2-1_R05_Nov_2011.pdf

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Code No: X0505/R05 Set No. 1

II B.Tech I Semester Supplementary Examinations, November 2011COMPUTER ORGANIZATION

( Common to Computer Science & Engineering, Information Technologyand Computer Science & Systems Engineering)

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

All Questions carry equal marks⋆ ⋆ ⋆ ⋆ ⋆

1. (a) What is meant by normalization in floating point representation?. Why doneed it? What is bias? What normalization is used in IEEE 754 standard?

[10]

(b) Explain about NaN and denormalised numbers in IEEE 754 standards. [6]

2. Design a circuit which can be used to transfer data from any register to any otherregister out of four 4-bit registers A,B,C,D which uses D flip-flops. [16]

3. (a) Hardwired control unit is faster than microprogammed control unit. Justifythis statement. [8]

(b) Explain the terms control word, control memory, control address register andcontrol buffer register. [8]

4. (a) How many bits are needed to store the result addition, subtraction, multipli-cation and division of two n-bit unsigned numbers. Prove. [8]

(b) What is overflow and underflow. What is the reason?. If the computer isconsidered as infinite system do we still have these problems?. [8]

5. (a) What is Cache Mapping? Why is it needed?

(b) Differentiate between direct and associative mapping techniques [8+8]

6. (a) What is daisy chaining? Explain with neat sketch.

(b) What is parallel priority interrupt method? Explain with neat sketch. [8+8]

7. Explain three segment instruction pipeline. Show the timing diagram and show thetiming diagram with data conflict. [16]

8. (a) Explain how Flynn classified the processors into different streams by givingan example for each stream.

(b) Explain tightly coupled and loosely coupled systems with suitable examples.[8+8]

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1. (a) Explain the terms compiler, linker, assembler, loader and describe how a Cprogram or any other high level language program is executed in a system.Indicate entire process with a figure.

(b) Distinguish between high level and low level languages?. What are the re-quirements for a good programming language? [16]

2. (a) What is the use of buffers. Explain about tri-state buffers. Explain abouthigh impedance state. [6]

(b) Explain commonly employed bit shift operators such as shift left, right, circularshift left/right and arithmetic shift left/right. Assume an 8-bit register, givean example for each [10]

3. (a) Hardwired control unit is faster than microprogammed control unit. Justifythis statement. [8]

(b) Explain the terms control word, control memory, control address register andcontrol buffer register. [8]

4. (a) How many bits are needed to store the result addition, subtraction, multipli-cation and division of two n-bit unsigned numbers. Prove. [8]

(b) What is overflow and underflow. What is the reason?. If the computer isconsidered as infinite system do we still have these problems?. [8]

5. Explain two-way set associative mapping and four-way set associative mappingtechniques with an example for each. [16]

6. (a) Explain bit oriented and character oriented protocols in serial communication

(b) What are the different issues behind serial communication? Explain. [8+8]

7. Explain three segment instruction pipeline. Show the timing diagram and show thetiming diagram with data conflict. [16]

8. (a) What are the different physical forms available to establish an inter-connectionnetwork? Give the summary of those. [6]

(b) Explain time-shared common bus Organization [5]

(c) Explain system bus structure for multiprocessors [5]

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1. (a) Explain about different buses in a practical computer system and their impli-cations on accuracy, precision and addressability. [10]

(b) What is Amdhal?s Law? [6]

2. . Design a circuit to implement the following RTL instructions. Mention aboutcontrol logic. Assume A,B are 4-bit registers using JK flip-flops. [16]A ← A + B

B ← A + B

3. (a) Why do we need subroutine register in a control unit?. Explain. [8]

(b) Why do we need some bits of current microinstruction to generate address ofthe next microinstruction. Support with a live example. [8]

4. (a) Explain single precision and double precision calculations. In general howmany bytes are uses for both and what is the precision we get. Give someexamples where double precision calculations are needed. [8]

(b) Explain booths algorithm with its theoretical basis. [8]

5. (a) Explain how the Bit Cells are organized in a Memory Chip. [8]

(b) Explain the organization of a 1K x 1 Memory with a neat sketch‘ [8]

6. Explain the following:

(a) Isolated Vs Memory mapped I/O

(b) I/O Bus Vs Memory Bus

(c) I/O Interface

(d) Peripheral Devices [4+4+4+4]

7. Explain the following with related to the Instruction Pipeline

(a) Pipeline conflicts

(b) Data dependency

(c) Hardware interlocks

(d) Operand forwarding

(e) Delayed load

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(f) Pre-fetch target instruction

(g) Branch target buffer

(h) Delayed branch [8×2=16]

8. Write short notes on the following

(a) Time-shared common bus organization [6]

(b) Multiport memory organization [5]

(c) System bus structure for multiprocessors [5]

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1. (a) Explain about sign magnitude and 2’s complement approaches for representingthe fixed point numbers. Why 2’s complement is preferable.

(b) Give means to identify whether or not an overflow has occurred in 2s comple-ment addition or subtraction operations. Take one example for each possiblesituation and explain. Assume 4 bit registers.

(c) Distinguish between tightly coupled microprocessors and tightly coupled Mi-croprocessors. [16]

2. (a) Explain about stack organization used in processors. What do you understandby register stack and memory stack? [10]

(b) Explain how X=(A+B)/(A-B) is evaluated in a stack based computer. [6]

3. (a) Explain the functioning of a control unit explaining the terms control word,control memory, control address register and control buffer register. [8]

(b) Support the statement ?Instruction Set Architecture has impact on the pro-cessors microarchitecture?. [8]

4. (a) Draw a circuit for 9?s complement of a number. [8]

(b) Explain sign magnitude and 2’s complement representation of numbers. Ex-plain why 2’s complement method is in wide use. [8]

5. Compare and contrast Asynchronous DRAM and Synchronous DRAM. [16]

6. (a) Explain bit oriented and character oriented protocols in serial communication

(b) What are the different issues behind serial communication? Explain. [8+8]

7. Explain the following with related to the Instruction Pipeline

(a) Pipeline conflicts

(b) Data dependency

(c) Hardware interlocks

(d) Operand forwarding

(e) Delayed load

(f) Pre-fetch target instruction

(g) Branch target buffer

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(h) Delayed branch [8×2=16]

8. (a) What is the need of interprocessor synchronization? Explain.

(b) Explain hardwarelock mechanism. [8+8]

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Code No: W0201/R05 Set No. 1

II B.Tech I Semester Supplementary Examinations, November 2011FLUID MECHANICS AND HYDRAULIC MACHINERY

(Electrical & Electronic Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

? ? ? ? ?

1. (a) Why does the viscosity of a gas increases with the increasing temperaturewhile that of liquid decreases with increasing temperature.

(b) Glycerin has a density of 1260 Kg/m3 and kinematic viscosity of 0.00183m2/sec. What shear stress is required to deform this fluid at a strain rate of104sec−1?

(c) A thin plate is placed between two flat surfaces ‘h’ cm a part such that the vis-cosity of liquids on the top and bottom of the plate are µ1 and µ2 respectively.Determine the position of the thin plate such that the viscous resistance touniform motion of the thin plate is minimum. Assume ?h? to be very small.- [4+4+8]

2. (a) What are the body forces considered in fluid flow problems?

(b) A 15-cm diameter pipe is reduced to 7.5 cm diameter through a gradual con-traction. The difference between the piezometric heads at the main and con-tracted section is 4 cm of mercury. By neglecting losses, calculate the dischargeof water. [8+8]

3. (a) Describe the principle and working of orifice meter with the help of a neatsketch.

(b) In a calibration test of an orifice meter of with orifice diameter 4cm is insertedin a pipe of 10cm diameter the mercury differential U-guage connected to themeter gives a reading of 38cm when 7.5 lit/sec of water flows through themeter. Compute the coefficient of discharge. [8+8]

4. (a) Derive an expression for the force exerted by a jet striking the curved plate atone end tangentially when the plate is symetrical.

(b) A jet of water 120 mm in diameter and moving with a velocity of 25m/secstrikes normally on a flat plate. Determine the power developed and theefficiency of the system when

i. the plate is stationary

ii. the plate is moving with a velocity of 8m/sec in the direction of the jet.And

iii. the plate is moving with a velocity of 8m/sec towards the jet. [7+9]

5. (a) Compare elaborately the different types of hydroelectric power stations spec-ifying the merits and demerits of one type over the others. Explain withsketches where necessary

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(b) A turbine runs at speed of 150 rpm. Its hydraulic, mechanical and volumetricefficiencies are 91%, 88% and 85% respectively. The head and discharge avail-able at the plant are 40m and 25 m3/sec respectively. The turbine has to runat 120rpm. Find the power developed and what is the type of turbine basedon specific speed. [8+8]

6. (a) How is flow controlled and regulated in Reaction turbines and Impulse turbines? Explain with a neat sketch

(b) State different efficiencies of a reaction turbine. What are the uses of providinga draft tube in a reaction turbine? Explain with a diagram [8+8]

7. (a) How can we compare the performance of a turbine under different workingconditions

(b) A Pelton wheel turbine works under different working conditions in a hy-dropower installation. The head changes from 100 m to150 m . What changescan be expected in speed, discharge and power if the efficiency is to remainsame under homologous conditions. [6+10]

8. (a) Draw a neat sketch of an indicator diagram for a single acting reciprocatingpump and explain its features.

(b) A reciprocating pump has a 20 cm diameter cylinder and a stroke of 120 cm.The pump delivers 5000 litres / minute of water at a static head of 80m.Friction losses in suction and delivery pipe are 2m and 18m respectively. Theslip of pump is 2% and efficiency is 90%. Determine the speed of the pumpand power required neglecting velocity head in delivery pipe [8+8]

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1. (a) Enunciate Newton’s law of Viscosity. Explain the importance of viscosity influid motion. What is the effect of temperature on viscosity of water and thatof air?

(b) A glass tube 20 mm in diameter contains a mercury column with water abovethe mercury. The surface tension of mercury in contact witht water is 0.36N/m. Datermine the capillary depression of the mercury. Take θ= 1300.[8+8]

2. (a) Distinguish between:

i. Steady and Un-steady flow.

ii. Uniform and Non-uniform flow.

iii. Compressible and incompressible flow.

(b) A 400 m long pipe has a slope of 1 in 100 and tapers from 1.2 m dia at highend to 0.6 m dia at the low end. The discharge is 100 lit/sec. If the pressureat high end is 100 kN/m2, find the pressure at the low end. Neglect friction.

[8+8]

3. (a) Describe major and minor losses in pipe flow in detail.

(b) Discuss how friction factor various with Reynolds Number.

(c) Two pipes one of 10cm diameter, 200m long and another 15cm diameter, 400mlong are connected in parallel. The friction factors are 0.0075 for the smallerpipe and 0.006 for the large pipe. The total discharge through the system is 50lit/sec. Find the discharge and head loss in each pipe. Neglect minor losses.Calculate the equivalent length of a 20cm diameter having f=0.005. [4+3+9]

4. (a) Derive the expressions for force and work done per second by the jet when itstrikes a curved plate moving in the direction of the jet.

(b) A jet of water 20cm in diameter and moving with a velocity of 20m/sec im-pinges normally on a series of flat vanes mounted on the periphery of a wheel.If the velocity of the vanes is 8m/sec, determine

i. the force exerted by the jet on the wheel

ii. work done by the jet on the wheel per second and

iii. hydraulic efficiency. [7+9]

5. (a) What are the elements of hydro electric power plants? Describe about waterways and penstocks with neat sketches if necessary.

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(b) The catchment area at a proposed site for a hydropower plant is 200 Km2 andpossible head of water is 140 m. The average annual rainfall is 145 cm andthe losses are 16%. How much power can be developed? [8+8]

6. (a) Define a turbine and bring out the differences between reaction turbine andimpulse turbine in a tabular form.

(b) The details of a Pelton wheel turbine installation are given below. Find thepower developed and hydraulic efficiency.Gross head = 510 mLoss of head in penstock = 30%Discharge through nozzle = 2.2 m3 / secAngle of deflection of jet = 1650

Coefficient of velocity Cv = 1Speed ratio Ku= 0.45 [8+8]

7. (a) Why is governing of turbines required ? What are the main components ofgoverning mechanism for a Pelton wheel turbine ? Draw a neat sketch andexplain.

(b) A hydraulic turbine generates 7500 Kw under a net head of 150m at a speedof 300 rpm. Hydraulic efficiency and mechanical efficiency are 92 % and 85%. Determine the discharge, specific speed of the turbine and type of turbine.

[8+8]

8. (a) What are the characteristic curves of centrifugal pumps ? What are theiruses.. Explain with neat sketches.

(b) A centrifugal pump has an impeller of outer diameter 30cm. The vane tipsare radial at the outlet. For a rotation speed of 1450 rpm calculate the nethead developed. The manometric efficiency is 0.62. [8+8]

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1. (a) The pressure at a point in a fluid is 13.6 cm of mercury vacuum. Express itin N/m2 of absolute pressure, gauge pressure and also in metres of water.

(b) A 6 m deep tank is square in plan of size 2 m x 2 m. It contains water up toa depth of 4 m and oil of relative density 0.88 for the remaining height of 2m. Determine the pressure on the bottom of the tank. [8+8]

2. (a) Write three important basic equations of fluid flow. Explain them.

(b) What are the different types of fluid flow? Explain. [8+8]

3. (a) Explain how the following flow problems are analyzed.

i. Series pipe connection

ii. Parallel pipe connection

iii. Equivalent pipe connection.

(b) Water flows through a 10cm diameter, 30m long pipe at a rate of 1400 rpm.What percent of head would be gained by replacing the central one thirdlength of pipe by another pipe of 20cm diameter. Assume that the changesin section are abreept and f = 0.008 for all pipes. Neglect entrance and exitlosses but consider major loss and losses due to sudden contraction and suddenexpansion. [9+7]

4. (a) Derive an expression for force exerted by a jet on stationary inclined flat plate.

(b) A nozzle of 50mm diameter delivers a stream of water at 20m/sec perpendic-ular to a plate that moves away from the Jet at 5m/sec.find

i. the force on the plate

ii. work done and

iii. the efficiency of jet. [7+9]

5. (a) What are the types of hydroelectric power plants? Describe elaborately aboutpumped storage plants.

(b) The following details pertain to a hydropower plant. What is power developedin Kw.Available head = 130 m, Catchment area = 220Km2, Annual averagerainfall = 150 cm, Percolation and evaporation losses = 18%, Turbine efficiency= 86%, Generator efficiency = 91% [8+8]

6. (a) Why is the end of a draft tube immersed below the tail water level. Explainwith a neat sketch. Define draft tube efficiency and derive its equation

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(b) A Kaplan turbine has the following details about its draft tube. Find thepressure at inlet of the draft tube.Inlet diameter of draft tube = 2mOut let diameter of draft tube = 3mVelocity of water at outlet = 4.2 m /secAtmosphere pressure = 10.1 m of waterHeight of draft tube above tail race = 3.5mLoss of head in draft tube = 0.2 times the velocity head at outlet. [8+8]

7. (a) How is geometric similarity obtained between model and prototype ? Explainwith sketches and give examples.

(b) A Francis turbine works under the following conditions. Estimate its perfor-mance when the head drops down to 45 m.The head = 60m, Speed = 1200 rpm, Discharge = 12 m3 / sec, Efficiency =88 % [8+8]

8. (a) Draw a neat sketch of an indicator diagram for a single acting reciprocatingpump and explain its features.

(b) A reciprocating pump has a 20 cm diameter cylinder and a stroke of 120 cm.The pump delivers 5000 litres / minute of water at a static head of 80m.Friction losses in suction and delivery pipe are 2m and 18m respectively. Theslip of pump is 2% and efficiency is 90%. Determine the speed of the pumpand power required neglecting velocity head in delivery pipe [8+8]

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1. (a) State the Newton?s law of viscosity and give examples of its applications?

(b) U gives the Velocity distribution near the solid wall at a section in laminarflow = 5 Sin(5πY)forY ≤ 0 . Compute the shear stress at a section (i) Y=0,(ii)Y=0.05m and (iii) Y=0.1m.The dynamic viscosity of fluid is 5 poise.[8+8]

2. (a) Distinguish between rotational and irrotational flow. [4+12]

(b) A pipe line, 600 mm diameter carrying oil of specific gravity 0.85 at the flowrate of 1800 lit/s has a 900 bend in the horizontal plane. The pressure at theentrance to the bend is 1.471 bars and loss of head in the bend is 2 m of oil.Find the magnitude and direction of the force exerted by the oil on the bendand show the direction of the force on a sketch of the bend.

3. (a) Describe different laws of fluid friction.

(b) Sketch the flow pattern and show how the hydraulic gradiant and total energyline vary as the flow takes place through the pipe contraction.

(c) Water flows through a 25cm diameter pipe which contracts suddenly to 10cmdiameter. The rate of flow is 75lit/sec. If CC is 0.62 determine the head loss.The pressure of water before the contraction is 80Kpa. What is the pressureafter contraction. [4+4+8]

4. (a) Derive the expressions for force and work done per second by the jet when itstrikes a flat vertical plate moving in the direction of the jet and away fromthe jet.

(b) A jet of water of 75mm diameter strikes a curved vane at its center with avelocity of 20m/sec. The curved vane is moving with a velocity of 8m/sec inthe direction of jet. Find the force exerted on the plate in the direction of thejet power and efficiency of the jet. Assume the plate to be smooth. [8+8]

5. (a) What are the types of hydroelectric power stations? Write about each of them.

(b) At the site where hydroelectric plant is proposed the following details areavailable. Calculate the power that can be developed. Available head = 28 mCatchment area = 420 Km2

Yearly rainfall = 140 cmRainfall utilization rate = 68%Penstock efficiency = 94%Turbine efficiency = 80%Generator efficiency = 84% [8+8]

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6. (a) What is the classification of turbines ? How do you differentiate among lowhead, medium head and high head turbines ?

(b) A Pelton wheel is working under a head of 45m and the discharge is 0.8m3/sec.The mean bucket speed is 14m/sec. Find the power produced if the jet isdeflected by the blades through an angle of 1650. The coefficient of velocity is0.985 [10+6]

7. (a) Show the governing mechanism of a reaction turbine with a schematic diagramand explain how it works

(b) In a hydroelectric station water is available at the rate of 175 m3/sec under ahead of 18m. The turbines run at a speed of 150 rpm with overall efficiency of82%. Find the number of turbines required if they have the maximum specificspeed of 460. [8+8]

8. (a) If the rate and the height to which a liquid is to be delivered are known , howdo you find the number of pumps to be connected either in series or parallel ?

(b) What are the uses of constant efficiency curves ? Sketch typical curves anddiscuss. What is NPSH. [8+8]

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II B.Tech I Semester Supplementary Examinations, November 2011MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE



All Questions carry equal marks? ? ? ? ?

1. (a) Construed a truth table for each of there (easy) compound statements

i. (p → q) Λ (7p → q)

ii. p → (7qV r)

(b) Write the negation of the following statements.

i. Jan will take a job in industry or go to graduate school.

ii. James will bicycle or run tomorrow.

iii. If the processor is fast then the printer is slow.

(c) What is the minimal set of connectives required for a well formed formula.[8+6+2]

2. (a) Let P(x) denote the statement. “x is a professional athlete” and let Q(x)denotethe statement” “x plays soccer”. The domain is the let of all people. Writeeach of the following proposition in English.

i. ∀x (P (x) → Q (x))

ii. ∃x (P (x) ΛQ (x))

iii. ∀x (P (x)V Q (x))

(b) Write the negation of each of the above propositions, both in symbols and inwords. [6+10]

3. (a) Consider f; Z+ → Z+ define by f (a)= a2. Check if f is one-to-one and / orinto using suitable explanation.

(b) What is a partial order relation? Let S = x,y,z and consider the power setP(S) with relation R given by set inclusion. ISR a partial order.

(c) Define a lattice. Explain its properties. [4+8+4]

4. (a) H is a non-empty complex of a group G. Prove that the necessary and sufficientcondition for H to be a subgroup of G is a, b ∈ H ⇒ ab - 1 ∈ H, where b - 1 isthe inverse of b in G

(b) Prove that the mapping f: Z → Z such that f(x) = -x for x ∈ Z where Z is anadditive group of integers is an automorphism. [If f: G → G is an isomorphismfrom a group G to itself then f is called on automorphism of G.] [10+6]

5. (a) A committee is to be chosen from a set of 5 women and 9 men. Howmany waysare there to from the committee, if the committee has 6 people and atleast 3are women.

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(b) Howmany ways can a person invite 3 of his 6 friends to lunch every day for 20days. [16]

6. (a) Solve an - 5an - 1 + 6an - 2 = 2n + n

(b) Solve an - 4an - 1 + 4an - 2 = (n + 1)2 given a0 = 0, a1 = 1 . [8+8]

7. (a) Derive the directed spanning tree from the graph shown Figure 7a

Figure 7a

(b) Explain the steps involved in deriving a spanning tree from the given undi-rected graph using breadth first search algorithm. [8+8]

8. (a) Prove that in any non directed graph there is an even numbers of vertices ofadd degree.

(b) Distinguish between cycle and circuit. Give suitable examples for each.

(c) What are the steps followed in discovering the isomorphism? [6+4+6]

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1. (a) Let p,q and r be the propositions.P: you have the fleeq: you miss the final examination.r: you pass the course.Write the following proposition into statement form.

i. P → q

ii. 7p→ r

iii. q → 7r

iv. pVqVr

v. (p→ 7r)V (q →∼ r)

vi. (pΛq)V (7qΛr)

(b) Define converse, contrapositive and inverse of an implication. [12+4]


i. ∀x (P (x)→ Q (x))

ii. ∃x (P (x) ΛQ (x))






4. Let G be a multiplicative group and f : G→G such that for a ∈ G,f(a) = a - 1,Prove that f is one-one onto. Also prove that f is homomorphism iff G is commu-tative. [16]

5. (a) A palindrome is a word that reads the same forward or backward. How many9-letter palindromes are possible using English alphabets?

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(b) There are five different roads form city A to city B, three different roads formcity B to city C, and three different roads that go directly form A to C.

i. How many different ways are there form A to C altogether?

ii. How many different trips are there form A to C and back to A that visitB at least once. [16]

6. (a) Imagine n lines in a plane such that no two lines are parallel, and no three areconcurrent. Let fn denote the number of distinct regions into which the planeis divided by them. Define fn recursively.

(b) Solve the recurrence relations:

i. ar - 4ar - 1 + 4ar - 2 = 0

ii. ar - 5ar - 1 + 6ar - 2 = 0. [10+6]

7. (a) Explain about the adjacency matrix representation of graphs. Illustrate withan example.

(b) What are the advantages of adjacency matrix representation.

(c) Explain the algorithm for breadth first search traversal of a graph. [5+3+8]

8. (a) Prove that in any non directed graph there is an even numbers of vertices ofadd degree.

(b) Distinguish between cycle and circuit. Give suitable examples for each.

(c) What are the steps followed in discovering the isomorphism? [6+4+6]

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i. P → q

ii. 7p→ r

iii. q → 7r

iv. pVqVr

v. (p→ 7r)V (q →∼ r)

vi. (pΛq)V (7qΛr)



i. ∀x (P (x)→ Q (x))

ii. ∃x (P (x) ΛQ (x))






4. Show that the set G = x/x = 2a 3b and a, b ∈ Z is a group under multiplica-tion. [16]

5. (a) Find the total number of positive integers that can be formed from the digits1, 2, 3, 4 and 5 if no digit is repeated in any one integer

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(b) In Pascal language, an identifier is a sequence of from 1 to up 8 characterswith the restriction that first character must be a letter of English alphabetand the remaining characters may be either a letter or a digit. [16]

6. (a) Solve an - 8an - 1 + 16 an - 2 = 0 given a2 = 6 and a3 = 80.

(b) Solve an + 5an - 1 + 6 an - 2 = 3n2 - 2n + 1. [8+8]

7. (a) Explain about the adjacency matrix representation of graphs. Illustrate withan example.

(b) What are the advantages of adjacency matrix representation.

(c) Explain the algorithm for breadth first search traversal of a graph. [5+3+8]

8. (a) How to determine whether a graph contains Hamiltonian cycle or not usingGrin berg theorem.

(b) Prove or disprove that there is an Hamiltonian cycle in the following graph.Figure 8b [16]

Figure 8b

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i. P → q

ii. 7p→ r

iii. q → 7r

iv. pVqVr

v. (p→ 7r)V (q →∼ r)

vi. (pΛq)V (7qΛr)


2. Prove using rules of inference or disprove.

(a) Duke is a Labrador retrieverAll Labrador retriever like to swinTherefore Duke likes to swin.

(b) All ever numbers that are also greater than2 are not prime2 is an even number2 is primeTherefore some even numbers are prime.UNIVERSE = numbers.

(c) If it is hot today or raining today then it is no fun to snow ski todayIt is no fun to snow ski todayTherefore it is hot todayUNIVERSE = DAYS. [5+6+5]

3. (a) Define partial order and total order of relations.

(b) If R is a relation defined on the set Z by a R b if a-b is a non negative eveninteger. Determine if R define a partial order and total order. [4+12]

4. (a) Show that the operation o given by aob = ab is a binary operation on the setof natural numbers N. Is this operation associative and commutative in N?

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(b) If G is the set of all positive rational numbers, then G is an abelian groupunder the composition defined by o such that aob = (ab)/3 for a, b ∈ G withusual addition as the operation. Find

i. the identity of (G,o) and

ii. inverse of each element of G

(c) Let G = -1, 0, 1. Verify whether G forms a group under

i. usual addition and

ii. usual multiplication. [6+6+4]

5. (a) Howmany out comes are obtained from rolling in distinushable dice.

(b) Find the number of distmct triples (x1,x2,x3)of non-negative integers satisfy-ing x1 + x2 + x3 < 15.

(c) Howmany integers between 1 and 1,000 have a sum of digits of integer numbersequal to 10. [16]

6. (a) Find recurrence relation for number of subsets of an n- element set.

(b) Solve the recurrence relation ar - 5ar - 1 + 6ar - 2 = 2r + r , r ≥ 2 with theboundary conditions a0 = 1 and a1 = 1, using generating function.

[4+12]

7. (a) Explain the steps involved in deriving a spanning tree from the given graphusing depth first search algorithm.

(b) Derive the spanning tree from the following graph using depth first searchalgorithm Figure 7. [8+8]

Figure 7

8. (a) Define the following graphs with one suitable examples for each graph.

i. Complement graph

ii. Sub graph

iii. Induced sub graph

iv. Spanning sub graph.

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(b) Determine whether the following two graphs are isomorphic or not. If isomor-phic, give the one to one mapping. Figure 8b, 8b [8+8]

Figure 8b

Figure 8b

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II B.Tech I Semester Supplementary Examinations, November 2011MATHEMATICS-III

( Common to Electrical & Electronic Engineering, Electronics &Communication Engineering, Electronics & Instrumentation Engineering,

Electronics & Control Engineering, Electronics & Telematics, Electronics &Computer Engineering and Instrumentation & Control Engineering)



1. (a) Evaluateπ/2∫0

sin2 θ cos4 θ dθ = π32

using β − Γ functions.

(b) Prove that∞∫0

√x e−x

2dx = 2

∞∫0

x2e−x4dx using β − Γ functions and evaluate.

(c) Show that∞∫0

xm−1

(x+a)m+ndx = a−nβ(m,n). [5+6+5]

2. (a) Show that Jn−1 (x) + Jn+1(x) = 2nxJn(x).

(b) Prove that J−1/2(x) =√

2πx

cosx.

(c) Show that (n+1) Pn+1 (x) - (2n+1) x Pn(x) + n Pn−1 (x) = 0. [5+5+6]

3. (a) Define analyticity of a complex function at a point P and in a domain D.Prove that the real and imaginary parts of an analytic function satisfy Cauchy? Riemann Equations.

(b) Show that the function defined by f(z) = x3(1+i)−y3(1−i)x2+y2

at z 6= 0 and f(0) = 0

is continuous and satisfies C-R equations at the origin but f ′(0) does not exist.[8+8]

4. (a) Evaluate∫C

(ez sin 2z−1) dzz2(z+2)2

where C is | z | = 1/2 using Cauchy’s integral formula.

(b) Evaluate∫C

(e−2z)z2 dz(z−1)3(z+2)

where C is | z + 2 | = 1 using Cauchy’s integral formula.

[8+8]

5. (a) Find the Laurent series expansion of the function z2−1z2+5z+6

about z = 0 in theregion 2 < |z| < 3.

(b) Evaluate f(z) = 2(2z+1)3

about (i) z = 0 (ii) z = 2. [8+8]

6. (a) Find the poles of f(z) and the residues at the poles which lie on imaginary axis

if f(z) = (z2+2z)(z+1)2(z2+4)

.

(b) Evaluate∫C

(z2−z+2)dzz4+10z2+9

where C is the circle |z| = 2 by using residue theorem.

[8+8]

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7. (a) Evaluate∞∫−∞

cosxdx(x2+16) (x2+9)

using residue theorem.

(b) If a>e, use Rouche’s theorem to prove that the equation ez= a zn has n rootsinside the circle |z| = 1. [8+8]

8. (a) Find the image of the rectangle R: -π <x< π;1/2<y<1, under the transfor-mation w = sin z.

(b) Find the bilinear transformation that maps the points ,(∞ i, 0), into the points(0, i, ∞) . [8+8]

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1. (a) Show that∞∫0

xme−axndx = 1

n a(m+1n )

Γ((m + 1)/n) where n and m are positive

constants.

(b) Prove that∞∫o

e−y1/mdy = mΓ(m).

(c) Show thatb∫a

(x− a)m(b− x)ndx = (b− a)m+n+1β(m+ 1, n+ 1). [5+5+6]

2. (a) Prove that P ′n(x) = x P ′n−1 (x) + nPn−1 (x).

(b) Show that J1/2(x) =√

2πx

sin x.

(c) Show that ddx

[xnJn(x)] = xnJn−1(x). [6+5+5]

3. (a) Find the analytic function whose imaginary part v is e−x(x siny–y cos y) andalso prove that v is harmonic.

(b) Prove that log (a+ib)a−ib = 2i tan−1 b

a

hence evaluate cos[i log (a+ib)

(a−ib)

]. [8+8]

4. (a) Evaluate∫c

(z2−2z−2) dz(z2+1)2z

where c is | z − i | = 1/2 using Cauchy’s integral for-

mula.

(b) Evaluate∫C

(z2 + 3z+ 2) dz where C is the arc of the cycloid x = a(θ + sin θ),

y = a (1− cos θ) between the points (0,0) to (πa, 2a). [8+8]

5. (a) Expand logz by Taylor’s series about z=1.

(b) Expand 1(z2 +1)(z2+2)

in positive and negative powers of z if 1 < |z| <√

2. [8+8]

6. (a) Find the poles and the residue at each pole of f (z) = sin2 z(z−π/6)2

(b) Find the poles and the residue at each pole of f (z) = zez

(z−1)3 . [5+5+6]

(c) Evaluate∫C

cosπ z 2dz(z−1)(z−2) where C is |z | = 3/2. [5+5+6]

7. (a) Show that2π∫0

dθa+bsinθ

= 2π√a2−b2 , a > b> 0 using residue theorem.

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(b) Evaluate by contour integration∞∫0

dx(1+x2)

. [8+8]

8. (a) Show that the region in the z plane between the lines y=0 and y =π corre-sponds toupper half of the w-plane under the transformationw= ez.

(b) Find the image of exterior of the unit circle in z-plane under the transformationW = z + 1/z. [8+8]

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1. (a) Evaluate1∫0

x2dx√1−x5 interms of β function.

(b) Prove that1∫0

(1− xn)1/ndx = 1n

[Γ( 1n)]

2

2Γ(2/n).

(c) Prove that Γ(

1n

)Γ(

2n

)Γ(

3n

).........Γ

(n−1n

)= (2

∏)n−12

n1/2 . [5+5+6]

2. (a) Prove that 1+zz√

1−2xz+z2− 1

z=∞∑n=0

(Pn(x) + Pn+1(x)) zn.

(b) Prove that ddx

(xJn Jn+1) = x(J2n − J2

n+1).

(c) Prove that cos x=J0–2J2+ 2J4+............ [6+5+5]

3. (a) Determine the analytic function f(z) =u+iv given that3u + 2v = y2 – x 2 + 16x.

(b) If sin (α + iβ) = x + iy then prove that x2

cosh2 β+ y2

sinh2 β= 1 and x2

sin2 α− y2

cos2 α= 1.

[8+8]

4. (a) Evaluate5+i∫−2+i

z3dz using Cauchy’s integral formula along y = x.

(b)∫

(x+ y)dx + ix2y dy along y=x2 from (0,0) to (3,9).

(c) Evaluate2+i∫−1+i

(x2 − y2 + i xy) dz using Cauchy’s integral formula along y=x2.

[5+5+6]

5. (a) Find the Laurent series expansion of the function z2−1z2+5z+6

about z = 0 in theregion 2 < |z| < 3.

(b) Evaluate f(z) = 2(2z+1)3

about (i) z = 0 (ii) z = 2. [8+8]

6. (a) Find the poles and residues at each pole of the function zez

(z−1)3.

(b) Evaluate∫C

2ezdzz(z−3)

where C is |z| = 2 by residue theorem. [8+8]

7. (a) Evaluate2π∫0

dθa+b cos θ

, a>0, b>0 using residue theorem.

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(b) Evaluate∞∫0

dx(1+x2)2

using residue theorem. [8+8]

8. (a) Under the transformation w=1/z, find the image of the circle |z-2i|=2.

(b) Under the transformation w = z−i1−iz , find the image of the circle |z|=1 in the

w-plane. [8+8]

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1. (a) Show that1∫0

xm (log x)n dx = (−1)nn!(m+1)n+1 where n is a positive interger and m>-1.

(b) Show that β(m,n)=∞∫0

yn−1

(1+y)m+ndy.

(c) Show that∞∫0

x4e−x2dx = 3

√π

8. [6+5+5]

2. (a) Show that Jn−1 (x) + Jn+1(x) = 2nxJn(x).

(b) Prove that J−1/2(x) =√

2πx

cosx.

(c) Show that (n+1) Pn+1 (x) - (2n+1) x Pn(x) + n Pn−1 (x) = 0. [5+5+6]

3. (a) Show thatf (z) = xy2(x+iy)

x2+y2, if z 6= 0

= 0 if z = 0is not analytic at z =0 although C –R equations are satisfied at the origin.

(b) If ( x + iy )1/3= a + ib, then prove that 4 ( a2–b2) = xa

+ yb. [8+8]

4. (a) Evaluate∫C

(y2 + 2xy)dx+ (x2 − 2xy)dy where c is the boundary of the region

by y=x2 and x=y2.

(b) Evaluate using Cauchy’s theorem∫c

z3 e−z dz(z−1)3 where c is | z − 1 | = 1/2 using

Cauchy’s integral formula.

(c) Evaluate(1,1)∫(0,0)

(3x2 + 5y + i(x2 − y2))dz along y2=x. [6+5+5]

5. (a) Expand f(z) = e2z

(z−1)3 about z=1 as a Laurent series. Also find the region ofconvergence.

(b) Find the Taylor series for zz+2

about z=1, also find the region of convergence.[8+8]

6. (a) Find the poles and the residue at each pole of f (z) = sin2 z(z−π/6)2

(b) Find the poles and the residue at each pole of f (z) = zez

(z−1)3 . [5+5+6]

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(c) Evaluate∫C

cosπ z 2dz(z−1)(z−2) where C is |z | = 3/2. [5+5+6]

7. (a) Show thatπ∫0

Cos2θ1−2aCosθ+a2 = πa2√

1−a2 , (a2 < 1) using residue theorem.

(b) Show by the method of contour integration that∞∫0

Cosmx(a2+x2)2

dx = π4a3

(1 +ma)e−ma,

( a > 0 , b > 0 ). [8+8]

8. (a) Under the transformation w=1/z, find the image of the circle |z-2i|=2.

(b) Under the transformation w = z−i1−iz , find the image of the circle |z|=1 in the

w-plane. [8+8]

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II B.Tech I Semester Supplementary Examinations, November 2011ADVANCED DATA STRUCTURES AND ALGORITHMS

( Common to Information Technology and Computer Science & SystemsEngineering)



1. (a) Each class has some special member-functions, which calls can be insertedby the compiler into a code without explicit instruction of the programmer.Enumerate such functions, members and cases, when implicit calls can arise.

(b) If when creating a variable the programmer explicitly did not initialize it, insome cases, the compiler itself would give it a certain, predefined initial value,and in some cases the initial value would be unpredictable. What does itdepend on? [8+8]

2. (a) Explain about operator overloading? Explain the rules to be followed onoverloading the operators?

(b) Explain about the function overriding with suitable examples. [8+8]

3. (a) How should we handle resources if constructors may throw exceptions?

(b) How do we change the string-length of an array of char to prevent memoryleaks even if/when someone throws an exception?

(c) What should we throw? What should we catch? [5+5+6]

4. (a) Explain in detail about probabilistic algorithm and amortized algorithm.

(b) Write the Union Find algorithms and also Explain with an example. [8+8]

5. (a) Explain about the skip list representation of dictionary with an example?

(b) What are the data members of skipList class? Write the constructor forskipList. [8+8]

6. Define a class called binarySearchTree to represent a Binary search tree. Extendthis class by adding a public method outputInRange (Low,High) that outputs,in ascending order of key, all elements in a binary search tree whose key lies betweenLow and High. Use recursion and avoid entering sub trees that cannot possiblycontain any elements with keys in desired range. [16]

7. Prove the equation T( N ) + a T ( N /b ) + θ(NklogpN) [16]Where a≥1, b≥1 and P≥0 is

T(N) = O(Nlogb a)ifa > bk

O (Nklogp+1N) if a = bk

O(NklogpN) if a < bk.

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8. Explain the Job Sequencing with dead line algorithm and also write the algorithmthe same. [16]

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1. (a) What are the two steps that happen with delete p?

(b) What are the advantages of new operator than malloc in C?

(c) Explain about the C++ classes in detail and design a class for playing cards?[5+5+6]

2. (a) What special considerations do we need to know about when I use VirtualInheritance?

(b) What special considerations do we need to know about when I inherit from aclass that uses virtual inheritance?

(c) What special considerations do I need to know about when I use a class thatuses virtual inheritance? [5+5+6]

3. What is an Error and Exception? Explain the exception handling mechanism inC++ ? [16]

4. (a) What is heap? Write an algorithm for implementing priority Queue usingheap.

(b) If f(n) + amnm+............a1n + a0 and am > 0 then prove that f(n) =θ(nm).[8+8]

5. Develop a class for hash table using linear probing and neverUsed concept to handlean erase operation. Write complete C++ code for all the methods. Include amethod to reorganize the table when (say) 60% of the empty buckets have neverused equal to false. The reorganization should move pairs around as necessary andleave a properly configured hash table in which neverUsed is true for every emptybucket. [16]


7. (a) Show that the inorder and post order sequences of a binary tree uniquelydefine the binary tree.

(b) Explain the AND/OR graph with an example. [8+8]

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8. (a) Write a linear time algorithm that generates the OBST from the root table.

(b) Prove that the greedy method always obtains an optimal solution to the job-sequencing problem. [8+8]

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1. (a) When are copy constructors called?

(b) What is Virtual Destructor?

(c) What is the diff between “new” and “operator new” ?

(d) What is a local class? Why can it be useful? [4+4+4+4]

2. (a) What is a virtual function? Why would you need a virtual destructor?

(b) What is a pure function and pure virtual function? When would you employthem? Can they improve the design?

(c) What function gets executed when we inherit from a class with the samefunction name? What about multiple inheritance? [5+5+6]

3. Create a program that opens a file (the first argument on the command line) andsearches it for any one of a set of words (the remaining arguments on the commandline). Read the input a line at a time, and print out the lines (with line numbers)that match. [16]

4. (a) Explain in detail about probabilistic algorithm and amortized algorithm.

(b) Write the Union Find algorithms and also Explain with an example. [8+8]

5. Develop a class for hash table using linear probing and neverUsed concept to handlean erase operation. Write complete C++ code for all the methods. Include amethod to reorganize the table when (say) 60% of the empty buckets have neverused equal to false. The reorganization should move pairs around as necessary andleave a properly configured hash table in which neverUsed is true for every emptybucket. [16]


7. Write an algorithm of Biconnected Components and also analyze its time complex-ity. [16]

8. (a) Show how Prim’s algorithm can be implemented using heap. What would bethe time complexity of the algorithm.

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(b) What is the time complexity of traveling sales person problem using dynamicprogramming. [10+6]

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1. (a) When are temporary variables created by C++ compiler?

(b) What is a local class? Why can it be useful?

(c) Can a copy constructor accept an object of the same class as parameter,instead of reference of the object?

(d) What is a class? [4+4+4+4]

2. (a) What is multilevel inheritance? Write a program to illustrate the concept ofMultilevel Inheritance.

(b) What is Hybrid inheritance? Write a program to illustrate the concept ofHybrid Inheritance. [8+8]

3. (a) Write a program to read the student details from a file and to store the studentdetails into a file.

(b) Write a program to count the no of characters in a given text file. [8+8]

4. (a) Show that [f(n)] is O(f(n)) is f(n) is a positive non decreasing function that isalways greater than 1.

(b) Define Theta notation. Explain the terms involved in it with an example.[8+8]

5. (a) How will you represent a node in a skip list. Write the constructor for skipList

(b) Write a method in C++ to perform insertion in a dictionary using skip listrepresentation. Explain its complexity? [8+8]

6. Define a class called binarySearchTree to represent a Binary search tree. Extendthis class by adding a method split(theKey, lessThan, greaterThan) that splitsthe binary search tree *this into two binary search trees - lessThan contains allelements of *this whose keys are less than theKey and greaterThan conatinsall elements of *this whose keys are greater than theKey. If the binary searchtree *this has a pair whose key equals theKey, a pointer to this pair is returnedas by the split method; otherwise NULL is returned. [16]

7. Write and explain the algorithm for evaluating a game tree using alpha-beta prun-ing. [16]

8. (a) Solve the following 0/1 Knapsack problem using dynamic programming P =(11,21,31,33) W = (2,11,22,15), C = 40, n = 4

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(b) What are the general characteristics of Greedy algorithms and the problemssolved by these algorithms. [8+8]

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II B.Tech I Semester Supplementary Examinations, November 2011PULSE AND DIGITAL CIRCUITS

( Common to Electrical & Electronic Engineering, Electronics &Communication Engineering, Electronics & Instrumentation Engineering

and Electronics & Telematics)Time: 3 hours Max Marks: 80


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1. (a) Derive the conditions necessary for good integrator:

(b) A square wave whose peak to peak amplitude is 1V extends ±0.5V with respectto ground. The duration of the positive section is 0.1 Sec. and of the negativesection is 0.2 Sec. If this wave form is impressed on RC high pass circuitswhose time constant is 0.2 Sec. what are the steady state maximum andminimum values of the output waveform? [6+10]

2. (a) Explain transfer characteristics of the emitter coupled clipper and derive thenecessary equations.

(b) Draw the basic circuit diagram of positive peak clamper circuit and explainits operation. [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. In the monostable circuit of the given figure 4 the resistor R is connected toan auxiliary supply V1 instead of VY Y . If A2 is in saturation or clamp andif A1 is OFF in the stable state, verify that the gate time T is given by Eq.T =τ ln(VYY+I1RY−Vσ)/(VYY−Vγ) with VY Y replaced by V1. [16]

Figure 4

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5. (a) Draw the circuit diagram and waveforms of a transistor bootstrap time basegenerator and explain principle of operation

(b) Why short recovery time is required? Draw and explain bootstrap sweepcircuit with this time. [8+8]

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 frequencydivision by an astable multivibrator? [8+8]

7. (a) Why are sampling gates called linear gates?

(b) What are the other names of a gate signal?

(c) Compare the unidirectional and bi-directional sampling gates. [6+4+6]

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) Prove that an RC circuit behaves as a reasonably good integrator if RC > 15T,Where T is the period of an input ‘Em sinωt’.

(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) Explain transfer characteristics of the emitter coupled clipper and derive thenecessary equations.

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

3. (a) What is non-saturating switch and where is it used?

(b) Write about diode switching times. [8+8]

4. Draw the circuit diagram for Schmitt trigger and explain its operation. What arethe applications of the above circuit? Derive the expressions for UTP and LTP.

[16]

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

(b) The specifications of UJT are given as η = 0.6 Vv = 2V, RBB= 5 K ohms,Iv = 1.5 mA, Ip = 8µA 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) 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) Explain the effect of circuit capacitances on the operation of a bi-directionaldiode gate.

(b) In the circuit of figure 7 consider that RL=RC=100K ohms and that R2=2 Kohms, Rf=50 ohms for Vs=25V, compute A, Vnmin, and Vcmin. [8+8]

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Figure 7

8. (a) Draw and explain the circuit diagram of a diode AND gate for negative logic.

(b) Derive the output equation for a diode OR gate for negative logic. [8+8]

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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 sinωt’.

(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) Draw the circuit diagram of slicer circuit using Zener diodes and explain itsoperation with the help of its transfer characteristic.

(b) Draw the circuit diagram of emitter coupled clipper. Draw its transfer charac-teristics indicating all intercepts, slopes and voltage levels derive the necessaryequations. [8+8]

3. (a) What is non-saturating switch and where is it used?

(b) Write about diode switching times. [8+8]

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) Explain how the deviation from linearity of linear sweep signals can be ex-pressed?

(b) In the UJT sweep circuit VBB = 20 V, VY Y = 50 V, R=5 k ohms RB1 =RB2

= 0 ohms, and C =0.01µF. Find

i. the amplitude of sweep signal

ii. the slope and displacement errors

iii. the duration of the sweep

iv. the recovery time?

( UJT fires when Vc =10.6 V and goes to off state when Vc=2.8 V). [8+8]

6. (a) How does the synch signal amplitude will affect the frequency of operation ofthe sweep generator?

(b) With the help of a circuit diagram and waveforms, explain frequency divisionby an Astable blocking oscillator. [8+8]

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7. (a) Explain the effect of circuit capacitances on the operation of a bi-directionaldiode gate.

(b) In the circuit of figure 7 consider that RL=RC=100K ohms and that R2=2 Kohms, Rf=50 ohms for Vs=25V, compute A, Vnmin, and Vcmin. [8+8]

Figure 7

8. (a) Draw and explain the circuit diagram of a diode OR gate for negative logic.

(b) Derive the output equation for a diode AND gate for negative logic. [8+8]

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1. Wtite short note on the following:

(a) Attenuators

(b) RC Double differentiator.

(c) RLC ringing circuit. [5+6+5]

2. (a) For the circuit shown in figure 2a an input voltage Vi linearly from 0 to 150Vis applied. Sketch the output waveform V0 to the same time scale. Assumeideal diodes.

Figure 2a

(b) What in meant by a d.c restoration circuit and explain? [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. (a) Draw the circuit of a bistable multivibrator with symmetrical collector trig-gering.

(b) Design a monostable circuit that produces a pulse width of 10msec. (Assumethe required date) [8+8]

5. (a) What is a Linear time base generator? Give its Applications

(b) Write the differences between the voltage and current time base generators?

(c) Why the time base generators are called sweep circuits? [6+6+4]

6. (a) What do you mean by synchronization on a one to one basis?

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(b) Explain how pulse synchronization differ from sine wave synchronization?

(c) Explain the relation between range of synchronization and sync signal ampli-tude? [4+6+6]

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) Explain the wired OR logic with the help of circuit diagram.

(b) Explain the significance of Clamping diode in AND logic. [8+8]

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II B.Tech I Semester Supplementary Examinations, November 2011ENVIRONMENTAL STUDIES

( Common to Electronics & Communication Engineering, Electronics &Telematics, Electronics & Computer Engineering and Aeronautical

Engineering)Time: 3 hours Max Marks: 80


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1. (a) Explain the need for students from all courses to be aware of environmentalissues.

(b) Write briefly about the scope of environmental studies. [6+10]

2. (a) What are the major development activities which threaten the stability of theenvironment and what are their effects and problems?

(b) Write briefly on the use of renewable & non-renewable resources. [8+8]

3. (a) Explain the significance of preserving balance in various kinds of ecosystems.Illustrate with examples.

(b) Describe the structure and functions of an ecosystem. [8+8]

4. Discuss the aesthetic value of nature with respect to the following statements.

(a) A true wilderness experience is an incredible learning experience.

(b) The beauty of nature encompasses every aspect of the living and non-livingpart of our earth. [8+8]

5. (a) Enumerate the diseases and other problems caused by soil pollution.

(b) How do you control soil pollution? [8+8]

6. (a) What are the major issues associated with resettlement and rehabilitation?

(b) Bring out the main elements of water conservation. [8+8]

7. (a) Describe the problems created by the growing population of the earth.

(b) Explain briefly the pattern of global population growth in recent years whichis causing alarm to environmental experts. [8+8]

8. (a) Explain the step by step procedure to record and document the environmentalfeatures and resource assets of an ecosystem during a field visit.

(b) Describe, in the format given above, the features of any type of any ecosystemyou have studied during field visit. [8+8]

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1. What is the role played by the following individual environmental thinkers?

(a) M.S. Swaminathan

(b) Medha Patkar

(c) Madhav Gadgil

(d) M.C. Mehta [4+4+4+4]

2. Discuss the importance of environmental studies with respect to the following state-ments.

(a) We live in a world wherein natural resources are limited.

(b) Green spaces and gardens are vital to the psychological and physical healthof city dwellers. [8+8]

3. How do different development activities, including construction of dams, affect thevarious aquatic ecosystems and what actions need to be taken to conserve them?

[8+8]

4. (a) Explain the concept of ex-situ conservation and illustrate your answer withexamples.

(b) What is an Integrated Protected Areas and how does it help in conservationof biological diversity. [10+6]

5. (a) List the types of hazardous wastes and their methods of disposal.

(b) Write about the health risks associated with these, giving examples to illus-trate your answer. [8+8]

6. Why should natural ecosystems and various forms of species be protected ? Howdoes indiscriminate exploitation of these areas lead to damage ? [16]

7. (a) Though population growth shows a global decline, there is still cause for worry.Explain why.

(b) What are the reasons for differences in the rate of population growth in variouscountries. [8+8]

8. (a) Describe how you would methodically record the elements and resources in anecosystem and assess its functioning.

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(b) Based on your filed visits, summarize your observations and findings of thewater resource ecosystem in your region. [8+8]

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1. Explain the different areas of environmental conservation to which people belongingto different disciplines can contribute. [16]

2. Discuss the importance of nature with respect to the following statements.

(a) There is an urgent need to protect all living species.

(b) Nature provides us with various options on how we utilize its goods and ser-vices. [8+8]

3. (a) What are the different tropic levels of organisms in an ecosystem ?

(b) Why is a complex ecosystem more stable than one with few species? [10+6]

4. (a) Write briefly about the different types of diversity in ecosystems.

(b) Explain what is value of biodiversity and what are the different types of valuesof biodiversity? [8+8]

5. (a) Oceans are ultimate sink for most of the waste we produce. Explain.

(b) List off shore sources of Marine Pollution.

(c) Explain the effects of oil pollution on the ocean. [8+4+4]

6. (a) Define watershed management and explain its objectives.

(b) Discuss various water conservation techniques that can be practiced by indi-viduals. [8+8]

7. (a) Write a brief note on health hazards related to climatic factors.

(b) What are the infectious diseases which have emerged /re-emerged recently andwhat are the reasons for this ? [6+10]

8. (a) Explain the aspects to be studied and the procedure for collecting informationwhen you want to document the environmental features and resource assetsof a water resoure ecosystem during a field visit.

(b) Describe, in the format given above, the features of any such ecosystem youhave studied during field visit. [8+8]

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1. Explain the different areas of environmental conservation to which people belongingto different disciplines can contribute. [16]

2. (a) Discuss the uses and exploitation of forest resources.

(b) Write about the consequences of deforestation. [8+8]

3. (a) Explain the significance of preserving balance in various kinds of ecosystems.Illustrate with examples.

(b) Describe the structure and functions of an ecosystem. [8+8]

4. (a) Explain the concept of ex-situ conservation and illustrate your answer withexamples.

(b) What is an Integrated Protected Areas and how does it help in conservationof biological diversity. [10+6]

5. (a) List the wastes that are prohibited from processing along with municipal solidwaste. Discuss.

(b) Briefly describe the methods of heating and disposal of solid waste. [8+8]

6. (a) Explain the phenomenon of Global Warming and the factors contributing toit.

(b) Explain the possible impacts of Global Warming on the food supply.

(c) What are the measures taken at Global level to control the emmission of GreenHouse Gases? [6+5+5]

7. (a) Write briefly about the environmentally caused diseases which affects children.

(b) How can these be reduced? [8+8]

8. (a) Describe how you would methodically record the elements and resources in anecosystem and assess its functioning.

(b) Based on your filed visits, summarize your observations and findings of thewater resource ecosystem in your region. [8+8]

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II B.Tech I Semester Supplementary Examinations, November 2011ELECTROMAGNETIC FIELDS

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



1. (a) E is the electric field due to a point charge Q C at the origin in free space.Find ∫

S

E.da where S is a spherical surface of radius R m and center at origin.

(b) Using Gauss’s law, show that the electric field due to an infinite straight line ofuniform charge density λ C/m along the z-axis in free space is (λ/2πε0r) ar N/C.

(c) An infinitely long cylinder of radius 1m in free space is filled with a uniformcharge density of 1nC/m3. If the potential on the axis of the cylinder is 100V, find the potential variation inside the cylinder. [6+6+4]

2. (a) A conducting body is in the electric field of static charges. Explain why thenet electric field at any point inside the conducting body will be zero.

(b) Use the result of (a) to show that

i. the net volume charge density at any point inside the conductor is zero,and

ii. the conductor is an equipotential body. [8+4+4]

3. (a) Derive the expression for the energy of charges q1 C, q2 C, ......qn C located atpoints 1,2,. . . . n.

(b) A sphere of radius 2.3 m has a uniform volume charge density of 300 µC/m3.Find the energy density of the field at a distance of 50 cm from the center ofthe sphere. The sphere is in free space. [8+8]

4. (a) State Biot - Savart’s law for the magnetic field B due to a steady line currentin free space.

(b) Find B due to a straight conductor length ℓ m and steady current I A at adistance of y m from the center of the line current. [6+10]

5. The planes z = 0 and z = 0.1 m are perfect conducting. A voltage of 2 V ismaintained between them, such that E is in az direction. For 0 < z < 0.1 m thereis a conducting material for which σ = 1000e - 100ρ Siemens/m. Find E and J. Alsofind current enclosed in cylinder of radius ρ . Use Ampere’s law to find H. [16]

6. (a) What is magnetic dipole? How it differs from electric dipole?

(b) In a certain region of space B = 0.1xax - 0.2yay - 0.3az T. Find the total forceon a rectangular loop carrying a current of 20 A, lying in z = 0 plane andbounded by 1 < x < 3 & 2 < y < 5 m. [6+10]

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7. (a) Prove that inductance of coil is given by L = µ0µrN2A

lHenry. Where N =

number of turns of coil, A = cross sectional area of coil and l = length ofmagnetic path.

(b) A spiral straight spring consists of 1000 turns of copper wire. The length ofspring is 10 cm. Find the inductance of spring if the current flowing throughspring is 5 Amp and radius of spring is 1cm. If this spring is bent in to a circlefind the new inductance of spring. (Neglect elongation of spring). [8+8]

8. If σ = 0, ε = 2.5εo and µ = 10µo determine whether following pairs of field satisfyMaxwell’s equation or not.

(a) E = 2y ay v/m, H = 5x ax A/m

(b) E =100 sin 6 * 107 t sin z ay V/m, H = - 0.1328 cos 6 * 107t cos z ax A/m.[8+8]

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1. (a) State and explain Coulomb’s law for the vector force between two point chargesin free space.

(b) A straight line with a uniform charge density of λ C/m extends from the originupto a length ℓ m along the z-axis in freespace. Find the component of theelectric field in the y-direction at (0,y,0) m. [6+10]

2. (a) For a conducting body in the electric field of static charges, explain what willbe the

i. net electric field the conductor, and

ii. distribution of any external charge given to the conductor.

(b) Three thin, concentric, spherical conducting shells of radii 1 m, 2 m and 3m respectively are in air. Charges of 1

9nC and −

19nC, are placed on the

inner two shells, while the outer shell is grounded. Find the magnitude of thepotential difference between the two inner shells. [8+8]

3. (a) Define polarization. Explain how a dielectric acquires polarization.

(b) A long straight line of uniform charge density λ C/m is surrounded by aninsulating medium out to a radius R m. Find D. Also find the electric fieldin the region outside the insulation. Explain why the electric field cannot befound in the insulation region. [8+8]

4. (a) A steady current of I A extends along the z-axis from −ℓ

2m to ℓ

2m in free

space. Find the magnetic field B at a point on the y-axis y m from the origin,using Biot-Savart’s law.

(b) Extend the result of (a) to an infinite straight line of steady current. Expressthe result in cylindrical co ordinates. [10+6]

5. Applying Ampere’s current law to differential element obtain the Maxwell’s equa-tion ∇ X H = J. [16]

6. In region 1, where r. (2ax - 3ay + az) > 5, let µr1 = 10 and in region 2 where r(2ax - 3ay + az) < 5, let µr2 = 2. B1 = 10ax + 20ay + 30az mT everywhere in re-gion 1.

(a) Find the angle θ1 that B1 makes with the unit normal aN21.

(b) Find the angle θ2 that B2 makes with the unit normal aN21. [8+8]

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7. (a) Explain the characteristic of permanent magnets. What are the specific re-quirements to obtain permanent magnetism?

(b) A co-axial cable has conductor dimensions 1 and 5 mm. the region betweenconductors is air for 0 < ϕ < π/2 and π < ϕ 3π/2 and a non-conducting ma-terial having µr = 8 for π/2 < ϕ < π and 3π/2 < ϕ < 2π . Find the induc-tance per meter length. [4+12]

8. Given the magnetic flux density B = 6 cos(106 t) sin (0.01)x az mT, find

(a) The magnetic flux passing the surface z=0, 0 < x < 20 m, 0 <y <3 m, at t =1 µs.

(b) The value of the closed line integral of E around the perimeter of the surfacespecified above at t = 1 µs. [8+8]

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1. (a) State and prove Gauss’s law in integral form, considering static charges in freespace.

(b) Given that E (r, φ, z) = 1

∈o

(2r cos φ) aφ −(

1

3rsin φ

)

az

N/C ( in cylin-

drical co ordinates), find the flux of E crossing the portion of the z = 0 planedefined by r ≤ a, 0 ≤ φ ≤ π/2 in the + ve z -direction.

(c) ∇V = xax + yay + zaz. If point (1,1,1) m is at zero volts, find the potentialV(x,y,z). [6+6+4]

2. (a) For a conducting body in the electric field of static charges, explain what willbe the

i. net electric field inside the conductor, and

ii. potential difference between any two points inside the conductor.

(b) A solid conducting sphere of radius 10 cm is surrounded by a thick concentricspherical conducting shell of inner radius 15 cm and outer radius 20 cm. Thespace between the two spheres is filled with air. If a charge of 5 nC is takenfrom the outer conductor and placed on the inner conductor, find the potentialdifference between the two conductors. What is the capacitance between thespheres? [8+8]

3. (a) Obtain the continuity equation. How does it get modified for steady currents?

(b) J (r, θ, φ) is given as J = 4

r2cos θar + 20e−2r sin θaθ − r sin θ cosφaφ A/m2 (in

spherical co ordinates). Find the total current passing through the sphericalarea r =3 m, 0 < θ < 200, 0 < φ < 2π. [8+8]

4. (a) State Biot-Savart’s law for the magnetic fieldB due to a steady current elementI dl A-m situated in free space.

(b) Find B due to an infinite plane sheet of steady current on the xy - plane, witha uniform surface current density of K(-ax) A/m in free space. [Hint: B dueto an infinite straight steady line current I A at a point y m from the line is(µ0I/2πy)T , in a direction given by the right hand rule]. [6+10]

5. Obtain the expression for the magnetic field intensity and sketch the same for aco-axial cable. [16]

6. Explain the nature and behavior of magnetic material. Define and explain the termmagnetization. [16]

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7. (a) Explain the concept and obtain the unit of scalar magnetic potential. Whatis the role of scalar magnetic potential in magnetic circuits?

(b) The region 3.5 < ρ 4.5 cm, 0< ϕ < 2π , 0< z < 2 cm, is current free andcontains the field Hϕ = 70/ρ A/m. Find Scalar magnetic potential at ρ =3.8 cm, ϕ = 110o, z = 0.5 cm. If scalar magnetic potential is 0 at ϕ = 0 andbarrier is at ϕ= 90o; and scalar magnetic potential is 0 at ϕ = 0 when barrieris at ϕ= 180o. [8+8]

8. (a) Explain why conduction current is absent through the capacitor.

(b) Find the displacement current within a parallel plate capacitor whereε = 100 εo, A = 0.1 m2, d= 0.05mm and the capacitor voltage is 100 sin2000π t Volts. [6+10]

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1. (a) Explain the superposition principle governing the forces between charges atrest.

(b) For the vector function A (x, y, z) = yay + zaz, f indP :(0,1,1)

∫0:(0,0,0)

A.dℓ.

(c) i. A line charge of 20 nC / m lies along the entire z - axis, in free space Findthe electric field at (0,4,0) m.

ii. A point charge of 20 nC is now added at (3,0,0) m. What is the new fieldat (0,4,0) m? [6+6+4]

2. (a) For a pure dipole paz C- m at the origin in free space, find the potential at apoint A (r, θ, φ = π

2) (in spherical co-ordinates).

(b) In (a) Find the electric field at the point A.(

∇V in spherical coordinates = ∂V∂r

ar + 1r

∂V∂θ

aθ + 1r sin θ

∂ V∂φ

aφ

)

(c) What is the electric field at(

r = 5m, θ = π2, φ = π

2

)

due to a pure dipole 5aznC-m located at the origin? [6+6+4]

3. (a) Define polarization. Explain how a dielectric acquires polarization.

(b) A long straight line of uniform charge density λ C/m is surrounded by aninsulating medium out to a radius R m. Find D. Also find the electric fieldin the region outside the insulation. Explain why the electric field cannot befound in the insulation region. [8+8]

4. (a) State Biot - Savart’s law for the magnetic field B due to a steady line currentin free space.

(b) Find B due to a straight conductor length ℓ m and steady current I A at adistance of y m from the center of the line current. [6+10]

5. A solenoid of 10cm diameter and 30 cm in length is wound with 150 turns andcarries a current of 5 A. Find the magnetic flux density at the mid point of thesolenoid and at distance 10 cm from either side of solenoid. [16]

6. (a) For the boundary between the two magnetic media, show that the boundaryconditions on the magnetization vectors areM1t

Xm1

− M2t

Xm2

= k and µ1

Xm1

M1n = µ2

Xm2

M2n

(b) If µ1 = 2µo for region 1 (0 < ϕ < π) and µ2 = 5µo for region1 (π < ϕ < 2π) and B2 = 10aρ + 15aϕ - 20az mT, calculate B1 . [8+8]

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7. With the help of Vector magnetic potential obtain the expression for mutual in-ductance for two current carrying loops. [16]

8. Given the magnetic flux density B = 6 cos(106 t) sin (0.01)x az mT, find

(a) The magnetic flux passing the surface z=0, 0 < x < 20 m, 0 <y <3 m, at t =1 µs.

(b) The value of the closed line integral of E around the perimeter of the surfacespecified above at t = 1 µs. [8+8]

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II B.Tech I Semester Supplementary Examinations, November 2011SWITCHING THEORY AND LOGIC DESIGN

( Common to Electrical & Electronic Engineering, Electronics &Instrumentation Engineering, Bio-Medical Engineering, Electronics &

Control Engineering, Electronics & Computer Engineering andInstrumentation & Control Engineering)



1. A 12-bit Hamming code word containing 8-bits of data and 4 parity bits is read frommemory. What was the original 8-bit data word that was written in to memory if12-bit words read out is as follows. [4 ×4 = 16]

(a) 000011101010

(b) 101110000110

(c) 101111110100

(d) 110011010010

2. (a) Express the following functions in sum of minterms and product of maxterms.[8]

i. F (A,B,C,D) = B’D + A’D + BD

ii. F(x,y,z) = (xy + z)(xz + y)

(b) Obtain the complement of the following Boolean expressions. [8]

i. (AB’ + AC’)(BC + BC’)(ABC)

ii. AB’C + A’BC + ABC

iii. (ABC)’(A + B + C)’

iv. A + B’C (A + B + C’)

3. Using K-map Simplifyf(x1, x2, x3, x4, x5, x6) =

∑m· (0, 3, 4, 5, 7, 8, 12, 13, 20, 21, 28, 29, 31, 34,

35, 38, 39,42, 45, 46, 50, 54, 58, 61, 62, 63) [16]

4. Implement the following Boolean function by a Hazard free OR- AND network.f =

∑m(2, 3, 5, 7) and explain in detail what the Hazards are encountered in

implementing the above function. [16]

5. (a) Derive the PLA programming table for the combinational circuit that squaresa 3 bit number.

(b) For the given 3-input, 4-output truth table of a combinations circuit,tabulatethe PAL programming table for the circuit. [8+8]

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Inputs Outputx y z A B C D0 0 0 0 1 0 00 0 1 1 1 1 10 1 0 1 0 1 10 1 1 0 1 0 11 0 0 1 0 1 01 0 1 0 0 0 11 1 0 1 1 1 01 1 1 0 1 1 1

6. (a) Using the method of flip flop conversion carry out the following conversions.

i. S-R to T

ii. J-K to D [4x2=8]

(b) Verify that the circuit and explain its function. With the timing waveforms.Shown in figure 1 [8]

Figure 1:

7. A clocked sequential circuit is provided with a single input x and single output Z.Whenever the input produce a string of pulses 1 1 1 or 0 0 0 and at the end of thesequence it produce an output Z = 1 and overlapping is also allowed.

(a) Obtain State - Diagram.

(b) Also obtain state - Table.

(c) Find equivalence classes using partition method & design the circuit using D- flip-flops. [4+4+8]

8. (a) Draw the ASM chart for the following state transistion, start from the initialstate T1, then if xy=00 go to T2, if xy=01 go to T3, if xy=10 go to T1, otherwise go to T3.

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(b) Show the exit paths in an ASM block for all binary combinations of controlvariables x, y and z, starting from an initial state. [8+8]

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1. Convert the following to Decimal and then to Binary.

(a) 101116

(b) ABCD16

(c) 72348

(d) 77668

(e) 12810

(f) 72010. [3+3+3+3+2+2]

2. (a) Simplify the following Boolean expressions. [8]

i. A’C’+ABC+AC’ to three literals

ii. (x’y’+z)’+z+xy+wz to three literals

iii. A’B(D’+C’D)+B(A+A’CD) to one literal

iv. (A’+C)(A’+C’)(A+B+C’D) to four literals

(b) Obtain the complement of the following Boolean expressions. [8]

i. B’C’D+(B+C+D)’+B’C’D’E

ii. AB+(AC)’+(AB+C)

iii. A’B’C’+ABC’+AB’C’+ABC’

iv. AB+(AC)’+AB’C

3. Reduce the following function using six variable K- mapF =

∑m(0, 2, 5, 7, 9, 11, 14, 16, 18, 21, 23, 27, 30, 32, 34, 36, 41, 43, 44, 48, 50, 52, 53, 59, 60, 61).

[16]

4. (a) Draw and explain the truth table and Logic diagram of a 1 line to 8 lineDemultiplexer.

(b) Draw and explain the truth table and Logic diagram of a 3 line to 8 lineDecoder. [8+8]


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6. (a) Using the method of flip flop conversion carry out the following conversions.

i. S-R to T

ii. J-K to D [4x2=8]

(b) Verify that the circuit and explain its function. With the timing waveforms.Shown in figure 1 [8]

Figure 1:

7. For the minimal state ? table:

(a) Give proper Assignment.

(b) Design the circuit using D - Flip-Flops. [8+8]

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Present State Next state out - putqv qv+1 Z

X=0 X=1A B,0 A,0B C,0 A,0C D,0 E,0D D,0 A,0E B,1 A,0



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1. (a) List the first 20 numbers in base12. Use the letters A and B to represent thelast two digits. [4]

(b) Convert the following numbers with the given radix to decimal. [4 × 3 = 12]

i. 44335

ii. 119912

iii. 56547

iv. 6128

2. (a) Reduce the following Boolean expressions. [8]



iii. (ABC)’(A + B + C)’

iv. A + B’C (A + (B’C)’)

(b) Obtain the Dual of the following Boolean expressions. [8]

i. ABC + A’B + ABC’

ii. (BC’ + A’D)(AB’ + CD’)

iii. x’yz + xz

iv. xy + x (wz + wz’)

3. Plot the following Boolean function on a K-map.F = (ABCDEF )+(ABCDE)+(BCDEF )+(ABCDF )+(ABCDF )+(ABCE)+(ACDF ) + (ABDE) + (ACD) + (EF ),. [16]

4. (a) Implement the following Boolean function using a 8:1 multiplexer considering‘C’ as the input and A,B,C as selection lines. f(ABCD) = AB +BD+ BCD

(b) Draw the Gate level diagram of a Decimal to BCD encoder. [10+6]


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6. (a) Explain the operation of 5 - stage twisted ring counter with circuit diagramState transition diagram & state table

(b) Find a ring code for a module - 5 shift counter using D-flip flops. Explainwith the waveforms. [8+8]

7. A clocked sequential circuit is provided with a single input x and single output Z.Whenever the input produce a string of pulses 1 1 1 or 0 0 0 and at the end of thesequence it produce an output Z = 1 and overlapping is also allowed.

(a) Obtain State - Diagram.

(b) Also obtain state - Table.

(c) Find equivalence classes using partition method & design the circuit using D- flip-flops. [4+4+8]



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1. (a) List the first 20 numbers in base17. Use the letters A, B, C, D, E, F and Gto represent the last seven digits. [4]

(b) Convert the following numbers with the given radix to decimal. [4 × 3 = 12]

i. 12345

ii. 12347

iii. 123411

iv. 3334

2. (a) Draw the NAND logic diagram that implements the complement of the fol-lowing function. [8]F(A,B,C,D) = Σ (0,1,2,3,4,8,9,12)

(b) Obtain the complement of the following Boolean expressions.

i. AB+A(B+C)+B’(B+D)

ii. A+B+A’B’C [4]

(c) Obtain the dual of the following Boolean expressions.

i. A’B+A’BC’+A’BCD+A’BC’D’E

ii. ABEF+ABE’F’+A’B’EF [4]

3. (a) Design a logic circuit Using minimum number of Basic gates for the followingBoolean expression.F = (ABCD) + (ABCD) + (ABCD) + (ABCD) + (ABCD) + (ABCD)+(ABCD) + (ABCD) + (ABCD) + (ABCD) + (ABCD)

(b) Reduce the following expression using Karnaugh map. F = (BA+ AB +AB)

(c) Find the out put of a four variable K-map, when all the cells are filled withlogic LOW. [10+4+2]

4. What are the advantages of a carry look ahead adder? Draw logic diagram of carrylookahead adder of a bit and explain the working of it. [4+!2]

5. Write a brief note on:

(a) Architecture of PLDs

(b) Capabitation and the limitations of threshold gates. [8+8]

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6. (a) Compare synchronous & Asynchronous circuits

(b) Design a Mod-6 synchronous counter using J-K flip flops. [6+10]

7. A clocked sequential circuit is provided with a single input x and single output Z.Whenever the input produce a string of pulses 1 1 1 1 or 0 0 0 0 and at the end ofthe sequence it produce an output Z = 1 and overlapping is also allowed.

(a) Obtain State- Diagram.

(b) Also obtain state -Table.

(c) Find equivalence classes using partition method. [4+4+8]

8. (a) For the given ASM chart obtain its equivalent state diagram 8.

(b) Design the circuit using mulitiplexes. [8+8]

Figure 8

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II B.Tech I Semester Supplementary Examinations, November 2011DIGITAL LOGIC DESIGN




1. Convert the following to Binary and then to gray code. [2+2+2+2+4+4]

(a) 101016

(b) AB3316

(c) 33238

(d) 17648

(e) 18710

(f) 226610.

2. (a) Explain the concept of positive logic and negative logic. Also draw the truthtables for positive logic AND gate and negative logic OR gate.

(b) Obtain the complement of the following Boolean expressions.

i. B’C’D + (B + C + D)’ + B’C’D’E

ii. AB + (AC)’ + (AB + C).

(c) Obtain the dual of the following Boolean expressions. [8+4+4]

i. A’B’C’ + A’BC’ + AB’C’ + ABC’

ii. AB + (AC)’ + AB’C.

3. (a) IfF1(A,B,C) = A⊕ B ⊕ C

F2 (A,B,C) = AΘC ΘBShow that = F1 = F2

(b) Show that A⊕ B ⊕ AB = A + B

(c) Obtain minimal SOP expression for the complement of the given expression:F (A,B,C) =

∏(1, 2, 5, 7) And draw the circuit using NOR - gates. [4+4+8]

4. (a) For a Full adder the input bits are Ai, BiCi, show that for a look-a-head carryAdder circuit.Si = Sumi = Ai ⊕Bi ⊕ Ci = Pi ⊕ Ci

Carryi+1 = AiBi + PiCi = Ci + PiCi.And draw the circuit for C3

(b) For BCD to Excess - 3 code converter the Boolean expression are as follows:E3E2E1E0 is the excess - 3 code & ABCD is BCD code.

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E3 = A + BC + BD

E2 = BC + BD + BCD

E1 = CD + CD

E0 = DWrite HDL data - flow description. [8+8]

5. (a) Explain the operation of D-flip-flop with negative edge triggering using NANDgates.

(b) Obtain the state diagram for the synchronous sequential circuit with two in-puts (X, Y) and one output ‘Z’. The input represents alphabet letters as 00-A, 01-B, 10-C and 11-D. The output is one if the most recent two inputs arein alphabetic order, i.e., AB, BC, CD. [6+10]

6. (a) Write the HDL behavioral description of the 4- bit up down counter.

(b) Design a counter with the following repeated binary sequence: 0, 2, 4, 6, usingD flip-flops. [8+8]

7. (a) Show the memory cycle timing waveforms for the write and read operations.Assume a CPU clock of 50 MHz and a memory cycle time of 50 ns.

(b) The following memory units are specified by the number of words times thenumber of bits per word. How many address lines and input-output data linesare needed in each case? [8+8]

i. 4K * 16,

ii. 2G * 8 ,

iii. 16M * 32,

iv. 256K * 64.

8. (a) Describe the operation of the SR Latch using NAND gate with the help oftruth table, transition table and the circuit.

(b) Explain the operation and use of De bounce circuit. [8+8]

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1. Convert the following to Decimal and then to Binary.

(a) 187616

(b) AB2216

(c) 12128

(d) 15568

(e) 97710

(f) 66410 [3+3+3+3+2+2]

2. (a) Reduce the following Boolean expressions.



iii. (ABC)’(A + B + C)’

iv. A + B’C (A + (B’C)’)

(b) Obtain the Dual of the following Boolean expressions. [8+8]

i. ABC + A’B + ABC’

ii. (BC’ + A’D)(AB’ + CD’)

iii. x’yz + xz

iv. xy + x (wz + wz’).

3. (a) Obtain Boolean expression for a two input Ex-OR gate in POS form and drawthe circuit with two-level NOR-NOR form and AND- OR form.

(b) Implement the following function with Excusive - OR and AND gates:F = ABCD + ABCD + AB CD + ABCD. [8+8]

4. (a) Using 3 to 8 line de- multiplexers, construct 5 to 32 line de- multiplexers.Use active - low Enable input. If necessary use additional logic gates.

(b) Design a combinational logic circuit with three inputs x, y, z and three outputsA, B, C. when the binary input is 0,1,2,or 3, the binary output is one greaterthan the input. When the binary input is 4,5,6,or 7 the binary output is oneless than the input. Draw the circuit using one- full adder and an inverter.(Use only block diagram of Full adder). [8+8]

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5. A circuit is to be designed with two inputs (X, Y) and one output ‘Z’. The logicis Z = X if Y = 1, but if Y = 0, ‘Z’ is remain fixed at its last value before ‘Y’becomes zero. Derive state diagram and state table and design the circuit using D-flip-flops. [16]

6. (a) Explain the following systems

i. shift registers

ii. counters.

(b) Draw and explain 4-bit binary ripple counter using D- flip-flops. [10+6]

7. (a) Give the HDL code for a memory read, write operations if the memory size is64 words of 4 bits each. Also explain the code.

(b) A 16K * 4 memory uses coincident decoding by splitting the internal decoderinto X-selection and Y-selection. [8+8]

i. What is the size of each decoder and how many AND gates are requiredfor decoding the address?

ii. Determine the X and Y selection lines that are enabled when the inputaddress is the binary equivalent of 6,000.


(b) An asynchronous sequential circuit has two internal states and one output.The excitation and output functions describing the functions are:Y1 = x1x2 + x1y

′2 + x′

2y1Y2 = x2 + x1y

′1y2 +x′

1y1z= x2 + y1 Implement the circuit defined above with NAND SR latches. [8+8]

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1. (a) Express the Decimal Digits 0 - 9 in BCD, 2421, 84-2-1 and Excess-3.

(b) Convert the Hexadecimal number 1010 to Decimal and then to Binary. [12+4]

2. (a) Reduce the following Boolean expressions.

i. B’C’D + (B + C + D)’ + B’C’D’E

ii. AB + (AC)’ + AB’C(AB + C)

iii. A’B’C’ + A’BC’ + AB’C’ + ABC’

iv. A + B + A’B’C.

(b) Obtain the complement of the following Boolean expressions. [8+8]

i. x’y’ + xy + x’y

ii. xy’ + y’z’ + x’z’

iii. x’ + xy + xz’ + xy’z’

iv. (x + y)(x + y’).

3. (a) Construct K-map for the following expression and obtain minimal SOP ex-pression. Implement the function with 2-level NAND -NAND form.f (A,B,C,D) = (A + C + D)

(A + B + D

) (A + B + C

) (A + B + D

) (A + B + D

)(b) Implement the following Boolean function F using the two - level form: [8+8]

i. NAND-AND

ii. AND-NOR F (A,B,C,D) = Σ0, 1, 2, 3, 4, 8, 9, 12

4. (a) Design a code converter to convert BCD code to 9’s complement code usingsuitable Decoder and OR - gates.

(b) Design a 4- bits 2’s complement circuit to generate 2’s complement for thegiven 4 - bit binary number. Use Decoder and OR - gates. [8+8]

5. (a) Draw the circuit diagram of positive edge triggered D- flip-flop with NANDgates and explain its operation using truth table.

(b) Write an HDL behavioural description of a D- flip-flop and D- flip-flop withsynchronous preset and clear. [8+8]

6. (a) Write the HDL behavioral description of the 4- bit up down counter.

(b) Design a counter with the following repeated binary sequence: 0, 2, 4, 6, usingD flip-flops. [8+8]

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7. (a) What is parity checking? Explain its necessity and how is it implemented?

(b) If the Hamming code sequence 1100110 is transmitted & due to error in oneposition, is received as 1110110, locate the position of the error bit using paritychecks and give the method for obtaining the correct sequence. [8+8]


(b) An asynchronous sequential circuit has two internal states and one output.The excitation and output functions describing the functions are:Y1 = x1x2 + x1y

′2 + x′

2y1Y2 = x2 + x1y

′1y2 +x′

1y1z= x2 + y1 Implement the circuit defined above with NAND SR latches. [8+8]

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1. (a) Express the Decimal Digits 0 - 9 in BCD, 2421, 84-2-1 and Excess-3.

(b) Convert the Hexadecimal number 1010 to Decimal and then to Binary. [12+4]

2. (a) Simplify the following Boolean expressions.

i. A’C’ + ABC + AC’ to three literals

ii. (x’y’ + z)’ + z + xy + wz to three literals

iii. A’B(D’ + C’D) + B(A +A’CD) to one literal

iv. (A’ + C)(A’ + C’)(A + B + C’D) to four literals.

(b) Obtain the complement of the following Boolean expressions. [8+8]

i. B’C’D + (B + C + D)’ + B’C’D’E

ii. AB + (AC)’ + (AB + C)

iii. A’B’C’+ A’BC’ + AB’C’ + ABC’

iv. AB + (AC)’ + AB’C.

3. (a) Construct K-map for the following expression and obtain minimal SOP ex-pression. Implement the function with 2-level NAND -NAND form.f (A,B,C,D) = (A + C + D)

(A + B + D

) (A + B + C

) (A + B + D

) (A + B + D

)(b) Implement the following Boolean function F using the two - level form: [8+8]

i. NAND-AND

ii. AND-NOR F (A,B,C,D) = Σ0, 1, 2, 3, 4, 8, 9, 12

4. (a) A multiple output combinational logic circuit is defined by the following func-tions. Draw the schematic circuits for F1 and F2.

F1 (A,B,C,D) = A • AD •(A + BC

)F2 (A,B,C,D) = AD •

(A + BC

)Using K-Maps simplify F1 and F2 and draw the reduced diagram circuit.

(b) Design a full - subtractor circuit with three inputs x,y,z and outputs D, B.The circuit subtracts X - Y - Z where Z is the input borrow, B is the outputborrow and D is the difference draw the circuit using NAND gates. [8+8]

5. (a) Draw the circuit diagram of clocked D- flip-flop with NAND gates and explainits operation using truth table. Give its timing diagram.

(b) Explain the procedure for the design of sequential circuits with example. [8+8]

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6. Design a circuit with three 4-bit registers A,B and C to perform the followingoperations.

(a) Transfer two binary numbers to A and B when a start signal is enabled,

(b) If A <B, shift left the contents of A and transfer the result to register C.

(c) If A >B, shift right the contents of B and transfer the result to register C.

(d) If A=B, transfer the number to register C unchanged.

Explain the procedure. [16]

7. (a) Explain the block diagram of a memory unit. Explain the read and writeoperation a RAM can perform.

(b) i. How many 32K * 8 RAM chips are needed to provide a memory capacityof 256K bytes.

ii. How many lines of the address must be used to access 256K bytes? Howmany of these lines are connected to the address inputs of all chips?

iii. How many lines must be decoded for the chip select inputs? Specify thesize of the decoder. [8+8]

8. (a) i. Explain the difference between asynchronous and synchronous sequentialcircuits.

ii. Define fundamental-mode operation.

iii. Explain the difference between stable and unstable states.

iv. What is the difference between an internal state and a total state.

(b) Explain critical and non critical races with the help of examples. [8+8]

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II B.Tech I Semester Supplementary Examinations, November 2011ELECTRONIC CIRCUIT ANALYSIS

( Common to Electronics & Communication Engineering and Electronics &Telematics)



1. (a) For a single stage transistor amplifier, RS = 10K and RL= 10K. The h-parameter values are hfc = −51, hic =1.1KΩ, hrc ≈ 1, hoc = 25 µA/V FindAI , AV , AV S, Ri, and Ro for the CC transistor configuration.

(b) For a single stage transistor amplifier, RS=1KΩ, andRL= 10K The h-parametervalues are hfe = 50, hie =1.1KΩ, hre = 2.5x10−4, hoe = 25 µ A/V. FindAI , AV , AV S, Ri, and Ro for the CE transistor configuration. [8+8]

2. (a) Draw the circuit diagram of CASCODE amplifier , deriving its importantcharacteristics.

(b) The bandwidth of an amplifier extends from 20 Hz to 20 KHz . Find thefrequency range over which voltage gain is down less than 1 dB from its midband value. [8+8]

3. (a) Show that in Hybrid - π model, the diffusion capacitance is proportional tothe emitter bias current.

(b) What is the frequency range to consider Giacolletto model of a transistor athigh frequencies? What is the significance of fT in discussing the frequencyrange of a transistor at high frequencies? [8+8]

4. (a) Classify large signal amplifiers based on its operating point. Distinguish theseamplifiers in terms of the conversion efficiency. [8]

(b) Draw the push-pull power amplifier circuit. Derive the expression for theoutput current in push ?pull amplifier with base current as ib = Ibm sinwt. [8]

5. A single tuned direct coupled amplifier feeds a load RL=100KΩ.The resonant fre-quency is 1 MHz, L=500 µH, Q=50. The transistor has the following parametersgm=1.5 mA/V , rO= 50kΩ. Find

(a) Gain at resonance with load RL not connected.

(b) Gain at resonance with load RL connected.

(c) Bandwidth with load

(d) Bandwidth without load. [16]

6. (a) Explain in detail about the Instability caused in tuned amplifiers at highfrequencies?

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(b) What is the importance of Stagger tuning? Explain briefly about Staggertuned amplifiers? [8+8]

7. (a) Explain how zener diode is used for voltage regulation and also find its powerdissipation?

(b) An unregulated dc power supply provides a dc voltage that can vary be-tween 18 and 22V. Design a 15 Volt zener voltage regulator for a load havingIL(min)=20mA and. IL(max)=120mA. Specify resistor and zener diode valuesincluding power ratings. [8+8]

8. (a) Using three pin voltage regulator, design a current source that will deliver0.25A current to 48 ohms 10W load. From data sheet IQ =4.2 mA and VR

=5V [6]

(b) Compare IC 723 and IC78XX Voltage Regulators [4]

(c) What is UPS and explain how it differs from regulated power supply? [6]

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1. (a) Draw the circuit diagram of CB- amplifier and its h-parameter equivalentcircuit. List out the characteristics of a CB amplifier.

(b) In a single stage CB amplifier circuit, RE = 20K,RC = 10K,VEE = −20V, VCC =20V,RL = 10KandRS = 0.5K. Find AI , Ri, Ro, AV . (8+8)

2. (a) Explain the significance of Miller’s theorem in transistor circuit analysis.

(b) Draw the circuit diagram of Difference amplifier and explain its operation.

(c) Write a short note on Gain-Bandwidth product of amplifiers. [6+5+5]

3. Derive all components in the Hybrid - π model in terms of h parameters in CEconfiguration. [16]

4. (a) In transformer coupled Class - A power amplifier, show that the conversionefficiency is 50%. [8 ]

(b) Discuss in detail the cross-over distortion. How do you avoid the cross overdistortion in power amplifier circuit? Discuss in detail. [8]

5. (a) Why do we use tuned amplifiers in the IF and RF range?

(b) Explain in detail how do you alter the bandwidth of an RF amplifier which is

i. Single tuned

ii. Double tuned

iii. Stagger tuned. [8+8]



7. (a) The voltage regulator in Figure 7amaintains an output voltage of 25 V.

i. What value of Rsc should be used to limit the maximum current to 0.5A?

ii. With the value of Rsc found in (i) what will be the output voltage whenRL= 100 ohms? When RL =10 ohms?

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Figure 7a

(b) Draw and explain the regulator which will provide the foldback limiting .[8+8]

8. (a) The basic Switching regulator is designed to maintain a 12V dc output whenthe unregulated input voltage varies from 15V to 24V. When pass transistoris conducting, its collector to emitter saturation voltage is 0.5V. Assumingthat the load is constant and the LC filter is ideal, find the minimum andmaximum duty cycles of the pulse width modulator.

(b) Write the Features and Applications of DC/DC converters [8+8]

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1. (a) Draw the circuit of an Emitter follower and its equivalent circuit. List out itscharacteristics.

(b) Design a single stage Emitter follower having Ri=500K Ω and Ro=20Ω. As-sume hfe = 50, hie = 1K, hoe = 25µA/V. [8+8]

2. A two stage FET RC coupled amplifier has the following parameters: gm = 10mA/V,rd = 5.5K and Rg = 0.5 M for each stage. Assume CS is arbitrarily large.

(a) What must be the value of Cb in order that the frequency characteristic ofeach stage be flat within 1 dB down to 10 Hz ?

(b) Repeat the above part if the overall gain of both stages is to be down 1 dB at10 Hz.

(c) What is the overall mid band voltage gain ? [8+4+4]

3. (a) What are the typical values of various components in Hybrid - π model? Showthat at low frequencies the Hybrid - π model with rb′e and rce taken as infinitereduces to the approximate CE h- parameter model.

(b) The following low- frequency parameters are known for a given transistor atIC = 10mA, VCE =10 V, and at room temperature,hie = 500 Ωhoe = 4x10−5 A/Vhfe = 100hre = 10−4.At the same operating point, fT = 50MHz and Cc=3PF, compute the valuesof all the Hybrid - π parameters [8+8]

4. (a) Draw the circuit of class -A series fed power amplifier and derive the expressionfor output power Po. [10]

(b) Draw and discuss the operation of Class - C power amplifier. [6]

5. (a) Draw the circuit of a Single tuned Inductively coupled amplifier?

(b) Derive the expressions for

i. Effective Q-factor (Qe)

ii. Voltage gain (A)

iii. Voltage gain at resonance (Ares). [6+10]

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6. Draw and explain the circuit diagram of two tuned amplifier configurations that donot suffer from Miller effect? [16]

7. (a) What is Voltage regulator? Explain with the help of neat circuit diagram howzener diode is used as a shunt voltage regulator?

(b) In figure 7 shown Vi=20V, Rs=200 ohms and Vz=12V, VBE =0.65V findoutput voltage, collector to emitter voltage of the transistor and the currentin 200 ohms resistor? [8+8]

Figure 7

8. (a) Explain how three terminal IC 7805 is used as a current source with a neatcircuit diagram. [8]

(b) What is a Voltage multiplier? Draw and explain any one circuit of it and giveits applications. [8]

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1. (a) Draw the circuit diagram and low frequency equivalent circuit of commonsource amplifier and derive an expression for its voltage gain.

(b) For the emitter follower circuit with RS = 0.5K and RL = 5K, calculateAI , Ri, AV , AV S, and R0. Assume , hfe = 50, hie =1K, hoe = 25 µA/V.[8+8]

2. (a) For the Cascode transistor configuration, which consists of CE stage in serieswith CB stage, verify that the cascode combination acts like a single CEtransistor with negligible internal feedback.

(b) If two identical cascaded stages have an overall upper 3-dB frequency of 20KHz and a lower 3-dB frequency of 20 Hz. What are fL and fH of each stage?Assume non interacting stages? [8+8]

3. (a) Draw Hybrid - π model for a transistor in the CE configuration and explainthe significance of every component in this model.

(b) Given a germanium p-n-p transistor whose basewidth is 10−4 cm. At roomtemperature and for a dc emitter current of 2 mA, find

i. emitter diffusion capacitance,

ii. fT [Assume Diffusion constant as 47 cm2/sec]. [8+8]

4. (a) Discuss distortions in large signal amplifier circuits. Show that in power ampli-fiers, the total power output is approximately1% higher than the fundamentalpower, when the distortion is 10%. [8]

(b) Discuss the push pull complementary circuit and show that no even harmonicsare present [8]

5. (a) Draw the circuit of a Single tuned Inductively coupled amplifier?

(b) Derive the expressions for

i. Effective Q-factor (Qe)

ii. Voltage gain (A)

iii. Voltage gain at resonance (Ares). [6+10]



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7. (a) The voltage regulator in Figure 7amaintains an output voltage of 25 V.

i. What value of Rsc should be used to limit the maximum current to 0.5A?

ii. With the value of Rsc found in (i) what will be the output voltage whenRL= 100 ohms? When RL =10 ohms?

Figure 7a

(b) Draw and explain the regulator which will provide the foldback limiting .[8+8]

8. (a) Using three pin voltage regulator, design a current source that will deliver0.25A current to 48 ohms 10W load. From data sheet IQ =4.2 mA and VR

=5V [6]

(b) Compare IC 723 and IC78XX Voltage Regulators [4]

(c) What is UPS and explain how it differs from regulated power supply? [6]

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II B.Tech I Semester Supplementary Examinations, November 2011ELECTRICAL MACHINES - I



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1. (a) Explain the mechanical energy and work done in singly excited system whenactual displacement occurs?

(b) An electromechanical device has following self and mutual inductances.L11= L22= 1.6 + cos2θ andL12= 1 + 0.4cosθ. Find the expression for torque asa function of θ. Find Tav forθ = 30o. when coils are connected to a voltagesource of 160 sin 314t, find Tav for θ= 30o.

[8+8]

2. (a) A DC generator is connected with lap winding. The numbers of poles inmachine are 6. If the resistance of each conductor is 2 milliohm and if thereare 60 slots with 4 conductors in each slot, find the resistance of armature.Repeat the calculation if the winding is wave winding.

(b) Explain the terms equalizer rings and dummy coils? With which windingsthey are related? [10+6]

3. (a) Explain about demagnetizing Ampere turn per pole and Cross magnetizingAmpere Turn per pole.

(b) What is the purpose of compensating winding? Explain in detail. [8+8]

4. What is critical speed? How do you draw magnetization characteristics in labora-tory. [16]

5. (a) Enumerate the reasons which cause terminal voltage under load conditions tobe different from terminal voltage under no-load conditions for a DC shuntgenerator. Give the applications of shunt generator

(b) A separately excited generator with constant excitation is connected to a con-stant load. When the speed is 1200 rpm, it delivers 120A at 500V. At whatspeed will the current be reduced to 60A ? Armature resistance is 0.1 ohm,Contact drop/brush is 1V. Armature reaction may be ignored. [8+8]

6. (a) Define torque. Derive the expression for torque developed by a D.C. motorfrom fundamentals.

(b) Determine the torque developed when a current of 30A passes through thearmature of a motor with the following particulars: lap winding, 310 conduc-tors, 4-pole, pole-shoes 16.2 cm long subtending an angle of 600 at the centre,bore radius 16.2 cm, flux density in air gap 0.7 tesla. [8+8]

7. (a) Explain the ’above normal speed’, speed control of DC motor. How this controlis achieved? Explain why speed is above normal?

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(b) A 220 V series motor runs at 700 RPM when operating at full load current of 20Amp. The motor resistance is 0.5 Ω. Assume magnetic path is un-saturable.What will be the speed if:

i. Load torque is increased by 44%

ii. Motor current = 10 Amp. [6+10]

8. (a) Explain constant and variable losses. Draw the graph of losses v/s load.

(b) A 60 kW, 250 V shunt motor takes 16 Amp, when running light at 1440 RPM.The hot resistance of the armature and field are 0.2 Ω and 125 Ω respectively.

i. Estimate the efficiency of the motor when taking 152 A.

ii. Also estimate the efficiency if working as generator and delivering a loadcurrent of 151 A at 250 V. [6+10]

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1. With the help of neat diagram obtain the expression for the energy stored in amagnetic system for a simple attracted armature type relay. Explain the operationof system. [16]

2. (a) Explain the construction of brushes in DC machines. Explain the type ofmaterial used and specific reason for the same?

(b) A DC generator is operating at a voltage of 200 V and supplying a load of300 Amps. When the load was thrown off, the terminal voltage raises to 213Volts. Find the resistance of armature if brush voltage drop is 0.5 Volts perbrush. Also find the total conductors required to obtain the rated voltage, ifarmature is wound with lap winding and flux per pole is 30 mwb, and whenarmatune is to rotated at 1000 RPM. [6+10]

3. (a) What are the causes of sparking in a d. c. machine? Explain how commutationis improved by use of inter poles.

(b) A 22.38 kW, 400-V, 2-pole wave-wound d.c., shunt motor has 840 armatureconductors and 140 commutator segments. Its full-load efficiency is 88% andthe shunt field current is 1.57A. If brushes are shifted backward through 1.5segments from the geometrical neutral axis, find the demagnetizing and dis-torting amp-turn /pole.

[8+8]

4. What is critical speed? How do you calculate the critical speed in laboratory. [16]

5. (a) What are the reasons for the parallel operation of DC generators?

(b) What are the conditions necessary for parallel operation of DC shunt genera-tors?

(c) Explain the procedure of parallel operation of DC shunt generators. [4+4+8]

6. (a) What is the significance of back e.m.f in a DC motor?

(b) Deduce the condition for maximum power of a DC motor.

(c) A 12-pole lap connected 230V shunt motor has 410 conductors. It takes 41A onfull-load. The flux per pole is 0.05 Wb. The armature and field resistances are0.1 ohm and 230 ohms respectively. Contact drop per brush is 1V. Determinethe speed of motor at full-load. [6+6+4]

7. (a) Explain what would happen if DC motor is switched ON to supply directly.

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(b) A 4 pole DC series fan motor takes an armature current of 60 Amp, whenrunning steadily at 2000 RPM on a 220 V supply. The four field coils arenow connected in two parallel groups of two in series. Assuming that the fluxproduced is directly proportional to the exciting current and the load torqueincreases as the square of the speed, find the new speed and the armaturecurrent. Assume there is no change in supply voltage. [6+10]

8. (a) A 220 V, 12 kW shunt motor has a maximum efficiency of 91% and a speedof 750 rpm., when delivering 85 % of its rated out put. The resistance of itsshunt field is 120 Ω. Determine the efficiency and speed when motor draws acurrent of 75 A from the mains.

(b) A 400 V shunt motor develops an out put of 20 kW when taking 23.25 kW.Field resistance is 210 Ω and the armature resistance is 0.32 Ω. What is theefficiency and power input when, output is 11.5 kW. [8+8]

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1. (a) With i−λ curve explain the coenergy and importance of coenergy.

(b) Two coupled coils have self and mutual inductances ofL11= L22= 4+, 1

2xand L12 = 1

4x=.IfI1= 5AmpandI

2= −2Amp. Find the ex-

pression for force of field origin as function of x and mechanical work done, asx changes from 1 m to 30 cm. [8+8]

2. (a) Explain why carbon and graphite are preferred as brush material? What areadvantages of these materials above any other material?

(b) A 6 pole DC generator has flux per pole of 0.03 wb and winding is connectedin lap with 600 conductors. Calculate the generated EMF on open circuitwhen it runs at 800 rpm. If the armature is wave wound what should be thechange in flux to obtain double the voltage as in previous. [8+8]

3. (a) Explain the effects of armature reaction in a d. c. generator.

(b) Determine per pole the number

i. of cross-magnetizing ampere-turns

ii. of back ampere-turns and

iii. of series turns to balance the back ampere-turns in the case of a.d.c.generator having the following data500 conductors, total current 100A, 4 poles, 2-circuit wave winding, angleof lead = 100, leakage coefficient = 1.3. [8+8]

4. (a) What is the necessity of residual pole flux in a self excited generator?

(b) Explain the various methods of connection of the field winding to the armaturein a DC generator. [6+10]

5. Six DC generators are running in parallel, each having an armature resistance of0.15 ohm, running at the same speed and excited to give equal induce e.m.f(s).All generators share load equally at a terminal voltage of 500V. The total load is360KW. If the field current of one generator is raised by 5% and the speed remainsconstant, Calculate

(a) New Terminal Voltage

(b) Output of each machine. [16]


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7. (a) Compare the speed control of DC motor by rheostat control method and speedcontrol by semiconductor devices.

(b) A DC shunt motor is required to supply a load requiring a constant torque of120 Nm, over a speed of 500 to 2000 RPM.

i. Explain the three methods of obtaining the required speed range.

ii. For each method above specify the base speed and power rating. [8+8]

8. (a) With neat diagram explain the Swinburne’s test conducted on DC shunt mo-tors. What are the advantages and limitations of this test? Enumerate allcalculations.

(b) The Hopkinson’s test on two machines gave the following results for full load:Line voltage 250 V, line current (excluding field current) = 50 A. Motor ar-mature current = 380 Amp. Field currents are 5 A and 4.2 A. Calculate theefficiency of each machine. Armature resistance of each machine = 0.02Ω.

[6+10]

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1. (a) Explain the operational differences of singly excited and multiple excited sys-tems.

(b) In a rectangular electromagnetic relay, the exciting coil has 2000 turns andcross sectional area of 30 cm2. Neglect reluctance of magnetic path, resistanceof coil. When the coil is excited with a sinusoidal voltage source of 45 V(RMS), 60 Hz and armature is held at 1.5 cm, find the force on the armature.

[8+8]

2. (a) What is duplex winding? How it differs from simplex winding. What are theadvantages and limitations of duplex winding?

(b) A 4 pole DC generator has a lap wound armature with 42 slots. The ratedoutput voltage of generator is 400 V when supplying a current of 150 Ampat a speed of 1000 RPM. The resistance of armature circuit is 25 milliohmsand brush drop is 0.75 volts/brush. The flux per pole is 50 mWb. Calculatethe effective number of conductors per slot and then find the actual fluxesrequired. [8+8]

3. (a) What are the causes of sparking in a d. c. machine? Explain how commutationis improved by use of inter poles.

(b) A 22.38 kW, 400-V, 2-pole wave-wound d.c., shunt motor has 840 armatureconductors and 140 commutator segments. Its full-load efficiency is 88% andthe shunt field current is 1.57A. If brushes are shifted backward through 1.5segments from the geometrical neutral axis, find the demagnetizing and dis-torting amp-turn /pole.

[8+8]

4. What is critical speed? How do you draw magnetization characteristics in labora-tory. [16]

5. (a) Discuss in detail the characteristics and applications of DC Shunt, series andcompound generators

(b) Explain the conditions necessary for the parallel operation of DC generators.[10+6]


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7. (a) A DC shunt motor is running at certain speed. Discuss the effect on the speedof this motor, if its

i. Line voltage is reduced to half.

ii. Armature voltage is reduced to half keeping field voltage constant

iii. Armature voltage kept constant and field voltage reduced to half.

iv. Armature voltage doubled and field voltage halved.

(b) A 200 V DC shunt motor takes 27 A at rated voltage and runs at 800 RPM.Its field resistance is 100 Ω. If an additional resistance of 20 Ω is inserted inthe armature circuit, compute the motor speed and the line current in casethe load torque varies as the square of the speed. [8+8]

8. (a) Explain the Testing method to separate rotational losses in DC machine.

(b) Two identical DC machines when tested by Back to back method gave thefollowing test results: Field currents are 2.5 A and 2 A. Line voltage is 220V. Line current including both field current is 10 A. Motor armature currentis 73 A. The armature resistance of each machine is 0.05 Ω. Calculate theefficiency of both machines. [6+10]

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II B.Tech I Semester Supplementary Examinations, November 2011SIGNALS AND SYSTEMS

( Common to Electronics & Communication Engineering, Electronics &Instrumentation Engineering, Bio-Medical Engineering, Electronics &

Control Engineering and Electronics & Telematics)Time: 3 hours Max Marks: 80


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1. (a) Define mean square error and derive the expression for evaluating mean squareerrors.

(b) A rectangular function f(t) is defined by

f (t) =

1 0 < t < Π−1 Π < t < 2Π

Approximate above function by a waveform Sin t over the interval (0,2π) suchthat the mean square error is minimum. [8+8]

2. (a) Derive polar Fourier series from the exponential Fourier series representationand hence prove that Dn = 2 |Cn|

(b) Show that the magnitude spectrum of every periodic function is Symmetricalabout the vertical axis passing through the origin. [8+8]

3. (a) Find the Fourier Transform of the time function given figure 3a.

Figure 3a

(b) Find Fourier Transform of x(t) = e−a|t|, a > 0 [8+8]

4. (a) What is a LTI System? Explain its properties. Derive an expression for thetransfer function of a LTI system.

(b) Find the impulse response to the RL filter shown figure 4b. [8+8]

Figure 4b

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5. (a) A waveform m(t) has a Fourier transform M(f) whose magnitude is as shownin figure 5a. Find the normalized energy content of the waveform.

Figure 5a

(b) The signal V(t) = cos ω0t + 2sin 3 ω0t + 0.5 sin 4ω0t is filtered by an RC lowpass filter with a 3 dB frequency.fc =2f0. Find the output power So.

(c) State parseval’s theorem for energy X power signals. [6+6+4]

6. (a) Consider the signal x(t) =(

sin 50Πt

Πt

)2which to be sampled with a sampling

frequency of ωs = 150Π to obtain a signal g(t) with Fourier transform G(jω ).Determine the maximum value of ω0 for which it is guaranteed thatG(jω) = 75× (jω) for |ω| ≤ ω0 where X(jω) is the Fourier transform of x(t).

(b) The signal x(t) = u(t + T0) − u(t − T0) can undergo impulse train samplingwithout aliasing, provided that the sampling period T< 2T0. Justify.

(c) The signal x(t) with Fourier transform X(jω) = u(ω + ω0) − u(ω − ω0) canundergo impulse train sampling without aliasing, provided that the samplingperiod T < π/ω0. Justify. [6+5+5]

7. (a) State the properties of the ROC of L.T.

(b) Determine the function of time x(t) for each of the following laplace transformsand their associated regions of convergence. [8+8]

i. (s+1)2

s2−s+1Re S > 1/2

ii. s2−s+1(s+1)2

Re S > −1

8. (a) Find the Z-transform and ROC of the signalx[n] = [4. (5n)− 3 (4n)] u(n)

(b) Find the Z-transform as well as ROC for the following sequences: [8+8]

i.(

13

)

n

u(−n) and

ii.(

13

)

n

[u(−n)− u(n− 8)]

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1. (a) Sketch the following signals

i. Π(

t−12

)

+Π(t− 1)

ii. f(t) = 3u(t) + tu(t)− (t− 1)u(t− 1)− 5u(t− 2)

(b) Evaluate the following Integrals [8+8]

i.5∫

0

δ(t)Sin2Πtdt

ii.α∫

−α

−αt2

e δ(t− 10)dt

2. (a) Use the defining equation for the Fourier Series Coefficients to evaluate theFourier series representation for the following signals.

i. x(t) = Sin(3πt) + Cos(4πt)

ii. x (t) =α∑

m=−α

δ (t−m/3) + δ (t− 2m/3) [5+5]

(b) Determine the time domain signal represented by the following coefficients.[6]

Cn = −jδ (n− 2) + j δ (n+ 2) + 2 δ (n+ 3) + 2 δ (n+ 3) , ω0 = π

3. (a) Find the Fourier Transform of the following time function f(t) = e−at cos w0tu(t)

(b) State and prove frequency differentiation and integration properties of FourierTransform. [8+8]

4. (a) Explain how input and output signals are related to impulse response of a LTIsystem.

(b) Let the system function of a LTI system be 1jw+2

. What is the output of the

system for an input (0.8)t u (t). [8+8]

5. (a) The waveform V(t)= e−t/Γ u(t) is passed through a high pass RC circuit havinga time constant Γ.

i. Find the energy spectral density at the output of the circuit.

ii. Show that the total output energy is one half the input energy.

(b) Find the cross correlation of the functions sin ωt and cos ωt. [8+8]

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sin 50ΠtΠt







i. (s+1)2

s2−s+1Re S > 1/2

ii. s2−s+1(s+1)2

Re S > −1

8. (a) Using the Power Series expansion technique, find the inverse Z-transform ofthe following X(Z):

i. X(Z) = Z2Z2

−3Z+1|Z| < 1

2

ii. X(Z) = Z2Z2

−3Z+1|Z| > 1

(b) Find the inverse Z-transform of [8+8]X(Z) = Z

Z(Z−1)(Z−2)2|Z| > 2

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1. (a) Define and sketch the following signals

i. Real exponential signals for C 6= 0α > 0

ii. Even continuous time signal

iii. Unit doublet

iv. Real part of damped complex exponential for α 0

(b) Evaluate the following integrals

i.∫

α

αδ (t+ 3)

−t

e dt

ii.∫

α

α[δ (t) cos t+ δ (t− 1) sin t] dt

(c) Discuss the signal with a neat sketch. [8+4+4]



3. (a) State and prove time convolution and time differentiation properties of FourierTransform.

(b) Find and sketch the Inverse Fourier Transform of the Waveform shown infigure 3b. [8+8]

Figure 3b

4. (a) Transfer function of a LPF is given by

H (w) =

1, |w| < wc

0, |w| > wc

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Show that its impulse response is non-causal. What do you do to make itcausal? What is its physical significance.

(b) Find the response e(t) of the electric circuit shown figure 4b below for theinput i (t) = e−tu (t). [8+8]

Figure 4b

5. Find the power of periodic signal g(t) shown in figure 5c. Find also the powers of[4×4]

(a) -g(t)

(b) 2g(t)

(c) g(t).

Figure 5c


sin 50Πt

Πt

)2

which to be sampled with a samplingfrequency of ωs = 150Π to obtain a signal g(t) with Fourier transform G(jω ).Determine the maximum value of ω0 for which it is guaranteed thatG(jω) = 75× (jω) for |ω| ≤ ω0 where X(jω) is the Fourier transform of x(t).



7. (a) Determine the Laplace transform and the associate region convergence foreach of the following functions of time.

i. x(t) = 1 0 ≤ t ≤ 1

ii. x(t) =t 0 ≤ t ≤ 1

2− t 1 ≤ t ≤ 2

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(b) State and prove initial value theorem of L.T. [10+6]

8. (a) State the properties of the ROC of Z.T.

(b) Find the Z-transform of the sequences. [8+8]

i. δ [n]

ii. u[n].

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1. (a) Define and sketch the unit step function and signum function bring out therelation between these two functions.

(b) Explain the Graphical Evaluation of a component of one function in otherfunction. [6+10]



3. (a) Explain the concept of Fourier Transform for periodic signals.

(b) Find out the Fourier Transform of the periodic pulse train shown figure 3b.[8+8]

Figure 3b

4. (a) Explain the difference between the following systems.

i. Time invariant and time invariant systems.

ii. Causal and non-causal systems.

(b) Consider a stable LTI system characterized by the differential equation d2y(t)dt2

+

4dy(t)dt

+3y (t) = dx(t)dt

+2x (t). Find its impulse response and transfer function.[8+8]

5. (a) For the signal g(t) = 2a/(t2+a2 ),determine the essential Band width B Hzof g(t) such that the energy contained in the spectral components of g(t) offrequencies below B Hz is 99% of signal energy Eg.

(b) Show that the auto correlation function of g(t)=C cos (ω0t+ θ0) is given byRg(τ)=(c2/2) cos ω0 τ ,and the corresponding PSD isSg (ω) = (c2π/2) [δ (ω − ω0) + δ (ω + ωo) . [8+8]

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sin 50ΠtΠt







i. (s+1)2

s2−s+1Re S > 1/2

ii. s2−s+1(s+1)2

Re S > −1

8. (a) Find the inverse Z-transform of the following X(z).

i. X(Z) = log(

11−az−1

)

, |z| > |a|

ii. X(Z) = log(

11−a−1z

)

, |z| < |a|

(b) Find the Z-transform X(n) x[n] =(

12

)nu[n] +

(

13

)nu[−n− 1]. [8+8]

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II B.Tech I Semester Supplementary Examinations, November 2011DATA BASE MANAGEMENT SYSTEMS




1. (a) Explain the Transaction management in a database.

(b) Discuss the Query Processor of Database system structure. [8+8]

2. (a) What is a relation? Differentiate between relation schema and relation in-stance. Define the terms unity and degree of relation. What are domainconstraints?

(b) What SQL construct enables the definition of a relation? What constructsallow modification of relation instances? [8+8]

3. Write the Equivalence Rules for the transportation of Real Expressions. [16]

4. (a) Explain about 4 Nf? Give one example?

(b) Explain about 5 Nf? Give one example? [8+8]

5. (a) Define the concept of schedule for a set of concurrent transaction. Give asuitable example. [8]

(b) Explain read-only, write-only & read-before-write protocols in serialazability.[8]

6. (a) What are the merits & demerits of using fuzzy dumps for media recovery. [6]

(b) Explain the phases of ARIES Algorithm. [4]

(c) Explain 3 main properties of ARIES Algorithm [6]

7. Explain about various physical storage media in detail. [16]

8. Explain about the B -tree and the structure of B+

−tree in detail with an example.

[16]

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1. Explain the advantages of a database system over conventional file-processing sys-tem. [16]

2. (a) What is a foreign key constraint? Why are such constraints important? Whatis referential integrity?

(b) How many distinct tuples are in a relation instance with cardinality 22? [8+8]

3. Describe the multi valued dependency. Is the decomposition in 4NF always depen-dency preserving and loss less justify your answer with the help of an example.

[16]



5. Give an example schedule wit actions of transactions T1 & T2 on objects X & Ythat results in a

(a) Write-read conflict

(b) Read-write conflict

(c) Write-write conflict [16]

6. (a) What are the merits & demerits of using fuzzy dumps for media recovery. [6]

(b) Explain the phases of ARIES Algorithm. [4]

(c) Explain 3 main properties of ARIES Algorithm [6]

7. (a) Explain about tertiary storage media in detail.

(b) Explain about Buffer Manager. [8+8]

8. Why is a hash structure not the best choice for a search key on which range queriesare likely. [16]

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1. (a) Describe about the three levels of Data Abstraction.

(b) What are the types of languages a database system provides? Explain. [8+8]

2. (a) Define all the variations of join operation, why special attention is given forthis?

(b) Define the division operation in terms of basic relational algebra operations.Describe a typical query that calls for division. Unlike join, the division oper-ator had not special attention in database, Explain. Why? [8+8]

3. (a) Explain in detail the 2 ways of executing pipeline?

(b) Write the SQL expressions for the following relational database? [6+10]sailor schema (sailor id, Boat id, sailorname, rating, age)Recerves (Sailor id, Boat id, Day)Boat Schema (boat id, Boatname, color)

i. Find the age of the youngest sailor for each rating level?

ii. Find the age of the youngest sailor who is eligible to vote for each ratinglevel with at lead two such sailors?

iii. Find the No.of reservations for each red boat?

iv. Find the average age of sailor for each rating level that at least 2 sailors.

4. (a) What is Normaliztion?give types of normalization

(b) What are the advantages of normalized relations over the un normalized rela-tions? [8+8]

5. (a) Define the concept of schedule for a set of concurrent transaction. Give asuitable example. [8]

(b) Explain read-only, write-only & read-before-write protocols in serialazability.[8]

6. (a) What information does the dirty page table & transaction table contain. [6]

(b) Explain how does crash & media failure occurs [10]

7. (a) Explain about Clustering File Organistaion.

(b) Explain about Heap File Organization. [8+8]

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8. What are the causes of bucket overflow in a hash file organization? What can bedone to reduce the occurrence of bucket overflows? [16]

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1. (a) What are the types of languages a database system provides? Explain.

(b) What are the five main functions of a Database Administrator? [8+8]

2. (a) What is a foreign key constraint? Why are such constraints important? Whatis referential integrity?

(b) How many distinct tuples are in a relation instance with cardinality 22? [8+8]

3. (a) What is functional dependency ? how it is useful in dbms?

(b) Normalize the relation R (A, B, C, D, E, F, G, H) into the 3NF using thefollowing set of FDs ABC, BCD, CDEABH, BHA, DEF is the decompositiondependency preserving? [8+8]



5. (a) Define Transaction & Schedule with suitable Example. [8]

(b) With suitable example explain ACID properties. [8]

6. (a) can a second end checkpoint record be encountered during the Analysis phase.[5]

(b) How is checkpointing done in ARIES. [6]

(c) What are the similarities & difference between checkpoint & fuzzy dumps.[5]

7. Give an example of a database application in which the pointer method of repre-senting variable-length records is preferable to the reserved-space method. Explainyour answer. [16]

8. Explain all the operations on B+

−tree by taking a sample example. [16]

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