# Computer Science and Information Technology - GATE 2008 Paper Solution

$\underset{x\to \infty }{\mathrm{lim}}\frac{x-sinx}{x+\mathrm{cos}x}$ equals

If P, Q, R are subsets of the universal set U, then (P ∩ Q ∩ R) ∪ (Pc ∩ Q ∩ R) ∪ Qc ∪ Rc is

The following system of equations

x1+x2+2 x3 = 1
x1+2 x2+3 x3 = 2
x1+4 x2+
$\alpha$ x3 = 4

has a unique solution. The only possible value(s) for $\alpha$ is/are

In the IEEE floating point representation the hexadecimal value 0x00000000 corresponds to

In the Karnaugh map shown below, X denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map? Let r denote number system radix. The only value(s) of r that satisfy the equation $\sqrt{{121}_{r}}={11}_{r}$ is / are

The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and edges has time complexity

Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit f1 = ${\sum }_{}$m (4, 5, 6, 7, 8)
f3 = ${\sum }_{}$m (1, 6, 15)
f = ${\sum }_{}$m (1, 6, 8, 15)
then f2 is

Which of the following is true for the language {ap | p is a prime}?

Which of the following are decidable?
I. Whether the intersection of two regular languages is infinite
II. Whether a given context-free language is regular
III. Whether two push-down automata accept the same language
IV. Whether a given grammar is context-free

Which of the following describes a handle (as applicable to LR-parsing) appropriately?

Some code optimizations are carried out on the intermediate code because

If L and  $\overline{L}$ are recursively enumerable then L is

What is the maximum size of data that the application layer can pass on to the TCP layer below?

Which of the following tuple relational calculus expression(s) is/are equivalent to $\forall t\in r\left(P\left(t\right)\right)$?

I. $¬\exists t\in r\left(P\left(t\right)\right)$
II.$\exists t\notin r\left(P\left(t\right)\right)$
III. $¬\exists t\in r\left(¬P\left(t\right)\right)$
IV. $\exists t\notin r\left(¬P\left(t\right)\right)$

A clustering index is defined on the fields which are of type

Which of the following system calls results in the sending of SYN packets?

Which combination of the integer variables x, y and z makes the variable a get the value 4 in the following expression?

a = (x > y) ? ((x > z) ? x : z) : ((y > z) ? y : z) 