Sub: EM-III (14MA301) Section: A & B Date: 13/07/17 One Mark Questions: 1. a) Write the iterative formula to compute 3 N by Newton s method.

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1 Bapatla Engineering College:: Bapatla (Autonomous) Department of Information Technology Assignment-I Question Paper - III Sem Class: 2/4 B.Tech Section: A Sub: EM-III (14MA301) Section: A & B Date: 13/07/17 a) Write the iterative formula to compute 3 N by Newton s method. b) Write Newton s back ward interpolation formula. c) State divided difference formula. d) Write simpson s one-third rule. e) Write Lagrange interpolation formula. f) When can the Simpson s rule be applied to evaluate an integral? g) What is the order of the Newton iteration method. h) Can Lagrange interpolation method be used for the data in which x values are equally spaced? i) Distinguish between Newton s forward interpolation formula and Newton s divided difference interpolation formula. j) When can we use Newton s forward interpolation formula and Newton s backward interpolation formula? 3 2 Using fixed point iteration find a solution of x + x 1= 0 correct to 5 decimal places. 2. Find a root of 2x log10x= 7 using fixed point iteration. 3. Design a Newton iteration for cube roots and compute Find a positive root of xsinx+ cosx= 0 correct upto six decimal places by Newton-Raphson s method. 5. Find the real roots of the equation x 4 -x-9 = 0 by Newton-Raphson s method. 6. Use Newton s Divided difference formula to find f(7) if f(-4)=1245, f(-1)=33, f(0)=5, f(2)=9 and f(5)= Using Lagrange interpolation formula find f(0.75), given f(0.25) = f(0.5) = f(1) = Find (410), f(210) by using Newton s interpolation formulas for the data: () Apply i) Trapezoidal rule ii) Simpson s one third rule of x dx, by taking six equal sub intervals. Compare it with the exact value. dx 10. Evaluate I = 1 + x 0 error correct to 6D. 1, using Trapezoidal rule and Simpson s Rule with h = 0.25 and find the 2 3 3

2 Sub: DMS (14IT302) Section: A & B Date: 15/07/17 a) What is discrete mathematics? b) What is the power set of the empty set? What is the power set of the set {Փ}? c) Define subset and proper subset. d) How many elements does each of these sets have where a and b are distinct elements? e) P({Փ, a, {a}, {{a}}}) b) P(P(Փ)) f) Prove B-A c =B A g) Prove that the empty set is unique. h) What do you mean by well defined or single valued. i) Give one example for the relation does not satisfy symmetric and anti symmetric. j) Define constructive dilemma. k) Give contra positive, converse and opposite of the following: If triangle ABC is a right triangle, then AB 2 + BC 2 = AC 2. l) Define Pigeonhole principle. m) Construct truth table for (pᴧ q) q n) What is inference pattern? o) Define proposition and open proposition. p) Identify the type of fallacy for the following: AB is parallel to EF or CD is parallel to EF. AB is parallel to EF. Hence, CD is not parallel to EF. a) List the several ways of describing a set with suitable example. b) Describe various properties of binary relation with suitable examples. 2. a) Discuss about the types of functions with suitable example. b) Define Congruence relation. Check which of the following pairs is congruence modulo 5. (i) (-19,19) (ii) (-11,19) (iii) (7,19) (iv) (54,19) 3. a) Prove distributive and demorgan s laws using set builder notation. b) Prove that B-A is subset of AC. 4. Explain in detail about various methods of proof of an implication. 5. Prove or Disprove the following statements (i) The governor will call a special session only if the Senate cannot reach a compromise. If a majority of the cabinet are in agreement, then the governor will call a special session. The senate can reach a compromise. Hence, the governor will not call a special session. (ii) r pᴠq q->r p. 6. Check whether the following are tautologies or not (i) {[(pᴠq)->r]ᴧ( p)}->(q->r) (ii) [(p->q)ᴧ(r->s)ᴧ(pᴠr)]->(qᴠs) 7. a) Describe the rules of inferences for quantified propositions.

3 b) Prove the validity of the following arguments: Every living thing is plant or an animal. David s dog is alive and it is not a plant. All animals have hearts. Hence, David s dog has a heart. Sub: DLD (14IT303) Section: A Date: 18/07/17 a) What do you mean by a positional weighted system? b) Why is the binary number system used in digital systems? c) How negative numbers are represented and give one example? d) What do you mean by end around carry? e) State the principle of duality? f) Find x if (A2C) 16 =(x) 8? g) If 52/4=12 find the base of this number system? h) What is the minimum number of bits required to encode the decimal digits 0 through 9? Justify your answer. i) What do you mean by sequential code? Name two sequential codes. j) What do you mean by self-complementing code? k) What do you mean by reflective code? l) Disadvantages of BCD code. m) What are the applications of gray code? Discuss about r s and (r-1) s complement methods of subtraction with an example. 2. Explain about the following conversions with suitable examples. a) Binary fraction to decimal b) octal to hexadecimal c) decimal fraction to octal 3. a) Write a short note on self complementing and reflected codes with an example? b) Differentiate 1 s and 2 s complement methods. 4. How to perform binary to gray and gray to binary code conversions. Explain with an example? 5. State and prove demorgan s laws using postulates of an algebra. 6. State and prove a) commutative b) distributive c) consensus theorem 7. Explain in detail about three variable and four variable k-map with suitable examples. Sub: OS (14IT304) Section: A Date: 20/07/17 One mark questions: a) Define Operating System. b) Define Process. c) What is Dual mode Operation? d) What is system call?

4 e) List any two Operating System goals. f) List any three Scheduling Queues. g) What is the work of scheduler? h) Differentiate mechanism and policy. i) Differentiate Command Interpreter and GUI j) What is process control block? Six mark questions: Discuss various services of operating system. 2. Explain following a) Storage management b) Process management 3. Demonstrate various structures of operating system. 4. Explain about Interprocess communication. 5. Discuss Multithreading Models 6. Explain Process concept. Sub: DS (14IT305) Section: A & B Date: 22/07/17 Part-I Answer any four questions. a) Need of data structure with an example. b) What is Stack Data Structure? Is stack a linear or non-linear? c) Mention the applications of Stack ADT. d) What are the different notations to represent a mathematical expression?which notation is most suitable for use in Computers? e) Convert infix expression c^d-e*(a+b) into post fix. f) Basic features of post fix expression. g) List the operations performed on Stack and Queue ADT. h) How circular queue is different than linear queue. i) Give any two applications of linear queue. j) Define delimiter. Name any four. k) Write the condition which satisfies Stack empty and Queue empty. l) Give the limitation of a linear queue and how to overcome. m) Write a formula to find the position at anytime of the REAR in circular queue. n) What is sorting? Name any four sorting techniques. o) Give the purpose of pivot element in quick sort. Answer any one question. Part-II a) Write a C-routine to implement PUSH and POP operations of a stack. b) Explain how to convert infix expression to postfix expression with an example. 2. a) Write a C-program to implement the conversion of infix to postfix expression. b) Describe the algorithm for evaluating post fix expression.

5 3. a) Write a C-routine for delimiter matching using stack. b) Implement the evaluation of post fix expression using C. 4. a) Explain in detail about Linear queue and Circular Queue ADT. b)write a C-routine to implement Circular Queue. 5. a) Perform merge sort on the following values 37,95,85,15,66,42,52,72,8,25. b) Implement merge sort algorithm using C. 6. Write a C-program to implement Quick Sort. Sub: OOP (14IT306) Section: A & B Date: 25/07/17 Answer any four questions. a) What is the use of this keyword? b) What the jagged array? c) Define class and object? d) Pillar of oops? Define each? Part-I e) What is the use of the break, continue, and exit? f) What is a constructor? Type of constructors. g) What is implicitly typed variable? h) What are short circuit logical operators? i) What is implicitly typed arrays with example? j) What is polymorphism? Type of polymorphism? Answer any one question. Part-II List and write about various data types, literals and variables in c# with their usage example. 2. List and write about various program control statements in c# with example program. 3. Define an Array and Type of arrays? Write a c# program to reverse the list of numbers by using one dimensional array. 4. a) Define class and Explain in details about class and object with example. b) Explain about static class and static members with example. 5. Explain about constructor overloading and method overloading with example. 6. What is string? Different string handling methods with suitable example?