# GATE CS 1998

• Last Updated : 11 Oct, 2021

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

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: 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 3-Explanation:
This method is guaranteed to convert to the root off if f is a continuous function in space [a, b] and f (a) and f (b) have opposing symbols. The total error is limited to half of each step so that the path is changed sequentially, which is relatively slow. Ref: http://en.wikipedia.org/wiki/Bisection_method#Analysis
 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 4-Explanation:
The function y = |x| in the interval [-1,1] is |x| is continuous and differentiable everywhere except at x=0, where it is continuous but not differentiable. since [-1,1] contains 0 , in this interval it is continues but not differentiables. Hence, option (B) is correct.
 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 5-Explanation:

Explanation:

The converse of the assertion "I stay only if you go" is:

(D) If I do not stay then you go.

The converse of an implication swaps the positions of the antecedent and the consequent. In the original assertion, "I stay" is the consequent and "you go" is the antecedent. Therefore, in the converse, "you go" becomes the consequent and "I do not stay" becomes the antecedent.

 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) R1R2 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 9-Explanation:
Some of the regular expression always equivalent to (0+1)* such that
(0+1)*
= (0*+1*)*
= (01*)*
= (0*+1)*
= (0+1*)*
= 0*(10*)*
= 1*(01*)* 
Since,
(01+1)* = ((01)* 1* )*
Therefore 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,.......}

Question 10-Explanation:
If there is a infinite language and for that language if their is no any pattern exist then we can surely say that given language is not regular, but if pattern is exist for that language then it may or may not be regular language and for ensuring a given language is regular, if we are able to draw DFA for that language then surely it will be regular otherwise not regular, Therefore option (A) is regular language as it can written in binary i.e.,
L = {1, 10, 100, 1000, 10000, …}
Regular expression is (10*), since, for this expression we can draw DFA. So, option (A) is correct.
There are 83 questions to complete.