MFCS MAIN QUIZ

Attempt any 6 questions. Each question carry 10 marks

1. a> All papers written by a student has at least one other author who is not a student.
Assume
paper(Y ) stands for Y is a paper,
author(X,Y ) stands for X is an author of Y and
std(X) stands for X is a student


b> x2 - y2 =1. Prove by Contradiction

2. The Boolean expression on variables A,B,C,D,E and simplified expression was given. Find out what are the don't
care conditions used to Simplify that expression

3. a> Give the result
5
i> E 2
i=0

ii> ......

iii> .......

iv> .......

..
b> 0.423 (Recurrence Relation)

4. a> Two relations R1 and R2 were given. Generate R1oR2 using the Boolean Matrix on zero and one
b> For what values of a and b the linear equations
x + 2y + 3z =6
..............
..............

will have
a> no solution
b> infinite number of solution
c> unique solution

5. a> Find inverse modulo 27 mod 11.
b> Explain RSA Algorithm with an example.

6. a> Poisson Distribution
An event occurs 2 times in one hour. What is the probability that event will not in occur between 8 am to 9 am.

b> How many 4 letter initial be created provided the last letter should me a consonant

7. Create a Turing Machine which accepts input {0,1} and the number of 0's and 1's should be equal to reach final state.
e.g. 0011, 1100, 0101, etc

8. a> Generate grammer for {ancbn | n>0 }
b> A sequence of productions were given and based on that

Q1. Which type of grammer this is?
Q2. Will this string "..........." be accepted
Q3. Which language best describes this
a> Turing Machine
b> Context Free
c> Context Sensitive
d> Regular Expression

9. a> Find mean, standard deviation and variance of Given Data
b> Probability that 3 persons will not have B'day on the same day?