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    
Discuss it


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-
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    
Discuss it


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    
Discuss it


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    
Discuss it


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    
Discuss it


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    
Discuss it


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    
Discuss it


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    
Discuss it


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    
Discuss it


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    
Discuss it


There are 83 questions to complete.


My Personal Notes arrow_drop_up


Writing code in comment? Please use ide.geeksforgeeks.org, generate link and share the link here.