Wednesday 25 July 2012

: MEASUREMENTS AND INSTRUMENTATION


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DEPT: II EEE
SUB/ CODE : MEASUREMENTS AND INSTRUMENTATION/EE33
2MARKS:
UNIT-I
INTRODUCTION
1. Define instrument.
An instrument is a device for determining the value or magnitude of a quantity.
2. What are the types of instruments?
a. Mechanical instrument
b. Electrical instrument
c. Electronic instrument
3. Write the dynamic characteristics of any measurement system.
a. Step change
b. Linear change
c. Sinusoidal change
d. Lag
e. Fidelity
f. Dynamic error
4. What is standard? What are the different types of standards?
A standard is a physical representation of a unit of measurement. A known accurate
measure of physical quantity is termed as standard.
Types:
a. Primary standard
b. Secondary standard
c. International standard
d. Working standard.
5. What is calibration?
Calibration is the process of checking the accuracy of instrument by comparing the
instrument reading with a standard meter of known accuracy.
6. Define arithmetic mean.
Arithmetic mean is calculated by taking the sum of all readings divided by the
number of readings.

7. Define the terms precision and sensitivity.
Precision:
It is a measure of the repeatability of a series of measurements.
Sensitivity:
It is the measure of change in reading of an instrument for a given change in
the measured quantity.
8. Define static error.
The static error of a measuring instrument is the numerical difference between the
true value of a quantity and its value as obtained by measurement.
9. Define accuracy.
The degree of closeness of a measurement compared to the true value.
10. Write the static characteristics of measuring instruments.
a. Accuracy
b. Precision
c. Sensitivity
d. Resolution
e. Error
11. What are the different calibration methodologies?
(i) Direct calibration
a. Meter calibration
b. Generator calibration
c. Transducer calibration
(ii) Indirect calibration
d. Meter calibration
e. Generator calibration
a. Transducer calibration
12. Define instrumental errors.
These errors arise due to inherent short coming in the instrument, misuse of the
instruments and loading effects.
13. List the different types of possible errors in measurements.
a. Gross error
b. Systematic error
c. Environmental error
d. Observational error
e. Random error
14. What is the need for measurement?
The need for the measurement is to know about the unknown magnitude.
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15. Write the need for calibration.
The need for calibration means is to check the accuracy and reliability.
16. What are the basic elements of a measurement system?
a. Primary sensing element.
b. Variable conversion element.
c. Variable manipulation element.
d. Data transmission element.
e. Data presentation element.
17. What is meant by measurement?
The process of determining the present value is called as measurement.
18. What are the methods of measurements?
a. Direct method.
b. Indirect method.
19. Define environmental error.
This error occurs due to external conditions to the measuring device, including
conditions in the area surrounding the instrument, such as the effects of change in
temperature, humidity, magnetic or electrostatic fields.
20. Define sensitivity
The ratio of the change in output of the instrument to a change of input or measured
value is called sensitivity.

UNIT-II
ELECTRICAL AND ELECTRONIC INSTRUMENTS
1. Write the classification of measuring instruments.
Electrical instruments are mainly classified as
a. Indicating instruments
b. Recording instruments
c. Integrating instruments
2. Define indicating instruments.
Indicating instruments are used to indicating the magnitude of unknown quantity.
The examples are ammeters, voltmeters etc.
3. Define recording instruments.
These instruments give a continuous record of the given input quantity. The
examples are various types of recorders.
4. Define integrating instruments.
These instruments measure the total quantity of electricity delivered over period
of time. Example: energy meter.
5. What are the requirements of an instrument?
The following systems must be present in an instrument
a. Deflecting system producing deflecting torque.
b. Controlling system producing controlling torque.
c. Damping system producing damping torque.
6. What are the types of instruments?
It consist of two types
(i) Permanent magnet moving coil instrument.
(ii) Moving iron instruments
a. Moving iron attraction type.
b. Moving iron repulsion type.
7. What are the advantages of digital instruments over analog instruments?
a. High accuracy.
b. High input impedance.
c. Reading speed is very high.
d. Digital output can be directly recorded.
8. Define gravity control.
It consists of a small weight attached to the moving system. Whose position is
adjustable. This weight produces a controlling torque due to gravity.
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9. Define spring control.
In this system two hair springs are attached to the moving system which produce
the controlling torque.
10. Explain the purpose of Schmitt trigger in digital frequency meter.
In a digital frequency meter, Schmitt trigger is connected between amplifier and
a gate, it is used to convert the analog voltage from the amplifier to train of pulses
which is fed to the gate.
11. Which torque is absent in energy meter? Why?
In energy meter, there is no controlling torque, as the driving torque alone is
enough to cause continuous revolution of the disc.
12. What are the various principles of analog type electrical instruments?
a. Magnetic effect
b. Heating effect
c. Electrostatic effect
d. Electromagnetic effect
e. Hall effect
13. What is the principle of ramp type digital voltmeter?
Ramp type digital volt meter works on the principle of comparison of unknown
voltage with the ramp signal and by counting the number of pulses passing
through till both the voltages become equal. This number of pulse will give the
direct indication of the voltage.
14. What is the purpose of instrument transformers?
The transformers used for measuring very large values of current or voltage
which can not be directly measured are called instrument transformer. Two types
of instrument transformers are
a. Current transformer
b. Voltage transformer.
15. How a PMMC meter can be used as voltmeter and ammeter?
When a resistance is connected across the basic PMMC meter then it will act as a
D.C ammeter and when a resistance is connected in series with the basic PMMC
meter then the meter will act as a D.C voltmeter.
16. What is volt ampere hour and watt hour?
Volt ampere hour is the reactive power consumed by the load where as watt
hour is the real power consumed by the load.
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17. What are the different methods of measurement of frequency in the power
frequency range?
a. Mechanical resonance type or vibrating reed type frequency meter.
b. Electrical resonance type frequency meter.
c. Weston frequency meter.
18. How are the analog instruments classified on the basis of method used for
comparing the unknown quantity?
a. Electrostatic type instruments.
b. Electromagnetic type instruments.
c. Instruments using magnetic effect.
d. Instruments using heating effect.
e. Instruments using hall effect.
19. Give the advantage of moving iron meters?
a. The same instrument can be used for both A.C and D.C measurement.
b. Torque /weight ratio is very high hence errors due to friction is very high.
c. These instruments are highly accurate.
d. These instruments are simple in construction.
20. What is creeping in energy meters?
A slow but continuous rotation of energy meter disc even when there is no
current flowing through the current coil but only the pressure coil is energised, is
called creeping. Some other factors that cause creeping are excessive voltage
across the pressure coil, vibrations and external magnetic fields.

UNIT-III
COMPARISION METHODS OF MEASUREMENTS
1. What is potentiometer?
A potentiometer is an instrument designed to measure an unknown voltage by
comparing it with a known voltage.
2. Mention the applications of potentiometers.
a. Measurement of small emfs (up to 2V).
b. Comparison of emf of two cells.
c. Measurement of high emfs (up to 250V).
d. Measurement of resistance.
e. Measurement of current.
3. What are the types of potentiometer?
a. D.C potentiometer
b. A.C potentiometer.
4. What are the types of DC potentiometer?
a. Simple potentiometer.
b. Direct reading potentiometer.
c. Crompton potentiometer.
d. Modern form of slide wire potentiometer.
5. What is the main difference between in operation between DC potentiometer and
AC potentiometer?
In the DC potentiometer only the magnitude of the unknown emf and slide
wire voltage drop must be made equal to obtain balance, where as in the AC
potentiometer the phases of the two voltages, as well as their magnitudes, must be
equal for balance to be obtained.
6. What are the types of AC potentiometers?
a. Polar potentiometer.
b. Co ordinate potentiometer
7. Mention some applications of AC potentiometers.
a. Measurement of self inductance
b. Calibration of ammeter
c. Calibration of voltmeter
d. Calibration of wattmeter
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8. What are the uses of bridge circuits?
The bridge circuits are mainly used for measuring unknown quantities such as
resistance, inductance and capacitance.
9. What are the two main types of bridges?
a. DC bridges
b. AC bridges
10. What are the types of DC bridges?
a. Wheatstone bridge
b. Kelvin’s bridge
c. Kelvin’s double bridge.
11. What is a Wheatstone bridge?
Wheatstone bridge is used for measurement of medium resistances in the range
of 1Ω to 100 k Ω.
12. What is Kelvin’s bridge?
Wheatstone bridge is not suitable for measurement of very low resistance.
Kelvin’s bridge is a modification of Wheatstone bridge and is used to measure
values of resistance below 1 Ω.
13. What is Kelvin’s double bridge?
This circuit consists of double bridge. This circuit is mainly used for measuring
very low resistances from 0.00001 Ω to 1 Ω.
14. What is Schering bridge?
The Schering bridge, one of the most important AC bridges, is used for
measurement of capacitors, it is also measures the insulating properties of the
electrical cables and equipments.
15. What is Maxwell’s bridge?
The Maxwell bridge is used to measure both a given inductance and its series
resistance by comparison to a standard capacitance.
16. What is Anderson bridge?
It is a modified version of the Maxwell’s inductance capacitance bridge. In this
method the self inductance is measured in terms of a standard capacitor.
17. What is earth loop?
Earth loops form a distinct part of the guarding system of electrical equipments.
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18. Define interference.
The instruments used for electrical measurements are in an environment which
contains many sources of electrical magnetic energy. These sources can produce
undesirable signals called interference.
19. Write the classification of interference signal.
a. Capacitive interference
b. Inductive interference
c. Electromagnetic interference
d. Electrostatic interference
e. Ground loop interference
20. What are the sources of electromagnetic interference?
a. Welding equipment.
b. Inductive or capacitive coupling
c. AC power circuits, radio frequency transmitters.

UNIT-IV
STORAGE AND DISPLAY DEVICES
1. Define recorder.
It is used to record all electrical and nonelectrical quantities as a function of time.
2. Define X-Y recorder.
It is used to study the behaviour of one variable with respect to another variable
instead of recording recording them separately as function of time. There are two
types of X-Y recorders namely.
a. Analog X-Y recorders.
b. Digital X-Y recorders.
3. List out the controllers normally found in XY recorder.
a. Servo controller.
b. Chopper controller.
4. What is magnetic tape recorder/
Magnetic tape recorder is a recorder which records analog data in such a manner
that they can be reproduced in electrical form again.
5. What is the basic operating principle of digital tape recording?
Digital data can be recorded and stored in magnetic tapes using a variety of
techniques. The basic principle used to modulate the digital data in some form and
then record this modulated data in the tape.
6. What are the various methods of recording data?
a. Direct recording.
b. Frequency modulated (FM) recording.
c. Pulse duration modulation (PDM) recording.
7. Write the basic components of magnetic tape recorder.
Following are the basic components of magnetic tape recorder:
a. Recording head
b. Magnetic tape
c. Reproducing head
d. Tape transport mechanism
e. Conditioning devices.

8. List the main parts of cathode ray tube.
a. Electron gun assembly
b. Deflection plate assembly
c. Fluorescent screen
d. Glass envelope.
9. List out the advantages and disadvantages of LCD.
Advantages:
a. Low cost
b. Low power consumption
Disadvantages:
a. Life time is very less compared with LED.
b. Reliability is low
c. It occupies large area.
10. What are the types of printers according to printing methodology?
(i) Impact printer
a. Line printer
b. Dot matrix printer
(ii) Non impact printer
a. Ink jet printer
b. Laser printer
11. In what ways line printers are advantage over dot matrix printer?
a. Prints one line at a time.
b. Printing speed is better
c. Printing quality is better
12. What are the different materials used in LED? Also name the colours emitted.
Materials:
a. Gallium arsenide phosphate
b. Gallium arsenide
c. Gallium Phosphide
Colours emitted:
Red, yellow, green, infrared
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13. Differentiate between LED and LCD.
No LED LCD
1.
2.
3.
4.
Consumes more power.
High cost.
More life time.
Capable of generating its own
light.
Consumes less power.
Low cost.
Less life time.
Requires an external or internal light
source.
14. State the features of ink jet printers.
a. They can print from two or four pages per minute.
b. The operating cost is quite low.
c. Resolution is about 360 dots per inch, therefore better printing quality is
achieved.
15. Define the deflection sensitivity of CRT.
The deflection sensitivity of a CRT is defined as the deflection of the screen per
unit deflection voltage.
16. What are the different types of amplifiers used for CRO?
a. Vertical amplifier
b. Horizontal amplifier
17. What are the advantages and disadvantages of FM method of magnetic tape
recording?
Advantages:
a. Accurately reproduces the wave form of the input signal.
b. Wide frequency range.
Disadvantages:
a. Requires a high tape speed
b. Limited frequency response
c. Requires a high quality of tape transport and speed control.
18. Write the advantages of LED on electronic display.
a. Low power consumption
b. Small size and weight.
c. Long life
d. Very fast action
19. Define data logger?
It is used to automatically record of the readings of instruments located at different
parts of the plant.
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20. What are the functions of a data logger?
The main function of the data logger is to measure electrical output from any type
of transducer.
The data logger is used to automatically record of the readings of instruments
located at different parts of the plant.
21. What are the functions of aluminium layer?
a. The aluminium layer acts as a heat sink for the phosphor and thus reduces
the chances of the phosphor burning.
b. It serves as a light scatter. When the beam strikes the phosphor with
aluminized layer, the light emitted back in to the tube is reflected back
towards the viewer which increases the brightness.

UNIT-V
TRANSDUCER AND DATA ACQUISITION SYSTEM
1. Define transducer.
It is a device which converts one form of energy into another form.
2. What are the classification of transducer?
The transducers are classified as
a. According to the transduction principle
b. Primary and secondary transducer
c. Active and passive transducer
d. Analog and digital transducer
e. Transducer and inverse transducer
3. Define active transducer.
Active transducers are self generating type of transducers. These transducers
develop an electrical parameter which is proportional to the input quantity.
4. Define passive transducer.
Passive transducer do not generate any electrical signal themselves. To obtain an
electrical signal from such transducers, an external source of power is essential.
5. What is analog transducer?
Analog transducer converts input signal in to output signal, which is a continuous
function of time such as strain gauge, LVDT, thermocouple.
6. What is digital transducer?
Digital transducer converts input signal in to the output signal, which is in the form
of pulses.
7. What is an inverse transducer?
An inverse transducer is defined as a device which converts an electrical quantity in
to a non electrical quantity.
8. Write the transducer selection factor.
a. Nature of measurement
b. Loading effect
c. Environmental conditions
d. Measuring system compatibility
e. Cost and availability.
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9. Define strain gauges.
The strain gauge is an example of a passive transducer that uses the variation in
electrical resistance in wires to sense the strain produced by a force on the wire.
10. Define gauge factor.
The gauge factor is defined as the ratio of per unit change in resistance to per unit
change in length.
Gauge factor : ΔR/R
ΔL/L
11. What are the main types of potentiometers?
a. Wire wound potentiometer
b. Non wire potentiometers
12. Mention the types of strain gauges
The strain gauges are mainly of four types namely
a. Wire strain gauges
b. Foil strain gauges
c. Thin film strain gauge
d. Semiconductor strain gauge.
13. What is an inductive transducer?
An inductive transducer is a device that converts physical motion in to a change in
inductance. Transducers on the variable inductance type work upon one of the
following principles.
a. Number of turns
b. Geometric configuration
c. Permeability of the magnetic material
14. Mention the advantages of LVDT
a. LVDT has high sensitivity.
b. The LVDT gives a high output.
15. Mention the applications of LVDT.
LVDT are used to measure
a. Displacement
b. Force
c. Weight
d. Pressure
e. Position
16. What are the types of DAS?
The DAS is mainly classified as
a. Analog data acquisition system (DAS).
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b. Digital data acquisition system (DAS).
17. What is piezoelectric effect?
A piezoelectric material is one in which an electric potential appears across certain
surfaces of a crystal if the dimensions of the crystal are changed by the application of
a mechanical force. This potential is produced by the displacement of charges. The
effect is reversible also if varying potential is applied to the proper axis of the crystal,
it will change the dimensions of the crystal there by deforming it. This phenomenon is
known as piezoelectric effect.
18. What are the materials used for piezoelectric transducers?
Common piezoelectric materials include ammonium dihydrogen phosphate , quartz
and ceramics made with barium titanate, potassium dihydrogen phosphate and lithium
sulphate are used in real applications.
19. Define smart sensor?
Smart sensors are sensors with integrated electronics that can perform one or more
of the following functions.
a. Logic functions
b. Two way communication
c. Make decision
20. Mention some applications of smart sensor.
Smart sensor enhances the following applications:
a. Self calibration
b. Computation
c. Communication
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FIFTH SEMESTER-ELECTRONICS & COMMUNICATION ENGG. CONTROL SYSTEMS




ANNA UNIVERSITY – COIMBATORE
B.E.\B.TECH.DEGREE-EXAMINATION-DECEMBER 2009
FIFTH SEMESTER-ELECTRONICS & COMMUNICATION ENGG.
CONTROL SYSTEMS
PART A-(2*20=40)
1. What is the use of mason’s gain formula.
2. Give two examples for open loop and closed loop systems.
3. What do you meant by analogous systems.
4. What are the frequency domain specifications.
5. What are the advantages and disadvantages of feedback control systems.
6. How can we classify second order system based on damping ratio.
7. Define gain margin.
8. Define resonant frequency.
9. State Routh stability criterion.
10. Define Nyquist stability criterion.
11. What are the difference between state space analysis and Transfer function analysis.
12. What are root loci.
13. What is servomechanism.
14. What are the different types of controller.
15. What is synchro.
16. Name the test signals used in control systems.
17. What is polar plot.

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18. Give examples for frequency response plot.
19. Write down state mode and output model of state space systems.
20. What do you mean by decomposition of transfer function.
PART B-(5*12=60)
21. A) A unity feedback system has an open loop transfer function G(s)=k/s(s+10). If the damping
ratio is 0.5 determine (i) the value of k, (ii) peak overshoot, (iii) time to peak overshoot, (iv) settling time.
(8) B) For a unity feedback whose G(s)=1/s(s+1) the input signal is r(t)= 4+6t+2t3. Find the generalized
error coefficients. (4)
22. For the given block diagram find corresponding signal flow graph and evaluate closed loop
transfer function relating to output and input.
23. Determine the value of k for a unity feedback control system have open loop transfer function
G(s)H(s)=k/s(s+2)(s+4) such that (i)gain margin =20db (ii) phase margin =600.
24. Investigate the F(s) for stability using RH criterion (i) F(s) =s4+ks2+(k+1)s+2 (ii)
F(s)=s4+s3+3s2+s+6 (iii) F(s)=s5+s4+2s3+2s2+6s+6
25. Obtain the state space model of the system with transfer function C(s)=s2+3s+2
in phase Variable form. R(s) s2+7s+12
26. A system characterized by the following state equation
Find (i) Transfer function of the system (ii) State transition matrix.
27. Sketch the root locus for the system with characteristic equation 1+G(s)H(s)=K(s+2)(s+3)
(s+1)(s-1)
28. Find transfer function of field controlled DC servo motor.

ENVIRONMENTAL SCIENCE AND ENGINEERING


B.E.IB Tech. Degree Examinations - November/December 2010

Fifth Semester Mechanical Engineering

ENVIRONMENTAL SCIENCE AND ENGINEERING 

(Common to B.E./B.Tech. Third Semester Computer Science and Engineering, Civil Engineering and Information Technology)

(Also common to Fourth Semešter Biomedical Engineering and FifthSemester/Aeronautical Engineering, Automobile Engineering, Electronics and Communication Engineering and Production Engineering)
(Regulation 2008)

1.What are the types of grasslands ecosystem?

Types of grassland ecosystem:

Depends upon climate condition,
1) Tropical grasslands.
2). Temperature grasslands.
3) Polar grasslands.
2. Define species diversity.
Species diversity is the diversity between differed species. The sum of varieties of all living organisms at the species level is known as species diversity.

3. What do you understand by soil pollution? 

Soil pollution is defined as, the contamination of soil by human and natural activities which may cause harmful effects on living beings.

4.What are the causes of noise pollution. .

Causes of Noise pollutions:
1) Noise pollution affects human health, comfort and efficiency. It causes contraction of blood vessels, makes skin page, leads in excessive scretion of adrenalin hormone into blood stream which is responsible for high blood pressure.

2) It causes muscles to contract leading to nervous breakdown, tension etc.

3) Recently it has been reported that blood is also thickend by excessive noises.
5.List the causes of deforestation.
Causes of Deforestation: .
1) Development projects.
2) Mining operations.
3) Raw materials for industries.
4) Fuel requirements.
5) Shifting cultivation.
6) Forest fires.

6.List the advantages and disadvantages of the hydel power.

7.Define urbanization.

Urbanization is the movement of humán population from rural areas to urban areas for the want of better education,communication, health, employment.

8.How can global warming be controlled?

Control of Global Warming: ‚
1) CO2 emission can be cut by reducing the use of fossil fels.
2) Implement energy conservation. measures.
3) Plant more trees.
4) Stabilize population growth.
5) Adopt sustainable agriculture.

9. What is population explosion?

The enormous increase in population, due to low death rate (mortaling) and high birth rate (Natating) , is termed as population explotion. The human population is not increasing at a  uniform rate in all parts of the world.

10.What are HIV and AIDS?

AIDs is the abbreviated form for Accquired Immuno Deficiency Syndrome caused by a virus called HIV (Human Immuno deficiency virus). Many Myths have been spread about AIDS and it is very important for eveiyone to know facts about HIV and AIDS.

Anna University - Data Structure and Algorithm (DSA) -



Anna University - Data Structure and Algorithm (DSA) - April / May 2011 - Question Paper Two Marks with Answers ~ V+ Blog - Anna University Study Material and Information Provider

B.Tech. DEGREE EXAMINATION, APRIL/MAY 2011 - Third Semester

Electrical and Electronics Engineering

DATA STRUCTURES AND ALGORITHMS - (Regulation 2008)


Two Marks with Answers

 1.Define Stack. What are the operations performed on a stack?

A stack is a linear data structure which follows Last In First Out (LIFO) principle, in which both insertion and deletion occur at only one end of the list called top.
The fundamental operations on the stack are :-

(j) PUSH - equivalent to insert

(ii) POP - equivalent to delete.
2.Mention the applications of list.

1. Polynomial ADT.
2. Radix sort.
3. Multilist,

3.Define tree. List the tree traversal techniques.


A tree is a collection of nodes. The collection can be empty, otherwise, a tree consists of a distinguished node r, called the root, and zero or more non empty (sub) trees T1, T2 Tk each of whose roots are connected by a directed edge from r.
Traversing means visiting each node only,once. Tree traversal is a method for visiting all the nodes in the tree exactly once.
There are three types of tree traversal techniques, namely:
1. Inorder traversal
2. Preorder traversal
3. Post order traversal.
4. Differentiate a binary tree from a binary search tree.

Binary search tree is a binary tree in which for every node X in the tree, the values of all the keys in its left subtree are smaller than the key value in X, and the values of all the keys in its right subtree are larger than the key value in X.

5. What is meant by binary heaps.


The efficient way of implementing priority queue is binary is Binary heap is merely referred as heaps, Heaps have two properties namely.
* Structure property .
* Heap order property

6. What is linear hashing? Specify its merits and demerits.


In linear hashing f (key) directly refers to value.
Best case time complexity 0(1)
Worst case time complexity 0(n) .


7.What is meant by digraph? Define the terms in-degree and out-degree with respect to a digraph.

A directed graph or digraph is a pair G = (V,E) where V is a set whose elements are called vertices (nodes) and E is a set of ordered pairs of elements of V (edges or directed edges or arcs). For directed edge (v, w) in E, v is its tail and w its head, (v;w) is represented in the diagrams as the arrow, v -> w, (ie)
simply vw.

Indegree of a Node = No.of incoming edges (nodes)
Outdegree of a Node = No. of outgoing edges (nodes)

8. Write the adjacency matrix for the following graph.
9.What is dynamic programming? Give two examples.

Dynamic programming is one of the optimal algorithm technique when comparing to other methods. What is the advantage of this method? From which classification it has been derived?
Examples:
Sorting by distribution counting.
Horspool's algorithm.

10.What is meant by NP-complete problem.


A problem L is NP-complete if & only if L is NP hard & L E NP.


Anna University MA2161 - MATHEMATICS – II


Anna University
MA2161 - MATHEMATICS – II

Semester : II
Year : 1st
Branch : Common to all branch

UNIT I ORDINARY DIFFERENTIAL EQUATIONS
1. Higher order linear differential equations with constant coefficients –(8 +2)marks
2. Method of variation of parameters -8 marks
3. Cauchy’s and Legendre’s linear equations-(8+2) marks
4. Simultaneous first order linear equations with constant coefficients -8 marks

UNIT II VECTOR CALCULUS
1. Gradient Divergence and Curl ,Directional derivative,Irrotational, solenoidal-8 marks
2. Green’s theorem ,Gauss divergence theorem,stokes’ theorem -16+8 marks

UNIT III ANALYTIC FUNCTIONS
1. Harmonic and orthogonal properties of analytic function-8 marks
2. conjugate Construction of analytic functions -8 marks
3. Conformal mapping : w= z+c, cz, 1/z, -8 marks
4. Bilinear transformation. -8 marks

UNIT IV COMPLEX INTEGRATION
1. Cauchy’s integral formula -8 marks
2. Taylor and Laurent expansions -8 marks
3. Residue theorem -8 marks
4. Contour integration-8 marks

UNIT V LAPLACE TRANSFORM
1. properties ,derivatives, integrals,unit step function ,impulse functions, Initial and Final value theorems-8marks
2. periodic functions-8 marks
3. Inverse Laplace transform –partial fraction and Convolution theorem -8 marks
4. Solution of linear ODE -8 marks

MATHEMATICS I question paper


DEPARTMENT OF MATHEMATICS
MA 2111 ENGINEERING MATHEMATICS -1
MATRICES
Part –A
1. Find the eigen values of the matrix A = ⎥⎦

⎢⎣

1 2
5 4
2. Find the constant a and b such that the matrix ⎥⎦

⎢⎣

b
a
1
4
has 3 and -2 as its
eigen values.
3. Show that if λ is a characteristic root of the matrix A, then λ + k is a
characteristic root of the matrix A + k I.
4. If λ be an eigen value of a non-singular matrix A, show that
λ
| A | is an
eigen value of adjA.
5. If the characteristic equation of a matrix A is λ2 - 4 λ+3 = 0, find the
characteristic equation of 3A−1 − 4 I
6. Are ⎥⎦

⎢⎣
⎡−
2
6
and ⎥⎦

⎢⎣
⎡−
1
6
eigen vectors of ⎥⎦

⎢⎣

1 4
2 3
.
7. Let A =
⎥ ⎥ ⎥


⎢ ⎢ ⎢


3 1 1
1 5 1
1 1 3
If ( 1, 0, -1)T is an eigen vector corresponding to some
eigen value λ of the matrix A. find λ.
8. Discuss the nature of QF 2xy + 2yz + 2zx.
9. Write down the matrices of the following QF 2x2 +3y2+6xy.
10. Write down the QF corresponding to the following matrices
⎥ ⎥ ⎥ ⎥


⎢ ⎢ ⎢ ⎢



− −


0 0 3 2
2 0 6 3
1 4 0 0
1 1 2 0
DEPARTMENT OF MATHEMATICS
MA 2111 ENGINEERING MATHEMATICS -1
ANALYTICAL GEOMETRY
PART – A
1. Find the equation of the sphere whose centre is ( 2, -3, 4) and radius 5?
2. Show that the spheres x2+y2+z2=25, x2+y2+ z2-18x-24y-40z + 225=0 touch
externally.
3. Find the equation of the sphere on this join ( 2,-3,1) and ( 1,-2,-1) as
diameter.
4. Find the equation of sphere having its centre on the plane 4x-5y-z=3 and
passing through the circle x2+y2+z2 -2x-3y+4z + 8=0,
x2+y2+z2+4x+5y-6z+2 = 0.
5. Prove that the plane x + 2y – z = 4 cuts the sphere x2+y2+z2 –x + z -2 =0 in
a circle of radius unity.
6. Find the equation of the tangent plane to the sphere 3(x2+y2+z2) -2x -3y -
4z -22 = 0 at the point ( 1,2,3).
7. Find the equation to the cone whose vertex is the origin and base the
circle x =a; y2 + z2 = b2.
8. Find the equation of the right circular cone whose vertex is at the origin,
whose axis is the line x = y / 2 =z / 3 and which has semi vertical angle of
30o
9. Find the equation of the quadric cylinder with generators parallel to
x – axis and passing through the curve ax2 + by2 + cz2 = 1, lx+ my+ nz = p.
10. Find the equation of the quadric cylinder whose generators intersect the
curve ax2 + by2 = 2z, lx+ my+ nz = p and are parallel to Z – axis.
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DEPARTMENT OF MATHEMATICS
MA 2111 ENGINEERING MATHEMATICS -1
FUNCTIONS OF SEVERAL VARIABLES
PART – A
1. Find the first order partial derivatives of the function u = yx
2. If Z = log( x2 + xy + y2), prove that = 2.


+


y
y z
x
x z
3. If U = f( y-z, z-x, x-y), prove that = 0


+


+


z
u
y
u
x
u
4. Given U = sin(x/y), x = et and y = t2 find
dt
du
5. If U = x2 + y2 + z2 and x = e2t, y = e2t cos3t, z = e2tsin3t find
dt
du
6. If
x y
w z
z x
V y
y z
U x

=

=

= , , show that 0.
( , , )
( , , ) =


x y z
u v w
7. If U = x (1-y); V = xy prove that JJ’ = 1.
8. Show that
2
log(1 )
x2 ey + x = x + xy − ( approximately)
9. Find the stationary points of xy ( a –x-y).
10. State necessary conditions for a maximum or a minimum.
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DEPARTMENT OF MATHEMATICS
MA 2111 ENGINEERING MATHEMATICS -1
DIFFERENTIAL CALCULUS
PART-A
1. Find the radius of curvature for a circle and straight line.
2. Find the radius of curvature at any point of the catenary y = c cosh (x / c).
3. Find the radius of curvature at any point of y = logsinx.
4. Find ρ at Ө on x = 3a cos Ө - a cos3 Ө, y = 3a sin Ө - a sin3 Ө.
5. Find ρ at ( -2,0) on y2 = x3 + 8.
6. Find the circle of curvature at (0,0) on x + y=x2+y2+x3.
7. Write the method to find the evolute of a given curve y = f(x).
8. State two important properties of the evolute.
9. Find the envelope of the family of straight lines y = mx +a/m.
10. Find the envelope of + = 1
b
y
a
x subject to a + b = c, where c is known
constant
DEPARTMENT OF MATHEMATICS
MA 2111 ENGINEERING MATHEMATICS -1
MULTIPLE INTEGRALS
PART –A
1. Evaluate ∫ ∫
2
1
5
2
xy dxdy
2. Evaluate ∫ ∫
2
0
2
0
π
rdrdθ
3. Evaluate ∫ ∫ x y dxdy + −
3
4
2
1
( ) 2
4. Evaluate ∫ ∫
π θ
θ
0
cos
0
rdrd
5. Shade the region of integration ∫ ∫


a a x
ax x
dxdy
0
2 2
2
6. Transform the integral ∫ ∫

0 0
y
dxdy to polar coordinates.
7. Change the order of integration ∫ ∫
1 −
0
2
2
( , )
x
x
f x y dydx
8. Express the region x > 0, y > 0, z > 0, x2 + y2 + z2 < 1 by triple integration.
9. Find the area enclosed by the circle x2 + y2 = a2.
10. Find the area of the region bounded by y2 = 4x and x2 = 4y.
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1. Find the eigen values and eigen vectors of the matrix
2
64
2 2 0
2 5 0
0 0 3
3
75
and
hence diagonalize it through orthogonal reduction.
2. Verify Cayley-Hamilton theorem for A =
2
64
2 0 −1
0 2 0
−1 0 2
3
75
and hence
find A−1 and A4.
3. Find the eigen values and eigen vectors of the matrix A =
2
64
2 −2 2
1 1 1
1 3 −1
3
75
.
4. Find the inverse of the matrix A =
2
64
7 2 −2
−6 −1 2
6 2 −1
3
75
by using Cayley-
Hamilton theorem.
5. show that
2
64
0 1 0
1 0 0
0 0 1
3
75
is orthogonal. Find its inverse. Verify that its
eigen values are of unit modulus.
6. Find the characteristic equation of A =
2
64
2 1 1
0 1 0
1 1 2
3
75
and hence express
the matrix A5 in terms of A2,A and I.
7. If (0, 1, 1)T , (2,−1, 1)T , (1, 1,−1)T be the eigen vectors of matrix A
corresponding to the eigen values −1, 1, 4 then find the matrix A.
8. Reduce the quadratic form 8x21
+7x22
+3x23
−12x1x2 +8x2x3 +4x1x3
to the canonical form through orthogonal transformation. Hence show
that it is positive semi-definite.
9. Reduce the quadratic form 6x21
+ 3x22
+ 3x23
− 4x1x2 − 2x2x3 + 4x1x3
into sum of squares by orthogonal transformation. Write also rank,
index and signature.
10. Reduce the quadratic form 17x2 − 30xy + 17y2 to a canonical form
and find the nature of conic 17x2 − 30xy + 17y2 = 128. Find also the
lengths and directions of the principal axes.
QUESTION BANK 1 MATHEMATICS I
11. Find the equation of the sphere which passes through the points (2, 0, 0),
(0, 2, 0) and (0, 0, 2) and which has its radius as small as possible.
12. Find the equations of the tangent planes to the sphere x2+y2+z2+2x−
4y+6z−7 = 0 which passes through the line 6x−3y−23 = 0 = 3z+2.
13. Find the equations of sphere which pass through the circle x+2y+3z =
8, x2 + y2 + z2 − 2x − 4y = 0 and touch the plane 4x + 3y = 25.
14. Find the center and radius of the circle x2+y2+z2−8x+4y+8z−45 = 0
and x − 2y + z − 3 = 0.
15. Show that the spheres x2 + y2 + z2 + 6y + 2z + 8 = 0 and x2 + y2 +
z2 + 6x + 8y + 4z + 20 = 0 cut orthogonally. Find their plane of
intersection. Also prove that this plane is perpendicular to the line
joining the center.
16. Find the equation of the sphere passing through the points (0, 3, 0),
(−2,−1,−4) and cutting orthogonally the two spheres x2 + y2 + z2 +
x − 3z − 2 = 0 and 2x2 + 2y2 + 2z2 + x + 3y + 4 = 0.
17. Find the equation of the cone whose vertex is (1, 2, 3) and guiding
curve is the circle x2 + y2 + z2 = 4, x + y + z = 1.
18. Prove that 9x2 + 9y2 − 4z2 + 12yz − 6zx + 54z − 81 = 0 represents a
cone. Find also its vertex.
19. Find the equation of the cylinder whose axis is x
1 = y
−2 = z
3 and whose
guiding curve is the ellipse x2 + 2y2 = 1, z = 3.
20. Find the equation of the right circular cylinder passing through A(3, 0, 0)
and having the axis x − 2 = z, y = 0.
21. Find , at (a, 0) on y2 = a3−x3
x .
22. Show that the curves y = a
2 (e
x
a + e
−x
a ) and y = a
2 (2 + x2
a2 ) have the
same curvature at their crossing with the Y-axis.
23. Show that at on x = 3a cos − a cos 3 , x = 3a sin − a sin 3 is
3a sin .
24. Show that the line joining any point on x = a( + sin ), y = a(1 −
cos ) to its center of the curvature is bisected by the line y = 2a.
QUESTION BANK 2 MATHEMATICS I
25. For the curve rn = an cos n , prove
= anr1−n
n + 1 .
26. Find the circle of curvature at (0, 0) on x + y = x2 + y2 + x3.
27. Obtain the equation of the evolute of the ellipse x2
a2 + y2
b2 = 1.
28. Show that the evolute of the tractrix x = a(cos t+log tan t
2 ), y = a sin t
is the catenary y = a cosh xa.
29. Given that x
2
3 + y
2
3 = c
2
3 is the envelope of x
a + y
b = 1. Find the
necessary relation between a and b.
30. Find the evolute of x2
a2 + y2
b2 = 1 considering it as the envelope of
normals.
31. Prove that if f(x, y) = p1
y e−(x−a)2
4y , then fxy = fyx.
32. If u = (1 − 2xy + y2)−1
2 prove that
@
@x

(1 − x2)@u
@x

+ @
@y

y2 @u
@y

= 0.
33. Verify Euler’s Theorem for the function
u = sin−1 x
y
+ tan−1 x
y
.
34. If u = log x4+y4
x+y , show that x@u
@x + y @u
@y = 3.
35. By changing the independent variables u and v to x and y by means
of the relations x = u cos − v sin , y = u sin + v cos , show that
@2z
@u2 + @2z
@v2 transforms into @2z
@x2 + @2z
@y2 .
36. If u = xyz, v = xy + yz + zx,w = x + y + z, show that @(u,v,w)
@(x,y,z) =
(x − y)(y − z)(z − x).
37. Expand tan−1( y
x ) in the neighborhood of (1, 1), using Taylor’s series.
38. Discuss the maxima and minima of x3y2(1 − x − y).
QUESTION BANK 3 MATHEMATICS I
39. Show that the rectangular solid of maximum volume that can be inscribed
in a given sphere is a cube.
40. Find the maximum and minimum distances of the point (3, 4, 12) from
the sphere x2 + y2 + z2 = 1.
41. Evaluate
R R
(x+y)2dxdy over the area bounded by the ellipse x2
a2+y2
b2 =
1.
42. Change the order of integration in
I =
Z 1
0
Z 2−x
x2
xydydx
and hence evaluate the same.
43. Evaluate
R 2
1
R 4−x2
0 (x + y)dydx by changing the order of integration.
44. Evaluate
R 1
0
R p
2−x2
x
p x
x2+y2
dydx by changing the order of integration.
45. Evaluate Z 1
0
Z 2−x
x
x
y
dxdy
by changing the order of integration.
46. Evaluate Z 1
0
Z 1−x
0
Z 1−x−y
0
xyzdzdydx.
47. Find the volume of the solid in the positive octant bounded by the
parabolic z = 36 − 4x2 − 9y2.
48. Change
Z pa
2
0
Z p
a2−y2
y
log(x2 − y2)dydx,
a > 0 into polar co-ordinates and hence evaluate it.
49. Evaluate Z a
0
Z p
a2−x2
p
ax−x2
dxdy p
a2 − x2 − y2
using polar co-ordinates.
50. Evaluate
R R
R xydxdy where R is the region in the first quadrant that
lies between the circles x2 + y2 = 4 and x2 + y2 = 25.
QUESTION BANK 4 MATHEMATICS I

THERMAL ENGINEERING2007 question paper


Reg. No. :
P 1330
B.E./B.Tech. DEGREE EXAMINATION. NO\IEMBEWDECEMBER 2007.
Fourth Semester
Mechanical Engineering
ME  237
-  THERMAL  ENGINEERING
Time : Three hours  Maximum  : 100 marks
(Use of Steam table/charts and refrigeration table/charts is permitted)
Answer ALL questions.
PART A
-  (10 x2  = 20 marks)
1.  What are the factors to be considered for selection of steam boilers?
2.  What is the function of superheater?
3.  Define two stage impulse turbine.
4.  What is meant by height of blades as applied to a reaction turbine?
5.  What is meant by injection lag?
6.  What are the requirements of a good carburetor?
7.  Define scavenging ratio.
8.  Define brake mean effective pressure.
9.  Define specific humidity.
10.  What is meant bv adiabatic saturation?
PARTB-(5x16=80marks)
11.  (a)  (i)  Explain  the  construction and working  of a Lancashire boiler with
the help of neat sketch.  (10)
(ii)  Compare water tube boiler with fire tube boiler.  (6)
www.VidyarthiPlus.in
www.VidyarthiPlus.in(b) (i) Differentiate
valve.
between  lever  safety  valve  and  dead  weight  safety
(8)
(ii)  Explain  the  working  of an  economiser rn  a
sketch.
boiler  plant  with  a neat
(8)
L2.
(a)  The  steam  enters  an  impulse  wheel  having  a  nozzle  angle  of  20"  at  a
velocity  of 450 m,/sec. The  exit  angle  of the  moving  blade  is  20o and  the
relative  velocity  of  the  steam  may  be  assumed  to  remain  constant  over
the  moving  blades.  If  the  blade  speed is  180 m./sec, determine
(i)  Blade
angle  at  inlet
(ii)  Work  done  per  kg  of  steam
(iii)  Power  of  the  wheel,
when  the turbine  is supplied  with  1.8 kg  of steam per  second.
(16)
Or
(b)  The  blade  angles  of  both  fixed  and  moving  blades  of  reaction  steam
turbine  are  35o at the  receiving  tips  and  20o at the  discharglng  tips'  At  a
certain  point  in  the  turbine,  the  drum  diameter  is  1.37  m  and  blade
height  ts  I27  mm.  The  pressure  of steam  supply  to  a ring  of fixed  blades
at  this  point  is  1.25 bar  and  the  drlmess  fraction  is  0.925. Find  the  work
d.one in  next  row  of  moving  blades  for  1  kg  of  steam  at  600  rpm,  the
steam  passing  through  the  blades without  shock. Assuming  an efficiency
of 8S7o for the  pair  of rings  of fixed  and moving  blades, find  the heat  drop
in  the  pair  and  state  the  properties  of steam  at  the  entrance  to  the  next
row offixed  blades.
18.
(a)  (i)  Explain  the magneto  ignition  system with  a neat  sketch-
(8)
(16)
influence  on
(8)
with  reference to  the
(r2)
good  fuel  for  a  petrol
(4)
(ii) Explain  the  significance of  flame  speed  and  its
combustion in S.I.engine.
(b)
Or
(i)  Compare  the  petrol  and  diesel  engines
following:
(1)  Porver to weight  ratio
(D  Accelerationresponse
(3)  Economy  in  road transPort
(4)  Maintenauce  and rePair.
(ii)  Enumerate  the  desirable  properties  of  a
engine.
P 1330
www.VidyarthiPlus.in
www.VidyarthiPlus.in14.  (a)  Explain briefly
(i)  Indicator card method
(ii)  Extrapolationmethod
(iii)  Retardationmethod
(iv)  Morse test.
Or
(b)  A four  stroke petrol engine has a piston displacement of 2210 cm3. The
compression ration  is  6.4. The  fuel  consumption is  0.13 kg/min'  The
caiorific value of fuel is 45000 KJfi<g. The brake power developed while
running  aL  2500 rev/min  is  50.25 KW.  Determine  the  brake  mean
effective pressure and  the  reiative  efficiency based on  brake  thermal
(16)
(16)
efficiency.
15.  (a)  A cinema hall of seating capacity 1500 persons has been provided with an
air conditioned plant with  the following data .
Outdoor conditions = 40"C DBT and 20'C WBT
Required conditions = 20"C DBT and 607o RH
Amount of air supplied = 0.3 m3/min/person.
If  the required condition is achieved first  by adiabatic humidifying  and
then  cooling, find  the  capacity of the  cooling coil  and  capacity of the
humidifier.
(16)
Or
(b)  (i)  Explain the winter  air  conditioning system with  the help of a neat
sketch.
(10)
(ii)  Explain the following terms :
(1)  Degree of saturation
(2)  Dew  point temperature
(3)  Humidity  ratio.
(6)
P 1330
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www.VidyarthiPlus.in

theory of computations important questions


Important Questions in Theory Of Computations CS2303 CS 2303 subject for NOV/DEC 2011 ANNA UNIVERSITY EXAMINATIONS FOR THIRD 3RD YEAR CSE Students

CS2303 – Theory Of Computations Important Questions For V SEMESTER CSE

UNIT I

1.      Consider the following ε–NFA. Compute the ε–closure of each state and find it’s equivalent DFA.                                                                                                  

ε
A
b
C
p
Ф
{p}
{q}
Ф
q
{p}
{q}
{r}
Ф
*r
{q}
{r}
ф
{p}
2.      Construct a NFA over the alphabet {0,1} that accepts all strings end in 01
3.      For the finite state machine M given in the following table, test whether the strings     101101,11111 are accepted by M.
4.      Consider the following ε–NFA. Compute the ε–closure of each state and find it’s equivalent DFA.


ε
a
b
c
    p
{q,r}
Ф
{q}
{r}
q
Ф
{p}
{r}
{p,q}
*r
Ф
ф
ф
ф
5.      Convert a NFA which accepts the string ends with 01 to a DFA.        


6.      Consider the following ε–NFA. Compute the ε–closure of each state and find it’s equivalent DFA.                                                              

ε
a
b
c
    p
{q}
{p}
Ф
Ф
q
{r}
ф
{q}
Ф
*r
Ф
ф
ф
{r}
7.      Convert the NFA string that ends with 01 to equivalent DFA


UNIT II

1.      Find The regular expression for the set of all strings denoted byR132 from the  DFA  given below. 
2.      Draw the table of distinguishabilities for this automaton & Construct the minimum – state equivalent DFA.
3.      Find the regular expression for the set of all strings denoted by R13from the deterministic finite automata  given below
4.      Construct the NFA –Σ For the given regular expression Using Thompson’s and Construct DFA For the  above  NFA –Σ and find the Minimized DFA?  (b/a)*bba

5.      Find whether the languages (ww, w is in (1+0)*} and {1k | k=n2, n ≥1} are regular or not. 




UNIT III
1.      Obtain the regular expression that denotes the language accepted by the following DFA
2.      Find the regular expression for the set of all strings denotes by R13 3    from the deterministic finite automata given below
3.  Find a derivation tree of a*b +a*b given that a*b+a*b is in L(G) where G is given by
                   S → S + S | S * S , S → a | b

4.  Suppose the PDA P= ({q,p},{0,1},{Z0,X}, δ,q, Z0,{p})  has the following transition function :                                                                       
                  1. δ(q,0, Z0)  ={(q, XZ0)}
                 2. δ(q,0, X) = {(q,XX)}
                 3. δ(q,1, X)  = {(q,X)}      
                 4. δ(q,ε, X)  = {(p,ε)}
                 5. δ(p,ε, X)   = {(p,ε)}     
                 6. δ(p,1, X) = {(p,XX)}
                 7. δ(p,1, Z0)  = {(p,ε)}  starting from the intial ID (q,w, Z0), show all the reachable ID’s when  
                         the input w is a) 01  b) 0011 c) 010.


UNIT IV

1.      Show that set of all strings over {a,b} consisting of equal number of a’s & b’s is accepted by a deterministic PDA.             
2.      Convert the grammar S → 0S1 | A, A→1A0 | S | ε  to a PDA that a accepts the same language by empty stack.
3.      The following grammar generates the language of regular expression 0*1(0+1)*                       S → A1B , A → 0A | ε,  B → 0B | 1B | ε. Give leftmost & rightmost derivation of   the following strings:     a) 00101     b) 1001   c)  00011
4. Design context free grammar for the following languages
a) The set {0n1n | n≥1}, that is the set of all strings of one or more 0’s followed by an equal number of 1’s.      


UNIT V

1.      Consider the Language Lwwr={wwR  | w is in (0+1)*}. Design the PDA P to accept the Lwwr.   Starting from the initial ID (q,w, Z0), show all the reachable ID’s when  the input w is a) 11111  b) 0011 c) 011.  
2.      Convert the PDA P= ({p,q},{0,1},{X,Z0},δ,q, Z0)  to a CFG , if is given by
                 1. δ(q,1, Z0)  ={(q, XZ0)}                    
                 2. δ(q,1, X) = {(q,XX)}
                 3. δ(q,0, X)  = {(p,X)}      
                 4. δ(q,ε,  X)  = {(q,ε)}
                 5. δ(p,1, X)   = {(p,ε)}     
                 6. δ(p,0, Z0)  = {(q, Z0)}           
  
3.     Prove the theorem, Let L be L(PF) for some PDA PF=(Q, ∑, Γ, δN, q, Z0,F), then there Is
                         a PDA PN such that L=L(PN)    

4  Convert the PDA P= ({q,p},{0,1},{Z0,X}, δ,q, Z0,{p}) to a Context free grammar.
                  1. δ(q,0, Z0)  ={(q, XZ0)}
                 2. δ(q,0, X) = {(q,XX)}
                 3. δ(q,1, X)  = {(q,X)}      
                 4. δ(q,ε, X)  = {(p,ε)}
                 5. δ(p,ε, X)   = {(p,ε)}     
                 6. δ(p,1, X) = {(p,XX)}
                    7. δ(p,1, Z0)  = {(p,ε)}