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Code No: X0122

II B.Tech I Semester (R07) Regular Examinations, Nov- 2009

ELECTRICAL AND ELECTRONICS ENGINEERING

(Com. to CE,ME, AME)

Time: 3 hours Max Marks: 80Answer any FIVE Questions

All Questions carry equal marks

1. a) Define ohms law.

b) When the resistance of two wires is 25 when connected in series and 6 hen

connected in parallel. Calculate the resistance of each wire. [6+10]

2. With neat sketches, explain the construction and functions of the various parts of a d.c.

Generator [16]

3. a) What is a transformer? [6+10]

b) A 25 kVA transformer has 500 turns on the primary and 50 turns on the secondary

winding. The primary is connected to 3000V, 50 Hz supply. Find the full-load primary

and secondary currents, the secondary emf and maximum flux in the core. Neglect

leakage drops and no-load primary current.

4. A 3-phase, star-connected, 5 kVA, 400 V, 50 Hz, 4-pole alternator has the following test

data at rated speed :

Excitingcurrent in(Amps)

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 8.0

Per phaseO.C volts(V)

75 140 173 202 224 240 250 257 260 263 266 271

S.C line

current(A)

3.6 7.2 10.8

Armature resistance per phase is 2 ,

a) Draw the O.C and S.C characteristics on a squared graph paper and then determineunsaturated value of synchronous reactance per phase in Ohms

b) Determine the percentage voltage regulation at rated load at 0.8 p.f lag and lead bysynchronous impedance method under un- saturated condition [16]

5. Explain the essential requirements of indicating instruments? Explain each of them[16]

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Code No: X0122

6. Draw and explain the V-I characteristics of a P-N junction diode. (16)

7. Briefly explain the working of Cathode Ray Oscilloscope with a neat sketch? ( 16)

8. a) One NPN transistor is used in the self biasing arrangement the circuit component

values are VCC = 4.5volts, Rc=1.5k,Re=0.27k ,and R1=27k if =44.Find the

stability factor and also determine the quiescent point Q (Vce, Ic)? (8)

b) What is the transistor biasing? (8)

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1. Two resistances of10 and 40 respectively are connected in parallel. A third

resistance of 5 is connected in series with the combination and a D.C supply of 240 V

is applied to the ends of the completed circuit. Calculate the current in each resistance.

[16]

2. a) Derive the equation for the voltage generated in a d.c generator.b) Calculate the emf generated by a 6 pole lap wound armature with 65 slots and 12

conductors per slot, when driven at 1000 rpm. The flux/pole is 0.02 Wb. [8+8]

3. a) What is the basic principle of a transformer? [6+10]

b) A 40 kVA , 2200/200V transformers has iron loss of 450 and a full load copper loss of

800W. Determine the percentage efficiency of the transformer at 0.8 p.f at half full load .

4. The OC and SC tests data on a 3-phase, 1MVA, 3.6 kV, star connected alternator is

given below

The resistance measured between the terminals is 2. Find the % regulation at full load

0.707 p.f lag and 0.8 p.f lead by synchronous impedance method. [16]

5. What is the essential torquess of an indicating instrument? Justify their necessity (16)

6. a) Explain the working of P-N junction diode. (12)

b) Explain the application of P-N junction diode. (4)

7. a) Define the following terms [6]

(i) Accuracy, (ii) Precision, (iii) Sensitivity

b) Describe the operation of Storage Oscilloscope? [10]

8. a) What is the emitter bias circuit? [8] b) Derive the stability factor of the self bias circuit? [8]

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IfAmps 60 70 80 90 100 110

OC Volts 2560 3000 3360 3600 3800 3960

SC Amps 180

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Code No: X0122




Time: 3 hours Max Marks: 80

Answer any FIVE Questions


1. a) Distinguish between

i). potential difference

ii). electromotive force.

(b) Two resistance R1 and R2 are connected in parallel and if the current entering the

parallel combination is I. Calculate the values of currents I1, I2 flowing in the resistance

R1, R2 in terms I, R1 R2. [8+8]

2. A lap connected d.c. generator has 8 poles and 120 slots with 8 conductors in each slot.If the flux/pole is 0.035 Wb. (i) Find the emf generated when the speed is 600 rpm.

(ii) What should be the speed of rotation if the induced emf is to be 500 V. [16]

3. a) Define step-up and step-down transformer? [6+10]

b) a 20 kVA, single-phase transformer has 20 turns on the primary and 40 turns on the

secondary. The primary is connected to 1000V, 50Hz supply .Determine

i) The secondary voltage on open circuit,

ii) The current flowing through the two windings on full-load,

ii) The maximum value of flux.

4. The following test results are obtained on a 6600V alternator.

A field current of 20Amps is required to circulate full load current as short circuit of

armature. Calculate full load regulation at 0.8 p.f lag by synchronous impedance method.

(Assume the rating of alternator as 1MVA) [16]

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OC voltage in volts 3100 4900 6400 7500 8300

Field current in amps 16 25 37.5 50 70

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5. Discuss the necessity of damping in indicating instruments and explain eddy current

damping. (16)

6. The turns ratio of a transformer used in a half-wave rectifier is n1:n2=12:1. The primary is

connected to the power mains: 220V, 50Hz, Assuming the diode resistance in forwardbias to be zero, calculate the dc voltage across the load. What is the Peak Inverse Voltage

(PIV) of the diode? (16)

7. a) Explain the principle of operation of a Dual beam Oscilloscope? [8]

b) Explain the principle of operation of Sampling Oscilloscope? [8]

8. a)Explain about the need for biasing in electronic circuits, what are the factors affecting

the stability Factor? [8]b) Draw the collector to base bias circuit and derive the expression for the stability

factor? [8]

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(Com. CE,ME, AME)




1. a) Define kirchoffs mesh law or voltage law.

b) Two batteries A and B are connected in parallel and a total load of10 is connected across

their terminals. Abattery has an e.m.f of 12V and internal resistance of 2 and B battery

has an e.m.f of 8V and an internal resistance of1 . Using Kirchoffs laws find the currentflowing in each battery and also find potential difference across the external resistance. [6+10]

2. An 8 pole DC generator has per pole flux of 40mWb and winding is connected in lap

with 960 conductors. Calculate the generated EMF on open circuit when it runs at 400rpm. If the armature is wave wound at what speed must the machine be driven to

generate the same voltage. [16]

3. a) What are the classifications of transformer? [6]

B) A 6600/440V, single phase 600 kVA transformer has 1200 primary turns. Find

i)Transformation ratio, ii)secondary turns, iii) voltage/turn, iv) secondary current when it

supplies a load of 400 kW at 0.8 p.f lagging . [10]

4. a) Why do we prefer field winding of an alternator as a rotating element and armature as

a stationary element, give reasons. [8+8]

b)A 3-phase star connected alternator is rated at 1500kVA, 12kV the armature effective

resistance and synchronous reactance are 2ohms and 10ohms respectively. Calculate %

regulation for a load of 120kW at 0.8 p.f lag and 0.707 p.f lead.

5. a) Explain how controlling torque is developed in indicating instruments? (8+8)

b) The torque of an ammeter varies as the square of the current through it. If a current of 5A

produces a deflection of 900, What deflection will occur for a current of 3A when the instrument

is i) spring controlled , ii) gravity controlled.

6. The turns ratio of the transformer used in a half-wave rectifier n1:n2 = 12:1. The primary

is connected to 220V, 50Hz power mains. Assuming that the diode voltage to be zero,

find the dc voltage across the load. What is the PIV of each diode? If the same dc voltage

is certained by using a centre-taped rectifier, what is the PIV? (16)

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7. a) Define error and resolution? [ 6]

b) Describe the applications of CRO? [10]

8. a) Draw the fixed bias circuits and derive the expression for the stability factor? [8]

b)Draw the self bias circuit and obtained the expression for the stability factor? [8]

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Code No: X0223/R07 Set No. 1

II B.Tech I Semester Regular Examinations, November 2009PULSE AND DIGITAL CIRCUITS

( Common to Electrical & Electronic Engineering and Electronics &Instrumentation Engineering)



1. (a) An ideal 1 -Sec pulse is fed to a low pass circuit. Calculate and plot theoutput waveform under the following conditions: The upper 3-dB frequencyis

i. 10 MHz

ii. .1 MHziii. .0.1 MHz.

(b) Explain RLC ringing circuit. [10+6]

2. (a) Determine Vo for the network shown in figure 2a for the given waveform.Assume ideal Diodes.

Figure 2a

(b) Draw the basic circuit diagram of positive peak clamper circuit and explainits operation. [8+8]

3. (a) Explain the terms pertaining to transistor switching characteristics.

i. Rise time.

ii. Delay time.

iii. Turn-on time.iv. Storage time.

v. Fall time.

vi. Turn-off time.

(b) Give the expression for risetime and falltime in terms of transistor parametersand operating currents. [6+10]

4. Consider the emitter-coupled binary of the figure 4 with silicon transistors hav-ing hFE=20. The circuit parameters are VCC=12V, Rs = 4K, Rc1=3K, Rc2=1K,R1=2K, R2=8K and Re=5K. Calculate

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(a) V1

(b) V2. [16]

Figure 4

5. (a) With the help of a neat circuit diagram and waveforms explain the working

of a UJT relaxation oscillator.(b) For the bootstrap sweep generator shown in figure 5 find the slope error, sweep

amplitude, retrace time and recovery time. Plot to scale the output and theinput on the same time scale. Assume hfe =50, hre=2x10

4, hoe =1/35 kohms, hie=1k ohms. Junction voltages are neglected. The input is a 1 kHzsymmetrical squarewave. [8+8]

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Figure 5

6. (a) What is relaxation oscillator? Name some negative resistance devices used asrelaxation oscillators and give its applications.

(b) With the help of a circuit diagram and waveforms, explain the frequency

division by an astable multivibrator? [8+8]

7. (a) In the circuit of figure 7 assume that RL = RC = 100K , R2=50K and thatthe signal has a peak value of 20V. The total shunting capacitance is 20pF.Find A, Vcmin Vnmin , Ri and the 3dB frequency of the gate. Assume diodesare ideal.

(b) Write the different capacitances which effect on the operation of the samplinggates. [10+6]

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Figure 7

8. (a) What are the basic logic gates which perform almost all the operations inDigital communication systems.

(b) Give some applications of logic gates.

(c) Define a positive and negative logic systems.

(d) Draw a pulse train representing a 11010111 in a synchronous positive logicdigital system. [4+4+4+4]

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1. (a) Prove that an RC circuit behaves as a reasonably good integrator if RC > 15T,Where T is the period of an input Em sint.

(b) What is the ratio of the rise time of the three sections in cascade to the risetime of Single section of low pass RC circuit. [8+8]

2. (a) Determine Vo for the network shown in figure 2a for the given waveform.Assume ideal Diodes.

Figure 2a(b) Draw the basic circuit diagram of positive peak clamper circuit and explain

its operation. [8+8]

3. (a) Explain the terms pertaining to transistor switching characteristics.

i. Rise time.

ii. Delay time.

iii. Turn-on time.

iv. Storage time.

v. Fall time.

vi. Turn-off time.(b) Give the expression for risetime and falltime in terms of transistor parameters

and operating currents. [6+10]

4. (a) Explain different triggering methods of binary circuits.

(b) A collector coupled Fixed bias binary uses NPN transistors with hFE = 100.The circuit parameters are VCC = 12v, VBB = -3v, RC = 1k , R1 = 5k ,and R2 = 10 k . Verify that when one transistor is cut-off the other is insaturation. Find the stable state currents and voltages for the circuit. Assumefor transistors VCE(sat) = 0.3V and VBE(sat) = 0.7V. [8+8]

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5. (a) Compare the voltage and current time base generators with some examples.

(b) What are the reasons for non linearity of sweep in current time base genera-

tors? Explain how to rectify this? [8+8]

6. (a) Why synchronization is required in digital systems? What are the differenttypes of synchronization? Give some examples.

(b) Explain the pulse synchronization of a sweep generator using UJT with thehelp of neat circuit diagram. [8+8]

7. (a) Draw and explain the unidirectional diode sampling gate for more that oneinput signal and also explain how to overcome the loading effect on controlsignal?

(b) What are the advantages and disadvantages of unidirectional diode sampling

gate? [10+6]8. (a) What are the basic logic gates which perform almost all the operations in

Digital communication systems.

(b) Give some applications of logic gates.

(c) Define a positive and negative logic systems.

(d) Draw a pulse train representing a 11010111 in a synchronous positive logicdigital system. [4+4+4+4]

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1. (a) A square wave of 5 V amplitude with an ON time of 1 msec and an OFF timeof 3 m sec is applied to a high pass RC circuit with R = 2K and C = 0.1 f.Sketch the steady state output waveform showing all the details

(b) Explain the operation of RC high pass circuit when exponential input is ap-

plied. [8+8]

2. (a) The input voltage vi to the two level clipper shown in figure 2a varies linearlyfrom 0 to 150 V. Sketch the output voltage vo to the same time scale as theinput voltage. Assume Ideal diodes.

Figure 2a

(b) Explain positive peak voltage limiters above reference level. [12+4]

3. Write Short notes on:

(a) Diode switching times

(b) Switching characteristics of transistors

(c) FET as a switch. [4+8+4]

4. Write short notes on:

(a) Gate width of mono-stable multivibrator.

(b) Astable multivibrator as a voltage to frequency converter with circuit andwaveform. [8+8]

5. (a) Define the terms solpe error, displacement error, and transmission error. Howare they related for an exponential sweep circuit? Derive the relation betweenthem.

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(b) The specifications of UJT are given as = 0.6 Vv = 2V, RBB= 5 K ohms,Iv = 1.5 mA, Ip = 8A and VBB = 18 V. Calculate the component values ofthe UJT Sweep circuit to generate an output sweep frequency of 10 kHz withsweep amplitude of 12V. [8+8]

6. (a) What do you mean by a relaxation circuit? Give a few examples of relaxationcircuits.

(b) With the help of neat waveforms, explain sine wave frequency division with asweep circuit. [8+8]

7. (a) Draw and explain a sampling diode whose response is not sensitive to theupper level of the control voltage.

(b) Draw and explain a unidirectional gate which delivers an output only at acoincidence of a number of control voltages. [8+8]

8. (a) Why totem pole is used in DTL? Draw the circuit diagram and explain a DTLgate with this.

(b) Verify the truth table of RTL NOR gate with the circuit diagram of two inputs.[8+8]

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1. (a) A 10Hz square wave is fed to an amplifier. Calculate and plot the output waveform under the following conditions the lower 3dB frequency is

i. 0.3 Hz.

ii. 3.0 Hz,

iii. 30 Hz.

(b) Draw the output waveform of an RC High pass circuit with a square waveinput under different time constants. Explain same. [8+8]

2. (a) A symmetrical 10 kHz square wave whose peak -to-peak excursion are 10Vwith respect to ground is impressed upon the diode clamping circuit shown infigure 2a. The Diodes has Rf = 100 , Rr = and V = 0. Sketch the steadystate output waveform Indicating clearly the voltage levels.

Figure 2a

(b) Explain positive peak voltage limiters above and below reference level. [8+8]

3. Write Short notes on:

(a) Diode switching times

(b) Switching characteristics of transistors

(c) FET as a switch. [4+8+4]

4. (a) Explain the working of a Bistable multivibrator circuit with the help of neatwaveforms. What are its applications?

(b) Design a collector coupled one-shot multivibrator circuit using n-p-n transis-tors. Neglect ICBO. Assume VCE(sat) to be 0v.,hFE(min) = 20. In the stablestate, the OFF transistor has VBE = -1v. The on transistor has base currentIB which is 50% in area of the IB(min) value. Vcc = 6v, IC(sat) = 2 mA. Delaytime is 3000 sec. Choose R1 = R2. [8+8]

5. (a) What type of Voltage input is required to obtain a linear current sweep?

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(b) The transistor bootstrap circuit shown in Figure 5 has the following parame-ters VCC = 10 V, VEE = -10V, RB = 30 K ohms, C=0.002 F, C1=0.25Fand CB may be taken as arbitrarily large. The input gate has an amplitudeof 1V and a width of 50s. The transistor parameters are hFE = hfe = 60,hie=2kohms, 1/hoe = 10 K ohms, hre = 10

4. ICBO = 0, and the forwardbiased junction voltages are negligible. The diode is ideal.

i. Plot the gate voltage, collector current iC1, and the output voltage Vo.

ii. Evaluate the sweep speed and amplitude of the sweep at its maximumvalue

iii. Find time it takes to discharge C at the end of the sweep,

iv. Find peak voltage change across C1 and the time required to replace thelost charge

v. Find slope error. [6+10]

Figure 5

6. (a) With the help of a neat circuit diagram and waveforms, explain synchroniza-tion of a sweep generator with pulse signals.

(b) Explain the use of a monostable relaxation device as a frequency divider. [8+8]

7. (a) What is sampling gate? Explain how it differ from Logic gates?

(b) What is pedestal? How it effects the output of a sampling gates?

(c) What are the drawbacks of two diode sampling gate? [6+6+4]

8. (a) Why totem pole is used in DTL? Draw the circuit diagram and explain a DTLgate with this.

(b) Verify the truth table of RTL NOR gate with the circuit diagram of two inputs.[8+8]

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Code No: X0422


ENVIRONMENTAL STUDIES

(Com to ECE, CHEM, ECC, AE)



1. a) Explain need for students from all courses to be aware of environmental issues.

b) Write briefly about the scope of Environmental issues.

2. a) Define renewable and non renewable resources? Explain in detail with examples.

b) Discuss about limits of renewable resources?

3. a) Describe the structure and function of a marine ecosystem with respect to Biodiversity,

Food Chains etc.

b) Describe the structure and function of a Pond Ecosystem.

4. a) Explain the terms: Environment, Genetic banks, species. Biodiversity, Hotspots,

Poaching, Endemic species and Environmental ethics.

b) Describe various In-situ and Ex-situ measurers of Conversation of Biodiversity

5. What are the major air pollutants?

6. Explain the mechanism of formation of acid rain.

7. Describe in detail different family welfare programs.

8. Write about six most honest guides while studying any ecosystem with an example.

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Code No: X0422



(Com to ECE,CHEM,ECC,AE)



1. a)Reasons for studying the state of environmentb) Define Environmental studies

c) Discuss about interrelated nature of environmental problems

2. a). Write about classification of resources?

b). Distinguish between reserves and resources

3. Assuming that youve visited a Forest ecosystem with mountains, streams and ponds,

write a detailed report on it w.r.t. Biodiversity, food chains, suggestions for improvementetc to make it an Eco tourism project.

4. Explain the terms: Species and Biodiversity. What is the significance of Biodiversity?What are the threats to Biodiversity? What are the various In-situ and Ex-situ

conversation measurers of Biodiversity?

5. Discuss the method of control of air pollution from automobiles

6. Explain the reaction of leading to the ozone layer depletion

7. What are the common methods in birth control?

8. What are possible alternatives to avoid a global ecological collapse?

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Code No: X0422II B.Tech I Semester (R07) Regular Examinations, Nov- 2009


(Com to ECE,CHEM, ECC,AE)




1. a) Write importance of education on environmental issuesb) Describe the multi disciplinary nature of environmental studies.

2. a)Write the concept of maximum sustainable yield

b) What are the reasons for exceeding maximum sustained yields?

3. Write a detailed note on:

a) Food Chains and Food Webb) Ecological Pyramids

c) Estuarine ecosystem

d) Ecological Succession

4. Explain the terms Environment, Spices and Biodiversity. What is the significance of

Biodiversity? What are the threats to Biodiversity? What are the various measurers of

Conversation of Biodiversity?

5. Soil pollution refers any physical or chemical change in soil condition.

6. Explain the green house effect and their climatic changes.

7. Give an account of the plight of children in developing countries?

8. What you will observe when visiting an industrial area, explain as case study.

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Code No: X0422



(Com to ECE,CHEM, ECC,AE)




1. What are the different activities that can be taken up to increase public awareness ofenvironmental issues? Explain how they help in better environmental management.

2. Explain in detail about forest resources

3. Write a detailed note on:

a) Ecological Pyramids

b) Marine Ecosystemc) Ecological Succession

d) Ideal Ecosystem

4. a) Describe various In-situ and Ex-situ measurers of Conversation of Biodiversity

b) Describe the Biogeographical distribution of Flora and Fauna.

5. What are the main sources of morine and coastal pollution?

6. Discuss the pollution control boards and pollution control actor in India.

7. What are the ways in which women are discriminated against?

8. What are the projects for field work?

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Code No: X0522


MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCES

(Com to CSE,IT,CSS)



1 a)Show that (p q) (p v q) is a tautology. (8m)b) Obtain the principal disjunction normal form of (p q) v ( p r) v (q r) (8m)

2 Which of the following terms are valid, satisfiable or unsatisfiable? (8m)i) (p ( p))(q q)ii)(a b) ( a)( b) ab

b)Show that x P(x) x Q(x)and x y(P(x) Q(y))are equivalent (8m)3 Define Relation? Explain about different types of Relations in detail? (16m)4 Explain the Algebraic structures Ring and Commutative Ring? (16m)5 a) How many integers between 1 and 10, 00, 000 have the sum of the digits as 18? (8m)

b) Find the number of distinct triples (x1+x2+x3) of non-negative integers satisfying

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Code No: X0522

8 (a) What is the minimum number of colours needed to colour the following graph? (8+8m)

(b) Find whether the following graphs: G1 and G2 are isomorphic or not:

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Code No: X0522



(Com to CSE,IT,CSS)



1. a)Show that (p ( q r)) V (q r) V (p r) r (8m)

b)Write formulae which are equivalent to the formulae given below and which contain theConnectives and only. ((p V q) r ) ( p V r) (8m)

2. a)Make the following terms as easy as possible! (8m)

(ab ( c)( d))(c ( a)d)(( a) ( c)

b)Show that x P(x) x Q(x)and x(P(x) Q(x)) are not logically equivalent (8m)3. Let A= {1,2,3,4,5,6,7} Determine a Relation R on A by a R b 3 divides (a-b).

Show that R is an Equivalence Relation. Also determine the Partition generated by R? (16m)

4. a) Define Semi group , abelian Semi group and Monoid (8m)

b) On the set Q of all rational numbers , the operation * is defined by

a*b = a + b - ab. Show that under this operation Q forms a commutative

monoid. (8m)

5. a) How many integers between 1 and 1000 inclusive have the sum of the digits?

(i) Equal to 7, (ii) Less than 10 (8m)

b) How many integers solutions are there to the equations x1+x2+x3+x4+x5 = 20 wherex1-3, x2 0, x3 4, x4 2 and x5 2 (8m)

6. a) Solve the recurrence relation an-6an-1+9an-2 = 0 where a0=1 and a1= 6. (8m)

b) Solve the recurrence relation an-3an-1+4an-2 = 0 where a0= a1= 1. (8m)

7. a) Consider the following digraph: (10+6m)

(i) What is the shortest distance for a path from A to K?

(ii) What is the weight of the minimal spanning tree for the above graph?

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Code No: X0522

b) Show that K3, 3 is non-planar graph.

8. a) Is the following a Eulerian graph? Is it a Hamiltonian graph? Justify your

answer.(8+8m)

b) How many vertices and how many edges do the following graphs have?

(i) Complete graph, Kn (ii) Cycle graph, Cn (iii) Wheel graph, Wn

(iv) Bipartite graph, Km, n (v) Cube graph, Qn

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Code No: X0522II B.Tech I Semester (R07) Regular Examinations, Nov- 2009


(Com to CSE,IT,CSS)




1. a)Show that p ( q v r) (p q) v (p r) (8m)b) Prove that the connectives NAND and NOR are commutative but not associative (8m)

2. a)Show that ( P ( Q R ) ) ( P Q ) R ) (8m)b) LetP(x) be the statement "x is happy," where the universe of discourse forx is the set of

students. Express each of the following quantifications in English. (8m)

i) x P(x)ii) x P(x)iii) x P(x)iv) x P(x)

3. Define and explain Equivalence and Compatibility Relation with examples? (16m)

4. a) Define and explain about Homomorphism and Isomorphism (8m). b) Define and explain about Group and Abelian group? (8m)

5. a) Suppose there are 50 distinguishable books including 18 English books, 17 Frenchbooks, 15 Spanish books

(i) How many ways can 3 books be selected so there is 1 book from each of the 3

languages.

(ii) How many ways are there to select 3 books where exactly one language is missing?

(8m)

b) There are 30 females and 35 males in junior class while there are 25 females and 20

males in the senior class. In how many ways can a committee of 10 be chosen so that there

are exactly 5 females and 3 juniors on the committee? (8m)

6. (a) Solve the recurrence relation an-7an-1+12an-2 = 0, for n 2 (8m)(b) Solve the recurrence relation s(n), 10s(n-1) + 9s(n-2) = 0, where s(0) = 3, s(1) =1 (8m)

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7. a) Consider the following connected, undirected graph: (8+8m)

(i) Which of the following sets of edges is a cut?

{(A, B), (E, F), (B, D), (A, E), (A, D)} and {(B, D), (C, F), (A, B)}

(ii) What is the cardinality of a min-cut in this graph?

(iii) Prove that if a connected undirected graph, G with n vertices has a min-cut of

cardinality k, then G has at least (nk/2) edges.

b) What is an articulation point? Find the number of articulation points of the following

graph:

8. Define isomorphism of directed graphs. Are the two digraphs shown in fig. A and fig. Bisomorphic? Justify your answer. (16m)

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(Com to CSE,IT,CSS)



1. a)Show that (p q) (r q) (p V r) q (8m)b) Write an equivalent formula for p (q r) which contains neither bi-conditional nor

Conditional. (8m)

2. a) What rule of inference is used in each of the following arguments? (8m)i)John likes apple pies. Therefore, John likes apple pies or ice-cream.

ii) Mary likes chocolate and ice-cream. Therefore, Mary likes chocolate.

iii) If it snows, then the roads are closed; it snows. Therefore, the roads are closed.

iv) If it snows, then the roads are closed; the roads are not closed. Therefore, it does not

snow.

v) To go to Tahiti, one must fly or take a boat; there is no seat on any flight to Tahiti this

year. Therefore, one must take a boat to go to Tahiti this year.

b) Express the following arguments using the symbols indicated. What rules of inferences

are used in each of them ? (8m)

3. Let A={1,2,3,4} and R= {(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(4,4)}Is R an Equivalence Relation? If Yes, find the Partition of A induced by R? (16m)

4. Let and be two semi-groups , If f: S1->S2 is an Isomorphism , thenshow that f

-1is an isomorphism from S2 onto S1. (16m)

5. a) Enumerating r-permutations without repetitions i.e. p(n,r) = n(n-1) (n-2) .. (n-r+1) = n!(8m)

b) How many 6 digit numbers without repetition of digits are there such that the digits are

all non-zero and 1 and 2 do not appear consequently in either order? (8m)

6. a) Solve the recurrence relation an-3an-1 = 5 x 3nfor n 1, given that a0 = 2 (8m)b) Find a recurrence relation and the initial condition for the sequence 2, 10, 50, 250, hence find the general term of the sequence (8m)

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7. (a) How many minimum spanning trees does the following graph have? Draw them

(b) What is the maximum number of edges in a planar graph with n vertices? What is theminimum number of vertices and edges in a non-planar graph? (8+8m)

8. (a) What is the difference between symmetric and asymmetric digraphs? Explain with asuitable example.

(b) Apply the Welch-Powell algorithm to paint the following graph and find the

chromatic number of the graph. (8+8m)

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