GATE CS question library

The data blocks of a very large file in the Unix file system are allocated using

The Breadth First Search algorithm has been implemented using the queue data structure. One possible order of visiting the nodes of the following graph is:

Which combination of the integer variables $x, y,$ and $z$ makes the variable $a$ get the value $4$ in the following expression? $$a=(x > y)?((x > z) ?x:z): ((y > z) ?y:z)$$

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

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

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

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

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

Some code optimizations are carried out on the intermediate code because

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

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

Which of the following is true for the language $$\left\{ a^p \mid p \text{ is a prime } \right \}?$$

Given $f_1$, $f_3$ and $f$ in canonical sum of products form (in decimal) for the circuit $f_1 = \Sigma m(4, 5, 6, 7, 8)$ $f_3 = \Sigma m(1, 6, 15)$ $f = \Sigma m(1, 6, 8, 15)$ then $f_2$ is

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

Let $r$ denote number system radix. The only value(s) of $r$ that satisfy the equation $\sqrt{121_r}={11}_r$ is/are

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?

In the IEEE floating point representation the hexadecimal value $0\text{x}00000000$ corresponds to

The following system of equations $x_1 + x_2 + 2x_3 = 1$ $x_1 + 2x_2 + 3x_3 = 2$ $x_1 + 4x_2 + αx_3 = 4$ has a unique solution. The only possible value(s) for $α$ is/are

If $P, Q, R$ are subsets of the universal set U, then $$(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$$ is

$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals