GATE CS question library

The Breadth First Search (BFS) algorithm has been implemented using the queue data structure. Which one of the following is a possible order of visiting the nodes in the graph below?

Match the following: …

Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____

The minimum possible number of states of a deterministic finite automaton that accepts the regular language $L$ = {$w_{1}aw_{2}$ | $w_{1},w_{2}$ $\in$ $\left \{ a,b \right \}^{*}$ , $\left | w_{1} \right | = 2, \left | w_{2} \right |\geq 3$} is ______________ .

An ER model of a database consists of entity types $A$ and $B$. These are connected by a relationship $R$ which does not have its own attribute. Under which one of the following conditions, can the relational table for R be merged with that of A?

Match the algorithms with their time complexities: …

Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold” is represented by

Let $L_1, L_2$ be any two context-free languages and $R$ be any regular language. Then which of the following is/are CORRECT? $L_1 \cup L_2$ is context-free $\overline{L_1}$ is context-free $L_1 - R$ is context-free $L_1 \cap L_2$ is context-free