Question 1 |

A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour is

\left(\dfrac{1}{36}\right) | |

\left(\dfrac{1}{6}\right) | |

\left(\dfrac{1}{4}\right) | |

\left(\dfrac{1}{3}\right) |

Question 1 Explanation:

Question 2 |

If the trapezoidal method is used to evaluate the integral obtained \int_{0}^{1} x^2dx, then the value obtained

is always > (1/3) | |

is always < (1/3) | |

is always = (1/3) | |

may be greater or lesser than (1/3) |

Question 2 Explanation:

Question 3 |

The determinant of the matrix given below is

\begin{bmatrix} 0 &1 &0 &2 \\ -1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& -2& 0& 1 \end{bmatrix}

\begin{bmatrix} 0 &1 &0 &2 \\ -1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& -2& 0& 1 \end{bmatrix}

-1 | |

0 | |

1 | |

2 |

Question 3 Explanation:

Question 4 |

Let L be a regular language and M be a context-free language, both over the alphabet \Sigma. Let L^c and M^c denote the complements of L and M respectively. Which of the following statements about the language L^c\cup M^c is TRUE?

It is necessarily regular but not necessarily context-free. | |

It is necessarily context-free. | |

It is necessarily non-regular. | |

None of the above |

Question 4 Explanation:

Question 5 |

Which of the following statements is TRUE about the regular expression 01*0?

It represents a finite set of finite strings. | |

It represents an infinite set of finite strings. | |

It represents a finite set of infinite strings. | |

It represents an infinite set of infinite strings. |

Question 5 Explanation:

There are 5 questions to complete.