List of top Miscellaneous Questions asked in GATE CS

The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is ............ \begin{center} \includegraphics[width=0.3\textwidth]{60.png} \end{center}

Let \(L_1\) be the language represented by the regular expression \(b^*ab^*(ab^*ab^*)^*\) and \(L_2 = \{ w \in (a + b)^* \mid |w| \leq 4 \\), where \(|w|\) denotes the length of string \(w\). The number of strings in \(L_2\) which are also in \(L_1\) is ............}

The relation schema, \( \text{Person(pid, city) \), describes the city of residence for every person uniquely identified by \( \text{pid} \). The following relational algebra operators are available: \texttt{selection}, \texttt{projection}, \texttt{cross product}, and \texttt{rename}.} To find the list of cities where at least 3 persons reside, using the above operators, the minimum number of \texttt{cross product operations that must be used is ...........\_.}

Let \(M\) be the 5-state NFA with \(\epsilon\)-transitions shown in the diagram below. \begin{center} \includegraphics[width=0.2\textwidth]{41.png} \end{center} Which one of the following regular expressions represents the language accepted by \(M\)?

Which of the following fields of an IP header is/are always modified by any router before it forwards the IP packet?}

What is the output of the following C program? \begin{verbatim} #include stdio.h int main() { double a[2] = {20.0, 25.0}, *p, *q; p = a; q = p + 1; printf("%d,%d", (int)(q - p), (int)(*q - *p)); return 0; } \end{verbatim}