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
Cross
1/6
Tick
3/8
Cross
1/8
Cross
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). P(E) = P(O) = \\frac{1}{2} P(\\text{Exactly 1 Odd Number}) = C(3,1) * P(E)^2*P(O)^1 = \\frac{3}{8}
Question 2
Consider the following set of equations
x+2y = 5
4x+8y = 12
3x+6y+3z = 15
This set-
Cross
has a unique solution
Tick
has no solutions
Cross
has finite number of solutions
Cross
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:
Cross
converges within a few iteration
Tick
guaranteed to work for all continuous functions
Cross
is faster than the Newton-Raphson method
Cross
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
Cross
continuous and differentiable
Tick
continuous but not differentiable
Cross
differentiable but not continuous
Cross
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.
Tick

I stay if you go

Cross

If I stay then you go

Cross

If you do not go then I do not stay

Cross

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
Cross
n
Tick
n^2
Cross
1
Cross
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?
Cross
both assertions are true
Cross
assertions (i) is true but assertions (ii) is not true
Tick
assertions (ii) is true but assertions (i) is not true
Cross
neither (i) nor (ii) is true


Question 8
The number of functions from an m element set to an n element set is
Cross
m+n
Cross
m^n
Tick
n^m
Cross
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 ?
Cross
A ⊂ B
Cross
B ⊂ A
Cross
A and B are incomparable
Tick
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?
Tick
The number 1, 2, 4, 8......,2^n,.......... written in binary.
Cross
The number 1, 2, 4,....., 2^n,.......... written in unary.
Cross
The set of binary strings in which the number of zeros is the same as the number of ones.
Cross
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.

  • Last Updated : 11 Oct, 2021

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