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:

Question 6 |

A processor takes 12 cycles to complete an instruction I. The corresponding pipelined processor uses 6 stages with the execution times of 3, 2, 5, 4, 6 and 2 cycles respectively. What is the asymptotic speedup assuming that a very large number of instructions are to be executed?

1.83 | |

2 | |

3 | |

6 |

Question 6 Explanation:

Question 7 |

Which of the following input sequences for a cross-coupled R-S flip-flop realized with two NAND gates may lead to an oscillation?

11, 00 | |

01, 10 | |

10, 01 | |

00, 11 |

Question 7 Explanation:

Question 8 |

The following circuit implements a two-input AND gate using two 2-1 multiplexers.

What are the values of X_1, X_2, X_3?

What are the values of X_1, X_2, X_3?

X_1 = b, X_2 = 0, X_3 = a | |

X_1 = b, X_2 = 1, X_3 = b | |

X_1 = a, X_2 = b, X_3 = 1 | |

X_1 = a, X_2 = 0, X_3 = b |

Question 8 Explanation:

Question 9 |

Consider an ambiguous grammar G and its disambiguated version D. Let the language recognized by the two grammars be denoted by L(G) and L(D) respectively. Which one of the following is true?

L (D) \subset L (G) | |

L (D) \supset L (G) | |

L (D) = L (G) | |

L (D) is empty |

Question 9 Explanation:

Question 10 |

Processes P1 and P2 use critical_flag in the following routine to achieve mutual exclusion. Assume that critical_flag is initialized to FALSE in the main program.

Consider the following statements.

i.It is possible for both P1 and P2 to access critical_region concurrently.

ii.This may lead to a deadlock.

Which of the following holds?

```
get_exclusive_access ( )
{
if (critical _flag == FALSE) {
critical_flag = TRUE ;
critical_region () ;
critical_flag = FALSE;
}
}
```

Consider the following statements.

i.It is possible for both P1 and P2 to access critical_region concurrently.

ii.This may lead to a deadlock.

Which of the following holds?

(i) is false (ii) is true | |

Both (i) and (ii) are false | |

(i) is true (ii) is false | |

Both (i) and (ii) are true |

Question 10 Explanation:

There are 10 questions to complete.