# GATE IT 2007

 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 ?
 A $\left(\dfrac{7}{8}\right)$ B $\left(\dfrac{1}{2}\right)$ C $\left(\dfrac{7}{16}\right)$ D $\left(\dfrac{5}{32}\right)$
Discrete Mathematics   Probability Theory
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?
 A 5 B $\frac{(5 + \sqrt{5})}{2}$ C 3 D $\frac{(5 - \sqrt{5})}{2}$
Engineering Mathematics   Linear Algebra
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?
 A Weight $(u,v) \leq 12$ B Weight (u,v) = 12 C Weight $(u,v) \geq 12$ D Weight (u,v) > 12
Algorithm   Shortest Path
Question 3 Explanation:
 Question 4
In the Spiral model of software development, the primary determinant in selecting activities in each iteration is
 A Iteration size B Cost C Adopted process such as Rational Unified Process or Extreme Programming D Risk
Software Engg
Question 4 Explanation:
 Question 5
Which of the following systems is a most likely candidate example of a pipe and filter architecture ?
 A Expert system B DB repository C Aircraft flight controller D Signal processing
Software Engg
Question 5 Explanation:

There are 5 questions to complete.