insulator but much greater than the receptivity of a conductor
and whose receptivity decreases with increase in temperature.
Q: What id doping?
A: The process of introducing impurity atoms in to a silicon crystal is called
doping.
112
113
114
115
Q: Diodes are to be selected for application listed below. Complete the table?
A: Application Diode Type
Q: What is a transistor?
A: The transistor is a device that can amplify an electrical signal, act as an
electronic switch, and perform number of other functions. Basically it consist of
a germanium or silicon crystal containing three separate regions.
116
117
Q: Complete the following table.
118
119
That surrounds the cathode, and two/three anodes. The grid is maintained at a
negative potential. The electrons emitted from cathode are subjected to
repulsive force by negative grid and an attractive force applied by the anodes
are much larger than the negative grid potential, typically + 1000V as opposed
to -20V, but since the grid is much nearer to cathode than are the anodes. Its.
Influence is sufficiently great for it to control the number of electrons that pass
thought small hole in the grid. These are electrons form the electron beam. The
electrons leaving the grid are accelerated to high velocity by positive anode
potentials and travel along the tube until they strike the screen.
120
DIGITAL ELEMENTS AND CIRCUITS
121
Q: Describe the Murray Code?
A: All characters have exactly the same number of signal elements and the signal
elements are of constant length. Each character is represented by a combination
of five signal elements that may be either a mark or space. The mark is
represented by a negative potential or the absence of tone. It is pace is
represented by a positive potential or the absence of tone. It is possible to
indicate 25 , or 32 combinations directly by the Murray code, but this number is
insufficient for general use, because 26 combinations are required for the letters
of the alphabet and there number of figures and punctuation marks also to be
transmitted. Two combinations therefore are used as letter shift and figure –
shift signals and they have the function of setting up the receiving teleprompter
to print either firuge3s or letters.
122
Q: Write a truth table for a two input AND gate?
A: input 1 0 1 0 1
Output 2 0 0 1 1
Output 0 0 0 1
Q: Describe the action of two input AND gate by the Boolean function?
A: L = S1 S2 where L is output and S1 and S2 are two input. The dot is the Boolean
symbol for AND logic function.
Q: There are three AND gates, the inputs of AND gate 1 are A and B while that of2
are A and C. The output of gate is 1 is D and of 2 is E. Write down the truth
table of the circuit. The output of two AND gates 1 and 2 are the inputs of
thirds. The output of the third gate is F.
A B A.B C A.C F
0 0 0 0 0 0
1 0 0 0 0 0
0 1 0 0 0 0
0 0 0 1 0 0
1 1 1 0 0 0
1 0 0 1 1 0
1 1 1 1 1 1
123
Q: Describe NOT-gate?
A: NOT logic is performed by a switch and one input. If the switch is open the
output will be 1, otherwise zero.
A 0 1 0 0 1 1 0 1
B 0 0 1 0 1 0 1 1
C 0 0 0 1 0 1 1 1
A.B.C 0 0 0 0 0 0 0 1
A.B.C 1 1 1 1 1 1 1 0
124
125
Q: What is a midi computer?
A: A computer having capability between min and main frame but usually applied
in dedicated real time application e.g., National grid control display system is
called midi computer.
Q: What is CPU?
A: There are logic circuits dealing with data grouped into words 8, 12, 16 or 24 bits
in length. Words are coped from locations in the memory into location in CPU.
These are of two types, instruction words of data words. Instruction words are
decoded in CPU which then operates on data words. The process of taking
instruction words decoding and executor is performed in a fixed time in
synchronous computer or in a time dependent for example on the efficiency of
the memory n a synchronous computers. Instruction time depends on the
complexity of the instruction and on other things and do not reliably indicate the
capability of a CPU. Typical times for micro and min are 1-20 micro seconds.
Many CPU’s have extra register (memories) which are not essential. The word
length of CPU us related to the maximum amount of memory that can be
accommodated e.g., a 16 bit word can distinguish (address) only 2 16 26x210 = 64
x 1024 = 64 K locations. A location is usually a word Failure of CPU is failure
of computer.
Q: What is memory?
A: it is place where information /data can be stored and as when required can be
recalled.
126
Q: Explain how magnetic memory works?
A: Each bit is represented by ferrite core (highly remanance) forcing the flux in a
particular direction produces a flux change (induced emf) in cores which have
opposite direction of the flux. Cores can by cycles in about 1 micro sec. per
word i.e. successive words can be accessed in 1 micro sec. The actual
information can be read in about half of this time. Cores memory can be
accessed for reading/writing quite randomly, therefore it is called Random
access memory RAM.
127
Q: What is an interface?
A: These are electronic circuits which connect external signal ( e.g. contacts lamps,
printers, tape reader) to resister, so that CPU can communicate with outside
world.
Q: How many number of registers are required in an interface?
A: AT least two registers are required
To indicate readiness of the interface to send or receive the data.
The register to actually contain the sent or received information.
Q: What is an interrupt?
A: When a peripheral requires. The attention of the CPU, it can initiate an interrupt
i.e. when an operator presses a key on a keyboard. This forces the CPU to give
attention to the interface after it has finished the instruction, it is currently
executing.
128
Q: What is the function of clock, describe its types?
A: Clocks are used by CPU to take account of time. There are of two types.
Line frequency clock generates an interrupt in every 20 ms (in 50Hz mains fed
computer). The interrupt program can keep a record of the number of interrupt
received.
Definite time clocks the CPU, places a number in an interface register. A crystal
clock (typically 100 KHz) counts down to zero and then interrupts the CPU.
129
Q: Write down the specification of computer system suitable for power system
applications?
A:
Scope:
A specification must define in detail what is required of the proposed system. In
addition customer will require certain engineering standards are met and these
can be included in usual way. The customer may include certain special
conditions.
Type of System:
e.g. integrated or segregated or dedicated or multi purpose.
Qualifications to tender:-
Some authorities may invite discussions and experience reports.
Reliability:
It is easy to include a particular MTBF figure but is not worth while.
Casts:-
Do not include an item (hardware or software) in a specification unless
approximate cost is known. Alternately include the item as an optional, to be
quoted separately.
Documentation:-
Drawings and manuals for hardware are expected with any equipment but
documents for software is often inadequate to enable to programmers to modify
the software system easily. One expects documentation for any specially written
task (this is included in 10 instructions/day figure) but it is advisable to check
the quality of documentation supplied by manufacturer certainly before placing
a contract. It is further required that a list of customers using systems of a
similar type as being proposed, be included in the tender, together with the
name of individuals in these organization who may be connected regarding
system performance.
130
Which of the three phase components of fault current is active on a ground fault.
Q:
Which of the following electronic device are closest to equivalent of an electric
switch.
Diac
Triac
SCR
RC Network
Q:
State kickoff’s laws?
Give two examples from daily life of the application of inductive voltage pulses?
Q: What is the difference between power and energy. Name their electrical units?
131
Q:
The shelf life of the battery can be extended by:
Strong it at higher temperature.
Strong it a low temperature.
None of the above.
The specific gravity of electrolyte in a lead acid battery changes as follows when it
gets discharged.
increases
remains unchanged
lowers
Q:
Give general specifications of a power transformer for purchasing purposes along
with the units of the terms used?
Why is the stat point of a transformer usually grounded through a reactor?
Is RF coils hysteresis losses have lower values then eddy current losses?
TRUE/FALES
Q:
Which type of motors shall be most efficient for the following application and
why?
Railway Electric Traction.
Contact speed drives.
Boiler feed water pump in a thermal power plant.
Q: Explain
Corona
Skin effect in a conductor.
Following are the characteristics of a particular type of capacitor. Name it;
132
Q:
What will happen if a 220 V, 50 c/s AC relay coil is connected to 220 V DC supply?
Current transformers should not be left open circuited. Why?
Why is the iron core of a transformer laminated?
Q:
Define power factor
Give four reasons why it should be improved?
Q:
A three phase induction motor is found to be running in the wrong direction. What
will you do correct the rotation?
Name the conditions to be fulfilled before two alternators are put in parallel
operation?
Q:
Relate the measured signal with the measuring device
Thermocouple a) Temperature
Float b) Level
Bellows c) Pressure
Orifice d) Flow
Which of the following storage devices lose their contents with power failure.
EPROM
RAM
Core Memory
Q:
How many nuclear reactors are working in Pakistan at present? Give their
location and purpose?
133
Q:
What are two methods for obtaining a 60 Hz frequency supply from 50 Hz supply
system? Show only by simple block diagrams. Also name the practical devices
used in each method?
Which of the following type of capacitors are generally used on the output of a power
rectifier.
Mica
Ceramic
Electrolytic
Q:
Number the following in descending order of their overall efficiencies:
A1000wattpetrolenginegenerator ___________________________
A 125 MWe gas fired, superheated steam turbine generator plant
_______________________________________________________
A125MWenuclearpowerplant______________________________
A125MWeGas–Turbine __________________________________
Q: What is the best method of measurement of power for 3-phase unbalance load?
A:
Three Watt meter method
Two Watt meter method
Single Watt meter method
134
Q: The starting of heavy motor on the distribution system creates the problem of
Frequency dips
Voltage dips
Over voltages
Q: When the conductors of a three phase system are not spaced equilaterally,
transposition is made to balance
Resistance
Capacitance
Inductance
135
Q: Which is correct?
A:
Max. Quantity of electric current flowing in a circuit for one hour is called Ampere
Hour.
Average quantity of electric current flowing in a circuit for one hour is called Ampere
hour.
Min. quantity of electric current flowing in a circuit for one hour is called Amp. Hour.
136
Q: Which of the following types of memory is used for temporary storage of data
during day-to-day software operations in a computer system?
A:
RAM
EPROM
ROM
137
Q: High-pass filter is used to,
Pass R.F and suppress I.F
Offer low impedance to high frequency signal and suppress lower frequency signals
Offer high impedance to high frequency signal and attenuate low frequency signals
Q: The power line carrier is connected with the transmission line through.
Special filters connected to transmission lines.
Breakers and isolators
Current Transformers
Q: The name of interface between a thermocouple and a computer is,
A/D converter
D/A converter
Serial to parallel converter
Q: A coil is wound on a magnetic core. Fist D.C volts are applied to the coil and
the current measured.
138
Q: Two similar capacitors are connected.
First in series and next in parallel.
The total capacitance will be greater when the capacitors are connected in;
Series
Parallel
Q: A three phase four wire system supplies three unbalanced loads connected in
stat, Will
Current flow from the neutral of the supply side to the neutral point of the load.
No current flow in the neutral circuit.
Current flow from the neutral point of the load to the neutral point of the supply.
Q: Large transformers have drums mounted on the top of the tank. This drum is
called a conservator and is used;
s an oil expansion chamber
o compensate for loss of oil in case the transformer tank leaks
tore spare oil
Q: Three phase induction motors are classified according to the winding of their
Stator
Rotor
139
Q: Two transmission lines of different length, are operated in parallel. The tv lines
share the load in;
i) Direct proportion to their respective impedances.
ii) Inverse proportion to their respective impedance.
Q: In high voltage circuit breakers the voltage rises across the contacts after the
are is interrupted. The breaker is then subjected to recovery voltageThe
frequency of the recovery voltage is;
The same as the supply frequency voltage (50 Hz)
Greater than the supply frequency.
Less than the supply frequency.
Q: If steel pole and wooden poles are equal in cost and maintenance which
would be preferred more.
i) Steel pole
ii) Wooden pole
140
8 0C
10 oC
36o C
45o C
141
Q: Multiplication by “i” rotates a vector E through:
i) 900 clockwise
ii) 900 counter clockwise
iii) 1800 clock wise
iv) 180o counter clockwise
i) 14.9%
ii) 25%
iii) 78.7%
iv) None of the above.
Q: If there is one deuterium atom for 6500 hydrogen atoms, the number of
deuterium atoms in 1 m3 of water is closest to
i) 6.5 x 109
ii) 6.02 x 1023
iii) 1.02 x 1025
iv) 1.84 x 1026
142
Q: An elevator cable will have its greatest tension when the elevator car is
moving?
i) Down but coming to rest
ii) upward at a constant speed
iii) upward but is coming to rest
iv) when it is at rest
i) 225
ii) 275
iii) 325
iv) 375
i) Doubled
ii) Decreased about 50%
iii) Increased about 40%
iv) Quadrupled
143
Q: If 15 cans of food are needed for seven men for two day’s, the number of cans
needed for four men for seven day is:
i) 15
ii) 20
iii) 25
iv) 30
ii) 4
4
iii) 4
5
144
Q: A man does piece of work in 9 days, while B can do it in 3 days. In how many
days, can the work be finished if both A and B work together?
1
i) 2
4
1
ii) 3
2
iii) 6 days
iv) None of the above
Q: Two cars travel along the same road, one going at 50 m.p.h starts a A.M.,the
other which runs at 60 m.p.h starts at 10 A.M. At what will time the faster car
overtake the slower car?
A:
i) 3 P.M
ii) 4 P.M
iii) 5 P.M
iv) Never.
Q: If shipping charges to a certain point are 62 cents for the first five ounce and 8
cents for each additional ounce, the weight of a package for which the charges
are $1.66 is:
i) 13 ounces
ii) 18 ounces
iii) 20 ounces
iv) 24 ounces
i) 9
ii) 11
iii) 13
iv) 14
145
Q: The radius r of a cylinder is increasing 1/2 inch per minute and the height is
increasing 1/8 inch per minute. How many cubic inches per minute is the
volume of the cylinder increasing when r = 4 inches and h = 6 inches,
i) 10 π
ii) 24 π
iii) 26 π
iv) None of the above.
Q: The average of four number is 45. If one of the numbers is increased by 6, the
average will remain unchanged if each of the other three numbers is reduced by
i) 1
ii) 2
iii) 3/4
iv) 4
Q: From a piece of tin in shape of a square, 2 inches one side, the largest possible
circle is cut out. Of the following, the ratio of the are of the original circle to the
are of the original square is closest in value to :
i) 4/5
ii) 2/3
iii) 3/5
iv) 3/4
146
Q: The tiles in the floor of a bathroom are 15/16 inch square. The cement b/w the
tiles is 1/16 inch. There are 3240 individual tiles in this flow. The area of
floor is.
i) 224 sq. yds.
ii) 2.50 sq. yds.
iii) 250 sq. ft.
iv) 22.50 sq. ft.
Q: A train running between two towns arrives at its destination 10 minutes late,
when it goes at 40 m.p.h and 16 minutes when it goes at 30 m.p.h. The distance
between the two towns is :
i) 720 miles
ii) 12 miles
6
iii) 8
7
Q: A merchant sold two watches for Rs. 120 each. One was sold at a loss of 25%
of the cost and the confer was sold at gain of 25% of the cost. On both
transactions combined the merchant lost:
i) Rs. 64.00
ii) Rs. 36.00
iii) Rs. 16.00
iv) None of the above
i) Rs. 4
ii) Rs. 24
iii) Rs. 6
iv) Rs. 60
147
Q: A number that is equal to the sum of all its positive divisors that are less than
the number itself is called a “perfect number”. Which of the following is a
perfect number?
i) 16
ii) 12
iii) 10
iv) 6
Q: A person earns twice as much in December as in each of the other months. What
part of his entire year’s earnings does he earn in December?
i) 2/11
ii) 1/6
iii) 2/13
iv) 3/14
i) 16
ii) 20
iii) 24
iv) 80
Q: A clock that gains two minutes each hour is synchronized at midnight with
a clock that loses one minute an hour. How many minutes apart will the
hands of the two clocks be at noon?
i) 30
ii) 24
iii) 14
iv) 36
148
Q: A house was rented to a man for a total of Rs. 3600 a month. Later 2 otmen
joined the groups and the amount paid by each men then living in thehouse was
Rs. 480 less than before. If the men shared equally and the rent did not
change, how much was each man’s share under the new arrangement?
i) Rs. 480/-
ii) Rs. 720/-
iii) Rs. 840/-
iv) Rs. 960/-
Q: Mr. Khan and his son have the same birthday. When Mr. Khan was 40 years
old, his son was 16. How old was the boy when Mr. Khan was 10 times as old as his
son?
A:
i) 2 years 5 months
ii) 2 years 8 months
iii) 2 years 9 months
iv) 3 years
Q: A boy at point X would have reached point Y if he had walked 3 meters north
and then 2 meters east. Starting at point S, he walked 2 meters west. From this
point, what is the shortest distance to point Y ?
i) 3m
ii) 2√3m
iii) 3√2m
iv) 5m
i) 10
ii) 50
iii) 20
iv) 12
149
A) all four.
B) (iv) only
C) (ii), (iii), (iv) only
D) (iii) and (iv) only
b
Q: a f (x) dx is
i) 3x
ii) x5
iii) x3
iv) 5 3x
150
Q: If the probabilities that A and B will die within a year are P and Q respectively,
what is the probability that only one of them will be alive atthe end of the year?
P+Q
P+Q
P+Q -2PQ
P+Q + 2PQ
Q: The cards numbered from 1 to 10 are mixed in a box, Two cards numbered
p and q are drawn from the box, what is the probability that p+q = 10?
2/5
4/9
7/45
4/45
0 -1 1
2 0 2 is:
3 0 4
+2
0
-2
None of the above
y = -3x + 1
y = 2x
y = x/2
y = x/3
151
Q: If the angles of triangle are in the ratio 2:3:7 the triangle is:
Acute
Isosceles
Obtuse
Right
Q: Given : if all X are Z ad no Z are y, it necessarily follows that;
all Y are Z
all Y are X
no X are Y
no Z are X
In order to remodel his house, Mr. Khan has hired a plumber, a brick-
mason, an electrician and painter. The plumber is available only Monday
morning, all day Tuesday, and on Wednesday afternoon.
The painter is available only all day Tuesday and on Friday morning.
152
(a) Red
(b) Violet
(c) Yellow
(d) None of the above.
A: A man has 40 ft. of wire fencing with which to form a rectangular garden.
providing the fourth side. Determine the maximum area that can beenclosed.
153
Q: One ball is drawn at random from a box containing 3 red balls, 2 white balls
and 4 blue balls. Determine the probability “p” that it is not a red bal?
A:
1/3
2/3
2/9
None of the above
Q: The water in a canal a point P is traveling 10 feet per second, but because of a
downgrade its speed is increasing 1/16 foot per second. If the rate of increase is
constant, how many feet will the water travel from point P in 1.1/15
minutes?
786 feet
644 feet
868 feet
None of the above.
SinX, CosX
e x ,e x
Sin hx, Cos hx
None of the above
Red
Yellow
Violet
None of the above.
154
W/m-oC
W/m2- oC
W/m- oC2
None of the above
kg/m3
1b/ft3
1b/oC
None of the above.
180000 BTU/hr
12000 BTU/hr
188000 BTU/hr
None of the above.
Q: e V is a unit of:
Power
Momentum
Force
Energy
10-4 cm
10-3 cm
10-6 cm
None of the above.
155
Q: When a flowing fluid enters the narrow section of nozzle, its pressure is:
Increased
Remains the same
Decreased
None of the above
Temperature
Humidity
Velocity
None of the above
Q: The property which resists the flow of a gas or a liquid or a solid is called:
Diffusion
Viscosity
Sublimation
None of the above.
Resistance
Reduction
Reluctivity
None of the above.
33 km/s
330 km/s
33 m/s.
33 cm/s
156
Water
Air
Iron
Copper
Q: For the same volume, the surface to volume ratio is minimum for:
Sphere
Cylinder
Cube
Parallelepiped
Q: When a kettle full of water is placed on a burner for boiling, it temperature rises
as:
Q: Two ships are 1550 miles apart sailing towards each other. One sails at rate
of 85 miles per day and other at a rate of 65 miles per day. How farapart they
will be at the end of 9 days?
180 miles
200 miles
220 miles
785 miles
Q: A cake is baked in a pan with a square bottom of side of length 24 cm. If the
cake is cut into bars 6 cm long and 4 cm wide, how many bars will there be?
12
24
36
None of the above.
157
18 kg
9 kg
2 kg
4 kg
128
16
64
None of the above.
Q: The specific heat of water may be taken as 1.0. of an oil as 0.5 and that of a
solid as 0.1 in CGS units. If the same quantity of heat is supplied to an equal
mass of the three, the temperature rise in the three cases may be:
158
2.0
0.2
20.0
None of the above.
Q: One mole of hydrogen and 0.5 moles of oxygen are in a bomb at 77oF. Thetotal
mass is 18.0 gms. A chemical reaction occurs and the temperature and pressure are
increased. The change in mass is approximately.
59.3 gms
18 gms
9 gms
No changes
33
330
3.3
0.33
Q: A cubical tank with each side 2 m long, is exactly half field with w cubical
block of wood of specific gravity 0.6 and measuring 1 m on the edge is then
placed in the tank, so as to float with one face horizontal. The level of the
water in the tank will now be:
1.10 m
1.15 m
1.20 m
1.30
159
15 N
49 N
147 N
184 N
25 kg-cm
1 Newton/m
9.8 Newton/m
None of the above.
17.9 cm
18.2 cm
18.9 cm
19.3 cm
1 kPa
2 kPa
6 kPa
16 kPa
160
Q: A house has two adjacent glass windows. Window A has area 3 m2 thickness 0.6
cm and window B has area 2 m2 and thickness 0.5 cm. The R Ratio of the
heat flow through the two windows qA/qB is:
0.69
0.83
1.0
1.25
0.3 F
0.33 F
0.333 F
0. IF
63 V
87 V
126 V
157 V
161
230
240
250
260
5/6, m/s
6/5, m/s
2, m/s
24/5, m/s
0.67
1.0
1.5
None of the above.
- 3/2
-2/3
3/2
None of the above.
n(n-1)/2
n(n+1)/2
n(n+1)
None of the above.
162
3.5
20/7
7.0
None of the above
Q: The sum of the two binary numbers 10110 and 10011 is:
101001
110011
111001
None of the above
-1/2 + 1/2
1 1
3 2 2 2
-1/ √2 + 1/√2
None of the above.
2/13
-7/13
-46/13
-49/13
No solution
Indeterminate
Z must be a complex number
None of the above
163
12/41 + i 26/41
12/41 - i 26/41
26/41 + i 12/41
None of the above.
Q: The number of samples of 5 light bulbs which can be selected from a lot c 10
bulb is:
250
252
254
256
Q: Three screws are drawn from a lot of 100 screws, 10 of which are defective.
The probability of the event that all 3 screws drawn ( we drawn without
replacement) are non-defective is nearest to:
92%
87%
82%
73%
2 and 6
0 and 5
3 and 4
1 an 7
164
y = dy/dx -4
y = 4 – dy/dx
y = dy/dx +4
None of the above
Q: The work done by the force F = 3i -2j + 4k (i, j and k being unit vectors along
x, y and z axes respectively) on a particle when it is displaced from P :(8, -2,-3)
to Q: (-2,0,6) is:
2 units
4 units
5 units
None of the above
1n(a+bx)/ab
1n(a+bx)/a
1n(a+bx)/b
None of the above
x 1n(x) - x
1n(x) - 1
x1n(x) + x
(x 1n(x) - x)/x
1/15
2/15
7/15
11/15