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PUNJAB TECHNICAL UNIVERSITY MCA - I (SEM 1) SEP 2010 : Computer Mathematical Foundation

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Roll No. ...................... Total No. of Questions : 13] [Total No. of Pages : 03 Paper ID [A0504] (Please fill this Paper ID in OMR Sheet) MCA (104) (S05) (O) (Sem. - 1st) COMPUTER MATHEMATICAL FOUNDATION Time : 03 Hours Maximum Marks : 75 Instruction to Candidates: 1) Section - A is Compulsory. 2) Attempt any Nine questions from Section - B. Q1) Section - A (15 2 = 30) a) What are distributive laws of set theory? b) What is a symmetric relation? c) What is relation partition? d) What are the ways of representing relations? e) What are identity laws of set theory? f) What are matrices? g) Explain scalar multiplication in a matrix. h) What are left and right distributive laws of matrix multiplication? i) How do you find transpose of a matrix? Give an example. j) What are the rules for matrix addition? k) What is a contradiction? l) What are propositions? m) What are multigraphs? n) o) A-522 What are the methods for representing a graph in computer memory? What are quantifiers? P.T.O. Section - B Q2) (9 5 = 45) Consider the following data for 120 mathematics students at a college concerning languages French, Germen and Russian : 65 study French, 45 study Germen, 42 study Russian, 20 study French and Germen, 25 study French and Russian, 15 study Germen and Russian and 8 study all the languages. Find the number of students who study one of the three languages? Q3) Which of the following sets are equal : A = {x:x2 -4x + 3 = 0}, B = {x:x2 -3x + 2 = 0},C = {x:x N,x<3} D ={ x: x N, x is odd, x<15}, E = {1,2}, F = {1 ,2,1}, H = {1,1,3} Q4) If A = {a,b}, B = {2,3}, C = {3,4} Show that Ax(BUC) = (AXB)U (AXC) Q5) Let R be the relation from A = {1,2,3,4,5} to B = {1,3,5} which is defined by x is less than y , write R as a set of ordered pairs. Q6) Write a procedure for finding the addition of the following matrices : 1 2 3 A= 4 5 6 Q7) 1 5 Let A = B= 3 1 Find (i) AB (ii) BA. 1 1 2 B= 0 3 5 2 0 4 3 2 6 Q8) Write procedure for solving a system of simultaneous equations using Gauss Jordon s method. Give an illustrative example also. Q9) Find 2A 3B 1 2 3 Where A = 4 5 6 3 0 2 B= 7 1 8 Q10) Verify the proposition P v (p q) is tautology. A-522 2 Q11) Let p be Ram reads Newsweek , q be Ram reads HT and r be Ram reads time . Write each of the following in symbolic form : (a) Ram reads Newsweek or HT, but not the Time. (b) Ram reads Newsweek or HT, or he does not read Newsweek and Time. (c) It is not true that Ram reads Newsweek but not the time. (d) It is not true that Ram reads Time or the HT but not Newsweek. Q12) By the Principle of Mathematical induction prove that : 1+3+5+...+(2n-l) = n2 Q13) Write a procedure to find all pairs shortest paths in a graph. kbkb A-522 3

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Additional Info : Mca - I (sem 1) September 2010 Question Paper - Computer Mathematical Foundation
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