Six Marks Questions: ( ) 3) Find the value of the derivative of f (z) = at z = i. r r r r. ( ) where C: z-a = r. (p). f ( z)

Size: px

Start display at page:

Download "Six Marks Questions: ( ) 3) Find the value of the derivative of f (z) = at z = i. r r r r. ( ) where C: z-a = r. (p). f ( z)"

Erik Henderson
5 years ago
Views:

1 Bapatla Engineering College:: Bapatla (Autonomous) Department of Information Technology Assignment-I Question Paper - IV Sem Class: 2/4 B.Tech Section: B Sub: EM-IV (14MA401) Section: A & B Date: 14/12/17 (a). Compute the imaginary part of sin z (b). What is the principal value of the argument of z = 1-i? (c). Which formula will help us to find the n th root of a complex number?. (d). Is f (z) = z analytic? (e). How can you check the analyticity of a complex function? (f). What are the necessary and sufficient conditions for the existence of analytic function?. (g). When do you find imaginary part in the case of knowing real part? (h). What are the C-R equations? (i) How can you check the derivability of a complex function? (j). Find a and b such that u = ax 3 + by 3 is harmonic. (k). When do you apply Cauchy s integral Theorem? (l). What is n th derivative of Cauchy s integral formula? (m). Integrate the following functions in the given regions 2 z e (m) f ( z) Where C: z = (n). f ( z) where C: z = 2. z 4 3 ( z 1) (o). f z 1 dz ( ) where C: z-a = r. (p). f ( z) where C: z =3 z a i 1) Find all roots of unity 3 8i. (Im z) 2) Check whether the function f ( z), z 0 with f(0)=0 is continuous or not.. (1 z ) 3) Find the value of the derivative of f (z) = at z = i. u 1 v v 1 u 4) Show that the polar form of Cauchy Riemann equations are,. r r r r 2 2 u 1 u 1 u Deduce that r r r r 5) Find the analytic function in terms of whose real part is Cosx Coshy 6) State and prove Cauchy s theorem. 7) Derive Cauchy s integral formula for f(z 0 ) and f (n) (z 0 ). 8) What is Cauchy s inequality? Find it. 9) Integrate f (z) = counter clockwise around the unit circle ( ) 10) Evaluate where C is = 3. ( )( ) 2 z 11) Evaluate 2 dz where (i).c: z-1 = (ii).c: z = 2. z 1 c 12). How can we extend Cauchy s integral Theorem from simply connected domain to multiply connection domain?. Derive it.

2 Sub: ATFL (14IT402) Section: B Date: 15/12/17 a) Define automaton. b) What is transition diagram? Give one example. c) Give any four applications of finite automaton. d) Construct Finite automaton for Փ and є. e) Difference between DFA and NFA. f) Design DFA for (a+b) n, n 0 over Σ= {0,1}. g) Limitations of DFA. h) What are the various symbols used to represent a finite automaton? i) Define є-closure. j) Name any two ways to represent finite automaton. Give one example. k) Define the language of DFA. l) Define ε-nfa. Give one example. a) Define DFA. Explain how DFA process the string with an example. b) Describe the central concepts of finite automaton with suitable examples. 2. Design DFA which accepts (i) All Strings that starts and ends with aba over Σ={a,b} (ii) All Strings contains even number of 1 s and 0 s is multiple of 3 over Σ={0,1}. (iii) All strings interpreted as binary integer is divisible by a) Define NFA. Construct NFA which accepts all strings contains three consecutive 0 s over Σ={0,1}. Also give the proliferation of states while processing the string b) Give the extended transition function for NFA. 4. a) Write down the procedure for converting NFA to DFA. b) Prove the language accepted by NFA also accepted by DFA i.e., L(D)=L(N). 5. a) Convert to DFA for the following NFA 0,1 start s 0,1 p q1 r2 final Also describe the language accepted by DFA. b) Write down the procedure for converting є-nfa to DFA. 6. a) Prove if L is accepted by є-nfa which is also accepted by DFA i.e., L(E)=L(D). b) Convert the following є-nfa to NFA without є and then convert to DFA. ε a b c p {q} {p} Ф Ф q {r} ф {q} Ф *r Ф ф ф {r}

3 Sub: CO (14IT403) Section: B Date: 16/12/17 a) Write the basic performance equation of a computer. b) Differentiate Big-endian and Little-endian assignments. c) How to access numbers, characters and strings from memory? d) What is super scalar operation? e) What is pipelining? f) What is the purpose of program counter? g) Differentiate logical shift and arithmetic shift operations. h) What is catche memory? i) Differentiate primary memory and secondary memory. j) What is CISC and RISC? Explain the difference. k) Write difference between multiprocessors and multicomputer. l) Define the system software Compiler and Loader. a) What are the basic functional units of a computer? b) Explain the operational concepts of a computer with a neat sketch. 2. What is an addressing mode? Explain various addressing modes with examples 3. Explain Shift and Rotate instructions. with examples 4. Explain performance issues of a computer? 5. Give means to identify whether or not an overflow has occurred in 2's compliment addition or subtraction operation. Take one example for each possible situation and explain. Assume 4 bit registers. 6. Explain the concept of subroutines. Sub: DAA (14IT404) Section: B Date: 18/12/17 a) Define Algorithm. b) List three properties of algorithm. c) Define Space Complexity. d) Define Time Complexity. e) What is the main functionality of D and C? f) Write the recurrence relation substitution method formula? g) Define Recursive Algorithm. h) Define Best case. i) Write about Average case? j) Differences between general matrix multiplication and Strassen s?

4 Explain Pseudo code conventions for algorithm. 2. Explain Quick sort algorithm with example. 3. Explain merge sort algorithm with example. 4. Explain Strassen s Matrix Multiplication with example. 5. List Asymptotic Notations with example. 6. Explain substitution method in recurrence relation with example. Sub: GUI (14IT405) Section: A & B Date: 19/12/17 a) How Encapsulation is achieved in Java? b) What is bytecode? c) Define polymorphism? d) What is the purpose of using finalize() method? e) What is dynamic initialization? f) Define abstract class? g) List out access specifiers? h) What is a final class and final method? i) Distinguish class and interface? j) Define class and object? Explain various Java buzzwords. 6M 2. a) Explain about Garbage Collection in Java. 2M b) Explain about super keyword in Java. 4M 3. a) Explain about static keyword in Java. 3M b) Discuss about method overriding in Java. 3M 4. Explain constructor overloading and parameterized constructor with an example. 6M 5. Define package. Discuss about importing packages with an example. 6M 6. a) Discuss about Method Overloading in Java. 3M b) Discuss about Dynamic method dispatch. 3M Sub: WT (14IT406) Section: A & B Date: 20/12/17 a) Define WWW and internet. b) What is HTML? c) Give the basic structure of HTML program. d) What is character entity? List any four character entities. e) What do you mean by row spanning and column spanning? f) Differentiate cell padding and cell spacing.

5 g) List various methods to specify colors in HTML document. h) Write the syntax for creating image map. i) Mention some text formatting tagsin HTML5. k) List some new features of HTML5. l) What is CSS? m) Mention some features of CSS. n) Write the format for CSS. o) What is the usage of BDO element? a) Explain in detail about Physical and Logical tags with suitable examples. b) Which elements are used to organize the text in a web page? Explain with an example. 2. a) Write an HTML code that describes all text formatting elements and explain the purpose of text formatting elements. b) Write a short note on various lists(nested lists) in HTML with an example. 3. a) Explain how to create image as a link, internal and external links in a web page with suitable example. b) What are the various elements used for representing multimedia files in a web page and explain with suitable example. 4. a) Describe all the table elements and their attributes with an example. b) Write an HTML code that describes image maps. 5. Explain in detail about all form controls with an example. 6. a) Write a short note on CSS. b) Design a web page with two frames, in which first frame represents list of contents and second frame represents the information related to list of contents in the first frame.

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.

Bapatla Engineering College:: Bapatla (Autonomous) Department of Information Technology Assignment-I Question Paper - III Sem Class: 2/4 B.Tech 2017-18 Section: A Sub: EM-III (14MA301) Section: A & B Date: