GATE CS 1998

Question 1

A die is rolled three times. The probability that exact one odd number turns up among the three outcomes is

• 1/6
• 3/8
• 1/8
• 1/2

Question 2

Consider the following set of equations

x+2y = 5
4x+8y = 12
3x+6y+3z = 15

This set-

• has a unique solution
• has no solutions
• has finite number of solutions
• has infinite number of solutions

Question 3

Which of the following statements applies to the bisection method used for finding roots of functions:

• converges within a few iteration
• guaranteed to work for all continuous functions
• is faster than the Newton-Raphson method
• requires that there be no error in determining the sign of the fuction

Question 4

Consider the function y = |x| in the interval [-1,1]. In this interval, the function is

• continuous and differentiable
• continuous but not differentiable
• differentiable but not continuous
• neither continuous nor differentiable

Question 5

What is the converse of the following assertion?

I stay only if you go.

• I stay if you go

• If I stay then you go

• If you do not go then I do not stay

• If I do not stay then you go

Question 6

Suppose A is a finite set with n elements. The number of elements in the largest equivalence relation of A is

• n
• n^2
• 1
• n+1

Question 7

Let R₁ and R₂ be two equivalence relations on a set. Consider the following assertions: (i) R₁ ∪ R₂ is an equivalence relation (ii) R₁ ∩ R₂ is an equivalence relation Which of the following is correct?

• both assertions are true
• assertions (i) is true but assertions (ii) is not true
• assertions (ii) is true but assertions (i) is not true
• neither (i) nor (ii) is true

Question 8

The number of functions from an m element set to an n element set is

• m+n
• m^n
• n^m
• m*n

Question 9

If the regular set \'A\' is represented by A= (01+1)* and the regular set \'B\' is represented by B= ((01)* 1*)*, which of the following is true ?

• A ⊂ B
• B ⊂ A
• A and B are incomparable
• A = B

Question 10

Which of the following sets can be recognized by a Deterministic Finite-state Automaton?

• The number 1, 2, 4, 8......,2^n,.......... written in binary.
• The number 1, 2, 4,....., 2^n,.......... written in unary.
• The set of binary strings in which the number of zeros is the same as the number of ones.
• The set {1, 101, 11011, 1110111,.......}