DISCRETE MATHEMATICAL STRUCTURES · b) Trace the execution of quick sort algorithm on the following data set {E, X, A, M, P, L, E}. 7M 2. a) Write the merge sort algorithm. 7M b)

Hall Ticket No: Question Paper Code : A3505

VARDHAMAN COLLEGE OF ENGINEERING

(AUTONOMOUS) B. Tech III Semester, End Semester Regular Examinations, November - 2016

(Regulations: VCE-R15) DISCRETE MATHEMATICAL STRUCTURES

(Common to Computer Science and Engineering & Information Technology) Date: 15 November, 2016 FN Time: 3 hours Max Marks: 75

Answer ONE question from each Unit All Questions Carry Equal Marks

Unit - I 1. a) If a proposition q has the truth value 1, determine all truth value assignments for the

primitive propositions p, r and s for which the truth value of the following compound proposition is 1.

qrssrpq

7M

b) Prove the following: i. rqprqp ii. rrprqrqp

8M

2. a) Test whether the following arguments are valid: .

________

i p qr sp s

q s

.

________

ii p qr s

q s

p r

8M

b) i. “The integer 58 is equal to the sum of two perfect squares”. Express this statement in symbolic form using quantifiers.

ii. Find the negation of the following quantified statement yxryxqyxpyx ,,,,,

7M

Unit – II 3. a) Define reflexive, symmetric and transitive relations and give examples for each. 7M b) Let P = 1, 2, 3, 4, 6, 12 and be the relation on P such that x y if and only if x

divides y. Draw the Hasse diagram for the poset (P, ).

8M

4. a) Prove that identity element in a group is unique. 7M b) If the functions CBgBAf :,: are one-one and onto, prove that CAfg :

is one-one and onto.

8M

Unit – III 5. a) Define distributive lattice and hence prove that every chain is a distributive lattice. 7M b) Define graph isomorphism. Verify that the following two graphs are isomorphic or not:

8M

Cont…2

::2::

6. a) i. Let G be a 4-regular connected planar graph having 16 edges. Find the number of regions of G.

ii. Show that if a planar graph G of order n an size m has r regions and k components, then n-m+r = k+1.

6M

b) Define chromatic number. Find the chromatic number of the following graph:

9M

Unit – IV 7. a) There are 30 females and 35 males in junior class while there are 25 females and

20 males in senior class. In how many ways can a committee of 10 be chosen so that there are exactly 5 females and 3 juniors in the committee?

8M

b) How many 6 digit numbers without repetition of digits are there such that the digits are all non zero and 1, 2 do not appear consequently in either order.

7M

8. a) State and prove Binomial theorem. Find the number of terms in (2a+5b)6 using Binomial theorem.

7M

b) State and prove multinomial theorem. Find the coefficient of x14x2

5x36x4

3 in (x1+x2+x3+x4)18 using multinomial theorem.

8M

Unit – V 9.

a) Find the solution of 3

16;4,2,0124 1021 aanaaa nnn by the method of

Characteristic roots.

8M

b) Solve the recurrence relation 121 nfornaa nn , where 70 a by substitution

method.

7M

10. a) Solve the recurrence relation 308126 321 nforaaaa nnnn using generating functions.

8M

b) If a0=0, a1=1, a2=4, a3=37 solve the recurrence relation an+2+ban+1+can=0 for n≥0. 7M




(Regulations: VCE-R15) COMPUTER ORGANIZATION AND MICROPROCESSORS

(Computer Science and Engineering) Date: 17 November, 2016 FN Time: 3 hours Max Marks: 75


Unit - I 1. a) Illustrate the responsibilities of the functional units of a computer. 7M b) A digital computer has a common bus system for 4 registers of 4 bits each. The bus

constructed with multiplexers: i. How many selection lines are there in each multiplexer ii. What size of multiplexers are needed iii. How many multiplexers are there in the bus? Also draw the bus system

8M

2. a) Explain register transfer language with control function and block diagram. 8M b) Represent the following conditional control statement by two register transfer

statements with control functions: If(P=1) then(R1←R2) else if (Q=1) then (R1←R3)

7M

Unit – II

3. a) Describe how microinstructions are arranged in control memory and how they are Interpreted.

8M

b) Explain the difference between hardwired control and micro programmed control. Is it possible to have a hardwired control associated with a control memory.

7M

4. a) What do you mean by micro operations? Explain arithmetic micro operations in details. 8M b) Draw a flowchart for adding and subtracting two fixed point binary numbers where

Negative numbers are signed 1’s complement presentation.

7M

Unit – III

5. a) List the addressing modes of 8086 with one example each. 8M b) Tabulate the differences between minimum and maximum mode of operations.

7M

6. a) Explain the memory organization of 8086 microprocessor. Draw the timing diagram of a typical memory write machine cycle.

8M

b) Briefly explain about the flag register of 8086 microprocessor.

7M

Unit – IV

7. a) What are different branch transfer instructions? Explain them with examples. 7M b) Write an assembly language program in 8086 to sort the given numbers in ascending

order. 8M

8. a) Write a program to calculate the sum of series of numbers. The length of the series is in

memory location 4200H and the series begins from memory location 4201H. Consider the sum to be 8 bit number. So, ignore carries. Store the sum at memory location 4300H.

8M

b) What is MACRO? Explain nested macro with examples.

7M

Cont…2

::2::

Unit – V 9. a) Explain the control word format for 8255 PPI. Write initialization sequence for 8255 PPI in

I/O mode, mode 0 with port A, port B as output and port C as input with address of port A as FFOOH.

8M

b) Write an assembly language program to rotate the stepper motor in anticlockwise direction by N steps.

7M

10. a) Elaborate the procedure for interfacing 4X4 keyboard with 8086 processor. 8M b) Interface two 8255 PPI’s to 8086 microprocessor in order to access 16 bit data using the

I/O space 3000H to 3007H. 7M



(AUTONOMOUS) B. Tech III Semester End Semester Regular Examinations, November - 2016

(Regulations: VCE-R15) DESIGN AND ANALYSIS OF AGORITHMS

(Common to Computer Science and Engineering & Information Technology) Date: 22 November, 2016 FN Time: 3 hours Max Marks: 75


Unit – I

1. a) Set up and solve a recurrence relation for the number of calls made by F(n), the recursive algorithm for computing n!.

8M

b) Trace the execution of quick sort algorithm on the following data set E, X, A, M, P, L, E.

7M

2. a) Write the merge sort algorithm. 7M b) Design a recursive algorithm for computing 2n for any non-negative integer n which is

based on the formula: 2n = 2n-1 + 2n-1. Draw a tree of recursive calls for this algorithm and count the number of calls made by the algorithm.

8M

Unit – II

3. a) Write the pseudo code for Kruskal’s algorithm. Solve the following graph for its minimum spanning tree:

9M

b) Explain the problem of Job sequencing with deadlines using an example.

6M

4. a) Explain Optimal storage on tapes using greedy technique. 6M b) Solve the following 0/1 knapsack problem where M=40 and N=4 using greedy technique.

Weights [W1, W2, W3, W4] = [20, 25, 10, 15] Profits [P1, P2, P3, P4] = [20, 40, 35, 45]

9M

Unit – III

5. a) Explain matrix chain multiplication. 6M b) Find the optimal tour by using travelling sales person problem using dynamic

programming:

0 10 15 205 0 9 106 13 0 128 8 9 0

9M

6. a) What is the Dynamic Programming? Write algorithm for generating optimal solution of the knapsack problem.

7M

b) Discuss about all pairs shortest path problem and find optimal path for each pair of nodes for the following graph.

8M

Cont…2

::2::

Unit – IV

7. a) Describe in detail how to traverse a graph by using breadth first traversal. 7M b) Draw and explain the tree organization of the 4-queen solution space.

8M

8. a) Apply backtracking to the problem of finding a Hamiltonian circuit in following graph:

9M

b) Write the implementation of the above algorithm.

6M

Unit – V 9. a) Explain the LC branch and bound solution for the following knapsack instance with n=4

and capacity m=15:

Object i Pi Wi 1 10 2 2 10 4 3 12 6 4 18 9

9M

b) Justify how all comparison-based sorting algorithms require nlog2(n) time.

6M

10. a) Differentiate between NP-Complete and NP-Hard problems. Give example for each category.

7M

b) Explain Cook’s theorem and its significance for NP-Hard and NP- Complete problems. 8M


VARDHAMAN COLLEGE OF ENGINEERING (AUTONOMOUS)

B. Tech III Semester End Semester Regular Examinations, November - 2016 (Regulations: VCE-R15)

OBJECT ORIENTED PROGRAMMING (Common to Computer Science and Engineering & Information Technology)

Date: 24 November, 2016 FN Time: 3 hours Max Marks: 75 Answer ONE question from each Unit

All Questions Carry Equal Marks

Unit – I

1. a) What is data type? Explain Different data types in detail. 7M b) Write a program that will read an unspecified number of integers and will determine

how many positive and negative values have been read. Your program ends when the input is 0.

8M

2. a) What is the purpose of a Method? How do you declare and invoke a method? 7M b) What is Method Overloading? Explain with an example program.

8M

Unit – II

3. a) Define Package. Write a sample program to demonstrate packages. 8M b) Create three classes with the names Shape, Rectangle and Circle and make use of

functions getdata(), printdata() and area(). To find the area of circle and rectangle, which type of inheritance is suitable? Why? Explain.

7M

4. a) How to Create Interface? When they are implemented and extended? Explain with Example.

7M

b) Write a program to calculate student grade using Inheritance.

8M

Unit – III

5. a) What is Multithreading? Explain life cycle of a thread with neat diagram. 7M b) What is file? Explain different file operations with their syntaxes.

8M

6. a) What is Priority? Explain thread priorities in detail with an example program. 8M b) What is an Exception? Explain try, catch, and throw keywords with examples.

7M

Unit – IV

7. a) What is secure applet? Differentiate applet and application. 7M b) Write an applet code to fill colors in Rectangle, circle and Square.

8M

8. a) Write a program to handle Mouse Events with Different methods. 7M b) Explain different layout managers with examples.

8M

Unit – V

9. a) How to pass parameters to applet from an HTML document? Give an example program. 8M b) What is JTree? Explain in detail with an example program.

7M

10. a) What are Swings? Explain different components available in swings. 9M b) Differentiate Swings and AWT components. 6M

Hall Ticket No: Question Paper Code: A3011



(Regulations: VCE-R15)

MANAGERIAL ECONOMICS AND FINANCIAL ANALYSIS

(Common to Computer Science and Engineering, Information Technology, Electrical and Electronics Engineering & Civil Engineering)



Unit – I

1. a) “Managerial economics is the discipline which deals with the application of economic theory to business management”. Explain.

7M

b) What is Law of Demand? Explain with the help of demand schedule and demand curve. What are the exceptions to this law?

8M

2. a) Explain the concept of income-elasticity of demand and explain its role in business decisions.

8M

b) Explain the Trend Projection method and Survey method of demand forecasting.

7M

Unit – II

3. a) Define production function. Explain the law of Variable Proportion. 7M b) Explain the concept of Least Cost Combination of Input. Why does Isoquant slope

downward and convex to origin?

8M

4. a) Describe Breakeven point with the help of diagram and its uses in business decision making.

6M

b) From the following data, you are required to calculate: i. P/V Ratio ii. Breakeven sales with the help of P/V Ratio iii. Sales required to earn a profit of Rs.4, 50, 000 Fixed Expenses = Rs.90, 000 Variable cost per unit Direct material = Rs. 5, Direct labour = Rs.2, Direct Overheads = 100% of direct labour Selling price per unit = Rs.12.

9M

Unit – III

5. a) What is Perfect Competition Market? Why is a firm under perfect competition is a price-taker and not a price-maker?

8M

b) What is monopoly? Explain features and causes of monopoly market.

7M

6. a) What is monopolistic competition? Explain its important features. 7M b) Explain any four methods of pricing with example?

8M

Unit – IV

7. a) Explain the factors affecting the requirements of Working Capital. 7M b) Define capital Budgeting. Discuss clearly the nature of capital budgeting problems. 8M

Cont…2

:: 2 ::

8. a) Define Time value of money and explain the advantages of discounted cash flow

techniques. 6M

b) XYZ Ltd. is considering two manually exclusive projects A and B whose cost of Capital is 15% the details of which are:-

Project A Project B Investments 3,00,000 3,00,000 Estimated Cash inflow

1st Year 80,000 70,000 2nd Year 1,00,000 1,20,000 3rd Year 1,30,000 1,40,000 4th Year 1,00,000 90,000 5th Year 80,000 60,000

Calculate the NPV @ 15% and profitability index. Which project should be chosen under each of these methods?

Year 1st Year 2nd Year 3rd Year 4th Year 5th Year Present value factor @15% 0.870 0.756 0.658 0.572 0.497

9M

Unit – V

9. From the following trial balance and adjustments of Swaraj Emporium, prepare trading and profit and loss account for the year ended December 31, 2015 and a balance sheet as on that date. Trial balance as on December 31, 2015

Debit balances(Dr) Rs Credit balances(Cr) Rs Sundry debtors 64,000 Sundry creditors 21,300 Opening stock 44,000 Sales 2,69,000 Cash in hand 70 Bills payable 15,000 Plant and Machinery 35,000 Capital 1,59,000 Trade expenses 2,150 Salaries 4,450 Carriage outwards 800 Rent 1,800 Purchases 2,37,740 Discounts 2,200 Land 69,000 Cash at bank 3,090 Total 4,64,300 Total 4,64,300

Adjustments: i. Closing stock was 24,900 ii. Outstanding rent Rs 170 iii. Outstanding trade expenses Rs.300 iv. Write off bad debts Rs. 800 v. Prepaid salaries Rs.450 vi. Depreciate plant and machinery @10% per annum vii. Land to be depreciated by 2% per annum

15M

10. a) What is ratio analysis? Discuss about different types of ratios. 9M b) A firm sold goods worth Rs 5,00,000 and its gross profit is 20 percent of sales value. The

inventory at the beginning of the year was Rs 16,000 and at the end of the year was Rs 14,000. Compute Inventory turnover ratio and also the inventory holding period.

6M





DATABASE MANAGEMENT SYSTEMS

(Information Technology)



Unit – I

1. a) Explain the characteristics that distinguish the database approach from traditional approach of programming with files.

7M

b) Write ER diagram for the following requirements (capture all the relationship constraints in the diagram): Consider a Mail-order database in which employees take orders for product from customers. The requirements are: i. Each Employee is identified by EMP_ID, EMP_Name and Address (Street num, area

name, city) ii. Each Customer is identified by CUST_ID, CUST_Name, Mobile Number (multiple

values) iii. Each Product is identified by Product_ID, Product_name, Price and Quantity. iv. Each Employee can take order from more than one Customer v. Each Customer can place request for more than one Product vi. Each Employee can deliver more than one Product

8M

2. a) Describe the architecture of DBMS. 8M b) Explain the functionalities of Database Administrator with examples.

7M

Unit – II

3. a) Show an example of violation of the integrity constraints. 8M b) Consider a relational database about hotels, customers (guests) and their bookings that

are maintained by an online hotel booking company. The database consisting of the following tables(where the primary keys are underlined): I. Hotel(hID, hName, hAddress, hCity) II. Guest(gID, gName, gAddress, gCity) III. Room(hID, roomNum, type, price) IV. Booking(gID, hID, roomNum, fromDate, year, noOfDays) Where, hID and gID are identifiers for the hotels and the guests, and the Booking relation indicates that a guest booked a hotel room for a specified number of days (noOfDays) starting from Date of a given year. i. Write a relational algebra expression that returns the IDs of the hotels located in

Bangalore which were not booked at all in the year 2016 ii. Write a relational algebra expression that returns the IDs of the guests who have

booked at least one room of type “suite” in every hotel located in Bangalore iii. List the guest Names whose booking count is greater than or equal to five

7M

4. a) Give a detailed account on importance and implementation of Views 7M b) Given two relations R1,R2 with N1,N2 tuples respectively state the assumptions in the

resultant about the schemas needed to make the expression meaningful and the number of tuples for the followingR1R2 , R1R2, R1 - R2 , R1 × R2 with examples

8M

Cont…2

:: 2 ::

Unit – III

5. a) What is the need for Normalization? Explain First, Second and Third normal form with example.

9M

b) What is Join dependency and Explain Fifth Normal form with example?

6M

6. a) Identify the lowest normal form the following STUDENT table instance violates and then convert to equivalent normalized form.

5M

b) Write the algorithm to find a minimum cover for a set of functional dependencies and find the minimal cover of the following set of functional dependencies R=(A, B, C, D, E, F.) AB->D, B->C, AE->B, A->D, D->EF.

10M

Unit – IV 7. a) Define Serializability. Explain the anomalies associated with Interleaved execution. 8M b) Define Time-Stamp? Explain Time-Stamp based concurrency control.

7M

8. a) Explain ARIES Recovery Algorithm. Discuss the principles behind ARIES Recovery Algorithm.

8M

b) Explain System Crash and Media Failure with example.

7M

Unit – V

9. a) Explain RAID levels. 8M b) What is the minimum space utilization for a B+ tree index? What is the minimum space

utilization for an ISAM index?

7M

10. a) Discuss Clustered indexing, Hash based indexing and tree based indexing 7M b) Consider the B+ tree index of order d = 2 shown in Fig.1.

Fig.1.

i. Show the tree that would result from inserting a data entry with key 9 into this tree. ii. Show the B+ tree that would result from inserting a data entry with key 3 into the

original tree. How many page reads and page writes does the insertion require

8M





MATHEMATICS-III

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



Unit - I

1.

a) Prove that 1 12

4 40 0

14 21 1

x dx dxx x

7M

b) Prove that: i. 1 !n n , where n is the positive integer

ii. 12

8M

2.

a) Prove that 1 2

2 sinJ x xx

7M

b) Prove that 1

1

0, if 2 ,

2 1m n

m np x p x dx

m nn

8M

Unit – II

3. a) Derive Cauchy - Riemann equations in polar form. 7M

b) If ( )f z u iv is an analytic function of z, prove that 2 2

22 2 Real ( ) 2 ( )f z f z

x y

8M

4.

a) Show that the function ( )f z defined by

)0(,0

)0(,)1()1()( 22

33

z

zyx

iyixzf

is continuous and C – R equations are satisfied at the origin , yet 0f does not exist.

10M

b) Find the analytic function whose real part is 22 yx

x

5M

Unit – III

5.

a) Show that 1 2sinh log 1z z z

7M

b) Find the real and imaginary parts of 1tan x iy

8M

6.

a) Find the bilinear transformation that maps the points 1, ,1i into the points 0, ,i

8M

b) Under the transformation 1wz

, find the image of the circle 2 2z i

7M

Con…2

:: 2 ::

Unit – IV

7.

a) Evaluate C

f z dz , where 2zf zz

, C is the semi-circle 2 iz e and

varies from 0 to

7M

b) Evaluate

2

41

z

C

e dzz , where C is 3z using Cauchy’s integral formula.

8M

8.

a) Find the Laurent’s series expansion of 2

1 3 2

f zz z

in the annulus region

1 2z

8M

b) Determine the zeros and poles of

2

211

zz

7M

Unit – V

9.

a) Find the residues of 3( 1)

zz ez

at its pole.

7M

b) Evaluate

4 31 2C

z dzz z z

where C is the circle 1.5z using residue theorem.

8M

10.

a) Evaluate 2

20

(0 1)1 2 cos

d aa a

8M

b) Evaluate dxbxax

x

)()( 2222

2

7M





ENVIRONMENTAL SCIENCE (Common to Electronics and Communication Engineering & Civil Engineering)



Unit – I

1. a) Discuss how environmental science is a multidisciplinary as well as interdisciplinary subject.

8M

b) Discuss the role of the individual in conservation of natural resources with respect to soil erosion and desertification.

7M

2. a) Differentiate between renewable and non renewable sources of energy. 8M b) Discuss the impact of overexploitation of mineral resources.

7M

Unit – II

3. a) What is an ecosystem? Describe the structure and function of an ecosystem. 9M b) Define ecological succession, discuss the various stages in the ecological succession.

6M

4. a) Describe the characteristics and function of forest ecosystem. 8M b) Explain the threats to biodiversity with reference to habitat loss and poaching of

wildlife.

7M

Unit – III

5. a) What do you understand by thermal pollution? List out the various sources and control methods of thermal pollution.

8M

b) Explain the various sources of noise pollution and list out the control methods.

7M

6. a) What do you understand by rain water harvesting and water shed management? 8M b) What is acid rain? List out the effects of acid rain on environment.

7M

Unit – IV

7. a) What are the approaches of green building? State the importance of LEED rating in the concept of green building.

8M

b) Write short notes on: i. Carbon foot print ii. Carbon sequestration

7M

8. a) Explain clean development mechanism and scope of ISO 14000. 8M b) Discuss role of Information technology on environment and human health.

7M

Unit – V

9. a) Give the salient features of wildlife protection Act and forest Act. 7M b) What is EIA? Explain briefly the steps followed in preparing EIA.

8M

10. a) Give the salient features of air Act and water Act. 8M b) Write a brief account on the role of NGO’s in creating awareness among the public

regarding the environmental issues. 7M



B. Tech III Semester, End Semester Regular Examinations, November - 2016 (Regulations: VCE-R15)

DIGITAL LOGIC DESIGN (Common to Computer Science and Engineering, Information Technology,

Electronics and Communication Engineering & Electrical and Electronics Engineering) Date: 19 November, 2016 FN Time: 3 hours Max Marks: 75


Unit – I

1. a) Perform the subtraction for the following: i. Using 10’s and 9’s complement (5230)10-(0321)10

ii. Using 2’s and 1’s complement (100)2-(110000)2

6M

b) Implement the following expression: , ,f a b c ac bc ab

i. Using NAND gates only ii. Using NOR gates only

9M

2. a) Realize Ex-NOR gate using only NOR gates. 6M b) Verify the following Boolean algebraic manipulation. Just each step with a reference to a

postulate or theorem.

i. 0x y xy x y xy

ii. AB C D C D C D E ABC D

9M

Unit – II

3. a) Obtain the essential prime implicants of following Boolean expression: , , , 1, 5, 6, 7, 11, 12, 13, 15f A B C D m

5M

b) Simplify the following function using K-map technique and implement using basic gates:

i. , , , 0, 1, 4, 8, 9, 10 2, 11ii. , , , 0, 2, 4, 10, 11, 14, 15

f P Q R S m df A B C D M

10M

4. a) Reduce the following Boolean expressions to a minimum number of literals: i. ii .

xy xyxyz xy xyz

6M

b) Construct the prime-implicant table and find the essential prime implicants of the function: , , , 0, 5, 7, 8, 9, 10, 11, 14, 15f D C B A m

9M

Cont…2

:: 2 ::

Unit – III

5. a) Convert SR–Flip Flop to D–Flip Flop. 5M b) Design the sequential circuit for the state diagram shown in Fig.1 using JK Flip-Flops. 10M

Fig.1

6. a) Implement the following Boolean function with a Multiplexer:

, , , (0,1,3, 4,8, )9,15F A B C D 6M

b) Design a sequential circuit whose state tables are specified in the below table using D – Flip Flops.

Present state

Next state Output X = 0 X = 1

Q0 Q1 Q0 Q1 Q0 Q1 X = 0 X = 1

0 0 0 0 0 1 0 0

0 1 0 0 1 0 0 0

1 0 1 1 1 0 0 0

1 1 0 0 0 1 0 1

9M

Unit – IV

7. a) Implement a 3 bit ripple down counter using edge triggered T flip-flops and also write the appropriate truth table.

5M

b) Using the smallest size ROM, implement the decimal arithmetic equation: 2 3, 0 7f a a a ; where f a and ‘ a ’ are in binary.

10M

8. a) Differentiate with appropriate diagrams the following PLDs: ROM, PLA and PAL. 5M b) Design a synchronous counter using D flip-flop that can function as a BCD up counter

when the mode control = 0 and when mode control = 1 it gives the count in the sequence as 0,3,6,2,4,9,7,11, 0,3,6,2…..

10M

Unit – V

9. a) Analyze the concept of an ASM chart with relevant diagram. 5M b) Two flip-flops A and B in a sequential circuit have an external input ‘ x ’ and output ’ y ’.

the flip-flop input functions and output function are as follows: i. ii. iii. , where is output

A

B

D x BxT B AxY AB Y

Obtain the logic diagram, state table and state diagram.

10M

Cont…3

:: 3 ::

10. a) What are synchronous sequential circuits? Analyze the different sequential machine models.

6M

b) Reduce the number of states in the following state table and tabulate the reduced state table:

Present State

Next State Output X=0 X=1 X=0 X=1

A F B 0 0 B D C 0 0 C F E 0 0 D G A 1 0 E D C 0 0 F F B 1 1 G G H 0 1 H G A 1 0

9M





ELECTRONIC CIRCUIT ANALYSIS

(Electronics and Communication Engineering)



Unit – I

1. a) Discuss the role of biasing resistances in reducing input impedance of self biasing circuit of CC configuration. How this defect can be eliminated using bootstrap principle?

6M

b) A CE Amplifier is drawn by a voltage source of internal resistance Rs=800 Ω and the load impedance is a resistance RL=1000 Ω. The h-parameters are hie=1kΩ, hre= 2x10-4, hfe=50 and hoe=25µA/V . Compute the current gain AI, input resistance Ri, voltage gain Av and output resistance Ro using exact analysis and using approximate analysis.

9M

2. a) Analyze the CE amplifier with un-bypassed RE with respect to Zi, AV, Z. 9M b) Find Av , AI, ZI and ZO for the following circuit.The transistor parameters at the

corresponding Quiescent points are hie=2K, hfe=50, hre=6x10-4 , hoe=25µA/V, hic=2K, hfc=-51, hrc=1, hoc=25 µA/V

Fig.1

6M

Unit – II

3. a) Explain Gain Bandwidth product of the CE transistor in Hybrid π model. 6M b) The following low frequency parameters are known for a given transistor at Ic=10 mA,

Vce=10V, and at room temperature hie=500 Ω, hfe=100, hoe=4x10-5A/V,hre=10-4 At the same operating point fT=50MHz and Cob=3pF. Compute the values of all the Hybrid π-parameters.

9M

4. a) At room temperature, A BJT has hie=6kΩ and hfe=224 at Ic=1mA with fT=80MHz and Cb’ç=12pF. Determine: i. gm ii. rb’e iii. rbb’ iv. Cb’e of small signal high frequency model of the BJT

6M

b) Derive gm, rb’e, rb’c , rce from h-parameters in CE Configuration

9M

Unit – III

5. a) What is the effect of negative feedback on input and output resistances? 7M b) A crystal L=0.4H, C=0.085pF and CM=1pFwith R=5kΩ Find:

i. Series resonant frequency ii. Parallel resonant frequency iii. By what percent does the parallel resonant frequency exceed the series resonant

frequency iv. Find the Q factor of the Crystal

8M

Cont…2

:: 2 :

6. a) Determine the frequency of oscillations for RC Phase shift Oscillator. 10M b) An Amplifier has voltage gain with feedback of 100. If the gain without feedback

changes by 20% and the gain with feedback should not vary more than 2%, determine the values of open loop gain A and feedback ratio β.

5M

Unit – IV

7. a) Show that conversion efficiency of class B-push pull amplifier is 78%. 8M b) A transformer-coupled class A amplifier drives a 16Ω loud speaker through a 4:1

transformer with Vcc=36 V the circuit delivers 2 W to the load. Find: i. Power across the transformer primary ii. RMS voltage across the load iii. RMS voltage across the transformer primary iv. RMS values of load current and primary current v. Conversion efficiency if the DC collector current is 150mA

7M

8. a) Draw the Circuit diagram of Class A transformer Coupled amplifier and derive the expression for conversion efficiency.

7M

b) For the circuit of Fig.2 shown below, calculate the input power, Output Power and Power handled by each Output transistor and the circuit efficiency for an input of 12Vrms.

Fig.2

8M

Unit – V

9. a) Explain tuned circuit with the frequency response. 7M b) A Single tuned RF amplifier uses a transistor with an output resistance of 50kΩ, Output

Capacitance of 15pF and input resistance of next stage is 20kΩ, The tuned circuit consists of 47pF capacitance in parallel with series combination of 1µH inductance and 2Ω resistance. Calculate:

i. Resonant Frequency ii. Effective Quality Factor iii. 3dB Band Width of the circuit

8M

10. a) Explain about classification of Tuned amplifier and their applications 7M b) A Single Tuned transistor amplifier is used to amplify modulated RF Carrier of 600kHz

and bandwidth of 15kHz. The Circuit has a total output resistance Rt=20kΩ and Output Capacitance Co=50pF. Calculate values of inductance and capacitance of the tuned circuit

8M





SIGNALS AND SYSTEMS

(Electronics and Communication Engineering)



Unit – I

1. a) Sketch the following signals, where x(t) is shown in Fig.1.

Fig.1

i. 2 2x t

ii. 0.5 02x t

iii. 2x t

iv. 2x t

8M

b) Determine the convolution of the following signals by graphical method 3 tx t e u t and 3 5h t u t u t

7M

2. a) State and prove the properties of Cross correlation function for power signals. 7M

b) Find the energy or power of the following signals i. 2cos 0.25x n n

ii.

5, 5 41.5, 4 45 , 4 50, otherwise

t tt

x tt t

8M

Unit – II

3. a) State the Dirchelt’s conditions for Fourier series. Explain with suitable examples. 6M b) Obtain the exponential Fourier series for the square waveform shown in the Fig.2, also

draw magnitude spectrum and phase spectrum .

Fig.2

9M

:: 2 ::

4.

a) The impulse response of a system is given as 1h t t t . Determine the step response of the system.

5M

b) What are the types of symmetry that may present in a waveform? Explain with examples. How does the symmetry of a signal help in simplification of calculations? Obtain the exponential Fourier series for the square waveform shown in the Fig.3

Fig.3

10M

Unit – III

5. a) Obtain the conditions for distortion less transmission through an a system. Examine whether the following system is distortion less.

d y t x tdt

6M

b) For the signal x(t) is shown in Fig.4, evaluate the following quantities without explicitly computing X(흎).

Fig.4

i. X d

ii. 2| | jX e d

iii. 0X

9M

6. a) State and prove the properties of continuous time Fourier transform. i. Time shifting property ii. Frequency Reversal property iii. Time integral property.

6M

b) Determine the inverse Fourier transform of the spectrum given below in the Fig.5.

Fig.5

What are the merits and demerits of Fourier transform.

9M

Cont…3

:: 3 ::

Unit – IV

7. a) State and prove time differentiation property and the differentiation in s-domain property of Laplace transform.

8M

b) Find the inverse Laplace transform of X(s) = 3

2 1X s

s s

if the ROC is

i. 2 1Re s

ii. 1Re s

iii. 2Re s

7M

8. a) Find the inverse Laplace transform of the following.

2

2 2

3 22 273 2 2 5s sX s

s s s s

7M

b) Using Laplace transform, find the response of the response of the system described by

the differential equation 2

6 5d y t dy t dx t

y tdt dt dt

,

if 20

0 1, 2 tdyy and x t e u t

dt

8M

Unit – V

9. a) State sampling theorem. What are the several ways of sampling continuous-time signals. Explain any one method in detail.

7M

b) Using long division, determine the inverse Z-transform of,

2

3 2

2 ; :| z | 12 3 4

z zX z ROCz z z

8M

10. a) A difference equation of the system is given by 0.5 1y n y n x n Determine: i. System function H(z) ii. Pole-zero plot of the system function

6M

b) A low pass signal x(t) has a spectrum X(f ) given by, | |1 , | | 200200

fX f f . Assume

x(t) is ideally sampled at fs =300Hz. Sketch the spectrum of xs(t).

9M





RANDOM SIGNALS AND STOCHASTIC PROCESSES (Electronics and Communication Engineering)



Unit – I

1. a) What is the difference between random variables and deterministic variables? What is the diference between probability distribution function (CDF) and probability density function (PDF)? Define the PDF for Gaussian distribution and Rayleigh distribution.

8M

b) Find the mean of an exponential distribution.

7M

2. a) Writea short note on characteristic function. Define a random variable and random process.

9M

b) Assume automobile arrivals at a gasoline station are Poisson and occur at an average rate of 50/h. The station has only one gasoline pump. If all cars are assumed to require one minute to obtain fuel. What is the probability that a waiting line will occur at the pump?

6M

Unit – II

3. a) List and Prove all properties of Joint Density Function. 7M b) Two random variables x and y have a joint pdf:

2

,

5 , 0 2, 16

0 X Y

x y for y xf x y

Elsewhere

i. Find the marginal density functions of x and y ii. Are x and y statistically independent

8M

4. a) Statistically independent random variables X and Y have moments m10=2, m20=14, m02=12, m11=-6. Find the moment μ22.

8M

b) Two Gaussian random variables X1 and X2 are defined by mean and covariance matrices

[ X ]=21

, [Cx]=5 2 / 5

2 / 5 4

Two random variables Y1, Y2 are formed using transformation

[T]=1 1/ 2

1/ 2 1

Find matrices [ Y ], [Cy] and correlation coefficient of Y1 and Y2.

7M

Unit – III

5. a) Define the following: i. 1st order stationary random process ii. Wide-Sense Stationary (WSS) random process iii. Strict-Sense Stationary (SSS) random process

7M

b) Which are the parameters required to calculate the correlation between two signals ( )x t and y( )t ? Explain them with example. Consider a random process ( ) cos sinx t a t b t , where a and b are random variables. Find the sufficient

and necessary conditions for which ( )x t are a wide-sense stationary process.

8M

Cont…2

:: 2 ::

6. a) Define Cross-correlation function. State and prove its properties. 7M b) A random process is defined by ( ) ( )cos( )y t x t t , Where ( )x t is a wide sense

stationary random process that amplitude modulates a carrier of constant angular frequency ω with a random phase θ independent of ( )x t and uniformly distributed on (-π, π). i. Find E[Y(t)] ii. Find the autocorrelation function of Y(t) iii. Is Y(t) is Wide Sense Stationary

8M

Unit – IV

7. a) Explain power density spectrum. 7M

b) A random process X(t) can be defined as 0( ) cos( ),X t A t where A and 0 are constants and is uniformly distributed over (0,π/2). Find the average power.

8M

8. a) Explain the properties of cross power density spectrum. 7M b) A cross power density function is given below:

;( )

0;XY

a jb W WW

elseher

Find cross correlation function.

8M

Unit – V

9. a) Write short notes on the following: i. Thermal noise ii. Shot noise iii. Noise bandwidth

6M

b) Derive the expression for the Friss cascade formula.

9M

10. a) Explain the following: i. Extraterrestrial Noise ii. Thermal Agitation Noise iii. Shot Noise iv. Industrial noise

8M

b) A parallel tuned circuit at 200Mhz with a Q of 10, and a capacitance of 10pf. The temperature of the circuit is 17 degree Celsius. What noise voltage will be observed across the circuit by a wide band voltmeter?

7M





ELECTRICAL MACHINES-I (Electrical and Electronics Engineering)



Unit – I

1. a) What is armature reaction? Explain in detail with necessary diagrams. 7M b) A 4-pole dc generator has 1200 armature conductors and generates 250V on open

circuit when running at a speed of 500rpm. The diameter of the pole shoe circle is 0.35m and the ratio of pole arc to pole pitch is 0.7 while the length of the shoes is 0.2m. Find the mean flux density in the air gap. Assume lap connected armature winding.

8M

2. a) How do you compensate the armature reaction in DC machines? Explain in detail. 5M b) Explain the working principle of DC generator with neat sketches.

10M

Unit – II

3. a) Draw the OCC of a dc shunt generator and define critical speed and critical resistance. 7M b) A dc shunt generator has the following open circuit magnetization curve at its rated speed

1500rpm: Field current (A) : 0.5 1.0 1.5 2 3 4 EMF ( V ) : 180 340 450 500 550 570

The resistance of the field circuit is 200Ω. The generator is driven at its rated speed. Find the terminal voltage on open circuit. (Use graph paper)

8M

4. a) Distinguish between internal and external characteristic of a DC generator. How can the internal characteristic are derived from the external characteristic of a separately excited generator.

7M

b) In a110v, D.C. compound generator, the resistance of the armature, shunt field and series field are 0.06Ω, 25Ω and 0.04Ω respectively. The load consists of 200 lamps each rated at 55W, 110v. Find the total e.m.f. generated and the armature current when the machine is connected in: i. Long shunt ii. Short shunt

8M

Unit – III

5. a) Derive the torque equation of a dc motor from the fundamentals. 7M b) A 25KW, 250V DC shunt generator has armature and field resistance of 0.06Ω and 100Ω

respectively. Determine the total armature power developed when working: i. As a generator delivering 25KW output ii. As a motor taking 25KW input

8M

6. a) With a neat circuit diagram explain the Hopkinson's test. 7M b) When running on no load, a 400V shunt motor takes 5A. Armature resistance is 0.5Ω

and filed resistance 200Ω. Find the output of the motor and efficiency when running on full load and taking a current of 50A. Also find the percentage change in speed from no load to full load.

8M

Cont…2

:: 2 ::

Unit – IV

7. a) Derive the EMF equation of a transformer. 7M b) A 400 KVA distributed transformer whose copper and iron losses at full load are 5KW and

4KW respectively. During a day of 24 h it is loaded as under. Find the all-day efficiency.

Number of hours Loading in KW Power Factor 6 320 0.8

10 240 0.75 4 80 0.8 4 0 ---

8M

8. a) Derive the voltage regulation formulae for single phase transformer and obtain the condition for zero regulation.

7M

b) A 25KVA, 2200/220-V, 50Hz, single-phase transformer obtained the following test results OC test (LV side) = 220V, 1.2A, 100W SC test (HV side) = 100V, 7A, 310W Calculate the parameters of the equivalent circuit of the transformer referred to the LV side, and draw the equivalent circuit.

8M

Unit – V

9. a) What are the merits and demerits of a star-star, delta-delta, star-delta and delta star three phase transformer?

7M

b) A 3-phase 50Hz transformer has an iron cross section of 400cm2 (gross). If the flux density be limited to 1.2Wb/m2, find the number of turns per phase on high and low-voltage windings. The voltage ratio is 2200/110V, the hv side being connected in star and low voltage in mesh. Assuming stacking factor is 0.9.

8M

10. a) What are the disadvantages of current and voltage harmonics in transformers? Explain how these harmonics can be eliminated.

7M

b) It is desired to transform 2400V, 5000KVA three phase power to 2-phase power at 600V by Scott-connected transformers. Determine the voltage and current ratings of both primary and secondary of each transformer. Neglect the transformer no load currents.

8M




(Regulations: VCE-R15) ELECTRO MAGNETIC FIELDS

(Electrical and Electronics Engineering) Date: 22 November, 2016 FN Time: 3 hours Max Marks: 75


Unit – I

1. a) State and prove Maxwell’s first equation (not by divergence theorem). 8M b) Find the electric field intensity, flux density and volume charge density at a point (1, 0, 1)

if the given potential is V = 3x2y+2yz2+2xyz volt.

7M

2. a) Show that the electric field intensity E due to infinite sheet of charge is independent of the distance of the point from the sheet.

7M

b) A charge of -0.3μC is located at A (25, -30, 15) Cm and a second charge of 0.5 μ C is located at B (-10, 8, 12) Cm. Find the electric field intensity, E at: i. The origin ii. Point P (15, 20, 50) cm

8M

Unit – II

3. a) Obtain an expression of Magnetic field intensity H at a center of a circular conductor. 7M b) Find the magnetic field intensity at point ‘P’ for the circuit shown in below Fig.1 using

Biot-Savart’s law:

Fig.1

8M

4. a) State and explain Ampere’s circuital law. Also derive expression for it in differential form.

7M

b) Derive expression for magnetic field intensity H due to infinite sheet of current placed on XY Plane.

8M

Unit – III

5. a) Derive the expression for capacitance of a spherical capacitor using concept of capacitance.

7M

b) Semi-infinite conducting planes Ø=0 and Ø=π/6 are separated by insulating gap. If V(Ø=0)=0, Volts and V(Ø=π/6)=100 volts. Calculate potential V and electric field intensity E in the region between plates.

8M

6. a) Derive the expression for energy stored and energy density in a magnetic field. 8M b) Derive the expression for mutual inductance between a straight long wire and a square

loop wire in the same plane.

7M

Cont…2

::2::

Unit – IV

7. a) Explain Lorentz force equation and force on a differential current element. 7M b) A charge is placed midway between stationary line charge of density λ C/m and a straight

filament conductor carrying 18 Amps (placed parallel to the line charge on same plane).If the charge moves with uniform velocity of 106m/s. Find the charge density λ.

8M

8. a) Obtain the expression for torque on a current loop placed in a magnetic field. 6M b) Given vector magnetic potential A=-ρ2/4 azwb/m. Calculate total magnetic flux crossing

surface Ø=π/2, 1≤ρ≤2m, 0≤z≤5m.

9M

Unit – V

9. a) State and prove Poynting theorem. Write expression for average power density by using Poynting theorem.

8M

b) A straight conductor of 0.2m lies on the x-axis with one end at origin. The conductor is subjected to a magnetic flux density B =0.04 ya Tesla and velocity V=2.5 sin103t azm/s. Calculate the motional electric field intensity and emf induced in the conductor.

7M

10. a) Explain Faradays law and Lenz’s law. 7M b) In free space E =15cos(wt-훽푧)axV/m. Calculate the total power passing through a

rectangular area of sides 30mm and 15mm in z=0 plane. Assume Em/Hm=ɳ0 and ɳ0=( 120 )훺.

8M




(Regulations: VCE-R15) NETWORK ANALYSIS

(Electrical and Electronics Engineering) Date: 24 November, 2016 FN Time: 3 hours Max Marks: 75


Unit – I

1. a) Explain the concept of self and mutual inductance. 5M b) Calculate the Phasor currents I1 and I2 in the circuit shown in Fig.1.

Fig.1

10M

2. a) Explain the following: i. Bandwidth ii. Quality factor

5M

b) In the circuit shown in Fig.2, R=2Ω, L=1mH, and C =0.4µF i. Find resonant frequency and the half power frequencies ii. Calculate bandwidth iii. Determine the amplitude of the current at ω0,ω1 and ω2

Fig.2

10M

Unit – II

3. a) Derive the relation between the line and phase quantities in star connected system. 6M b) Each of the two wattmeters connected to measure the input to a 3-phase circuit reads

10KW when the power factor is unity. What does each wattmeter read when the p.f falls to: i. 0.866 lagging ii. 0.5 lagging, the total power remaining unchanged

9M

4. a) Briefly explain the different methods of solving the three phase, 3 wire unbalanced star connected load.

6M

b) A unbalanced star connected load with ZR=10Ω, ZY=15Ω and ZB=20Ω, is supplied from a 3-phase, 440V, symmetrical system. Determine the line currents, and the total power.

9M

Cont…2

:: 2 ::

Unit – III

5. a) In the circuit shown in Fig.3, find i0, v0 and I for all time, assuming that the switch was open for a long time.

Fig.3

7M

b) The switch is shown in Fig.4 has been closed for a long time, and it is opened at t =0. Find v(t) for t ≥ 0. Calculate the initial energy stored in the capacitor.

Fig.4

8M

6. a) Find the transient response of RL network with DC excitation. 6M b) In the circuit shown in Fig.5 the switch is moved from 1 to 2 at time t = 0. The steady-

state current having previously established in the R-L circuit, find the expression for the current i(t) after switching.

9M

Fig.5

Unit – IV

7. a) Explain the classification of filters and symmetrical attenuators. 5M b) Design a m derived T Section low pass filter having a cut off frequency of 7KHz and

R0=600Ω and frequency of infinite attenuation of 10.5KHz.

10M

8. a) Explain the design of constant-k low pass filter with circuit diagram. 6M b) Design a bandpass filter to match a load of 600Ω and which allows frequency between

3KHz to 6KHz.

9M

Unit – V

9. a) Draw the locus diagram of a series RL circuit with R Variable and L Variable. 7M b) Obtain current locus of the circuit shown in Fig.6.

Fig.6

8M

10. a) Draw the locus diagram of a series RLC circuit with L and C varying. 5M b) A series circuit consisting of R=500Ω, L=0.5H and C=18µF is connected to a variable

frequency supply of voltage of 120V. If the frequency is varied through 40 to 80Hz, draw the locus diagram of current. Determine the current and power factor at 40 and 80Hz.

10M




(Regulations: VCE-R15) MACHINE DRAWING

(Mechanical Engineering) Date: 15 November, 2016 FN Time: 3 hours Max Marks: 75


1. Draw the sectional view from the front and view from the side of a cotter joint with sleeve used to connect two rods of 50mm diameter each.

15M

2. Draw half sectional view from the front, top half in section and half sectional view from the side, left half in section of a split muff coupling, indicting proportions to connect two shafts, each of diameter 50mm.

15M

3. Draw the following: i. Sectional view from the front ii. View from above of the following riveted joint to join plates of thickness 10mm iii. Double riveted double strap, chain butt joint

15M

Cont…2

:: 2 ::

Unit – II

4. Assemble all parts of the stuffing box, as shown in Fig.1 and draw:

i. Half sectional view from the front with right half in section ii. Half sectional view from the right side iii. View from above

Fig.1

45M




(Regulations: VCE-R15) ELECTRICAL TECHNOLOGY



Unit – I

1. a) Find the equivalent resistance and total current flowing through the circuit shown below Fig.1 if V=100 V , R1 = 10Ω , R2 =50Ω and R3=20Ω:

Fig.1

7M

b) Calculate the equivalent resistance, total current and current flowing through each resistor that in the given a series-parallel combination circuit as shown in below Fig.2:

Fig.2

8M

2. a) A voltage wave is represented by v= 200 sin 314 t. Find: i. Maximum value ii. RMS value iii. Average value iv. Frequency

8M

b) Explain the procedure for conversion of star to delta transformation.

7M

Unit – II

3. a) State and explain maximum power transformer theorem. 7M b) Find the Norton’s equivalent circuit across A-B for the network shown in Fig.3 below?

Fig.3

8M

Cont…2

::2::

4. a) State and explain Thevenin’s theorem. 7M b) Find the current in the 5Ω resistor for the circuit shown below Fig.4 by using super

position theorem:

Fig.4

8M

Unit – III

5. a) What are the different types of DC generators based upon the excitation? 7M b) A short shunt compound generator supplied 7.5KW at 230V. The shunt field, series field

and armature resistances are 100Ω, 0.3Ω and 0.4Ω respectively. Calculate the induced emf and the load resistance.

8M

6. a) Write about the self and mutual inductance. 7M b) From the fundamental principles, calculate the torque developed by a 6-pole dc motor

having 1800 lap connected conductors, the armature current and the flux per pole being 15A and 30 mWb respectively.

8M

Unit – IV

7. a) Differentiate between core type and shell type transformers. 7M b) A 600 kVA, single phase transformer when working at u.p.f has an efficiency of 92% at

full load and also at half load. Determine its efficiency when it operates at unity p.f and 60% of full load.

8M

8. a) Explain the various losses in a transformer and explain how to minimize the losses. 7M b) In no load test of a single Phase transformer, the following test data were obtained.

Primary Voltage : 220 V Secondary Voltage : 110 V Primary current : 0.3A Power Input : 20 W Find the following The Turns ratio The Magnetizing component of no load current Its Working component The iron loss. Resistance of the primary winding 0.6 Ω.

8M

Unit – V

9. a) What are the total loss in induction machine and draw the power flow diagram. 7M b) Explain the types of three phase induction motors with a neat sketch.

8M

10. a) Derive the starting torque equation in induction motor. 8M b) A three phase, 415V, 50hz, 4 pole induction motor has star connected stator winding.

The rotor resistance and reactance are 0.2ohm and 2 ohm respectively. The full load speed is 1440rpm. Calculate the torque developed on full load by the motor. Assume stator to rotor ratio is 2:1.

7M





MECHANICS OF SOLIDS

(Mechanical Engineering)



Unit – I

1. a) Explain stress – strain diagram for mild steel and show salient features. 6M b) A round stepped bar is subjected to an axial force 30KN. Diameter and length of first

portion are 40mm and 200mm respectively and those that of second portion are 20mm and 100mm respectively. Determine change in deformation when a uniform bar with same volume and length as that of stepped bar is subjected to 30KN? Take E=200GPa.

Fig.1

9M

2. a) Derive the relationship 퐸 = 3퐾(1 − 2μ) with usual notations start from the fundamentals.

5M

b) A circular bar of 250mm2 cross-sectional area and 2.6m long is rigidly fixed at its top in vertical position. An axial force of 20KN is applied vertically downwards at a distance of 0.8m from upper support. If there is an initial gap of 0.1mm between the lower support and bottom surface of the member as shown in Fig.2, determine the stresses and deformation induced in the portions AB and BC. Take E = 200GPa.

Fig.2

10M

Unit – II

3. a) What are types of beams? Write SF diagram for any one type of beam. 3M b) Draw SF and BM diagram for the loading pattern on the beam shown in Fig.3, indicate

where the inflection and contra-flexure points are located? Also locate the maximum BM with its magnitude.

Fig.3

12M

Cont…2

:: 2 ::

4. a) What are the sign conventions used for shear force and bending moment in general? 4M b) A cantilever of length 2m carries a uniformly distributed load of 1.5kN/m run over the

whole length and a point load of 2KN at a distance of 0.5m from the free end. Draw the S.F and B.M diagrams for the cantilever.

11M

Unit – III

5. a) Briefly explain different types of supports and types of beams. 5M b) A cantilever beam has a length of 2.5m and has T-section C.S with flange dimension

100mmx20mm and web 12mmx200mm, with flange being in tension. What concentrated load can be applied at the free end if the maximum tensile stress is 30MPa? What then is the Maximum compressive stress?

10M

6. a) Explain pure bending and non-uniform bending. 4M b) A simply supported beam with overhang is loaded with point load as shown in Fig.4.

The cross section of the beam is I- section. The allowable bending stresses in tension and compression are σt=150MPa and σc=100MPa. Find the safe load ‘W’ on the overhang.

Fig.4

11M

Unit – IV

7. a) Using double integration method, obtain maximum deflection in a cantilever beam subjected to concentrated load at free end.

5M

b) Find the maximum deflection for the beam loaded as shown in Fig.5. Take EI=15x109KN-mm2.

Fig.5

10M

8. a) Derive the expression for the deflection at the load point for a simply supported beam subjected to central concentrated load.

9M

b) Cantilever beam of 2m length carries a UDL of 5KN/m for the entire length along with an end load of 30KN. The beam has a cross section of b=100mm and h=200mm. Take E=200GPa and determine the maximum deflection.

6M

Unit – V

9. a) From first principles prove that volumetric strain in a cylinder is given by

5 44pdEt with usual notations.

10M

b) A water pipe with 500mm diameter supplies water at 51m head. Taking allowable stress for pipe material as 30MPa and efficiency of circumference riveted joint as 80%, determine the thickness of the pipe. Specific weight of water is 9.81KN/m3.

5M

10. a) Derive the expression for radial pressure in the wall of thick cylinder. 5M b) A thick cylinder with internal diameter 80mm and external diameter 120mm is

subjected to an external pressure of 40KN/m2. Calculate circumferential stress at internal and external surfaces of the cylinder. Plot the variation of circumferential stress and radial pressure on the thickness of the cylinder.

10M





MECHANICS OF FLUIDS (Mechanical Engineering)



Unit – I

1. a) State hydrostatic law and derive the expression for the same. 7M b) A differential manometer is connected at the two points A and B of two pipes as centre B

is 2m from left limb mercury level and centre A is 5m from left limb mercury level. The pipe A contains a liquid of sp. gr.=1.5 while pipe B contains a liquid of sp. gr.=0.9. The pressures at A and B are 1kgf/cm2 and 1.8kgf/cm2 respectively. Find the difference in mercury level in the differential manometer.

8M

2. a) Define surface tension on liquid jet. 6M b) Calculate the dynamic viscosity of oil, which is used for lubrication between a square plate

of size 0.8mx0.8m and inclined plane with angle of inclination 300 as plate is moving towards down. The weight of the square plate is 300N and it slides down the inclined plane with a uniform velocity of 0.3m/s. The thickness of oil film is 1.5mm.

9M

Unit – II

3. a) Distinguish between: i. Steady and unsteady flow ii. Uniform and non-uniform flow with examples

7M

b) Derive the continuity equation for three dimensional flows.

8M

4. a) Explain the terms: i. Path line ii. Streak line iii. Stream line iv. Stream tube

7M

b) A 40cm diameter pipe, conveying water, branches into two pipes of diameters 30cm and 20cm respectively. If the average velocity in the 40cm diameter pipe is 3m/s. Find the discharge in this pipe. Also determine the velocity in 20cm pipe if the average velocity in 30cm diameter pipe is 2m/s.

8M

Unit – III

5. a) Obtain an expression for Euler equation and state the assumptions made 7M b) Three pipes of 400mm, 200mm and 300mm diameters have lengths of 400m, 200m and

300m respectively. They are connected in series to make a compound pipe. The ends of this compound pipe are connected with two tanks whose difference of water level is 16m. If co-efficient of friction for these pipes is same and equal to 0.005, determine the discharge through the compound pipe neglecting first the minor losses and then including them.

8M

6. a) Derive an expression for discharge through venturimeter. 7M b) Water flows through a 300mmX150mm venturimeter at the rate of 0.037m3/s and the

differential gauge is deflected by 1m. S.G of the gauge liquid is 1.25. Determine the coefficient of discharge of the water.

8M

Cont…2

:: 2 ::

Unit – IV

7. a) What is boundary layer? Explain the growth of boundary layer along a thin flat plate, with a neat sketch.

7M

b) A fluid of viscosity 0.7 N-s/m2 and specific gravity 1.3 is flowing through a circular pipe of diameter 100mm. The maximum shear stress at the pipe wall is given as 196.2N/m2, find: i. Average velocity ii. Reynolds number of the flow

8M

8. a) Define the following: i. Laminar boundary layer ii. Turbulent boundary layer iii. Laminar sub layer iv. Boundary layer thickness

7M

b) A thin plate is moving in still atmospheric air at a velocity of 5m/s. The length of the plate is 0.6 m and width 0.5m. Calculate the: i. Thickness of the boundary layer at the end of the plate ii. Drag force on one side of the plate Take density of air 1.24 kg/m3 and kinematic viscosity 0.15 stokes.

8M

Unit – V

9. a) Define the terms: sub-sonic flow, super-sonic flow, sonic flow, mach angle and mach cone.

7M

b) A projectile is traveling in air having pressure and temperature as 8.829N/cm2 and -20C. If the Mach angle is 400, find the velocity of the projectile. Take K=1.4 and R=287J/kg K.

8M

10. a) Derive an expression for velocity of sound for an adiabatic process. 10M b) Find the speed of the sound wave in air at sea level where the temperature and pressure

are 200C and 1.0kgf/cm2 respectively. Take R=287J/kg K and k=1.4. 5M



B. Tech III Semester End Semester Regular Examinations, November - 2016 (Regulations: VCE-R15) THERMODYNAMICS



Unit – I

1. a) Classify thermodynamic systems with an example. 8M b) A system of volume V contains a mass M of gas at pressure P and temperature T. the

macroscopic properties of system obey the following relationship (P+a/V2)(V -b)=mRT where a, b and R are constant. Obtain an expression for displacement work done by the system during a constant temperature expansion from volume V1 to V2. Calculate the work done by the system which contains 10kg of this gas expanding from 1m3 to 10m3 at a temperature of 293K. Use the values a=15.7*10Nm4, b=1.07810-2m3 and R= 0.0278kJ/kgK.

7M

2. a) Describe the concept of thermodynamic equilibrium. 8M b) A gas of piston cylinder assembly undergoes an expansion process for which the

relationship between pressure and volume is given by Pvn=constant. The initial pressure is 0.3MPa, the initial volume 0.1m3 and the final volume is 0.2m3. Determine work done for process in kJ if: i. n = 1.5 ii. n = 1 iii. n = 0

7M

Unit – II

3. a) List out the limitations of first law of thermodynamics. 4M b) Show that energy is a property of the system.

A stationary mass of gas is compressed without friction from an initial state of 0.3m3 and 0.15MPa to a final state 0.15m3 and 0.15MPa, the pressure remains constant during process. There is transfer of 37.5kJ of heat from the gas during the process. How much does the internal energy of the gas change?

11M

4. a) Derive steady flow energy equation for single stream entering and single stream leaving a control volume.

8M

b) 0.5kg of air is compressed reversibly and adiabatically from 80kPa, 60oC to 0.4MPa and is then expanded at constant pressure to original volume. Sketch these processes on P-v and T-s plane, compute heat transfer and work transfer for whole path.

7M

Unit – III

5. a) Derive the Maxwell relations and explain their importance in thermodynamics. 7M b) A reversible heat engine operates between two reservoirs at 6000C and 400C. The engine

drives a reversible refrigerator which operates between the same 400C reservoir and a reservoir at -180C. The heat transfer to the heat engine is 2100kJ and there is a net work output of 370kJ from the combined plant. Evaluate the heat transfer to the refrigerator and the net heat transfer to the 400C reservoir.

8M

Cont…2

::2::

6. a) Prove that the Kelvin plank and Clausius statements of the second law of

thermodynamics are equivalent to each other. 7M

b) Heat is supplied from two constant temperature sources at 1000K and 800K to a reversible engine and it rejects heat to a constant temperature sink at 310K. The engine develops work equivalent to 110kW and rejects heat at the rate of 62kW. Find the heat supplied by each source and the thermal efficiency of the engine.

8M

Unit – IV

7. a) Write a short on the following: i. Sensible heating ii. Latent heating iii. Critical point iv. Triple point

8M

b) A pressure cooker contains 1.5kg of steam at 5 bar and 0.9 dryness. When the gas was switched off, determine the quantity of heat rejected by the pressure cooker when the pressure in the cooker falls to 1 bar.

7M

8. a) What is quality of steam? What are the different methods to measurement of quality and discuss the throttling calorimeter for measurement of quality of steam?

9M

b) A sample of steam from a boiler drum at 3MPa is put through a throttling calorimeter in which the pressure and temperature are found to be 0.1MPa, 120o C. Find the quality of the sample taken from the boiler.

6M

Unit – V

9. a) With P-V and T-S diagrams, derive an expression for efficiency of Diesel cycle. 8M b) In an air standard diesel cycle, the compression ratio is 15. Compression begins at 0.1

MPa, 40oC. The heat added is 1.675MJ/kg. Find: i. The maximum temperature of the cycle ii. The work done per kg of air iii. The cycle efficiency iv. The temperature at the end of isentropic expansion

7M

10. a) For the same compression ratio and heat rejection, which cycle is most efficient: Otto, Diesel or Dual? Explain with p-v and T-s diagrams.

7M

b) With the help of line diagram, p-V and T-s diagram explain Bell-Coleman cycle. 8M



B. Tech III Semester End Semester Regular Examinations, November - 2016 (Regulations: VCE-R15)

METALLURGY AND MATERIAL SCIENCE (Mechanical Engineering)



Unit – I

1. a) Find the relationship between the radius of atom (r) and lattice constant (a) for BCC and FCC crystal structures.

7M

b) Write a note on edge and screw dislocation giving suitable sketches. What is Burgers vector? Explain its significance.

8M

2. a) Write a brief note on effect of grain boundaries on mechanical properties of metals and alloys.

6M

b) Write a note on Hume – Ruthery rules.

9M

Unit – II

3. a) Explain Iron-Ironcarbide equilibrium diagram with neat sketch. 7M b) Explain experimental methods for construction of equilibrium diagram.

8M

4. a) State phase rule and write about Eutectic, Eutectoid and Peritectic alloy systems with reactions.

10M

b) What is the difference between TTT diagram and equilibrium diagram?

5M

Unit – III

5. a) Mention at least three different types of cast iron. How do they differ with respect to composition and structure?

7M

b) Write short notes on: i. Annealing ii. Normalizing

8M

6. a) With the help of neat sketch, explain the T.T.T diagram for an eutectoid steel. 7M b) Explain the properties, compositions and applications of Hadfield steel and die steel.

8M

Unit – IV

7. a) Explain the characteristics and applications of aluminium alloys. 7M b) Differentiate between brass and bronze. Explain different types of bronze briefly.

8M

8. a) Give the standard values for physical properties like density, melting point, tensile strength, crystal structure for titanium. What are different types of titanium alloys?

6M

b) Give the composition and applications of maraging steel. State its specialty.

9M

Unit – V

9. a) What are Glass ceramics and write the properties and applications of Glass ceramics? 8M b) Explain importance, types and uses of abrasive materials.

7M

10. a) Define composite with advantages and limitations. What is the role of matrix and reinforcement in a composite?

8M

b) Explain production of FRP by Hand Lay Up process with a neat sketch. 7M




(Regulations: VCE-R15) SURVEYING-I

(Civil Engineering) Date: 15 November, 2016 FN Time: 3 hours Max Marks: 75


Unit – I

1. a) What are the basic principles of surveying? With sketches, explain them briefly. 7M b) Sketch the conventional symbols for the:

i. Building ii. Temple iii. Railway track double line iv. Dam

8M

2. a) List the different sources and types of error in surveying. Explain them briefly. 7M b) Classify and explain different types of surveys.

8M

Unit – II

3. a) Write the differences between prismatic compass and surveyors compass. 7M b) Calculate the included angles of the following traverse and apply geometric checks:

Line : AB BC CD DE EA Bearing : 750 1370 1940 2450 336030

8M

4. a) What are the sources of error in compass? What precautions would you take to avoid them?

7M

b) The following are the interior angles of a closed traverse ABCDE: 0 0 0 0 078 15, 168 30; 84 30; 115 45 and 93 00.A B C D E If the

observed bearing of AB is 135000; and the traverse having been run counter-clockwise, determine the bearings of the remaining side.

8M

Unit – III

5. a) Discuss the advantages and disadvantages of plane table surveying over other methods. 6M b) Explain with sketches, the following methods of locating a point by plane table survey.

Also discuss the relative merits and application of the following methods: i. Radiation ii. Intersection iii. Resection

9M

6. a) Describe the various accessories of plane table along with function of each one of them. 7M b) List and explain different types of errors in plane table surveying.

8M

Unit – IV

7. a) Distinguish between: i. Horizontal plane and level surface ii. Line of collimation and line of sight iii. Rise and fall method and height of instrument (HI) method

7M

b) The following readings were taken with a 4m leveling staff on a continuously sloping ground. Calculate the R.L. of last point if that of first point is 102.345m. The readings are 0.945, 1.470, 1.950, 2.780, 3.655, 1.750, 2.655, 3.440, 0.780, 1.345 and 2.475 m.

8M

Cont…2

:: 2 ::

8. a) What are the common difficulties generally faced in leveling? How would you overcome them?

7M

b) The following reciprocal levels were taken with a dumpy level:

Instrument at Readings on Remarks A B

A 1.565 2.785 Distance AB=100M B 0.435 1.690 RL of A=200.00m

Find the corrected readings of A and B.

8M

Unit – V

9. a) Explain the characteristics of contours with neat sketches. 7M b) A series of offsets were taken at 3 m intervals in the following order from a chain line to a

curved boundary. 0, 2.2, 1.6, 2.8, 2.4, 1.0, 2.5, 0 meters. Find the area between chain line and curved boundary by trapezoidal rule.

8M

10. a) Explain various methods for determining area of a surface of land. Describe their merits and demerits.

7M

b) A railway embankment is 12 m wide. The ground is level in a direction transverse to the centre line. Calculate the volume contained in a 100 m length by trapezoidal rule and prismoidal rule, if the side slope is 1.5:1. The centre heights at 20 m interval are 3.7 m, 4.0 m, 3.4 m, 2.8 m, 3.0 m and 2.2 m.

8M





BUILDING MATERIALS AND CONSTRUCTION (Civil Engineering)



Unit – I

1. a) What precautions should be taken during stone quarrying while blasting? 7M b) Explain briefly the manufacturing of bricks.

8M

2. a) Explain the properties of Aluminum and its uses. 7M b) What are the disadvantages of clamp burning?

8M

Unit – II

3. a) Explain with a neat sketch about the structure of timber wood cut from tree. 7M b) Enumerate the different types of cement and discuss any two types briefly.

8M

4. a) Explain the process of natural seasoning of wood with a neat sketch. 8M b) List out various laboratory tests for cement and Explain the test procedure for consistency

test.

7M

Unit – III

5. a) Explain English bond and Flemish bond with neat sketches. 7M b) List out various types of stone masonry and Explain the construction of Random rubble

masonry with neat sketch.

8M

6. a) With neat sketches explain Ashlar masonry. 8M b) Explain various types of shallow foundations with neat sketch.

7M

Unit – IV

7. a) Mention the different types of floors and explain any two types briefly. 7M b) Enumerate the different types of roofs and discuss any two briefly.

8M

8. a) Write a short notes on: i. Panelled window ii. Swing ventilator

8M

b) Differentiate between King Post Truss and Queen Post Truss with neat sketches.

7M

Unit – V

9. a) Mention the different types of formwork and explain any two briefly. 8M b) Discuss the constituents of a good paint.

7M

10. a) Discuss the different methods of Pointing in building construction. 8M b) Explain the method of painting old and new wood work for doors and windows. 7M





FLUID MECHANICS (Civil Engineering)



Unit – I

1. a) Define surface tension. Derive expression for the pressure: i. Within a droplet of water ii. Inside a soap bubble

9M

b) A 50X50 mm plate is moving on a 0.2mm thick fluid layer with a velocity of 20mm/s. Determine the force and power required to maintain the constant velocity if the viscosity of the fluid film is 1 poise.

6M

2. a) State and prove Pascal’s law. 8M b) A circular plate 2.5m diameter is immersed in water, its greatest and least depth below

the free surface being 3m and 1m respectively. Find: i. The total pressure on one face of the plate ii. The position of centre of pressure

7M

Unit – II

3. a) A steady two dimensional flow has the following velocity fields u=2x+3y-5 and v=5x-2y-9. Determine the acceleration at the point (1, 1).

5M

b) For a two dimensional flow velocity potential is given by Ф = (푦 − 푥 ). Check whether it represents a possible case of fluid flow. If yes, determine the velocity components in the x and y directions. Also, determine the velocities at points (1, 3) and (4,4).

10M

4. a) For the velocity components in a fluid flow given by u=2xy and v=a2+x2-y2, show that the flow is possible.

5M

b) A stream function in a two dimensional flow is ψ = 2xy. Show that the flow is irrotational and determine the corresponding velocity potential Ф.

10M

Unit – III

5. a) What is a pitot-tube? How will you determine the velocity at any point with the help of pitot-tube?

9M

b) A 450 reducing bend is connected in a pipe line, the diameters at the inlet and outlet of the bend being 600mm and 300mm respectively. Find the force exerted by water on the bend if the intensity of pressure at inlet to bend is 8.829 N/cm2 and rate of flow of water is 600liters/s.

6M

6. a) Derive the expression for the rate of flow of fluid through a venturimeter. 7M b) Water flows through a triangular right-angled weir first and then over a rectangular weir

of 1m width. The discharge coefficients of the triangular and rectangular weirs are 0.6 and 0.7 respectively. If the depth of water over the triangular weir is 360mm, find the depth of water over the rectangular weir.

8M

Cont…2

:: 2 ::

Unit – IV

7. a) Obtain von-karmen momentum integral equation. 8M b) A flat plate of 1m width and 4m length is kept parallel to air flowing at 4.5m/s. Determine

the length of the plate over which the boundary layer is laminar, and the total force on both sides on the plate where the boundary layer is laminar. Assume density of air as 1.225kg/m3, kinematic viscosity=1.46X10-5m2/s.

7M

8. a) Define the following: i. Displacement thickness ii. Momentum thickness iii. Energy thickness iv. Drag and lift

8M

b) Calculate the friction drag on a plate 15cm wide and 45cm long placed longitudinally in a stream of oil ( specific gravity = 0.925 and kinematic viscosity of 0.9 stokes) flowing with a free stream velocity of 6m/s. Also find the thickness of the boundary layer and shear stress at the trailing edge.

7M

Unit – V

9. a) Explain the characteristics of laminar and turbulent flow in pipes 5M b) Derive an expression for the steady laminar flow through a long circular pipe.

10M

10. a) With a neat sketch explain the hydraulic grade line and total energy line for pipe flow. 5M b) A pipe 6cm in diameter, 1000m long and with f=0.018 is connected in parallel between

two points M and N with another pipe 8cm diameter, 800m long having f=0.020. A total discharge of 20 l/s enters the parallel pipes through division at M to rejoin at N. Estimate the division of discharge in the two pipes (Fig.1).

Fig.1

10M




(Regulations: VCE-R15) STRENGTH OF MATERIALS-I

(Civil Engineering) Date: 24 November, 2016 FN Time: 3 hours Max Marks: 75


Unit – I

1. a) Explain clearly the different types of stresses and strains. 5M b) A steel rod of 3cm diameter is enclosed centrally in a hollow copper tube of external

diameter 5cm and internal diameter of 4cm. The composite bar is then subjected to an axial pull of 45000N. If the length of each bar is equal to 15cm, determine: i. The stresses in the rod and tube ii. Load carried by each bar Take E for steel = 2.1×105 N/mm2 and for copper = 1.1×105 N/mm2.

10M

2. a) Define the terms: Elasticity, elastic limit, Young’s modulus and modulus of rigidity. 5M b) A tensile test was conducted on a mild steel bar. The following data was obtained from

the test: Diameter of the steel bar = 3cm Guage length of the bar = 20cm Load at elastic limit = 250kN Extension at a load of 150kN = 0.21mm Maximum load = 380kN Total extension = 60mm Diameter of the rod at the failure = 2.25cm Determine: i. The young’s modulus ii. The stress at elastic limit iii. The percentage elongation iv. The percentage decrease in area

10M

Unit – II

3. a) Write a short note on different types of loads. 5M b) A cantilever of the length 2m carries a UDL of 1.5KN/m run over the whole length and a

point load of 2KN at a distance of 0.5m from the free end. Draw the SFD and BMD for the cantilever.

10M

4. a) Explain sign convection for SF and BM. 3M b) A horizontal beam 10M long is carrying a UDL of 1KN/m the beam is supported on two

supports 6m apart. Find the position of the supports, so that BM on the beam is as small as possible. Also draw the SFD and BMD.

12M

Unit – III

5. a) What do you mean by ‘simple bending’ or pure bending? What are the assumptions made in the theory of simple bending?

5M

b) A rectangular beam 300mm deep is simply supported over a span of 4meters. Determine the uniformly distributed load per meter which the beam may carry, if the bending stress should not exceed 120N/mm2. Take I=8×106mm4.

10M

Cont…2

:: 2 ::

6. a) What do you mean by shear stresses in beams? 5M b) A timber beam of rectangular section is simply supported at the ends and carries a point

load at the centre of the beam. The maximum bending stress is 12N/mm2 and maximum shearing stress is 1N/mm2, find the ratio of the span to the depth.

10M

Unit – IV

7. a) Derive the relationship between bending moment and deflection of a beam subjected to flexure.

5M

b) A beam of length 6mtrs is simply supported at its ends and carries two point loads of 48kN and 40kN at a distance of 1meter and 3meters respectively from left support. Find the deflection under the first point load. Use Mc-auleys’s method.

10M

8. A simply supported beam of length 4meters carries a point load of 3kN at a distance of 1meter from each end. If E=2x105N/mm2 and I=1X108mm4for the beam, using conjugate beam method, determine the: i. Slope at each end and under point load ii. Deflection under each load and at the center of the beam

15M

Unit – V

9. a) Define the terms principal planes and principal stresses. 5M b) A point in a strained material the principal stresses are 100N/mm2(tensile) and 60N/mm2

(compressive). Determine the normal stress, shear stress and resultant stress on a plane inclined at 500 to the axis of major principal stress. Also determine the maximum shear stress at the point.

10M

10. a) Define the term ‘obliquity’ and write the expression. 5M b) The tensile stresses at a point across two mutually perpendicular planes are 120N/mm2

and 60N/mm2. Determine the normal, tangential and resultant stresses on a plane inclined at 300 to the axis of the minor stress.

10M

Documents

DISCRETE MATHEMATICAL STRUCTURES · b) Trace the execution of quick sort algorithm on the following data set {E, X, A, M, P, L, E}. 7M 2. a) Write the merge sort algorithm. 7M b)