©
SS
S
ಮ್ತ
2
٥ف‎

ಲ
Ws 111,

No. of Pages:2

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER M.TECH DEGREE EXAMINATION, NOV 2020
Branch:

Computer Science & Engineering

Stream(s):

1. Computer Science &Engineering
2. Information security
3. Network Security

Course Code & Name:
01CS6101 Mathematical Foundations of Computing Systems

Answer any two full questions from each part

Limit answers to the required points.

Max. Marks: 60 Duration: 3 hours
PARTA
1. a. Prove by exhausting cases ‏تہ‎ - 1 15 divisible by 3. (4)
ந. Prove by mathematical induction 2.4 2! + 337 is divisible by 11. (5)
2. a. Explain linear time temporal logic. (4)

ந. Using strong induction prove that ifn is an integer greater than 1, thenn canbe (5)

written as the product of primes.

3. a. Let P(n) be “ If n is an integer and 1345 is even , then n is even.” Prove P(n) using

contradiction technique. (4)
b. Solve the recurrence relation a, + ‏احم "312 - مد‎ (5)
PART 8
4. a. The continuous random variable X is uniformly distributed over the interval [-1, 4].
Find (a) P(X < 2.7) 6/8 (4)
1