# 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:
 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?
 A 1.83 B 2 C 3 D 6
Computer Organization   Pipeline Processor
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?
 A 11, 00 B 01, 10 C 10, 01 D 00, 11
Digital Logic   Sequential Circuit
Question 7 Explanation:
 Question 8
The following circuit implements a two-input AND gate using two 2-1 multiplexers.

What are the values of $X_1, X_2, X_3$?
 A $X_1 = b, X_2 = 0, X_3 = a$ B $X_1 = b, X_2 = 1, X_3 = b$ C $X_1 = a, X_2 = b, X_3 = 1$ D $X_1 = a, X_2 = 0, X_3 = b$
Digital Logic   Combinational Circuit
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?
 A $L (D) \subset L (G)$ B $L (D) \supset L (G)$ C L (D) = L (G) D L (D) is empty
Compiler Design   Parsing
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.
 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.