R13. II B. Tech I Semester Supplementary Examinations, June DATA STRUCTURES (Com. to ECE, CSE, EIE, IT, ECC)

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1 Code No: RT21042 SET - 1 DATA STRUCTURES (Com. to ECE, CSE, EIE, IT, ECC) PART A 1 a) Differentiate between time complexity and space complexity 3 M b) Give the analysis of Heap Sort Algorithm 4 M c) Describe any one method for representing sparse matrix. 4 M d) What are the advantages of Threaded Binary Tree 4M e) Draw a binary tree with five nodes and three leaves. 3M f) State the situation at which binary search algorithm is best applied. 4 M PART -B 2 a) Explain Divide and Conquer algorithmic strategy using Merge Sort as an example. b) Explain Towers of Hanoi problem with illustrative diagrams. 3 a) "Queues can be implemented using two stacks" - Support this statement with suitable programming example. b) Write an algorithm to convert infix expression into a postfix expression. Illustrate the same with the given infix expression: ( ( a + b ) / d - ( ( e - f ) + g ) 4 a) Explain how linked list can be used for representing polynomials using a suitable example. b) Write an algorithm to implement queue using linked list. 1 of 2

2 Code No: RT21042 SET a) Write a recursive procedure which finds the depth D of a binary tree T. b) Explain various methods in which a binary tree can be represented. Discuss their advantages and disadvantages. 6 a) With the help of diagrams construct a Binary Search Tree (BST) with the following keys: 86, 12, 42, 69, 38, 57, 74, 6, 49, 71. Also delete 42 from the constructed BST. b) Write a short note on the non-recursive tree traversals using stack. 7 a) What are different ways of representing a graph? Explain using suitable example. b) Define the following terms with respect of a graph: i) Degree of vertex ii) Incident edge iii) Directed edge iv) Path, 2 of 2

3 Code No: RT21042 SET - 2 DATA STRUCTURES (Com. to ECE, CSE, EIE, IT, ECC) PART A 1 a) List out the pros and cons of recursion. 4 M b) Write an algorithm to insert an element into circular queue. 3 M c) What is the running time of Quick sort and why. 4 M d) State how recursion is different from iteration? 3 M e) List out the properties of Binary Search Tree 4 M f) With respect to the graph below (a) Is it cyclic? (b) Is it connected? 4 M PART -B 2 a) Define an algorithm. Describe commonly used asymptotic notations and give their significance. b) Write an algorithm to implement Binary Search technique. Use the algorithm to search 32 in the following list of elements. Explain the process at each step. 12, 16, 17, 19, 20, 22, 24, 29, 30, 32, 37 3 a) What is a stack? Explain overheads caused by stack in recursion with a suitable example. b) Write the algorithm for evaluating a postfix expression using stack. Evaluate the following postfix notation * 8 4 / - 4 a) What is linked list? Write an algorithm for inserting an element E at the given position P of the linked list. b) What is a sparse matrix? Write an algorithm for finding the transpose of a sparse matrix. 1 of 2

4 Code No: RT21042 SET a) What is a binary tree? Construct a binary tree given the pre-order traversal and in-order traversals as follows: Pre-Order Traversal: G B Q A C K F P D E R H In-Order Traversal: QB K C F A G P E D H R b) Define the following terms with suitable examples i. Binary Tree ii. Strictly Binary Tree iii. Complete Binary Tree iv. Almost Complete Binary Tree 6 a) Write a procedure to search an element in a Binary Search Tree. b) Write a short note on various operations of the threaded binary tree. 7 a) Write an algorithm to traverse the graph using Breadth First Search with a suitable example? b) What is Adjacency Matrix? Draw the Adjacency Matrix of the following graph. Also give adjacency list representation for the same. A B C D 2 of 2

5 Code No: RT21042 SET - 3 DATA STRUCTURES (Com. to ECE, CSE, EIE, IT, ECC) PART A 1 a) What is an algorithm? List out the properties of an algorithm. 4 M b) Differentiate POP with PEEP operation of a stack. 3 M c) List out the advantages and disadvantages of using linked list over an array 4 M d) Write an algorithm to count the number of nodes in a circularly linked list. 4 M e) Draw the BST for the given list of elements 46, 21, 56, 89, 9, M f) Draw an undirected graph from the given adjacency matrix PART -B 2 a) Write a recursive function to find factorial of a given number. b) Explain radix sort with an algorithm. Discuss on its time complexity. 3 M 3 a) List out the applications of stack. Consider the usual algorithm for determining whether a sequence of parentheses is balanced. What is the maximum number of parentheses that will appear on the stack AT ANY ONE TIME when the algorithm analyzes: ( ( ) ( ( ) ) ( ( ) ) )? b) Explain various operations that are performed on queue with suitable algorithms. 4 a) Write algorithms for swapping two successive elements in a singly linked list with the first element placed at position P. b) What is a circular linked list? Write an algorithm to merge two circular linked lists. 1 of 2

6 Code No: RT21042 SET a) Consider the following tree i. How many leaves does it have? ii. How many of the nodes have at least one sibling? iii. List out the nodes that are siblings to node 5? iv. How many descendants does the root have? v. What is the depth of the tree? vi. How many children does the root have? vii. "Is it a complete binary tree" - Justify b) Write the iterative procedures for i. Post-Order Traversal of a binary tree ii. Level-Order Traversal of a binary tree 6 a) Define threaded binary tree. Explain inorder threading using suitable example. Discuss advantages of the threaded binary tree. b) Write a procedure to find the maximum and minimum elements of a Binary Search Tree (BST). 7 a) Write the Prim s algorithm for finding the minimum-spanning tree of a graph with an example. b) What is transitive closure of a graph. Explain Warshall s algorithm to find the transitive closure of the graph with a suitable example 2 of 2

7 Code No: RT21042 SET - 4 DATA STRUCTURES (Com. to ECE, CSE, EIE, IT, ECC) PART A 1 a) List out some examples for linear and non-linear data structures. 3 M b) Write the differences between stack and queue. 3 M c) What is singly linked list? Mention any two advantages of singly linked lists. 4 M d) State the scenario under which insertion sort should be used. 4 M e) Define threaded binary tree with an example. 4 M f) Does the minimal spanning tree of a graph give the shortest distance between any two specified nodes? Justify your answer. PART -B 2 a) Arrange the list of elements in ascending order using quick sort 45, 26, 31, 55, 77, 24, 42, 63, 99, 22, 88, 72? Write the value of left pointer l, right pointer r and pivot at each step and also draw the current scenario after each step? b) Write a recursive procedure to compute the n th Fibonacci number. 4 M 3 a) "One of the applications of stack is Reversing a List" Explain it with a suitable algorithm. b) List out various applications of queues. Explain how queue is used in Round Robin Algorithm with neat diagrams wherever necessary? 4 a) Discuss the advantages and disadvantages of representing a group of items as an array versus a linear linked list. b) Write an algorithm to insert a node at the end of a doubly linked list. 1 of 2

8 Code No: RT21042 SET a) Find the inorder, preorder and postorder traversals for the given binary tree. b) Write a procedure to display the nodes of a binary tree at a particular level. 6 a) Give the analysis of insertion and deletion operations of nodes in binary search tree. b) Write a short note on Balanced Binary Trees. Also discuss on the applications of Balanced Binary Trees. 10 M 6 M 7 a) Differentiate between the DFS and BFS graph traversal techniques. b) What are connected components of a graph? Is there a method to find out all the connected components of a graph? Explain. 2 of 2

9 Code No: RT21053 SET - 1 DIGITAL LOGIC DESIGN (Com. to CSE, IT) PART A 1 a) Convert the decimal number 46 to binary number system also explain the steps of 4M conversion b) Realize Ex-OR gate operation with minimal number of NAND gates 4M c) Compare serial adder and parallel adder 4M d) List the basic flip flop applications 3M e) Explain the concept of bidirectional shift register 4M f) What is programmable logic array? How it differs from ROM? 3M PART B 2 a) Perform the following arithmetic operation using l s complement method : i) Add (-19) 10 and (29) 10 ii) Add (21) 10 and (37) 10 b) The Hamming code is received at the receiving end. Correct the received data if there is any error. 3 Using Quine-Mc Cluskey method,obtain minimal expression for the following Boolean function F(A,B,C,D,E) = m(8,12,13,18,19,21,22,24,25,28,30,31) + φ(2,6,9,20,26,29) 16M 4 a) Implement the following using a multiplexer F(w,x,y,z) = m(0,1,2,3,4,9,13,14,15) b) Draw the logic diagram of 8:1 MUX with active low enable input using NAND gates 5 a) Draw the circuit diagram of J-K flip flop with NAND gates with positive edge 10M triggering and explain its operation with the help of a truth table. b) What is race around condition and how is it eliminated. 6M 6 a) What is the difference between serial and parallel transfer? Explain how to convert serial data to parallel and parallel data to serial. What type of register is needed? b) Draw the logic diagram of a MOD-10 count up ripple counter using count reset and explain its operation. 7 a) Draw the internal logic construction of 32X4 ROM and explain how an Boolean expression is implemented using it. b) Implement the following Boolean expressions using ROM F 1 (A,B,C) = m(0,2,4,7) F 2 (A,B,C) = m(1,3,5,7) 1 of 1

10 Code No: RT21053 SET - 2 DIGITAL LOGIC DESIGN (Com. to CSE, IT) PART A 1 a) (25.75) 10 to binary number 4M b) Find the compliment of the following expression (AB + C) D + E 4M c) Implement 1:8 demultiplexer using two 1:4 demultiplexer 4M d) Compare combinational circuits and sequential circuits 4M e) Write the applications of shift register 3M f) What are the programmable logic devices 3M PART B 2 a) Perform the following using BCD arithmetic. i) ii) b) Perform the following subtraction: i) (11010) 2 (10000) 2 using 1 s complement ii) ( ) 2 - ( ) 2 using 2 s complement 3 a) Using K-map determine SOP realization of the following F(w,x,y,z) = m(1,4,8,9,13,14,15) + φ(2,3,11,12). b) Realize a two level NAND-NAND circuit for the following F=(w.x.y) +(y.z) 4 a) Implement the following using 4 to 16 line decoder F(A,B,C,D) = (0,1,4,7,9,12,14) b) Design 4X1 MUX using 2X4 decoder and basic logic gates 5 a) Define the following terms of a flip flop.(i) Hold time (ii) Set up time (iii) Propagation delay time. b) Draw the circuit diagram of master-slave J-K flip flop and explain its operation with the help of a truth table. How is it different from edge trigged flip flop? Explain. 6 a) Draw the logic diagram of a four bit binary ripple counter and explain its operation. b) Explain the working of serial in parallel out shift register with logic diagram and waveforms. 6M 10M 7 a) Draw and explain the block diagram of PLA b) Implement following Boolean functions using PLA F 1 (A,B,C) = m(0,1,3,5) and F 2 (A,B,C) = m(0,3,5,7) 1 of 1

11 Code No: RT21053 SET - 3 DIGITAL LOGIC DESIGN (Com. to CSE, IT) PART A 1 a) Decimal number 86 to octal number system also explain the steps of conversion (4M) b) State and prove consensus theorem (3M) c) Realize f(x,y,z) = (0,1,5,7) using AND, OR and inverter gates (4M) d) Explain the difference between racing and toggling (4M) e) What is the difference between synchronous and asynchronous counter (3M) f) List the applications of PLA (4M) PART B 2 a) Briefly explain error detecting and error correcting codes with examples. () b) Convert the following to Decimal and then to Hexadecimal. i) ii) iii) a) Find the prime implicants, essential prime implicants and number of minimal expressions for the given function using K -map f(a,b,c,d) = m(1,3,5,7,8,10,12,13) b) Realize a two level OR-AND circuit for the following F = (x+y ).z + (x.y.z ) 4 a) Design and realize the combinational logic circuit for converting a BCD number to a seven segment display b) Design a full adder with two half adders and other logic gates and explain its operation. () () () (10M) (6M) 5 a) Compare latch and flip flop (6M) b) Realize D-latch using S-R latch. How is it different from D-flip flop? Draw the (10M) circuit using NAND gates and explain. 6 a) Explain the operation of universal shift register with suitable examples. () b) Explain operation of Johnson counter with a diagram () 7 a) Give the comparison between PROM, PLA and PAL (6M) b) Realize the BCD to EXCESS-3 code converter using PLA (10M) 1 of 1

12 Code No: RT21053 SET - 4 DIGITAL LOGIC DESIGN (Com. to CSE, IT) PART A 1 a) Convert 6ABC.2A to decimal number system 4M b) Convert the following expression to POS from (A+B+C) (AB+AC) 3M c) Realize the functionality of NAND gate using 2X1 multiplexer 4M d) Explain the difference between edge triggering and level triggering 4M e) Define counter? Write the classification of counter 4M f) What are the advantages of PLD 3M PART B 2 a) Using 2 s complement perform the following: i) (42) 10 - (68) 10 ii) (78) 16 (56) 16 b) Perform each of the following decimal subtraction in excess-3 code i) ii) iii) a) Using Boolean algebra rules simplify the following Boolean expression and implement in NAND logic f(a,b,c,d) = m(10,11,14,15) b) Find the minimal expression using K- map for given function F F(w,x,y,z) = (0,2,3,5,7,9)+ d (1,6,10,11) 4 a) Construct a 4X16 decoder using 2X4 decoder. Show the schematic diagram neatly. b) Realize full adder circuit using multiplexer. 5 a) Draw the truth table, logic diagrams of J-K, R-S, D and T type flip flops 10M b) Convert a T flip flop to D flip flop and write characteristic equations of T and D flip flops. 6 a) What is the procedure for designing a synchronous counter? b) The content of a 4-bit register is initially The register is shifted six times to the right with the serial input being What is the content of the register after each shift? 6M 7 a) Draw the internal construction of PLA having three inputs, three product terms and two outputs b) Tabulate the PLA programming table for the four Boolean functions listed below. Minimize the number of product terms i) A(x,y,z) = (1,2,4,6) ii) B(x,y,z) = (0,1,6,7) iii) C(x,y,z) = (2,6) iv) D(x,y,z) = (1,2,3,5,7) 1 of 1

13 Code No: RT21034 SET - 1 MANAGERIAL ECONIMICS AND FINANCIAL ANALYSIS (Com. to ME, ECE, CSE, IT, ECC, MTE) PART A 1 a) What is demand? And explain the types of demand. 3M b) Explain Cobb-Douglas Production function. 4M c) What is Oligopoly market? And significance of kinked demand curve. 4M d) Explain the salient features and types of partnership. 4M e) Describe the importance of ratio analysis. 4M f) Explain the meaning of capital. 3M PART B 2 a) Define managerial economics and explain its relation with other subjects. b) Explain the importance of demand forecasting and describe any two methods of demand forecasting. 3 a) Describe the salient features of law of variable propositions. b) Explain any four concepts of costs. 4 a) Explain the conditions of perfect competition and how the price and output determined in the short-run? b) Describe the importance of pricing and write any two methods of pricing. 5 a) What is business? And explain the merits and demerits of Joint-Stock Companies. b) Explain the causes and consequences of business cycles. 1 of 2

14 Code No: RT21034 SET a) Explain the limitations of ratio analysis. 6M b) The following is an extract of a balance sheet of a company during the last year. Compute current ratio and quick ratio. Also interpret the ratios. (Rs.) 10M Land and buildings 50,000 Plant and machinery 1,00,000 Furniture and fixtures 25,000 Closing stock 25,000 Sundry debtors 12,500 Wages prepaid 2,500 Sundry creditors 8,000 Rent outstanding 2,000 7 a) What is capitalization? And explain the need for capital budgeting. b) Briefly explain the techniques of capital budgeting. 2 of 2

15 Code No: RT21034 SET - 2 MANAGERIAL ECONIMICS AND FINANCIAL ANALYSIS (Com. to ME, ECE, CSE, IT, ECC, MTE) PART A 1 a) Explain the law of demand and types of demand. 4M b) Describe the salient features of Isoquants. 3M c) Explain the conditions of monopoly. 4M d) Describe the merits and demerits of sole trader. 4M e) Explain the double entry system. 4M f) What is Capitalization? 3M PART B 2 a) Define managerial economics and explain its scope. b) What is elasticity of demand? And explain its types and measurement. 3 a) Explain the importance production function and describe the salient features of Cobb-Douglas production function. b) Describe the importance of Break-even analysis and Break-even point. 4 a) Explain the conditions of perfect competition and monopolistic competition. b) Describe any three methods of pricing. 5 a) Explain the salient features of private limited and public limited companies. b) What is the meaning of business cycles? And explain different phases of business cycles. 1 of 2

16 Code No: RT21034 SET a) Explain the importance of funds flows and cash flow statements. 6M b) The following is an extract of a balance sheet of a company during the last year. Compute current ratio and quick ratio. Also interpret the ratios. (Rs.) 10M Land and buildings 1,50,000 Plant and machinery 3,00,000 Furniture and fixtures 1,25,000 Closing stock 25,000 Sundry debtors 62,500 Wages prepaid 7,500 Sundry creditors 18,000 Rent outstanding 12,000 7 a) Briefly explain the traditional methods of capital budgeting. b) Briefly describe the modern methods of capital budgeting. 2 of 2

17 Code No: RT21034 *** SET - 3 MANAGERIAL ECONIMICS AND FINANCIAL ANALYSIS (Com. to ME, ECE, CSE, IT, ECC, MTE) PART A 1 a) Define Managerial Economics. 3M b) Isoquants Vs. Iso costs. 4M c) Salient features of Oligopoly and kinked demand curve. 4M d) Merits and demerits of partnership. 4M e) Importance of ratio analysis. 4M f) Explain the need for capital budgeting. 3M PART B 2 a) What is demand? And explain the law of demand and its exceptions. b) Explain the significance of demand forecasting and describe any two methods of demand forecasting. 3 a) Explain the law of variable proportions. b) Describe any three cost concepts. 4 a) Explain the conditions of monopoly and how the price and output determined in the monopoly? b) Explain any three methods of pricing. 5 a) Describe the salient features, merits and demerits of public enterprises. b) Explain the meaning and phases of business cycles. 1 of 2

18 Code No: RT21034 SET a) Explain the limitations of financial analysis. 4M b) Calculate Funds from operations from the following Profit and Loss Account. 12M Dr. Cr. (Rs.) (Rs.) To salaries To printing and stationery To postage and telegrams To telephone charges To auditor s fee To other expenses To depreciation To loss on sale of furniture To discount To good will To trademarks To net profit 2,50,000 20,000 20,000 25,000 20,000 95,000 1,40,000 8,000 2,000 40,000 10,000 3,90,000 10,20,000 By gross profit By gain on sale of land 9,00,000 1,20,000 10,20,000 7 a) What is capitalization? And briefly explain the traditional methods capital budgeting. b) Describe the modern methods of capital budgeting. 2 of 2

19 Code No: RT21034 SET - 4 MANAGERIAL ECONIMICS AND FINANCIAL ANALYSIS (Com. to ME, ECE, CSE, IT, ECC, MTE) PART A 1 a) Explain the scope of Managerial Economics. 3M b) Explicit Vs. Implicit costs. 4M c) Oligopoly and kinked demand curve. 4M d) Salient features of partnership. 4M e) Significance of ratio analysis. 4M f) Explain the need for capital budgeting. 3M PART B 2 a) What is elasticity of demand? And explain its types and measurement. 10M b) Explain any two methods of demand forecasting. 6M 3 a) Describe the importance of Break-even analysis and Break-even pint. b) Briefly explain the salient features of law of variable propositions. 4 a) Describe the conditions and price-out-put determination in perfect completion. 10M b) Explain any two methods of pricing. 6M 5 a) Explain the salient features, merits and demerits of private and public limited 10M companies. b) Describe the phases of business cycle. 6M 1 of 2

20 Code No: RT21034 SET a) Explain the objectives of funds flows statement. 4M b) Calculate the funds from operations from the following profit and loss account for the year ending Dr. Cr. (Rs) (Rs) To salaries To rent To postage and telegrams To printing and stationery To telephone charges To audit fee To law charges To interest To bad debts To provision for bad debts To preliminary expenses written off To goodwill written off To provision for Tax To proposed dividend To general reserve To loss on sale of furniture To net profit 50,000 30,000 20,000 30,000 30,000 20,000 25,000 5,000 2,000 3,000 20,000 30,000 40,000 60,000 1,00,000 10,000 1,75,000 By gross profit By profit on sale of buildings 6,00,000 50,000 6,50,000 6,50,000 12M 7 a) Explain the traditional methods of capital budgeting. b) Describe the modern methods of capital budgeting. 2 of 2

21 Code No: RT21052 SET - 1 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE AND ENGINEERING (Com. to CSE, IT, ECC) PART-A 1. a) What is a Well Formed Formula? What are rules of the Well Formed Formulas? Explain b) Explain in brief about Greatest common divisor with an example? c) Draw the Hasse diagram for the poset (P(S), ), where S={1,2,3,4} d) Prove that if G is a non trivial tree then G contains at least 2 vertices of degree 1? e) In how many ways can we chose a black square and white square on an 8 X 8 chessboard? f) Explain in brief about Recurrence relation? (4M+3M+4M+4M+4M+3M) PART-B 2. a) Prove or disprove the validity of the following arguments using the rules of inference. i) All men are fallible ii) All kings are men iii) Therefore, all kings are fallible b) Show that the following statements is a tautology. (~P (P Q)) ~Q (+) 3. a) Explain the theorem of principle of inclusion and exclusion for three variables with an example? b) Explain in brief about Properties of integers? (+) 4. a) How many relations are there on a set with `n' elements? If a set A has `m' elements and a set B has `n' elements, how many relations are there from A to B? If a set A = {1, 2}, determine all relations from A to A. b) Draw the Hasse diagram of (P(S), ), where P(S) is power set of the set S={a,b,c}? (+) 5. a) Prove that a connected plane graph with 7 vertices and degree(v) = 4 for each vertex V of G must have 8 regions of degree 3 and one region of degree 4.? b) How many vertices will the graph contain 6 edges and all vertices of degree 3? (+) 6. a) Eight people enter an elevator at the first floor. The elevator discharges a passenger on each successive floor until it empties on The fifth floor. How Many different ways can this happen? b) 15 males and 10 females are members are seated in a round table meeting. How many ways they can seated if all the females seated together? (+) 7. a) Solve the recurrence relation un+2-un+1-12un=10, u1=13, u0=0. b) Solve the recurrence relation un+2+4un+1+3un=5(-2)n,u0=1,u1=0 using gen-erating function. (+) 1 of 1

22 Code No: RT21052 SET - 2 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE AND ENGINEERING (Com. to CSE, IT, ECC) PART-A 1. a) Find the truth table for the propositional formula (P ~Q) (Q P)? b) Explain in brief about principle of inclusion with an example? c) Draw the Hasse diagram of (P(S), ), where P(S) is power set of the set S = {a, b, c}? d) Discuss graph coloring problem with required examples.? e) Find the sum of all 4 digit numbers that can be obtained by using the digits 2, 3, 5 and 7 (without repetition)? f) Find the generating function of n^2-2? (4M+3M+4M+4M+4M+3M) PART-B 2. a) Construct the truth table for the following statement (~P ~Q) (Q R)? b) Show that the following statements are logically equivalent without using truth table. (P Q) (P R) P (Q R)? (+) 3. a) Explain in brief about Fermats theorem? b) Explain in brief about Division theorem? (+) 4. a) Draw the Hasse diagram for the poset (P(S), ), where S={1,2,3,4} b) Let X = {1, 2, 3, 4, 5, 6, 7} and R= {(x,y)/ x-y is divisible by 3} in X. show that R is an Equivalence Relation.? (+) 5. a) State the kruskal's algorithm for Finding Minimal Spanning Tree? Explain it with an Example? b) Describe an algorithm to decide whether a graph is bipartite? (+) 6. a) Compute the number of 10-digit numbers which contain only the digits 1,2 and 3 with the digit 2 appearing in each number twice? b) Let G be a group of order P, where P is a prime. Find all subgroups of G.? (+) 7. a) Find a particular solution for recurrence relation using the method of determined coefficients an- 7 an-1+12an-2=n.2^n b) Solve an=an-1 + n where a0 =2 by substitution? (+) 1 of 1

23 Code No: RT21052 SET - 3 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE AND ENGINEERING (Com. to CSE, IT, ECC) PART-A 1. a) What is the compound statement that is true when exactly two of the three statements P, Q and R are true? b) Explain in brief about principle of exclusion with an example? c) Prove that A (B C) = (A-B) (A-C)? d) Define and explain planar graphs with examples? e) Show that the identity element in a group is unique? f) Find the generating function of (n-1)2? (4M+3M+4M+4M+4M+3M) PART-B 2. a) Determine the truth value of each of the following statements i) = 7 and = 8. ii) four is even. iii) = 7 and = 8. b) Write each of the following statements in symbolic form i) Anil & Sunil are rich. ii) Neither Ramu nor Raju is poor. iii) It is not true that Ravi & Raju are both rich. (+) 3. a) Explain in brief about Eulers Theorem with Example? b) Explain in brief about Least common multiple with Example? (+) 4. a) Let A = {1, 2, 3, 4}and P ={{1, 2,3},{4}} be a partition of A. Find the equivalence relation determined by P.? b) If A, B, C are three sets such that A B. show that (A X C) (B X C)? (+) 5. a) Write the rules for constructing Hamiltonian paths and cycles? b) Write the difference between Hamiltonian graphs and Euler graphs? (+) 6. a) Consider the group G = {1,2,4,7,8,11,13,14} under multiplication Modulo 15.Construct the multiplication table of G and verify whether G is cycle or not? b) Prove that H = {0,2,4,}forms a sub group of < Z6,+6>? (+) 7. a) Solve the difference equation un-2un-1 2=(5).2? b) Find a particular solution for recurrence relation using the method of determined coefficients an- 5 an-1=3^n? (+) 1 of 1

24 Code No: RT21052 SET - 4 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE AND ENGINEERING (Com. to CSE, IT, ECC) PART-A 1. a) Using predicate logic, prove the validity of the following argument Everyhusband argues with his wife.`x' is A husband. Therefore,`X'argues With his wife".? b) Explain in brief about modular arithmetic? c) If A = {1,2,3}, B={4,5}.Find A X B and B X A? d) How many edges does a graph have if it has vertices of degree 4,3,3,2,2?Draw such a graph? e) State the binomial theorem? f) Solve the an - 6an-1+8 an-2 = n.4 where a0 =8 and a 1=22? (4M+3M+4M+4M+4M+3M) PART-B 2. a) Obtain the PCNF of the following formula (~P R) (Q P) i) Using Truth Table. ii) Without using Truth Table. b) What is the negation of the statement 2 is even and -3 is negative?" (+) 3. a) Explain in brief about Euclidean algorithm? b) Explain in brief about testing the prime numbers? (+) 4. a) A function f(z X Z) Z is defined by f(x,y)=4x=5y.prove that f is not one-to-one, but on to? b) Let f(x): x2-3x+2. Find f(x2) and f(x+3)? (+) 5. a) Prove that isomorphism is an equivalence relation on diagraphs? b) How many equivalence classes are there for loop-free diagraphs with three vertices? (+) 6. a) One type of automobile license plate number in Masachusetts consists of one letter and Five digits. Compute the number of such license plate numbers possible.? b) Find the number of positive integers less than are equal to 2076 and divisible by 3 or 4? (+) 7. a) Define recurrence relation? Show that the sequence {an} is a solution of re-currence relation an=-3an-1 +4an-2 if an =1? b) What is solution of the recurrence relation an = an-1+2 an-2 with a0 =2 and a1 =7? (+) 1 of 1

25 Code No: RT21051 SET - 1 OBJECT ORIENTED PROGRAMMING THROUGH C + + (Com. to CSE, IT) PART-A 1. a) Define stream b) What are the principles of function overloading? c) With a sample program create an array of objects? d) Give three operators that cannot be overloaded? e) What are the advantages of inheritance? f) What are the advantages of templates? PART-B 2. What the concepts are of object oriented programming? Explain in detail 3. Write a C++ program to find the area of a circle, rectangle and triangle using function overloading? 4. What is a friend function? Write a C++ program to add two complex numbers using friend functions? 5. a) What is copy constructor? Explain b) Discuss about anonymous objects? 6. a) Explain about virtual base class? b) Explain about virtual destructors? 7. a) Explain about file manipulators? b) Explain about adaptors in C++? 1 of 1

26 Code No: RT21051 SET - 2 OBJECT ORIENTED PROGRAMMING THROUGH C + + (Com. to CSE, IT) PART-A 1. a) Define class and object? b) What are the advantages of inline function? c) Give function prototype of a function foo which is having two objects of class sam as arguments and returning reference of an object as parameter? d) Give the order of calling of constructors? e) What are iterators? f) What are the different file opening modes? PART-B 2. Differentiate between C and C++ programs? Illustrate with sample programs? 3. a) Explain about scope resolution operator? b) Discuss about name space? 4. Write a C++ Program to demonstrate the usage of static data member and static member function? 5. Write a c++ Program to overload + operator to add two matrices using friend functions? 6. a) Explain about function overriding? b) What are the rules for virtual functions? 7. What is an Exception? Explain about try, throw and catch with example? 1 of 1

27 Code No: RT21051 SET - 3 OBJECT ORIENTED PROGRAMMING THROUGH C + + (Com. to CSE, IT) PART-A 1. a) Give examples of user defined manipulators? b) With a sample program explain about default arguments? c) Define friend function? d) Can we have more than one constructor in a class? Discuss? e) Explain about Pure virtual function? f) Explain about container classes? PART-B 2. a) What are the member functions of istream class? b) Discuss about flags without bitfields? 3. With a sample program explain the concept of return by reference? 4. a) Can we overload member function? Illustrate? b) Explain about constant classes? 5. Write a C++ Program to copy the contents of one object into another using copy constructor? 6. Define inheritance? Explain different types of inheritance? 7. Write a c++ Program to add two integers, two floats and two complex numbers using class templates? 1 of 1

28 Code No: RT21051 SET - 4 OBJECT ORIENTED PROGRAMMING THROUGH C + + (Com. to CSE, IT) PART-A 1. a) Discuss about the structure of C ++ program? b) Discuss about 4 operators in C++ which are not present in C? c) C++ allows nested classes are not? If Possible give an example? d) What is the purpose of destructor? e) Define abstract class? f) Define staic binding? PART-B 2. a) Discuss about formatted console I/O operations and unformatted console I/o operations b) Explain about manipulators? 3. Write a C++ Program to swap two number s using call by value, call by reference and call by address mechanism? 4. a) Explain about static classes? b) What happens if we declare all member functions as private in a class? 5. Write a C++ program to overload two increment operators (pre and post)? 6. Define virtual function? Illustrate with a C++ Program? 7. a) What are the principles of exceptional; handling? Explain b) Explain the need of templates? 1 of 1