GATE CSE 1998

Question 1
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is
A
\dfrac{1}{6}
B
\dfrac{3}{8}
C
\dfrac{1}{8}
D
\dfrac{1}{2}
Discrete Mathematics   Probability Theory
Question 2
Consider the following set of equations
x+2y=5\\ 4x+8y=12\\ 3x+6y+3z=15
This set
A
has unique solution
B
has no solution
C
has finite number of solutions
D
has infinite number of solutions
Engineering Mathematics   Linear Algebra
Question 3
Which of the following statements applies to the bisection method used for finding roots of functions:
A
converges within a few iterations
B
guaranteed to work for all continuous functions
C
is faster than the Newton-Raphson method
D
requires that there be no error in determining the sign of the function
Engineering Mathematics   Numerical Method
Question 4
Consider the function y=|x| in the interval [-1, 1]. In this interval, the function is
A
continuous and differentiable
B
continuous but not differentiable
C
differentiable but not continuous
D
neither continuous nor differentiable
Discrete Mathematics   Functions
Question 5
What is the converse of the following assertion?
I stay only if you go
A
I stay if you go
B
If I stay then you go
C
If you do not go then I do not stay
D
If I do not stay then you go
Discrete Mathematics   Propositional Logic
Question 6
Suppose A is a finite set with n elements. The number of elements in the largest equivalence relation of A is
A
n
B
n^2
C
1
D
n+1
Discrete Mathematics   Relation
Question 7
Let R_1 and R_1 be two equivalence relations on a set. Consider the following assertions:
I. R_1 \cup R_2 is an equivalence relation
II. R_1 \cap R_2 is an equivalence relation
Which of the following is correct?
A
Both assertions are true
B
Assertions (i) is true but assertions (ii) is not true
C
Assertions (ii) is true but assertions (i) is not true
D
Neither (i) nor (ii) is true
Discrete Mathematics   Relation
Question 8
The number of functions from an m element set to an n element set is
A
m + n
B
m^n
C
n^m
D
m*n
Discrete Mathematics   Functions
Question 9
If the regular set A is represented by A = (01 + 1)^* and the regular set B is represented by B = \left(\left(01\right)^*1^*\right)^*, which of the following is true?
A
A \subset B
B
B \subset A
C
A and B are incomparable
D
A=B
Theory of Computation   Regular Expression
Question 10
Which of the following set can be recognized by a Deterministic Finite state Automaton?
A
The numbers 1, 2, 4, 8, \dots 2^n, \dots written in binary
B
The numbers 1, 2, 4, 8,\dots 2^n, \dots written in unary
C
The set of binary string in which the number of zeros is the same as the number of ones.
D
The set \{1, 101, 11011, 1110111, \dots\}
Theory of Computation   Finite Automata
There are 10 questions to complete.

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