GATE CS 1998

Question 51

Suppose the domain set of an attribute consists of signed four digit numbers. What is the percentage rate of reduction in storage space of this attribute if it is stored as an integer rather than in character form?

• 80%
• 20%
• 60%
• 40%

Question 52

[Subjective type] 1Two friends agree to meet at a park with the following conditions. Each will reach the park between 4:00 p.m. and 5:00 p.m. and will see if the other has already arrived. If not, they will wait for 10 minutes or the end of the hour whichever is earlier and leave.  What is the probability that the two will not meet? 

• 25/36

Question 53

[Subjective type] Given a regular expression for the set of binary strings where every 0 is immediately followed by exactly k 1\'s and preceded by atleast k 1\'s (k is a fixed integer).

Question 54

[Subjective type] Design a deterministic finite state automaton (using minimum number of states) that recognizes the following language:

 L = { w ∈ {0,1}* | w interpreted as a binary number (ignoring the leading zeros) is divisible by 5 }

Question 55

a.  The implication gate shown below, has two inputs (x and y), the output is 1 except when x=1 and y=0. Realize f=x\'y  + xy\' using only four implication gates. b.  Show that the implication gate is functionally complete.  

Question 56

Solve the following recurrence relation:

xn = 2xn-1 -1, n>1
x1 = 2

Question 57

Consider the grammar

S →  Aa | b
A → Ac | Sd | ε

Construct an equivalent grammar with no left recursion and with minimum number of production rules.

Question 58

Suppose we have a database consisting of the following three relations.

FREQUENTS(student, parlor) giving the parlors each student visits.
SERVES(parlor, ice-cream) indicating what kind of ice-creams each parlor serves.
LIKES(student, ice-cream) indicating what ice-creams each parlor serves.

(Assuming that each student likes at least one ice-cream and frequents at least one parlor)

Express the following in SQL: Print the students that frequent at least one parlor that serves some ice-cream that they like.

Question 59

In a computer system where the \'best-fit\' algorithm is used for allocating \'jobs\' to \'memory partitions\', the following situation was encountered: When will the 20K job complete? Note - This question was subjective type.

• 8
• 18
• 11
• None of these

Question 60

a.  Prove by induction that the expression for the number of diagonals in a polygon of n sides is n(n-3) /2. b.  Let R be a binary relation on A = {a, b, c, d, e, f, g, h} represented by following two component digraph. Find the smallest integers m and n such that m<n and  R^m = Rⁿ