Nalanda Open University 2010 M.C.A Computer Aplications Master of Computer Application Part–I, –III (Discrete Mathematics) Annual , - Question Paper
Master of Computer Application Part–I, Paper–III (Discrete Mathematics) Annual Examination, 2010
IN ALAIN DA OPEN UNIVERSITY Master of Computer Application Part-1, Paper-Ill
Annual Examination, 2010 Full Marks : 80 Time : 3 Hours.
Answer any Five Questions.
Ali questions carry equal marks.
1. (a) Define proposition and define Bi-condition with example.
(I)) Prove that {p a q)-> {p v q) is a tautology.
2. I low many different 7 Persons committee can be formed, each containing 3 women and 4 men from a set of 20 women and 30 men ?
3. Prove bv mathematical induction that
12 + 32 +'52 +.....+ (2n - l)2 - /}n (2n - 1) (2n + 1)
4. If f, g, h: R -> R are defined bv f(x) x3 - 4x
g{x) = mid h(x) = .v4 find x2 + 1
{{fof*}t>h)x anil {ftf{soh})x and check if they are equal.
5. Find the sets A and B if A - B (1,3,7,11), B - A (2, 6,8) and A fi B (4, 9).
6. Defme (a) Surjective map, (I)) Bijective map, (c) Injective Map.
7. An urn contains 15 balls, 8 of which are red and 7 are black. In how mam- wavs can
(i) 5 balls be chosen so that all 5 are red ?
(ii) 7 balls be chosen so that atleast 5 are red ?
8. In how manv wavs can 20 Identical books be placed in 4 Identical lx>xes ?
9. Find the value of n and r.
(a) If *Pr - 6720 and "C, - 56
(b) If ISC, l8C, .2 then find the values of 'C0.
10. Prove that is not rational.
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