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IGNOU UNIVERSITY MCA - I (SEM 1) DEC 2009 : Discrete Mathematics

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I MCS-013 I MCA (Revised) Term-End Examination December, 2009 oo MCS-013 : DISCRETE MATHEMATICS Time : 2 hours Maximum Marks : 50 Note : Question number 1 is compulsory. Attempt any three questions from the rest. 1. (a) If a five digit number is chosen at random, what is the probability that the product of the digits is 20 ? If the function f : R -* R is defined by f (x) = x2 . Find r 1 (4) and r 1 ( - 4). In how many ways can a prize winner choose any 3 CDs from the 'Ten Best' list ? Let A= {a, b} be a given set and R = ((a, a), (b, a), (b, b)} and S= {(a, b), (b, a), (b, b)} be relations on A. Then verify (s0R)-1_, R -1 o s-1. Find contrapositve of : If John is a poet then he is poor. Only if Marc studies will he pass the test. (f) Show that r > n 3 for n.?-. 10. MCS-013 1 3 4 3 3 3 4 P.T.O. 2. (a) Construct the logic circuit for X1 ( X2 V X3 3 What is the sum of the coefficients of all the terms in expansion of (a + b + c) 7 ? Show that the relation 'equality' defined in any set A is an equivalence relation. 3. (a) Find CNF form of ---1(P v Q) H P n Q Establish the equivalence P--->(Q >R)E(PAQ)-4R. 4 4 for 3 Show that if any 20 people are selected, then we may choose a subset of 3 so that all 3 were born on the same day of the week ? 3 4. (a) Use induction to prove that any integer 4 n 3 2 is either a prime or a product of primes. Given the set A = {1, 2, 3}, consider a relation in A : R = {(1, 1), (2, 2), (2, 3), (3, 2)). Find RoR. In how many ways can 12 balloons be distributed at a Birthday party among 10 children ? MCS-013 3 3 2 5. (a) Among the integers 1 to 200 find the number of integers that are 4 divisible by 2 or 5 or 9. not divisible by 5. Determine the number of integer solutions to the equation x 1 + x 2 + x3 + x4 = 7, where x/. ?... 0 for all i= 1, 2, 3, 4. . 3 Find the number of ways of placing n people in n 1 rooms, no room being empty. 3 -o0o- MCS-013 3

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Additional Info : Mca - I (sem 1) December 2009 Question Paper - Discrete Mathematics(Revised Course)
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