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 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 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 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 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   




There are 5 questions to complete.

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