Gate IT 2007

Question 1

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

• 7/8
• 1/2
• 7/16
• 5/32

Question 2

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

• 5
• (5 + √5)/2
• 3
• (5 - √5)/2

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) < 12
• weight (u, v) ≤ 12
• weight (u, v) > 12
• weight (u, v) ≥ 12

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 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 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 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 8

The following circuit implements a two-input AND gate using two 2-1 multiplexers. What are the values of X₁, X₂, X₃ ?

• X₁=b, X₂=0, X₃=a
• X₁=b, X₂=1, X₃=b
• X₁=a, X₂=b, X₃=1
• X₁=a, X₂=0, X₃=b

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) ⊂ L (G)
• L (D) ⊃ L (G)
• L (D) = L (G)
• L (D) is empty

Question 10

Let a memory have four free blocks of sizes 4k, 8k, 20k, 2k. These blocks are allocated following the best-fit strategy. The allocation requests are stored in a queue as shown below.

The time at which the request for J₇ will be completed will be

• 16
• 19
• 20
• 37