# GATE CS 1998

Please wait while the activity loads.

If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled.

If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled.

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 |

**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).

Question 2 |

Consider the following set of equations

x+2y = 5 4x+8y = 12 3x+6y+3z = 15This set-

has a unique solution | |

has no solutions | |

has finite number of solutions | |

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:

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 |

**Numerical Methods and Calculus**

**GATE CS 1998**

**Discuss it**

Question 4 |

Consider the functiony = |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 |

**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.

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 |

**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 isn | |

n^2 | |

1 | |

n+1 |

**Set Theory & Algebra**

**GATE CS 1998**

**Discuss it**

Question 7 |

Let

*R*and_{1}*R*be two equivalence relations on a set. Consider the following assertions: (i)_{2}*R*∪_{1}*R*is an equivalence relation (ii)_{2}*R*∩_{1}*R*is an equivalence relation Which of the following is correct?_{2}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 |

**Set Theory & Algebra**

**GATE CS 1998**

**Discuss it**

Question 8 |

The number of functions from an

*m element*set to an*n element*set ism+n | |

m^n | |

n^m | |

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(i) | |

(ii) | |

(iii) | |

(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?

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,.......} |

**Regular languages and finite automata**

**GATE CS 1998**

**Discuss it**

There are 83 questions to complete.