Download JNTUA MCA 2019 May Reg-Supply 1st Sem 17F00101 Mathematical Foundations for Computer Science Question Paper

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Code: 17F00101

MCA I Semester Supplementary Examinations May/June 2019

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MATHEMATICAL FOUNDATIONS FOR COMPUTER SCIENCE

(For students admitted in 2017 & 2018 only)

Time: 3 hours Max. Marks: 60

Answer all the questions

1. Using mathematical induction prove that 1³ + 2³ + 3³ + ...+ n³ = ?
   

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   OR
   With example, explain the properties of binary relations.
2. (a) State and prove Lagrange’s theorem.
   (b) Write about group codes.
   OR
   

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   Find all the cosets of the cyclic subgroup H = {id, (1 2)} of the symmetric group S₃.
3. With example, explain the rules of sum and product.
   OR
   What is a recurrence relation? Solve the recurrence relation T(n) = 2T(n/2) + n for n > 1 and T(1) =1.
4. With example, explain about graph traversal techniques.
   

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   OR
   What is Hamiltonian circuit? Check whether the following graph has Hamiltonian circuit or not.
5. What is binary search tree? Write algorithms to insert and remove a node in binary search tree.
   OR
   With the help of following graph, explain Prim’s algorithm.

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