# 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
 A 1/6 B 3/8 C 1/8 D 1/2
Probability    GATE CS 1998
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Question 1 Explanation:
The question is an example of Binomial Experiment, with two possibilities- Number is Even(E) or Number is odd(O).  Question 2
Consider the following set of equations
x+2y = 5
4x+8y = 12
3x+6y+3z = 15
This set-
 A has a unique solution B has no solutions C has finite number of solutions D has infinite number of solutions
Linear Algebra    GATE CS 1998
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Question 2 Explanation:
When the given set of equations are represented in matrix form, the coefficient matrix A is singular. Since the determinant value of A is 0, the system of equations is inconsistent. Therefore, option (B) is correct. This explanation is provided by Chirag Manwani.
 Question 3
Which of the following statements applies to the bisection method used for finding roots of functions:
 A converges within a few iteration 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 fuction
Numerical Methods and Calculus    GATE CS 1998
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 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
Numerical Methods and Calculus    GATE CS 1998
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 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
Propositional and First Order Logic.    GATE CS 1998
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 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
Set Theory & Algebra    GATE CS 1998
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 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) R1R2 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
Set Theory & Algebra    GATE CS 1998
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 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
Set Theory & Algebra    GATE CS 1998
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 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? (i) A ⊂ B (ii) B ⊂ A (iii) A and B are incomparable (iv) A = B
 A (i) B (ii) C (iii) D (iv)
Regular languages and finite automata    GATE CS 1998
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 Question 10
Which of the following sets can be recognized by a Deterministic Finite-state Automaton?
 A The number 1, 2, 4, 8......,2^n,.......... written in binary. B The number 1, 2, 4,....., 2^n,.......... written in unary. C The set of binary strings in which the number of zeros is the same as the number of ones. D The set {1, 101, 11011, 1110111,.......}
Regular languages and finite automata    GATE CS 1998
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There are 83 questions to complete.

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