Question 1 |

A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is

\dfrac{1}{6} | |

\dfrac{3}{8} | |

\dfrac{1}{8} | |

\dfrac{1}{2} |

Question 1 Explanation:

Question 2 |

Consider the following set of equations

x+2y=5\\ 4x+8y=12\\ 3x+6y+3z=15

This set

x+2y=5\\ 4x+8y=12\\ 3x+6y+3z=15

This set

has unique solution | |

has no solution | |

has finite number of solutions | |

has infinite number of solutions |

Question 2 Explanation:

Question 3 |

Which of the following statements applies to the bisection method used for finding roots of functions:

converges within a few iterations | |

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 function |

Question 3 Explanation:

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:

Question 5 |

What is the converse of the following assertion?

I stay only if you go

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:

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 6 Explanation:

Question 7 |

Let R_1 and R_1 be two equivalence relations on a set. Consider the following assertions:

I. R_1 \cup R_2 is an equivalence relation

II. R_1 \cap R_2 is an equivalence relation

Which of the following is correct?

I. R_1 \cup R_2 is an equivalence relation

II. R_1 \cap R_2 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 7 Explanation:

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 8 Explanation:

Question 9 |

If the regular set A is represented by A = (01 + 1)^* and the regular set B is represented by B = \left(\left(01\right)^*1^*\right)^*, which of the following is true?

A \subset B | |

B \subset A | |

A and B are incomparable | |

A=B |

Question 9 Explanation:

Question 10 |

Which of the following set can be recognized by a Deterministic Finite state Automaton?

The numbers 1, 2, 4, 8, \dots 2^n, \dots written in binary | |

The numbers 1, 2, 4, 8,\dots 2^n, \dots written in unary | |

The set of binary string in which the number of zeros is the same as the number of ones. | |

The set \{1, 101, 11011, 1110111, \dots\} |

Question 10 Explanation:

There are 10 questions to complete.