VARDHAMAN COLLEGE OF ENGINEERING...a) Probability that a man will be alive 25 years hence is 0.3 and the probability that his wife will be alive 25 years hence is 0.4. Find the probability

Hall Ticket No: Question Paper Code: A4012

VARDHAMAN COLLEGE OF ENGINEERING (AUTONOMOUS)

II B. Tech I Semester Regular Examinations, November - 2019 (Regulations: VCE-R18)

PROBABILITY AND STATISTICS (Computer Science and Engineering)

Date: 20 November, 2019 FN Time: 3 hours Max Marks: 100

Answer All Questions

1. a) Define the following: i. Critical Region ii. Critical value

2M

b) What is the probability for a leap year to have 52 Mondays and 53 Sundays? 2M

c) The joint distribution of two random variables X and Y is as follows.

X \Y -2 -1 4 5

1 0.1 0.2 0 0.3

2 0.2 0.1 0.1 0

Find the marginal distribution of X and Y.

2M

d) If the life of ball bearings has the density f(x) = ke-0.2x if 0 ≤ x ≤ 10 and 0 otherwise, What is k? What is the probability P (X ≥ 5) ?

2M

e) The students in a class are selected at random one after the other for an examination. Find the probability that the boys and girls sit alternately if class consists of 4 boys and 3 girls.

2M

f) Let X be normal with mean 10 and variance 4. Find P(X > 12), P (X < 10). 2M

g) A random variable X has the following probability functions:

X=x 1 2 3 4 5 6

P(x) k 3k 5k 7k 9k 11k

Find the value of k.

2M

h) Assuming that =20.0 how large a random sample be taken to assert with probability 0.95 that the sample mean will not differ from true mean by more than 3.0 points?

2M

i) State clearly the assumptions for F – test. 2M

j) State clearly the assumptions in t- Test difference of means.

2M

2. a) Probability that a man will be alive 25 years hence is 0.3 and the probability that his wife will be alive 25 years hence is 0.4. Find the probability that 25 years hence: i. Both will be alive ii. Only the man will be alive iii. Only the women will be alive iv. None will be alive

8M

b) Two sets of candidates are competing for the positions on the Board of Directors of a company. The probabilities that the first and second sets will win are 0.6 and 0.4 respectively. If the first set wins, the probability of introducing a new product is 0.8 and the corresponding probability if the second win is 0.3. What is the probability that the product will be introduced?

8M

3. a) The joint probability distribution of two discrete random variables X and Y is given by

f(x,y)=k(2x+y) where x and y are integers such that 0 2 , 0 3 :x y

i. Find the value of the constant k ii. Find the marginal probability distributions of X and Y iii. Show that the random variables X and Y are dependent

8M

b) If x is a normal variate with mean 1 and standard deviation 3. Find the probability that:

i. 3 .43 6 .19x

ii. 1.43 6 .19x

8M

Cont...2

:: 2 ::

(OR)

c) In a normal distribution 7% of the items are under 35 and 89% are under 63. Determine the mean and variance of the distribution.

8M

d) A sample of 64 students has a mean weight of 70kgs. Can this be regarded as a sample from a population with mean weight 56kgs and standard deviation 25kgs?

8M

4. a) The mean and variance of a binomial distribution are 3 and 2, respectively. Find the

probability that the variate takes place: i. Less than or equal to 2 ii. Greater than or equal to 7

8M

b) A car hire firm has two cars which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson variate with mean 1.5. calculate the proportion of days on which: i. Neither car is used ii. Some demand is refused

8M

5. a) A sample of 10 cam shafts intended for use in gasoline engines as an average eccentricity of 1.02 and a standard deviation of 0.044 inch. Assuming the data may be treated random sample from a normal population. Determine a 95% confidence interval for the actual mean eccentricity of the cam shaft.

8M

b) A continuous random variable x as the distribution function

4

0 , 1

1 , 1 3

1, 3

i fx

F x k x if x

i f x

Determine:

i. f x

ii. k iii. Mean

8M

(OR) c) Two bolts are drawn from a box containing 4 good and 6 bad bolts. Find the probability that

the second bolt is good if the first one is found to be bad. 8M

d) If X and Y are continuous random variable having the joint density function

2 2, , 1

, .

0 ,

c x y o x yf x y

o th e rw is e

Determine:

i. Constant c

ii. 1 1

,2 2

p x y

iii. 1

2p y

8M

6. a) A random sample of 20 daily workers of state A was found to have average daily earning of Rs. 44 with sample variance 900. Another sample of 20 daily workers from state B was found to earn on an average Rs. 30 per day with sample variance 400. Test whether the workers in state A are earning more than those in state B.

7M

b) The time taken by workers in performing a job by method I and method II is given below:

Method I 20 16 26 27 23 22 -

Method II 27 33 42 35 32 34 38

Do the data show that the variances of time distribution from population from which these samples are drawn do not differ significantly?

9M




DISCRETE MATHEMATICAL STRUCTURES

(Common to Computer Science and Engineering & Information Technology)



1. a) “If x is even and a perfect square, then x is not divisible by 3 ”. Express this statement in symbolic form using quantifiers.

2M

b) Prove the following pqqrqqp using the truth table. 2M

c) Define the partial order relation; give an example of not partial order relation. 2M d) Discuss about the uniqueness of the inverse element in a group. 2M

e) Define the order of group and give an example of group of order two. 2M f) Define Semigroup with example 2M

g) Let G be a 4-regular connected planar graph having 16 edges. Find the number of regions of G. 2M h) Define Chromatic number. Find the chromatic number of the complete

graph(Kn) and wheel graph(W5). 2M

i) Discuss about degree sequence of a graph and find the following degree sequence represent the simple undirected graph or not 5, 5, 4, 4, 3, 2, 2, 1 and 1.

2M

j) What is the general solution of a recurrence relation, find the general solution of

1 24 4 2

n

n n na a a

2M

2. a) Without using truth table show that (( ) ( ( ))) ( ) ( )P Q P Q R P Q P R is a tautology

8M

b) Show that following are equivalent: i. ( )P P Q P

ii. ( )P P Q P Q

8M

3. a) Prepare the meet and join table for the set A=1,2,3,12. Is ,A a lattice. 8M

b) Apply suitable technique to solve recurrence relation

.7,221021

aawithaaa

nnn

8M

(OR) c) Find the chromatic number of the following graph.

Fig.1

8M

d) Draw the Hasse-diagram for ,20

D where 20

D is the set of all possible divisible of 20. Is

,20

D a lattice?

8M

Cont…2

:: 2 ::

4. a) Let 2, 3, 6,12A and let R and S be the following relations on A: xR y if and only if

2 divides x y ; x S y if and only if 3 d ivides x y . Compute:

i. R ii. R S

iii. R S

8M

b) Let 1, 2 , 3A and 1, 2, 3, 4B . The relations R and S from A to B are represented by the

following matrices.

1 0 1 0

0 0 0 1

1 1 1 0

RM

,

1 1 1 1

0 0 0 1

0 1 0 1

SM

Determine the relations , ,R R S R S and 1R

.

8M

5. a) Find the solution of recurrence relation

26,6,844210321

aaawithaaaa

nnnn

8M

b) Solve the recurrence relation, 2 1 0 1

, 0 , 0 , 1n n n

F F F fo r n F F

. 8M

(OR) c) Determine the suitable method for ]11......2,1,0[

12Z , the group under addition modulo12,

let H=0,3,6,9, Show that H is a subgroup of 12

Z under 12

.

8M

d) Determine the suitable method to verify, whether (Z,*) is a group. Define the binary operation * on Z by x*y=x+y+1.

8M

6. a) Prove that complete bipartite graph 3 ,3

K a non-planar graph. 8M

b) Demonstrate the steps to be followed to determine whether the following two graphs are isomorphism or not?.

Fig.2

8M




DATA STRUCTURES (Common to Computer Science and Engineering & Information Technology)



1. a) Write the conditions for checking stack overflow and underflow. 2M b) Discuss the advantages and disadvantages of Arrays over Linked Lists. 2M

c) What operations can be performed on stacks? 2M d) Write recursive function for tower of Hanoi problem. 2M

e) What is a queue in data-structure? 2M f) Briefly explain tower of Hanoi. 2M

g) What is a stack? Why do we use stacks? 2M h) What is an AVL Tree? 2M

i) Convert the expression ((A + B) * C - (D - E) ^ (F + G)) to equivalent postfix notation. 2M j) Explain any two hash functions.

2M

2. a) Write a C program for evaluating a valid postfix expression. Trace the same on the postfix expression: A B + C –B A + C ^ - where A = 2, B = 1, C = 3.

8M

b) Write a C program to implement Circular queue operations using array.

8M

3. a) Using singly linked list, write C functions: i. To create two ordered (ascending) lists ii. To merge these two lists

8M

b) Write a C program to implement linear Queue operations using Singly Linked Lists. 8M (OR)

c) Write a C program to implement linear queue operations using arrays and check for queue overflow and underflow conditions.

8M

d) Write C functions to implement the following operations on a Doubly linked list: i. Store a string into the list ii. Delete a particular character from the list iii. Display the string

8M

4. a) Construct a binary tree given the following preorder and inorder traversals: Preorder: A B D G C J M E H I F K L Inorder: D G B J C A H E I M K F L

8M

b) For the following graph Fig.1, starting at vertex “a” traverse the graph using BFS and DFS.

Fig.1

8M

5. a) Along with C program compare the efficiency of following searching algorithms: i. Linear search ii. Binary Search

8M

b) Write Recursive C functions for each of the following: i. Find the maximum element in a Binary Search Tree ii. Count the number of nodes in a Binary tree

8M

Cont…2

::2::

(OR)

c) Write a C program to sort the given characters in alphabetical order using Bubble sort technique. Also derive expression of its time efficiency.

8M

d) Summarize the following Hashing techniques: i. Linear Probing ii. Quadratic Probing iii. Double Hashing

8M

6. a) Illustrate RL and LR rotations of AVL tree with an example for each. Construct an AVL tree given the data: 1, 8, 6, 5, 3, 7, 4

8M

b) Write an algorithm for sorting elements of an array using the Merge Sort technique. Draw the tree structure of the recursive calls made for the input 23, 56, 9, 47, 78, 3, 89, 33. Analyze the efficiency of Merge sort algorithm.

8M




OBJECT ORIENTED PROGRAMMING

(Common to Computer Science and Engineering & Information Technology)



1. a) Define bytecode. What is the main benefit of generating bytecode? 2M b) What is the need of “this” keyword? Demonstrate its usage through sample code. 2M

c) Discuss the procedure to define and import a package. 2M d) How is multiple inheritance implemented in Java. Give an example. 2M

e) Define abstract class with an example. 2M f) What are the two ways of creating a thread in java? 2M

g) Give the output of the following program : import java.util.*; class HashSetEx public static void main(String args[]) //Creating HashSet and adding elements HashSet<String> hs=new HashSet<String>(); hs.add("B"); hs.add("A"); hs.add("D"); hs.add("E"); hs.add("C"); hs.add("F"); System.out.println(hs);

2M

h) What are the differences between a Class and an Interface? 2M

i) List two limitations of AWT. 2M j) Describe two key features of swing.

2M

2. a) Write a program to illustrate the uses of “final” keyword in multilevel inheritance. 8M b) Create a Java package to define a class Shape. The classes Rectangle and Triangle extend the

Shape class to find area. Write a program to access all the classes of package.

8M

3. a) Write a Java program to do the following: i. Create an Account class ii. Create two derived classes for Account class, namely SavingsAccount and

CurrentAccount iii. Create a BankClass, which has an array of Account objects iv. Create an update method in the BankClass, which gives 8% interest to SavingsAccounts

and 6% interest to CurrentAccount

8M

b) Explain the following with code snippets: i. Packages ii. Access Protection

8M

(OR) c) Differentiate between:

i. Abstract class and interface ii. Throw and throws

8M

d) Write a java program to create a 4X4 grid and fill it in with 15 buttons each labelled with its index from 1 to 15.

8M

Cont…2

:: 2 ::

4. a) Write a java program to display 1 to 100 for every 5 seconds in the main thread and childthread has to display A to Z for every 10 seconds. The main thread has to wait until childthread completes its task.

8M

b) Create a try block that is likely to generate ArithmaticExceptaion and NumberFormatException and then incorporate necessary catch blocks to catch and handle them appropriately.

8M

5. a) Describe Delegation Event Model in java. 8M b) Differentiate between usage of Thread class and Runnable interface for creating Threads. With

syntax, explain the uses isAlive() and join() methods. 8M

(OR) c) What is deadlock? Why is it difficult to handle it? Demonstrate deadlock condition through a

java program.

8M

d) Write a program using an applet which will print “Key pressed” on the status window when you press the key “Key released” on status window when you release the key and when type the character it should print “HELLO” at co-ordinate (50, 50) on applet.

8M

6. a) Explain JTable and its models. List the steps required to set up simple JTable that can be used to display data.

8M

b) Develop an applet program to add 2 buttons ‘X2’ and ‘X4’ and a text box. The user needs to enter a number in the text box and when he clicks ‘X2’ button, the number should be multiplied by 2. When he clicks ‘X4’ button the number should be multiplied by 4.

8M




COMPUTER ORGANIZATION (Computer Science and Engineering)



1. a) Convert (0.6875)10 to binary. 2M b) Find the 2’s complement of 1101100. 2M

c) Simplify using Karnaugh maps: f(x,y,z) = Ʃm (2,4,5,6,7). 2M d) Define Flip-flops. 2M

e) Write the truth table of JK flip-Flop. 2M f) Write example of Register notation. 2M

g) Define Micro-operation. 2M h) List various input and output instructions. 2M

i) Write the block diagram of a sequential circuit. 2M j) Describe the application of a decoder.

2M

2. a) Realize all logic gates using NAND gate. 8M b) Simplify the following expression in the POS form using K-map technique.

Y = (a’+b’+c+d) (a’+b’+c’+d) (a’+b’+c’+d’) (a’+b+c+d) (a+b’+c’+d) (a+b’+c’+d’) (a+b+c+d) (a’+b’+c+d’).

8M

3. a) Simplify the expressions: i. z=AB’C’+AB’C+ABC ii. F(w,x,y,z)= (0,1,2,4,5,6,8,9,12,13,14)

8M

b) Implement the following using 8 input multiplexer: i. f(A,B,C,D)= (0,1,3,4,6,8,15) ii. f(A,B,C)= ∑(0,1,3,4,6)

8M

(OR) c) Realize 16:1 multiplexer using two 8:1 multiplexer and 4:1 multiplexer. 8M d) Design a full adder circuit using K-maps.

8M

4. a) What is instruction cycle? Explain various steps involved in the instruction cycle. 8M b) With the help of a circuit diagram, graphic symbol and characteristic table, explain the working

of a JK flip-flop constructed using a D flip-flop and gates.

8M

5. a) List and explain any five addressing modes with an example. 8M b) With a neat block diagram, discuss the basic operational concepts of computer. 8M

(OR) c) With neat diagram explain clocked SR flip-flop, T flip-flop and D flip flop. 8M d) Design a mod 8 synchronous counter.

8M

6. a) Explain the following micro-operations in brief: i. Logical shift ii. Circular shift iii. Arithmetic shift

8M

b) Explain Booths algorithm and multiply 13 * 09 using Booths algorithm. 8M




FORMAL LANGUAGES AND AUTOMATA THEORY

(Information Technology)



1. a) Define the language of a DFA and NFA. 2M b) Construct NFA to accept the strings ending with ab. 2M

c) Identify the languages accepted by the following regular expressions: i. (a+b)*(abb+aa) ii. ((a+b)(a+b)(a+b))*

2M

d) What is power of an alphabet? 2M

e) Define homomorphism. 2M f) Construct a CFG for the language L = anbn | n>=0. 2M

g) When do we say the problem is undecidable? Give an example. 2M h) How do you determine whether the given grammar is ambiguous or not? 2M

i) Write any two major components of Turing Machine. 2M j) Define the language accepted by Turing Machine.

2M

2. a) Design a DFA to accept the following strings over the alphabet 0, 1: i. Odd number of 0’s or even number of 1’s ii. Divisible by 5

8M

b) Write regular expressions for the following languages: i. The set of all strings containing at least two 0’s ii. Set of strings of a’s and b’s ending with the string abb iii. Length of string is either even or multiple of 3 or both

8M

3. a) Construct the minimized automata for the following DFA.

a b

→A B A

B A C

C D B

*D D A

E D F

F G E

G F G

H G D

8M

b) Construct a Moor machine to print the residual modulo 4 over the binary string and find the output string for the given input sequence “101101“.

8M

(OR) c) Prove that every language defined by a regular expression is also defined by a finite

automaton. 7M

d) Design the regular expressions for the following languages: i. L= anbm | n>=1, m>=1, nm<=3 ii. L= a2nb2m | n>=0, m>=0 iii. L=, strings that are not ending with ‘01’ over an alphabet ,0,1--

9M

Cont…2

:: 2 ::

4. a) Obtain finite automata for the following regular expressions. i. (a+b)*(ab+a) ii. 0(0+1)*(01+11)

6M

b) Convert the following DFA to regular expression (Rijk) using Kleene’s method.

Fig.1

10M

5. a) Check whether the string "baaba " is acceptable by the following grammar or not by using CYK algorithm:

S A B B C

A B A a

B C C b

C A B a

8M

b) Construct PDA for the following grammar , , , .S aA A aA B C bB a B b C c

8M

(OR) c) Construct a CFG for the following language and convert the constructed grammar into CNF

L= 0i1j |i ≠ j, i≥ 0, j ≥ 0-. 8M

d) Design Turing machine that computes the following function:

0,

m n m n

m nf m n

8M

6. a) Explain the following: i. Context sensitive language ii. Linear bounded automata

6M

b) Design a Turing Machine that accepts the language L=wwR|wϵ,a, b*. Give the graphical representation for the Turing Machine obtained.

10M

Hall Ticket No: Question Paper Code : A4014



ENVIRONMENTAL SCIENCE (Common for Computer Science and Engineering, Information Technology &

Civil Engineering) Date: 22 November, 2019 FN Time: 3 hours Max Marks: 100

Answer One question from each Unit All Questions carry Equal Marks

UNIT-I

1. Define environment and discuss the scope and multidisciplinary nature of environment with a neat diagram.

20M

2. Discuss in detail about food chains, food webs and energy flow in the ecosystem with neat diagrams.

20M

UNIT-II

3. Explain in detail about the uses and over exploitation of forest resources with good examples and mention significant control measures of deforestation.

20M

4. Discuss natural resources and differentiate renewable and non-renewable resources with suitable examples.

20M

UNIT-III

5. Elaborate the in-situ and ex-situ conservation of biodiversity with suitable examples.

20M

6. Explain the reasons for man-wildlife conflicts with any four case studies regarding these issues.

20M

UNIT-IV

7. Discuss in detail about the causes, effects and control measures of air pollution with suitable examples.

20M

8. Explain in detail on the role of individual in controlling environmental pollution.

20M

UNIT-V

9. Explain in detail about the concept of sustainable development and sustainable development goals with suitable examples.

20M

10. Discuss the following in detail: i. Environmental protection act ii. Mission Kakatiya

20M




MANAGERIAL ECONOMICS AND FINANCIAL ANALYSIS (Common to Information Technology, Mechanical Engineering & Civil Engineering)



1. a) Define law of demand. 2M b) List out types of elasticity demand. 2M

c) Distinguish between Fixed cost &Variable costs 2M d) Describe the term Iso-quant. 2M

e) What is Peak load pricing? 2M f) Define Oligopoly. 2M

g) Define about Journal. 2M h) What is business entity concept in accounting? 2M

i) What is profitability ratio? 2M j) Define capital budgeting.

2M

2. What do you mean by Price Elasticity of demand? Explain the various types of measurement of Price elasticity.

16M

3. a) Explain diagrammatically the Law of Variable Proportions or production function with one variable input.

16M

(OR) c) Swag company manufactures of home use plastic items. The break-up of its cost and sales is

given below: The company produces total 5,000 unit per year Fixed cost Rs.50,000 per annum Variable cost per unit Rs.60 Selling Price per unit Rs.80 You are required to compute: Break Even Point PV Ratio Margin of Safety Number of units for a desired profit Rs.80,000. Find BEP, if the fixed increases by Rs.10,000.

16M

4. Explain the characteristics of Perfect Competition Market. Also explain Equilibrium price and output determination in both short run and long run.

16M

5. a) Journalize the following:

Jan 1 Started business with cash Rs.100,000

5 Deposited Rs.75,000 to bank

10 Purchased furniture Rs.20,000 and paid by cheque

16 Paid shop rent Rs.2,500 cash

21 Withdrew from bank for personal use Rs.1,000

8M

Cont…2

:: 2 ::

b) From the following balances extracted from the books of X Ltd., prepare Trial Balance as on 31st March, 2019:

Particulars Amount (Rs.)

Capital 7,000

Purchases 8,000

Rent paid 240

Drawings 1,200

Bills Receivables 400

Opening stock 1,000

Purchase Returns 280

Sales Returns 160

Plant & Machinery 4,000

Sales 9,600

Sundry Debtors 5,600

Furniture 500

Salaries 720

Sundry Creditors 5,600

Carriage 100

Insurance 40

Cash in hand 100

Cash at Bank 1,950

Commission Paid 40

Bills Payable 1,580

Discount Received 30

Discount Allowed 40

8M

(OR) c) What is financial statement analysis? Highlight the significance of financial analysis through

ratios and Bring out the different types of ratios used in ratio analysis.

16M

6. A company is considering two projects which are independent of each other requires an initial outlay of Rs.500 million. The expected cash flows from the project are given: You are required to calculate the payback period of the projects, NPV of the projects assuming a discount rate of 10%. Which of them should be opted?

Years CFAT

(Rs. Millions) M Project

CFAT (Rs. Millions)

N Project

1 110 380

2 190 220

3 320 180

4 370 100

16M




DIGITAL LOGIC DESIGN (Electronics and Communication Engineering)



1. a) Implement the Boolean function F1 = y’ + xy + x’yz’ using basic gates. 2M b) Implement AND gate using NOR gates. 2M

c) What is the drawback in binary parallel adder? How it can be rectified. 2M d) Realize 4X1 Mux using 2X1 mux. 2M

e) Convert JK Flipflop to T Flipflop. 2M f) What is the difference between Flipflop and Latch. 2M

g) Draw general structure of PAL and show structure of PAL when it is programmed for EX-OR gate.

2M

h) What is the capabilities and limitations of Finite State Machine? 2M

i) Differentiate between TTL and CMOS. 2M j) Compare IC Logic families

2M

2. a) Express the Boolean function F = A + B’C as a sum of minterms. 8M b) Simplify the Boolean function:

i. F (x, y, z) = ∑m (2, 3, 4, 5)

ii. F (x, y, z) = ∑m (3, 4, 6, 7)

8M

3. a) Design a circuit which can add or subtract two 4 bit binary numbers with overflow detection. 8M b) i. Implement 8:1 multiplexer using 4:1 multiplexers.

ii. Implement F (A, B, C, D) = ∑m (1, 3, 4, 11, 12, 13, 14, and 15) using 8:1 MUX (use A, B, C as

selection lines).

8M

(OR) c) Implement 1 bit full adder with following steps:

i. Symbolic representation ii. Truth table iii. K-map iv. Logic diagram

8M

d) Design a combinational logic that can add two 4 bit BCD numbers.

8M

4. a) Design synchronous counter using JK F/F to count 0 2 3 6 5 0 8M b) Design 4-bit ring counter and explain its working with the help of timing diagram.

8M

5. a) Implement the following Boolean function using PROM PLD

f1(x,y,z)=∑m(2,3,4,6) , f2(x,y,z)=∑m(0,1,5,7), f3(x,y,z)=∑m(4,5)

8M

b) Implement the following Boolean function using 3x4x2 PLA

f1(x,y,z)=∑m(1,2,3,6), f2(x,y,z)=∑m(0,1,3,6,7)

8M

(OR) c) Implement the function given using PAL

f1(x,y,z)=∑m(1,2,4,6,7), f2(x,y,z)=∑m(2,4,5,6), f3(x,y,z)=∑m(1,4,6)

8M

d) Realize the following Boolean function using n-mos transistor F(a, b, c)=a’b’ +ac.

8M

6. a) Explain CMOS gate. With neat circuit diagram, explain working of CMOS NOT gate. 8M b) Consider the family of logic gates which operates under static discipline with the following

voltage threshold: VIL=1.5V, VOL=0.5V, VIH=3.5V, VOH=4.4V. Does the choice of voltage threshold offer any immunity to noise? If so, determine the noise margin.

8M




ELECTRONIC DEVICES AND CIRCUIT ANALYSIS (Common to Electronics and Communication Engineering &

Electrical and Electronics Engineering) Date: 15 November, 2019 FN Time: 3 hours Max Marks: 100


1. a) Define forward bias. Draw silicon diode forward bias characteristics. 2M b) Draw the circuit diagram of half wave rectifier. 2M

c) Draw the block diagram of the regulated power supply. Name the function of each block. 2M d) Enumerate the operating regions of a transistor. In which regions it operates like a switch. 2M

e) Mention three different regions of operation of MOSFET. In which region MOSFET acts as resistor.

2M

f) Draw the drain characteristics of JFET. 2M

g) The operating point of a Class B amplifier is located at which portion in the load line. What is its maximum efficiency?

2M

h) A diode has 20nA of reverse saturation current at 20oC. If the temperature is raised to 40oC, determine its new value.

2M

i) When the amplifiers are connected in cascade how the overall gain and band widths are affected?

2M

j) Enumerate the conditions to obtain sustained oscillations.

2M

2. a) With a neat circuit, waveform and transfer characteristics, explain the working of positive peak clipper circuit with reference voltage.

8M

b) Design a circuit to perform the function shown in Fig.1 below, with: i. Ideal diode ii. Silicon diode

8M

Fig.1

3. a) Define static and dynamic resistance of a junction diode. Derive an expression for dynamic resistance.

8M

b) Determine R1 and RC for the network shown in Fig.2, given that ICQ=2mA & VCEQ=10 V. hfe of the transistor is 100.

Fig.2

8M

Cont…2

:: 2 ::

(OR)

c) Explain the working principle and operation of centre tapped transformer based full wave rectifier.

8M

d) Draw h-parameter model of CE amplifier and derive the expressions for voltage gain, current gain, input and output resistances.

8M

4. a) Explain the operation of n-channel enhancement type MOSFET in the following regions: i. Cut off ii. Linear iii. Saturation

8M

b) Sketch the transfer characteristic curve of JFET defined by IDSS =12mA and VP=6V.

8M

5. a) Explain the working principle of series-fed class A amplifier. Derive an expression for its efficiency. Show that it’s maximum efficiency 25%.

8M

b) A peak input signal of 20V driving a load of 16Ω through a Class B Push Pull amplifier biased with 30 V. Determine the input power, output power and circuit efficiency.

8M

(OR) c) Draw the circuit diagrams of cascade and cascode amplifiers and explain its advantages. 8M d) With a block diagram, explain voltage series feedback amplifier circuit. Derive the expressions

for input impedance, output impedance and gain with feedback.

8M

6. a) With neat circuit diagram and relevant expressions, explain BJT Hartley oscillator. 8M b) Determine the voltage gain, input, and output impedance with feedback for voltage series

feedback having A=-100, Ri =10kΩ, Ro = 20kΩ for feedback of: i. β= -0.1 ii. β= -0.5

8M




NETWORK THEORY-I

(Electrical and Electronics Engineering)



1. a) When is an element said to be a Passive element? 2M b) Define an ideal current source. 2M

c) Define Kirchoff’s current law. 2M d) Define a network graph. 2M

e) Define band width and Q-factor for series resonant circuit. 2M f) Define phase sequence in 3-phase system and list any two advantages of 3-phase systems. 2M

g) Write the dual elements of: i. Inductor ii. Capacitor iii. Voltage source iv. Current source

2M

h) A series RLC circuit has R=10Ω, L=0.01H and 0 .1 0C F Calculate the resonant frequency

and band width.

2M

i) Write procedure to draw dual of a network. 2M j) Sketch the frequency response of parallel RLC circuit.

2M

2. a) Use nodal analysis and write nodal equations at nodes a, b, c, d, e in network shown in Fig.1 below. All resistors are in ohms.

Fig.1

8M

b) For the network shown in Fig.2 below, write loop equations and then find all the loop currents.

8M

Fig.2

Cont…2

:: 2 ::

3. a) Using superposition theorem, obtain the current IAB for the following network.

Fig..3

8M

b) Consider the following circuit and apply circuit fundamentals to obtain Thevenin’s equivalent circuit between the terminals AB.

Fig..4

8M

(OR) c) Apply the necessary theorem to obtain the Thevenin’s equivalent circuit in the following

circuit at the terminals AB.

Fig.5

8M

d) Consider the following circuit and apply maximum power transfer theorem to find the impedance ZL and the value of maximum power.

8M

Fig.6

4. a) A 3-phase, 400V, 4-wire system has a star connected load with ZA=(10+j0)Ω, ZB=(15+j10)Ω, Zc=(0+j5)Ω. Determine the line currents and current through the neutral conductor.

8M

b) Three delta connected impedances 0 0 0

5 0 , 5 3 0 , a n d 1 0 6 0A B C

Z Z Z are

connected to a 3-phase, 200V, ABC system. Obtain the phase currents, line currents.

8M

5. a) Find the value of RL for maximum power transfer for the circuit given below. Also find the maximum power transferred to RL.

Fig.7

8M

Cont…3

:: 3 ::

b) Two coils, one of R1 = 0.51 Ω, L1 = 32mH, the other of R2 = 1.3 Ω and L2 = 15 mH and

two capacitors of 25 μF and 62 μF are all in series with a resistance of 0.24 Ω. Determine the following for this circuit: i. Resonance frequency ii. Q of each coil iii. Q of the circuit iv. Cut off frequencies

8M

(OR) c) In a series RLC circuit, C = 50uF. Determine BW, Q,R and L for the following cases.

given r

W = 100, BW= 120.

8M

d) For the following graph, write tie set matrix choosing 1, 2, 3, 6 branches as tree branches.

8M

Fig.8

6. a) A series RLC circuit has the following parameter values: R=10Ω, L=0.01H, 0 .1 0C F

Compute the resonant frequency, bandwidth, lower and upper frequencies of the band width and Q-factor of the CKt.

8M

b) Draw the current locus diagram of an R-L series circuit, when R is varied from zero to infinity. 8M




BASIC ELECTRICAL AND ELECTRONICS ENGINEERING

(Mechanical Engineering)



1. a) State ohm’s law. 2M b) Two resistances each of 32Ω are connected in parallel. What is the equivalent resistance of

this combination? 2M

c) State Thevenin's Theorem. 2M d) What is commutation? 2M

e) A sinusoidal voltage is given by v=20sinwt, what will the instantaneous value of voltage at t=0.002 secs when f=50?

2M

f) Name the different types of transformer with neat diagram. 2M

g) A 1phase transformer connected to 230V, 50Hz supply has 30 primary turns, and the net cross sectional area of the core is 250cm2. Calculate the peak value of flux density in the core.

2M

h) Find equivalent resistance between Point A-B.

Fig.1

2M

i) Mention the various losses in a DC machine. 2M j) Draw the input and output sinusoidal waveform for a 1phase half wave rectifier.

2M

2. a) In the network shown below Fig.2 find the current IX flowing in the circuit using super position theorem.

Fig.2

8M

b) Apply mesh analysis to determine current drawn from the source in the network shown below Fig.3.

Fig.3

8M

Cont…2

::2::

3. a) A 25 KVA transformer has 500 turns on the primary and 50 turns on thesecondary winding.

The primary is connected to 3000V, 50 Hz supply. Findthe full load primary and secondary currents, the secondary emf and the maximum flux in the core.

8M

b) Using KCL and KVL, determine the currents IX and IY in the network shown below Fig.4.

Fig.4

8M

(OR) c) State and explain Thevenin’s theorem with an illustrative example. 8M d) Write the construction and working principle of a transformer.

8M

4. a) Derive an EMF equation of a DC generator. 8M b) Determine the current in all the branches of the network.

Fig.5

8M

5. a) Derive the EMF equation of a transformer. 8M b) Mention the types of DC motors and explain each with neat circuits and equations. 8M

(OR) c) Explain the working principle of DC machine as a motor. 8M d) Explain, why the induced EMF in a DC motor is called back EMF?

8M

6. a) Explain how a D.C. generators converts mechanical energy into electrical energy. With suitable diagrams explain the principal parts of a D.C. generator.

8M

b) Discuss the operation of PN junction diode in forward and reverse bias condition. 8M




THERMODYNAMICS (Mechanical Engineering)



1. a) What is the difference between open system and closed system? 2M b) What do you understand by thermodynamic equilibrium? 2M

c) Define Enthalpy. 2M d) Differentiate reversible and Irreversible process. 2M

e) Define PMMK-I. 2M f) Define efficiency of heat engine. 2M

g) Give Clausius statement of second law of Thermodynamics. 2M h) Right P-V and T-S diagram for an Otto cycle. 2M

i) For the same compression ratio and equal heat input, which cycle is most efficient: Otto, Diesel or Dual?

2M

j) Define universal gas constant. 2M

2. a) Derive an Expression for work done and heat transfer in a polytropic Process. 8M b) A piston cylinder device contains 0.05m3 of gas initially at 200kPa. At this state, a linear spring

having a spring constant of 150kN/m is touching the piston but exerting the no force on it. Now heat is transferred to the gas, causing the piston to rise and to compress the spring until the volume inside the cylinder is thrice the initial volume. If the cross-sectional area of the piston is 0.25 m2. Determine: i. The final pressure inside the cylinder ii. The total work done by the gas

8M

3. a) Define First law of thermodynamics applied to closed system and prove that internal energy is a point function.

6M

b) During a constant pressure process in a closed system with p=105kPa and properties of the

system change from V1=0.25m3, T1=10°C to V2=0.45m3, T2=240C. The specific heat at

constant pressure is given by Cp=0.4+18/(T + 40) kJ/kg. Assuming the mass of the system as 2kg. Determine: i. Work transfer ii. Heat transfer iii. Change in internal energy

10M

(OR) c) What is Joule-Thomson coefficient? Discuss why it is zero for an ideal gas? 8M d) A fluid at the rate of 10 kg/min undergoes a reversible steady flow process. The properties

of fluid at the inlet are P1=1.4 bar, ρ1=25 kg/m3, V1=120 m/s and u1=920 kJ/kg and at the exit are P2=5.6 bar, ρ2=5 kg/m3, V2=180 m/s and u2=720 kJ/kg. During the passage, the fluid rejects 60 kJ/s and raises through 60 m. Determine the change in enthalpy and work done during the process.

8M

4. a) State and prove Clausius inequality. 8M b) An air Compressor takes in air at 1 bar and 350C and compresses it to 4 bar. Find the work

done, heat transfer and change in internal energy per kg of a compressed air when the compression process is: i. Isothermal ii. Adiabatic

iii. According to law PV1.25=C Take R=0.287 and =1.4 Neglect changes in kinetic energy and potential energy.

8M

Cont…2

:: 2 ::

5. a) Discuss with the help of T-h, p-v and p-T diagram for a pure substance. 8M b) A rigid closed tank of volume 3m3 contains 5 kg of wet steam at a pressure of 200kPa. The tank

is heated until the steam becomes dry saturated. Determine the final pressure and heat transfer to the tank.

8M

(OR) c) What is quality of steam? What are the different methods to measurement of quality and

discuss with neat sketch throttling calorimeter for measurement of quality of steam. 8M

d) 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.

8M

6. a) With the help of P-v and T-s diagrams, derive an expression for efficiency of Limited Pressure cycle in terms of compression ratio, pressure ratio and the ratio of specific heats.

8M

b) An engine working on Otto cycle as a clearance of 17% of the stroke volume and initial pressure of 0.95 bar and temperature 300C. If the pressure at the end of constant volume heating is 28 bar. Find: i. The air standard efficiency ii. The maximum temperature in the cycle iii. The ideal mean effective pressure Assuming working fluid to be air. If the relative efficiency of engine is 50%. Calculate the fuel consumption per Kwh. The calorific value of fuel used being 41900 KJ/kg.

8M




SIGNALS AND SYSTEMS (Electronics and Communication Engineering)



1. a) Define impulse function and step function with waveform. Write the relation between the two.

2M

b) Describe the time variance property of systems. 2M

c)

Plot the following discrete signal:

otherwise

nn

nn

nx

0

10510

50

][

2M

d) Find the step response of an LTI system given by 0 .5n

h n u n

2M

e) Describe in brief the procedure to find Fourier transform of periodic signals. 2M

f) What is Hilbert transform? Find Hilbert transform of 2x t A cos ft .

2M

g) Define Region of Convergence. State any two properties. 2M

h) Find the Z Transform of n

x n u n

2M

i) Find the Z -Transform of 1 3x n n n 2M

j) What is aliasing effect?

2M

2.

a) Given 2, 6, 3, 5, 0 , 8 ,x n sketch:

. 2

. 2 2

. 2 2

. 2 1 2

i x n x n

i i x n x n

i i i x n x n

iv x n x n

8M

b) Consider the triangular signal x t shown in Fig.1.

Fig.1

Sketch:

i. 2 3 x t

ii. 3 8x t

iii. 8 1x t

8M

3. a) Find the exponential Fourier series coefficients of the signal x t as shown in Fig.2 and draw

its spectra.

Fig.2

8M

Cont…2

::2::

b) Find the output of an LTI system whose impulse response t

h t e

u t when the input

3

2t

x t e u t u t

8M

(OR) c) If the system is represented by the following difference equation

22 1 .y n x n x n

Is the system: i. Linear ii. Stable iii. Time Invariant iv. Causal

8M

d) Find the exponential Fourier representation of the signal x t shown in Fig.3. Write the

expression for magnitude and phase.

Fig.3

8M

4.

a) Compute the Fourier transform of , 0a t

x t e t

and plot the magnitude and phase

spectra.

8M

b) Find the inverse Fourier transform of the function:

2

3 2

jX j

j j

8M

5.

a) The system function is given by 86

3)(

2

ss

ssH . Determine its impulse response & step

response.

8M

b) Let x t be a signal that has rational Laplace transform with exactly two poles at 1s and

3 .s If 2 t

g t e x t and G [the Fourier transform of g t ] converges, determine

whether x(t)is left sided, right sided or both sided .

8M

(OR) c) A signal 2 cos 400 6 cos 640x t t t is ideally sampled at 5 0 0 .

sf H z If the

sampled signal is passed through an ideal low pass filter with an ideal low pass pass filter with a cutoff frequency 400 Hz. What frequency components with appear in the output? Sketch the output spectrum.

8M

d) Obtain the frequency response and impulse response of the system described by 1

2[ ] [ 1] [ ] 2 [ 1] .y n y n x n x n

8M

6. a) What is Region of Convergence (RoC) in Z-transforms? Explain the properties of RoC. 8M

b) Determine the inverse Z-transform of 2

3 4 1

zX z

z z

for the RoCs:

i. 11,3

z z

ii. 1 13

z

8M




RANDOM VARIABLES AND STOCHASTIC PROCESSES

(Electronics and Communication Engineering)



1. a) A box of 40 diodes is known to contain five defective ones, if two diodes are selected at random without replacement. What is the probability of at least one of these diodes is defective?

2M

b) A random variable has a CDF given by fX(x) = (1- e-x) u(x). Find P(3<X<7). 2M

c) Define expectation. 2M d) Draw probability density function and its distribution function for Gaussian random variable. 2M

e) Define conditional distribution. 2M f) Write the expression for joint characteristic function. 2M

g) Discuss statistical independence of two random variables X and Y. 2M h) If X and Y are independent random variables then find E[XY]. 2M

i) List the properties of power spectral density. 2M j) Give the expression for bandwidth of power spectral density.

2M

2. a) Explain the following term with suitable examples: i. Mutually exclusive events ii. Joint and conditional probability iii. The cumulative distribution function

8M

b) State and Prove Total Probability and Baye’s theorem.

8M

3. a) Define: i. Moments about the origin ii. Central moment iii. Variance iv. Skew

8M

b) A random variable with a uniform probability density function given as fX(x)=1/b 0≤X≤b, 0 otherwise. Find Mean, Second Moment, nth Moment of this random variable.

8M

(OR) c) The joint PDF of (X,Y) is given by f(x,y)=K(2x+3y) 0≤x≤1 0≤y≤1; 0 elsewhere:

i. Determine K ii. Find P[(X,Y) ∈A where A is the region (x,y) such that 0<x<1/ 2 ; 1/4<x<1/ 2 iii. Marginal PDFs fX(x), fY(y).

8M

d) Given the joint PDF f(x,y) = x(1+3y2)/4 0<X<2, 0<Y<1; 0 elsewhere. Find fX(x), fY(y), fX/Y(x/y) and evaluate P(1/4 < X < 12 / Y=1/3).

8M

4. a) Show that the conditional PDF of a random variable X is fX/Y(x/y)=fX,Y(x,y)/fY(y). 8M b) Define the correlation coefficient of two random variables and prove that the correlation

coefficient is less than 1 in magnitude. 8M

5. a) Consider a linear transformation of Vector Random Variables of the form Y=AX +b, find: i. Relation between means of X and Y ii. The correlation matrices of X and Y iii. Co variance matrices of X and Y

8M

b) If X is a two element jointly Gaussian Vector with μX = [ μ1 μ2]T and CXX = [σ1

2 ρσ1σ2 , ρσ1σ2 σ2

2

]. Obtain the expression for joint PDF and Marginal PDFs. 8M

(OR) Cont…2

:: 2 ::

c) Discuss cross correlation and its properties. 8M

d) Given autocorrelation function of a stationary process2

61

425)(

XXR . Find the mean

value and variance of the process.

8M

6. a) Define Autocorrelation function of a random variable and discuss its properties. 8M b) Suppose we form a random process Y(t) by modulating a carrier with another random process,

X(t). That is, let Y(t)=X(t) cos(ωot+Φ) where Φ is uniformly distributed over*0, 2∏+ and independent of X(t). Test whether Y(t) is wide sense stationary or not?

8M




BUILDING PLANNING AND DRAWING

(Civil Engineering)



1. a) Define the following terms: i. Plinth area ii. Floor area

2M

b) Explain the following terms: i. Sanctioned Plan ii. Set back line

2M

c) Explain the following terms: i. Semi-detached house ii. Detached house.

2M

d) Explain the following: i. Open well ii. Dog-legged stair

2M

e) What are the requirements of a good stair? 2M f) Write different methods of scheduling. 2M

g) Define FAR. 2M h) Define event. 2M

i) Define Activity. 2M j) Define Pessimistic time.

2M

2. a) Describe briefly the main objectives of building bye laws. 8M b) Explain the limitations of built up area.

8M

3. a) Explain the various rooms and recommended minimum areas of a residential building. 8M b) Write a brief note on classification of public buildings. 8M

(OR) c) Write a model plan of a two bed room residential building and explain. 8M d) Identify the needs of lighting and ventilation requirements for a building.

8M

4. a) Write briefly about open space requirements of buildings. 8M b) What are the requirements of a Kitchen?

8M

5. a) Write the importance and necessity in planning of educational institutes. 8M b) What are the requirements of a Living room? 8M

(OR) c) List and explain various types of residential buildings. 8M d) Model a public building plan and explain briefly various rooms.

8M

6. a) What is scheduling and Explain various steps in project scheduling phase? 8M b) Distinguish between PERT and CPM. Explain the circumstances under which one is preferred

over the other. 8M




STRENGTH OF MATERIALS-I

(Civil Engineering)



1. a) Define Poisson’s ratio and bulk modulus. 2M b) Explain the different types of beams. 2M

c) Explain about point of contra flexure. 2M d) Explain the different types of loads. 2M

e) What are the different types of loading system in beams? 2M f) What is meant by principle of supper position? 2M

g) Draw bending stress distribution for rectangular and circular section. 2M h) Explain the concept of simple shear. 2M

i) Define pure bending. 2M j) What is meant by neutral axis?

2M

2. a) A bronze bar is fastened between a steel bar and an aluminum bar as shown in Fig.1. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140MPa in the steel, 120MPa in the bronze and 80MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use Est = 200 GPa, Eal = 70 GPa, and Ebr = 83 GPa.

Fig.1

8M

b) A steel tube of 30mm external diameter and 20mm internal diameter encloses a copper rod of 15mm diameter to which it is rigidly joined at each end. If, at a temperature of 10oC there is no longitudinal stress, calculate the stress in each rod and in tube when the temperature is raised to 200oC. Take E for steel and copper as 2.1x105 N/mm2 and 1x105 N/mm2 respectively. The value of co-efficient of linear expansion for steel and copper is given as 11x10-6 per oC and 18x10-6 per oC respectively.

8M

3. a) A cantilever of length 5.0m loaded as shown in the Fig.2. Draw the SF and BM diagram.

Fig.2

8M

b) A simply supported beam of length 10m carries the uniformly distributed load and two point loads as shown in Fig.3. Draw the SF and BM diagram and also calculate the maximum bending moment.

Fig.3

8M

Cont…2

:: 2 ::

(OR) c) The following data were recorded during the tensile test of a 14mm diameter mild steel rod.

The gauge length was 50mm. plot the stress strain diagram and determine: i. Proportional limits ii. Modulus of elasticity iii. Yield point iv. Ultimate strength

Load (N) Elongation (mm) Load (N) Elongation (mm)

0 0 46200 1.25

6310 0.010 52400 2.50

12600 0.020 58500 4.50

18800 0..030 68000 7.50

25100 0.040 59000 12.50

31300 0.050 67800 15.50

37900 0.060 65000 20.00

40100 0.163 61500 Fracture

41600 0.433

8M

d) Derive the expression for bending equation. M E

I y R

8M

4. a) An I section as shown in Fig.4 is simply supported over a span of 12m. if the maximum permissible bending stress is 80N/mm2, what concentrated load can be carried at a distance of 4m from one support?

Fig.4

8M

b) The shear force acting on a section of a beam is 50kN. The section of the beam is of T shaped of dimensions 100mm x 100mm x 20mm as shown in Fig.5. The moment of inertia about the horizontal neutral axis is 314.2x104 mm4. Calculate the shear stress at neutral axis and at the junction of web and flange.

Fig.5

8M

Cont…3

::3::

5. a) Derive an expression for slope and deflection of a simply supported beam carrying a point load

at the centre by Mohr’s theorem. 8M

b) Find the displacement of free end of cantilever beam shown in Fig.6 take E=2X105N/mm2, I=180X106mm4.

Fig.6

8M

(OR) c) A simply supported beam of 6m span is subjected to a concentrated load as show in Fig.7.

Calculate: i. The position and the value of maximum deflection ii. Slope at mid span iii. Deflection at the load point

Fig.7

8M

d) A 5 meters simply supported beam is subjected to downward point loads as show in Fig.8. Determine: i. Slope at the support ii. Deflection at the points of application of loads. Take E=200Gpa and I=80X10-5m4.

Fig.8

8M

6. a) A rectangular block of material subjected to a tensile stress on 110N/mm2 on one plane and a tensile stress of 47N/mm2 on plane right angles to the former. Each of the above stresses is accompanied by a shear stress of 63N/mm2 and that associated with the former tensile stress tends to rotate the block anticlockwise. Find: i. The direction and magnitude of major and minor principal stress ii. Magnitude of maximum shear stress

8M

b) At a certain point in a strained material, the intensities of stresses on the two planes at right angles to each other are 20N/mm2 and 10N/mm2 both tensile. They are accompanied by a shear stress of 10N/mm2. using Mohr’s circle find the principal planes and principal stresses.

8M




ELECTROMAGNETIC FIELD THEORY (Electrical and Electronics Engineering)



1. a) Specify the unit vector extending from the origin toward the point G(2,-2,-1). Also find the OG vector magnitude.

2M

b) Mention the applications of Gauss’s Law. 2M

c) Write the expression for divergence in spherical coordinates. 2M d) State Maxwell’s first equation. 2M

e) Define amperes circuit law. 2M f) Calculate the capacitance of a parallel plate capacitor having a mica dielectric of 6, a plate area

of 10cm2, and a separation of 0.01cm. 2M

g) What is a dipole? 2M h) State Gauss law with necessary equation. 2M

i) Define biotsavarts law. 2M j) State Fardays law.

2M

2.

a) What is a Gauss’s law and derive the point form of Gauss law ( .v

D ).

8M

b) Find the electric field intensity (E) at a point (0, 3, 1), if two point charges 1mc and -2mc are located at (3, 2, 1) and (-1, -1, 4) respectively.

8M

3. a) Derive an expression for electric field intensity (E) due to infinite line charge using Coulomb’s law.

8M

b) Determine electric field intensity at any point due to an infinite sheet of charge having uniform

surface charge density .s

8M

(OR) c) State Coulomb’s law. Explain its vector form. 8M d) Two point charges 5nC and -2nC are located at (2, 0, 4) and (-3, 0, 5) respectively. Find the

force on a 1nC point charge located at (1, -3, 7).

8M

4. a) Obtain Laplace’s equation. Using Laplace’s equation find the capacitance of parallel plate capacitors.

8M

b) Obtain the boundary conditions at the interface of a conductor and dielectric.

8M

5. a) Describe self inductance and mutual inductance. 8M b) Write a note on scalar magnetic potential and its limitations. 8M

(OR) c) Describe Lorentz force equation and derive the equation to represent the force between two

straight long and parallel current carrying conductors. 8M

d) The point charge Q=18nc has a velocity of 5X106m/s in the direction av=0.6ax+0.75ay+0.3 az. Calculate the magnitude of the forces exerted on the charge by the field: i. B= -3ax+4ay+6azmT (Magnetic force) ii. E= -3ax+4ay+6azKV/m (Electric force) iii. B and E acting together (Lorentz force)

8M

6. a) List out four Maxwell equations for time varying electromagnetic fields in integral and point form.

8M

b) Explain vector form of Faraday’s law of electromagnetic induction and derive Maxwell

equation Curl / .E B t

8M




ELECTRICAL MACHINES - I (Electrical and Electronics Engineering)



1. a) What is the necessity of starter in DC motors? 2M b) What is core loss? What is its significance in electric machines? 2M

c) Define slip of induction motor. 2M d) A 10 pole dc machine has a lap wound armature. It has 600 conductors, each of resistance

0.05Ω. What is the armature resistance? 2M

e) How short shunt and long shunt compound winding is selected? 2M

f) What are the conditions to be fulfilled for a dc shunt generator to build back emf? 2M

g) Under What circumstances a dc shunt generator does fails to generate? 2M

h) What is an induction generator? 2M

i) The power input to the 3-phase induction motor is 60kW. The stator losses total 1kW. Find the mechanical power developed at the slip of 3%.

2M

j) Explain the effect of increasing the poles of a 3-phase wound rotor induction motor.

2M

2. a) Discuss with neat diagram, the different methods to improve commutation in a DC machine.

10M

b) The brushes of a lap connected 400 kW, 6 pole DC Generator are given a lead of 21 degrees electrical. If the generator has 900 conductors and delivers full load current of 750A, determine: i. The demagnetizing AT ii. Cross magnetizing AT

6M

3. a) Describe the experimental set up for Hopkinson’s test and explain its advantages. 8M b) Explain with neat figure 3 point starter. 8M

(OR)

c) A 6-pole, 50Hz, 3-phase induction motor running on full load develops a useful torque of 160Nm when the rotor emf makes 120 complete cycles per minute. Calculate the shaft power output. If the mechanical torque lost in friction and that for core-loss is 10Nm. Compute: i. The copper-loss in the rotor windings ii. The input to the motor iii. The efficiency The total stator loss is given to be 800W.

8M

d) A 200V shunt motor takes 10A when running on no-load. At higher loads the brush drop is 2V and at light loads it is negligible. The stray-load loss at a line current of 100A is 50% of the no-load loss. Calculate the efficiency at a line current of 100A if armature and field resistances are 0.2Ω and 100Ω respectively.

8M

4. a) With neat circuit diagram explain Swinburne’s test. 8M b) Analyze how the speed is controlled by adding an external resistance in the rotor circuit of

slip ring induction motor. List the disadvantages. 8M

Cont…2

:: 2 ::

5. a) Explain Ward Leonard system of speed control with relevant diagram. 8M b) An 8-pole, 3-phase, 50Hz induction motor runs at a speed of 710rpm with an input power of

35kW. The starter copper loss at this operating condition is 1200W while the rotational losses are 600W. Find: i. Rotor copper loss ii. Gross torque developed iii. Gross mechanical power developed iv. Net torque and mechanical power output

8M

(OR) c) What is meant by the torque in synchronous watts? Write its expression in terms of circuit

model quantities. There from find the torque developed. 8M

d) A 150kW, 3000V, 50Hz, 6-pole star-connected induction motor has a star-connected slip-ring rotor with a transformation ratio of 3.6 (stator/rotor). The rotor resistance is 0.1W/phase and its per phase leakage inductance is 3.61mH. The stator impedance may be neglected. Find: i. The starting current and torque on rated voltage with short-circuited slip-rings ii. The necessary external resistance to reduce the rated-voltage starting current to 30A and

the corresponding starting torque

8M

6. a) Sketch and analyze the speed-current, speed-torque and torque - current characteristics of DC series motor and shunt motor.

10M

b) Derive an expression for the torque of a DC motor with usual notation. 6M




MECHANICS OF SOLIDS (Mechanical Engineering)



1. a) Differentiate between true stress and engineering stress. 2M b) Define:

i. Homogeneous materials ii. Isotropic materials

2M

c) Write the difference between beam subjected to point load and moment. 2M d) Write different types of beams. 2M

e) Explain the sectional modulus of hollow circular section. 2M f) Illustrate difference between UDL and UVL by drawing SFD. 2M

g) Define the terms: i. Deflection of beam ii. Slope

2M

h) Write an expression for the maximum deflection of a cantilever beam subjected to UDL of

intensity ‘’.

2M

i) Explain thermal stress and corresponding strain. 2M j) When a thin – walled cylinder is subjected to internal pressure, principal stresses in three

mutually perpendicular will be set up – name them and explain any one type of stress.

2M

2. a) Derive the relationship 3 1 2E K with usual notations start from the fundamentals. 10M

b) Draw stress-strain curve of: i. Ductile Material ii. Brittle Material Also locate the salient points on it.

6M

3. a) Obtain governing equations for finding stresses induced in a compound/composite bar when subjected to an axial load P.

6M

b) A member ABCD is subjected to point loads P1, P2, P3 and P4 as shown in Fig.1. Calculate the

force P3 necessary for equilibrium if P1 120 kN ; P2 220 kN and P4 160 kN. Determine

also the net change in length of member. Take E 2 105 N/mm2.

Fig.1

10M

(OR)

c) Derive bending equation R

E

YI

M b==

with usual notations.

9M

d) Draw SFD and BMD for the Cantilever Beam shown in Fig.2.

7M

Fig.2

Cont…2

::2::

4. a) Derive an expression for slope and deflection at any section when a simply supported beam

is subjected to uniformly distributed load. Also find maximum deflection and maximum slope 10M

b) A simply supported beam of span 5m has a cross section 150mm x250mm. If the permissible stress is 10 N/mm2, find: i. Maximum intensity of UDL it can carry ii. Maximum concentrated load P applied at 2m from one end it can carry

6M

5.

a) Derive an expression 2

2

d yM E I

d x with usual notations.

10M

b) A thin cylinder shell of 160 mm internal diameter is subjected to an internal pressure of 8N/mm2. Find the thickness of shell if the permissible or hoop stress in the section is not to exceed 35N/mm2.

6M

(OR) c) Using Double Integration method, determine the slope and deflection for a cantilever beam

subjected to concentrated load at free end. 8M

d) A beam of an I-Section consists of 180mm x 15mm flanges and a web of 280mm x 15mm thickness. It is subjected to a shear force of 60kN. Sketch the shear stress distribution along the depth of the section.

8M

6. a) A thin cylindrical shell, 2m long has 200mm diameter and 10mm thickness. It is completely filled with a fluid at atmospheric pressure. If an additional 25000mm3 fluid is pumped into the cylinder. Find the pressure developed and hoop stress developed. Determine also changes in diameter and length. Take E=2x105N/mm2, Poisson’s ratio = 0.3.

8M

b) A thick cylinder pipe outside diameter 300mm and internal diameter 200mm is subjected to an internal fluid pressure of 14N/mm2. Determine the maximum hoop stress developed in the cross section. Sketch the variation of hoop stress across thickness of the pipe.

8M




FLUID MECHANICS (Civil Engineering)



1. a) A Soap bubble of 50 mm diameter has a pressure difference of 20N/mm2 between inside and outside. Determine the coefficient of Surface tension of the Soap bubble.

2M

b) The head of water over an orifice of diameter 50mm is 12m. find the actual velocity and actual discharge of jet at Vena contracta. Take Cd as 0.6 and Cv as 0.9.

2M

c) Distinguish between Newtonian fluid and non-Newtonian fluid. 2M d) Express Pascal’s law, and give a real-world example of it. 2M

e) Define Stream function and Velocity potential. 2M f) List the forces acting on the fluid flow. 2M

g) Determine the gauge pressure and absolute pressure of water at a point which is 2m below the water surface. Take atmospheric pressure as10.1N/cm2

2M

h) An oil of Specific gravity 0.8 is contained in a vessel. At a point the height of oil is 20m. Find the corresponding height of water at that point.

2M

i) A Pitot tube is inserted in to the pipe line at its centre, which carries water The mercury manometer connected to the Pitot tube shows a deflection of 100mm. Find the Velocity at the centre of the pipe line if the coefficient of the tube is 0.75

2M

j) Explain the terms: Stream line, Path line, Streak line and Stream tube.

2M

2. a) Derive expression for force on an inclined plane submerged in fluid and obtain the expression for centre of pressure.

8M

b) A triangular Plate of base width 1m and height 1.5 m is immersed in water. The plane plate is making an angle of 30° with the free surface and the base is parallel to and at a depth of 2 meters from water surface. Determine the total pressure on the plate and the position of centre of pressure,

8M

3. a) Differentiate: i. Eulerian and Lagrangian methods ii. Pathlines, streamlines and streaklines

8M

b) Derive an expression for continuity equation for a three dimensional steady incompressible flow.

8M

(OR) c) Explain various types of fluid flows. 8M d) Velocity vector in a fluid flow is given by (6xt+yz2)i+(3t+x2y)j+(xy-2xyz-6tz)k

i. Verify whether continuity equation satisfied ii. Find the acceleration vector of fluid at point (2,2,2) at time t=2.0

8M

4. a) State and prove Bernoulli’s equation. Mention the various applications of Bernoulli’s theorem. 8M b) A venturimeter is installed in a pipeline carrying water and is 30cm diameter. The throat is

12.5cm. The pressure in the pipeline is 140kN/m2, and the vaccum in the throat is 37.5cm of mercury. Four percent of the differential head is lost between the gauges. Working from first principles find the flow rate in pipeline in litres/s assuming the venturimeter to be horizontal.

8M

5. a) Prove that, the loss of head in a pipe line due to sudden expansion is a function of velocity head.

7M

b) Determine the rate of flow through a pipe line of diameter 20cm and of length 50m, when one end of the pipe is connected to a tank and the other end is open to the atmosphere. The pipe line is horizontal and height of water in the tank is 4m above the pipe central line. Consider all losses and take f as 0.009

9M

(OR) Cont…2

:: 2 ::

c) Differentiate between a broad crested weir and a Sharp crested weir. Find the condition for maximum discharge over a broad Crested weir and derive an expression for maximum discharge

8M

d) During a test in a laboratory the water passing through the Venturimeter is made to flow over a 90˚ V-notch. The diameter of inlet and the throat of venturimeter is 250mm and 100mm respectively. The pressure head difference is 34 cm, when the head over the V-notch is steady at 18.2cm. If Cd for the Venturimeter is 0.95, what is the coefficient of discharge for the V-notch?

8M

6. a) Derive expression for drag and lift when forces when arbitrary solid body is placed in fluid. 8M b) For the following velocity profiles, determine whether the whether the flow has separated or

on theof separated or will attach with the surface. Also suggested method to prevent boundary layer.

i.

2

2

1

2

3

yy

U

u

ii.

32

2

12

yy

U

u

iii.

2

2

12

yy

U

u

8M




MATERIAL SCIENCE AND METALLURGY (Mechanical Engineering)



1. a) Compare fine grained metal with a coarse grained metal. 2M b) Define the following terms:

i. Material science ii. Metallurgy

2M

c) Define dislocations. List its types. 2M d) Define Hardness and Hardenability. 2M

e) Define Heat Treatment process. 2M f) Define Phase Rule. 2M

g) Write composition and properties of Low Alloy Steels. 2M h) Define interstitial solid solution. 2M

i) If the pure iron is heated to 9500 C and subjected for fast cooling. What will be the effect of grain size and why?

2M

j) Define Surface Hardening process.

2M

2. a) Determine the Atomic Packing Factor of FCC and HCP crystal structures. 8M b) Using neat sketches describe the line imperfections in crystal.

8M

3. a) State the Hume – Rothery rules for extensive solid solubility of one element in another. 8M b) Explain the Peritectic system with neat diagram. 8M

(OR) c) Explain the following reactions:

i. Eutectic Reaction ii. Peritectic Reaction iii. Eutectoid Reaction iv. Peritectoid Reaction

8M

d) Draw Fe-Fe3C equilibrium diagram and mark all the fields and microstructures in the diagram.

8M

4. a) Write the composition, preparation method, microstructure, properties and applications of Grey Cast Iron, Malleable Cast Iron, White Cast Iron, Spheroidal Graphite Cast Iron.

8M

b) Write the classification of steels. Write the properties, composition and applications of various Stainless Steels.

8M

5. a) Draw the T-T-T diagram for Eutectoid steel and show the cooling curves which represent various heat treatment processes.

8M

b) Enumerate the effect of Austenite stabilizers and Ferrite stabilizers on the transformation curves using a neat sketch.

8M

(OR) c) Using neat sketch explain the Jominy End Quench test to determine Hardenability of a

material. 8M

d) Compare and contrast Annealing, Hardening and Tempering heat treatment processes.

8M

6. a) Write the classification of Copper alloys. Write the composition and properties of various types of Bronzes.

8M

b) Write the classification of Wrought Aluminium alloys. Write the composition and properties of heat treatable wrought aluminium alloys.

8M




SURVEYING

(Civil Engineering)



1. a) Define the following: i. Whole circle bearing system ii. Quadrennial bearing system

2M

b) What are the accessories is plane table surveying. 2M

c) Define the following: i. Fore bearing ii. Back bearing

2M

d) Convert from W.C.B to Q.B. : (i) 220 30’ (ii) 3270 24’ Q.B. to W.C.B. : (i) N 120 24’ E (ii) S 680 6’ W

2M

e) Define contour interval and contour gradient. 2M f) Explain reciprocal ranging. 2M

g) Define the following: i. Level surface ii. Datum

2M

h) Classify the levelling staff. 2M

i) Define the following in leveling: i. Horizontal plane ii. Bench mark

2M

j) Explain an error is plane table survey.

2M

2. a) Explain the following types of chain: i. Surveyors chain ii. Engineers chain iii. Revenue chain iv Metric chain

8M

b) Choose any two methods to find the obstacle length when: i. Chaining is possible but ranging not possible ii. Ranging is possible but chaining not possible

8M

3. a) The following interior angles were measured with a sextant in a closed traverse. The bearing of the line AB was measured as 600 00’ with prismatic compass. Calculate the bearings of all other line if ∟A = 1400 10’, ∟B = 990 8’, ∟C = 600 22’, ∟D = 690 20’.

8M

b) The following bearings were observed while traversing with a compass. Mention which stations were affected by local attraction and determine the corrected bearings:

Line F.B. B.B.

AB 450 45’ 2260 10’

BC 960 55’ 2770 5’

CD 290 45’ 2090 10’

DE 3240 48’ 1440 48’

8M

(OR) c) What is local attraction? How is it detected and eliminated? 8M d) Explain the different types of compass.

8M

4. a) Explain the methods of plane table surveying employed for locating the details. 8M b) Explain the errors in Plane tabling. 8M

Cont….2

::2::

5. a) Explain the characteristics of contour with the help of neat sketches. 8M b) The following staff readings were observed successively with a level. The instrument have

been moved after 5th and 9th reading. 0.813, 2.170, 2.908, 2.630, 3.133, 3.752, 3.277, 1.899, 2.390, 2.810, 1.542: calculate the R.L of points, if the first reading was taken with a staff held on a 13m of 39.563m.

8M

(OR) c) Compare the rise and fall method of reducing leveling with height of collimation method. 8M d) Analyze the following cross staff survey of a field ABCDEFG and determine its area:

G

1220 110 F

E 190 980

724 220 D

C 180 475

150 62 b

0

A

8M

6. a) Identify advantages and disadvantages of various methods of contouring and describe them in detail.

8M

b) Discuss the uses of contour maps. 8M




DIGITAL DESIGN AND COMPUTER ORGANIZATION (Information Technology)



1. a) Convert (0.6875)10 to binary. 2M b) Find the 2’s complement of 1101100. 2M

c) Simplify using Karnaugh maps: f(x,y,z) = Ʃm (2,4,5,6,7). 2M d) Define Flip-flops. 2M

e) Write the truth table of JK flip-Flop. 2M f) Write example of Register notation. 2M

g) Define Micro-operation. 2M h) List various input and output instructions. 2M

i) Write the block diagram of a sequential circuit. 2M j) Describe the application of a decoder.

2M

2. a) Realize all logic gates using NAND gate. 8M b) Simplify the following expression in the POS form using K-map technique.

Y = (a’+b’+c+d) (a’+b’+c’+d) (a’+b’+c’+d’) (a’+b+c+d) (a+b’+c’+d) (a+b’+c’+d’) (a+b+c+d) (a’+b’+c+d’).

8M

3. a) Simplify the expressions: i. z=AB’C’+AB’C+ABC ii. F(w,x,y,z)= (0,1,2,4,5,6,8,9,12,13,14)

8M

b) Implement the following using 8 input multiplexer: i. f(A,B,C,D)= (0,1,3,4,6,8,15) ii. f(A,B,C)= ∑(0,1,3,4,6)

8M

(OR) c) Realize 16:1 multiplexer using two 8:1 multiplexer and 4:1 multiplexer. 8M d) Design a full adder circuit using K-maps.

8M

4. a) What is instruction cycle? Explain various steps involved in the instruction cycle. 8M b) With the help of a circuit diagram, graphic symbol and characteristic table, explain the working

of a JK flip-flop constructed using a D flip-flop and gates.

8M

5. a) List and explain any five addressing modes with an example. 8M b) With a neat block diagram, discuss the basic operational concepts of computer. 8M

(OR) c) With neat diagram explain clocked SR flip-flop, T flip-flop and D flip flop. 8M d) Design a mod 8 synchronous counter.

8M

6. a) Explain the following micro-operations in brief: i. Logical shift ii. Circular shift iii. Arithmetic shift

8M

b) Explain Booths algorithm and multiply 13 * 09 using Booths algorithm. 8M

VARDHAMAN COLLEGE OF ENGINEERING...a) Probability that a man will be alive 25 years hence is 0.3 and the probability that his wife will be alive 25 years hence is 0.4. Find the probability

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