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

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

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

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)

Question 5

A class of 24 students occupies a classroom containing 4 rows of seats, with 7 seats in each row. If the students seat themselves randomly, what is the probability that the 5th seat in the 4th row is empty?

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

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

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

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

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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