GATE IT 2006

Question 1

In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 25°C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 25°C, or at/below 25°C. What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 25°C?

• 0.4
• 0.6
• 0.8
• 0.9

Question 2

For the set N of natural numbers and a binary operation f : N x N → N, an element z ∊ N is called an identity for f, if f (a, z) = a = f(z, a), for all a ∊ N. Which of the following binary operations have an identity?

1. f (x, y) = x + y - 3
2. f (x, y) = max(x, y)
3. f (x, y) = x^y

• I and II only
• II and III only
• I and III only
• None of these

Question 3

In the automaton below, s is the start state and t is the only final state.               Consider the strings u = abbaba, v = bab, and w = aabb. Which of the following statements is true?  

• The automaton accepts u and v but not w
• The automaton accepts each of u, v, and w
• The automaton rejects each of u, v, and w
• The automaton accepts u but rejects v and w

Question 4

In the context-free grammar below, S is the start symbol, a and b are terminals, and ϵ denotes the empty string S → aSa | bSb | a | b | ϵ Which of the following strings is NOT generated by the grammar?  

• aaaa
• baba
• abba
• babaaabab

Question 5

Which regular expression best describes the language accepted by the non-deterministic automaton below?

• (a + b)* a(a + b)b
• (abb)*
• (a + b)* a(a + b)* b(a + b)*
• (a + b)*

Question 6

The addition of 4-bit, two\'s complement, binary numbers 1101 and 0100 results in  

• 0001 and an overflow
• 1001 and no overflow
• 0001 and no overflow
• 1001 and an overflow

Question 7

Which of the following DMA transfer modes and interrupt handling mechanisms will enable the highest I/O band-width?  

• Transparent DMA and Polling interrupts

• Cycle-stealing and Vectored interrupts

• Block transfer and Vectored interrupts

• Block transfer and Polling interrupts

Question 8

In a binary tree, the number of internal nodes of degree 1 is 5, and the number of internal nodes of degree 2 is 10. The number of leaf nodes in the binary tree is  

• 10
• 11
• 12
• 15

Question 9

Given a boolean function f (x₁, x₂, ..., x_n), which of the following equations is NOT true  

• f (x1, x2, ..., xn) = x1\'f(x1, x2, ..., xn) + x1f(x1, x2, ..., xn)
• f (x1, x2, ..., xn) = x2f(x1, x2, …, xn) + x2\'f(x1, x2, …,xn)
• f (x1, x2, ..., xn) = xn\'f(x1, x2, …, 0) + xnf(x1, x2, …,1)
• f (x1, x2, ..., xn) = f(0, x2, …, xn) + f(1, x2, .., xn)

Question 10

If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a  

• Hamiltonian cycle
• grid
• hypercube
• tree