# 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 1 Explanation:
 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 2 Explanation:
 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 3 Explanation:
 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 4 Explanation:
 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 5 Explanation:
 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 6 Explanation:
 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 7 Explanation:
 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 8 Explanation:
 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 9 Explanation:
 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
Question 10 Explanation:
There are 10 questions to complete.