Download JNTUH MCA 1st Sem R17 2019 April-May 841AA Aprilmay Mathematical Foundations Of Computer Science Question Paper

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA I Semester Examinations, April/May - 2019

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Time: 3hrs Max.Marks:75

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

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Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.

PART - A

5 x 5 Marks =25

1. Construct the truth table (P?Q) ? (Q?R) ? (P?¬R). [5]
2. Let G be the set of real numbers not equal to -1 and be defined by a*b=a+b+ab. Prove that < G,* > is an abelian group. [5]

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3. How many integers between 1 and 100 have a sum of digits of integer numbers equal to 10? [5]
4. Find the particular solution for the following difference equation a_n+5a_n-1+6a_n-2=42.4ⁿ [5]
5. What do you mean by Isomorphic graph? When will you say that two graphs are isomorphic? [5]

PART -B

5 x 10 Marks =50

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1. Obtain the Principal Disjunctive normal form of P ? [(P?Q) ? ¬(Q ? ¬P)] [10]

   OR

2. Show that the following argument is valid. If today is Tuesday, I have a test in Mathematics or Economics. If my Economics professor is sick, I will not have a test in Economics. Today is Tuesday and my Economics professor is sick. Therefore I have a test in Mathematics. [10]
3. 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. [10]

   OR

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4. Let f: R?R and g: R?R, where R is the set of real numbers. Find fog and gof, where f(x) = x²-2 and g(x) = x+4. State whether these functions are injective, surjective, and bijective.
5. Define Lattice and write various properties of Lattice. [5+5]
6. Using binomial identities evaluate the sum 1.2.3+2.3.4+...... +(n-2)(n-1)n. [10]

   OR

7. Suppose there are 15 red balls and 5 white balls. Assume that the balls are distinguishable and that a sample of 5 balls is to be selected.
   1. How many samples of 5 balls are there?

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   2. How many samples contain all red balls?
   3. How many samples contain 3 red balls and 2 white balls?
   4. How many samples contain at least 4 red balls? [10]
8. Solve the recurrence relation a_n-7a_n-1+10a_n-2=0 for n>2 where a₀=10 and a₁=41. [10]

   OR

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9. Explain and illustrate various ways of solving the recurrence relation. [10]
10. State and explain the 4-color problem for planar graphs. [10]

    OR

11. What is planar graph? Show that following graph is planar. [10]

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