II B.Tech I Semester (R07) Regular Examinations, Nov- 2009 ELECTRICAL AND ELECTRONICS ENGINEERING

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: 80
Answer any FIVE Questions
All Questions carry equal marks

1. a) Define ohm’s 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 :
Exciting
current 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 phase
O.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 determine
unsaturated 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 by
synchronous impedance method under un- saturated condition [16]
5. Explain the essential requirements of indicating instruments? Explain each of them[16]
1 of 2
SET - 1
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)


















2 of 2

SET - 1
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: 80
Answer any FIVE Questions
All Questions carry equal marks
1. Two resistances of 10 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 torques’s 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]
1 of 1

If Amps 60 70 80 90 100 110
OC Volts 2560 3000 3360 3600 3800 3960
SC Amps 180
SET - 2
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: 80
Answer any FIVE Questions
All Questions carry equal marks
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]
1 of 2

OC voltage in volts 3100 4900 6400 7500 8300
Field current in amps 16 25 37.5 50 70
SET - 3


Code No: X0122

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 forward
bias 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]
2 of 2
SET - 3
Code No: X0122
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009

ELECTRICAL AND ELECTRONICS ENGINEERING
(Com. CE,ME, AME)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) Define kirchoff’s mesh law or voltage law.
b) Two batteries A and B are connected in parallel and a total load of 10 is connected across
their terminals. ‘A’ battery 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 Kirchoff’s laws find the current
flowing 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 400
rpm. 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)
1 of 2

SET - 4
Code No: X0122


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]















2 of 2


SET - 4
Code No: X0223/R07 Set No. 1
II B.Tech I Semester Regular Examinations, November 2009
PULSE AND DIGITAL CIRCUITS
( Common to Electrical & Electronic Engineering and Electronics &
Instrumentation Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) An ideal 1 μ -Sec pulse is fed to a low pass circuit. Calculate and plot the
output waveform under the following conditions: The upper 3-dB frequency
is
i. 10 MHz
ii. .1 MHz
iii. .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 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. 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
1 of 4
Code No: X0223/R07 Set No. 1
(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 the
input on the same time scale. Assume hfe =50, hre=2x10−4, hoe =1/35 k
ohms, hie=1k ohms. Junction voltages are neglected. The input is a 1 kHz
symmetrical squarewave. [8+8]
2 of 4
Code No: X0223/R07 Set No. 1
Figure 5
6. (a) What is relaxation oscillator? Name some negative resistance devices used as
relaxation 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 that
the 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 diodes
are ideal.
(b) Write the different capacitances which effect on the operation of the sampling
gates. [10+6]
3 of 4
Code No: X0223/R07 Set No. 1
Figure 7
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 logic
digital system. [4+4+4+4]
? ? ? ? ?
4 of 4
Code No: X0223/R07 Set No. 2
II B.Tech I Semester Regular Examinations, November 2009
PULSE AND DIGITAL CIRCUITS
( Common to Electrical & Electronic Engineering and Electronics &
Instrumentation Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
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 sin !t’.
(b) What is the ratio of the rise time of the three sections in cascade to the rise
time 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 in
saturation. Find the stable state currents and voltages for the circuit. Assume
for transistors VCE(sat) = 0.3V and VBE(sat) = 0.7V. [8+8]
1 of 2
Code No: X0223/R07 Set No. 2
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 different
types of synchronization? Give some examples.
(b) Explain the pulse synchronization of a sweep generator using UJT with the
help of neat circuit diagram. [8+8]
7. (a) Draw and explain the unidirectional diode sampling gate for more that one
input signal and also explain how to overcome the loading effect on control
signal?
(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 logic
digital system. [4+4+4+4]
? ? ? ? ?
2 of 2
Code No: X0223/R07 Set No. 3
II B.Tech I Semester Regular Examinations, November 2009
PULSE AND DIGITAL CIRCUITS
( Common to Electrical & Electronic Engineering and Electronics &
Instrumentation Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) A square wave of 5 V amplitude with an ON time of 1 msec and an OFF time
of 3 m sec is applied to a high pass RC circuit with R = 2K and C = 0.1 μ 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 linearly
from 0 to 150 V. Sketch the output voltage vo to the same time scale as the
input 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 and
waveform. [8+8]
5. (a) Define the terms solpe error, displacement error, and transmission error. How
are they related for an exponential sweep circuit? Derive the relation between
them.
1 of 2
Code No: X0223/R07 Set No. 3
(b) The specifications of UJT are given as = 0.6 Vv = 2V, RBB= 5 K ohms,
Iv = 1.5 mA, Ip = 8μA and VBB = 18 V. Calculate the component values of
the UJT Sweep circuit to generate an output sweep frequency of 10 kHz with
sweep amplitude of 12V. [8+8]
6. (a) What do you mean by a relaxation circuit? Give a few examples of relaxation
circuits.
(b) With the help of neat waveforms, explain sine wave frequency division with a
sweep circuit. [8+8]
7. (a) Draw and explain a sampling diode whose response is not sensitive to the
upper level of the control voltage.
(b) Draw and explain a unidirectional gate which delivers an output only at a
coincidence of a number of control voltages. [8+8]
8. (a) Why totem pole is used in DTL? Draw the circuit diagram and explain a DTL
gate with this.
(b) Verify the truth table of RTL NOR gate with the circuit diagram of two inputs.
[8+8]
? ? ? ? ?
2 of 2
Code No: X0223/R07 Set No. 4
II B.Tech I Semester Regular Examinations, November 2009
PULSE AND DIGITAL CIRCUITS
( Common to Electrical & Electronic Engineering and Electronics &
Instrumentation Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) A 10Hz square wave is fed to an amplifier. Calculate and plot the output wave
form 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 wave
input under different time constants. Explain same. [8+8]
2. (a) A symmetrical 10 kHz square wave whose peak -to-peak excursion are ±10V
with respect to ground is impressed upon the diode clamping circuit shown in
figure 2a. The Diodes has Rf = 100
, Rr = and V
= 0. Sketch the steady
state 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 neat
waveforms. 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 stable
state, the OFF transistor has VBE = -1v. The on transistor has base current
IB which is 50% in area of the IB(min) value. Vcc = 6v, IC(sat) = 2 mA. Delay
time is 3000 μsec. Choose R1 = R2. [8+8]
5. (a) What type of Voltage input is required to obtain a linear current sweep?
1 of 3
Code No: X0223/R07 Set No. 4
(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 μF, C1=0.25μF
and CB may be taken as arbitrarily large. The input gate has an amplitude
of 1V and a width of 50μs. The transistor parameters are hFE = hfe = 60,
hie=2kohms, 1/hoe = 10 K ohms, hre = 10−4. ICBO = 0, and the forward
biased 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 maximum
value
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 the
lost 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 DTL
gate with this.
(b) Verify the truth table of RTL NOR gate with the circuit diagram of two inputs.
[8+8]
2 of 3
Code No: X0223/R07 Set No. 4
? ? ? ? ?
3 of 3
Code No: X0422
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009

ENVIRONMENTAL STUDIES
(Com to ECE, CHEM, ECC, AE)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
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.


SET - 1
Code No: X0422
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009

ENVIRONMENTAL STUDIES
(Com to ECE,CHEM,ECC,AE)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a)Reasons for studying the state of environment
b) 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 you’ve visited a Forest ecosystem with mountains, streams and ponds,
write a detailed report on it w.r.t. Biodiversity, food chains, suggestions for improvement
etc 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?


SET - 2
Code No: X0422
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009

ENVIRONMENTAL STUDIES
(Com to ECE,CHEM, ECC,AE)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) Write importance of education on environmental issues
b) 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 Web
b) 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.

SET - 3

Code No: X0422
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009

ENVIRONMENTAL STUDIES
(Com to ECE,CHEM, ECC,AE)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. What are the different activities that can be taken up to increase public awareness of
environmental 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 Ecosystem
c) 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?


SET - 4
Code No: X0522
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCES
(Com to CSE,IT,CSS)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
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
x1+x2+x3 <15. (8m)
6 a) Solve the recurrence relation an-5an-1+6an-2 = 0 where a0=2 and a1=5, n!0. (8m)

b) Solve the recurrence relation an-7an-1+10an-2 = 0 where a0=10 and a1= 41. (8m)

7 (a) Draw the graph for the following incidence matrix, M: (8+8m)



(b) What is a planar graph? Which of the following graphs is/are planar?



1 of 2
SET - 1
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:




























2 of 2
SET - 1
Code No: X0522
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCES
(Com to CSE,IT,CSS)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
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 the
Connectives 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 where
x1!-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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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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II B.Tech I Semester (R07) Regular Examinations, Nov- 2009

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCES
(Com to CSE,IT,CSS)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
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) Let P(x) be the statement "x is happy," where the universe of discourse for x 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 French
books, 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. B
isomorphic? Justify your answer. (16m)



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

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCES
(Com to CSE,IT,CSS)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
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 <S1 , *1> and <S2 , *2> be two semi-groups , If f: S1->S2 is an Isomorphism , then
show that f-1 is 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 3n for 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 the
minimum 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 a
suitable 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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