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

f(x1, x2, ..., xn) = f(0, x2, …, xn) + f(1, x2, ..., xn)

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)

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Question 1

In the working-set strategy, which of the following is done by the operating system to prevent thrashing?

It initiates another process if there are enough extra frames.
It selects a process to suspend if the sum of the sizes of the working-sets exceeds the total number of available frames.

I only
II only
Neither I nor II
Both I and II

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Question 2

A problem in NP is NP-complete if

It can be reduced to the 3-SAT problem in polynomial time
The 3-SAT problem can be reduced to it in polynomial time
It can be reduced to any other problem in NP in polynomial time
Some problem in NP can be reduced to it in polynomial time

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Question 3

The characters a to h have the set of frequencies based on the first 8 Fibonacci numbers as follows

a : 1, b : 1, c : 2, d : 3, e : 5, f : 8, g : 13, h : 21/

A Huffman code is used to represent the characters. What is the sequence of characters corresponding to the following code? 110111100111010

fdheg
ecgdf
dchfg
fehdg

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Question 4

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

f(x₁, x₂, …, x_n) = x₁'f(x₁, x₂, …, x_n) + x₁f(x₁, x₂, …, x_n)
f(x₁, x₂, ..., x_n) = x₂f(x₁, x₂, …, x_n) + x₂'f(x₁, x₂, …, x_n)
f(x₁, x₂, ..., x_n) = x_n'f(x₁, x₂, …, 0) + x_nf(x₁, x₂, …,1)
f(x₁, x₂, ..., x_n) = f(0, x₂, …, x_n) + f(1, x₂, ..., x_n)

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Question 5

When a coin is tossed, the probability of getting a Head is p,0<p<1. Let N be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are independent, the expected value of N is

1/p
1/(1−p)
1/p2
1/(1−p2)

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Question 6

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

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Question 7

Which of the following relational query languages have the same expressive power?

Relational algebra
Tuple relational calculus restricted to safe expressions
Domain relational calculus restricted to safe expressions

II and III only
I and II only
I and III only
I, II and III

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Question 8

Consider the relations r₁(P, Q, R) and r₂(R, S, T) with primary keys P and R respectively. The relation r₁ contains 2000 tuples and r₂ contains 2500 tuples. The maximum size of the join r₁⋈ r₂ is :

2000
2500
4500
5000

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Question 9

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?

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

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

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Question 10

What is the cardinality of the set of integers X defined below? X = {n | 1 ≤ n ≤ 123, n is not divisible by either 2, 3 or 5}

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