CSIT 2nd Semester
Discrete Structure Board Question Paper 2081 Old Course

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CSC 165-2081 ✡

Tribhuvan University

Institute of Science and Technology

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Bachelor Level/First Year/Second Semester/Science
Bachelors in Computer Science and Information Technology (CSC 165)
(Discrete Structure) <br> <b class="underline">(Old Course</b>)
Full Marks: 60 Pass Marks: 24 Time: 3 hours

Candidates are required to give their answers in their own words as far as practicable.
The figures in the margin indicate full marks.

Section A
Long Answer Questions
Attempt any Two questions.
[2x10=20]
1.

Define discrete probability. Solve the recurrence relation an = 5an-1 - 6an-2 with initial conditions a0 = 1 and a1 = 4.

2.

What is simple graph? How do you find forward and backward augmented path to calculate maximal flow? Explain with your own example.

3.

Define geometric and arithmetic progression. Prove that 1 + 3 + 5 + � + (2k - 1) = k2 using mathematical induction.

Section B

Attempt any Eight questions

[8×5=40]
4.

Define function and describe its types.

5.

What is primality test? Find all additive inverse pairs in Z10.

6.

Discuss about Universal and Existential quantifier with examples.

7.

State pigeon hole principle. Expand (a + b)5 using Binomial expansion.

8.

Define tree, spanning tree and minimum spanning tree with examples.

9.

Solve the following congruence using Chinese Remainder Theorem.
x = 5 MOD 7
x = 2 MOD 5

10.

How do you represent set? Explain.

11.

Using direct proof, show that the square of odd is odd.

12.

Describe relation and its properties.