Download JNTUH MCA 1st Sem R13 2017 August 811AA Mathematical Foundations Of Computer Science Question Paper

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Code No: 811AA R13

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA I Semester Examinations, August - 2017

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Time: 3hrs Max.Marks:60

Note: This question paper contains two parts A and B.

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Part A is compulsory which carries 20 marks. Answer all questions in Part A.

Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 8 marks and may have a, b, c as sub questions.

PART - A 5 x 4 Marks = 20

1. a) What do you mean by tautological implication? Give an example. [4]
2. b) Explain transitive closure property. [4]

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3. c) Write about binomial and multinomial theorems. [4]
4. d) What are generating functions? Give an example. [4]
5. e) Write about binary trees. [4]

PART -B 5 x 8 Marks = 40

1. a) Express P —( — P— Q) in terms of 1 only.
   

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   b) Define Universe of Discourse? Symbolize the given statement with and without using the set of positive numbers as the Universe of Discourse. Statement: “Given any positive integer there is a greater positive integer.” [4+4]
   OR
2. 3. Give an over view of theory of inference for predictive calculus. [8]
3. S={1,2,3,4} and A= SxS. Define a relation R on A by (a,b)R (a',b") & atb=a"+b"
   a) Show that R is an equivalence relation.
   

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   b) Compute A/R. [4+4]
   OR
4. a) Let (S,*) and (T,*’) be Semi Groups. Show that the function f: SXT — S defined by f(s,t)= s is a Homomorphism of the Semi Group SxT onto the Semi Group S?
   b) Give an over view of lattice as an algebraic structures. [4+4]
5. a) Explain pigeon hole principles and its applications.
   

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   b) Explain the principles of inclusion and exclusion. [4+4]
   OR
6. 7. Determine the coefficients of x⁶y⁷ and x⁷y⁶in (2x+3y)¹³. [8]
7. What are characteristic roots? Explain how characteristics roots can be used in solving recurrence relation using examples. [8]
   OR

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8. Write short notes on how each of the following can be used in solving recurrence relation.
   a) Function of sequences
   b) Coefficients of generating functions. [4+4]
9. Explain the following with examples:
   a) Hamiltonian Graphs
   

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   b) Planar graphs and multi —graphs. [4+4]
   OR
10. Write Kruskal’s Algorithm and explain. Find the minimum cost spanning tree for the given graph? And calculate its minimum cost. [8]

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