Question 1 |

Suppose there are two coins. The first coin gives heads with probability \dfrac{5}{8} when tossed, while the second coin gives heads with probability \dfrac{1}{4}. One of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads ?

\left(\dfrac{7}{8}\right) | |

\left(\dfrac{1}{2}\right) | |

\left(\dfrac{7}{16}\right) | |

\left(\dfrac{5}{32}\right) |

Question 1 Explanation:

Question 2 |

Let A be the matrix \begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}. What is the maximum value of x^TAx where the maximum is taken over all x that are the unit eigenvectors of A?

5 | |

\frac{(5 + \sqrt{5})}{2} | |

3 | |

\frac{(5 - \sqrt{5})}{2} |

Question 2 Explanation:

Question 3 |

Consider a weighted, undirected graph with positive edge weights and let uv be an edge in the graph. It is known that the shortest path from the source vertex s to u has weight 53 and the shortest path from s to v has weight 65. Which one of the following statements is always TRUE?

Weight (u,v) \leq 12 | |

Weight (u,v) = 12 | |

Weight (u,v) \geq 12 | |

Weight (u,v) > 12 |

Question 3 Explanation:

Question 4 |

In the Spiral model of software development, the primary determinant in selecting activities in each iteration is

Iteration size | |

Cost | |

Adopted process such as Rational Unified Process or Extreme Programming | |

Risk |

Question 4 Explanation:

Question 5 |

Which of the following systems is a most likely candidate example of a pipe and filter architecture ?

Expert system | |

DB repository | |

Aircraft flight controller | |

Signal processing |

Question 5 Explanation:

There are 5 questions to complete.