GATE CS question library

Let $G$ be a weighted graph with edge weights greater than one and $G'$ be the graph constructed by squaring the weights of edges in $G$. Let $T$ and $T'$ be the minimum spanning trees of $G$ and $G'$, respectively, with total weights $t$ and $t'$. Which of the following statements is TRUE?

Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to

Register renaming is done in pipelined processors:

The amount of ROM needed to implement a $4\text{-bit}$ multiplier is

Let $W(n)$ and $A(n)$ denote respectively, the worst case and average case running time of an algorithm executed on an input of size $n$. Which of the following is ALWAYS TRUE?

Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to

The recurrence relation capturing the optimal execution time of the $Towers \ of \ Hanoi$ problem with $n$ discs is

Which of the following statements are TRUE about an SQL query? P : An SQL query can contain a HAVING clause even if it does not have a GROUP BY clause Q : An SQL query can contain a HAVING clause only if it has a GROUP BY clause R : All attributes used in the GROUP BY clause must appear in the SELECT clause S : Not all attributes used in the GROUP BY clause …

What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational”

What is the complement of the language accepted by the NFA shown below? Assume $\Sigma = \{a\}$ and $\epsilon$ is the empty string.

Let A be the $2 × 2$ matrix with elements $a_{11} = a_{12} = a_{21} = +1$ and $a_{22} = −1$ . Then the eigenvalues of the matrix $A^{19}$ are

Given the basic ER and relational models, which of the following is INCORRECT?

The protocol data unit (PDU) for the application layer in the Internet stack is:

Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local minima of this function are

The decimal value $0.5$ in IEEE single precision floating point representation has

A process executes the code fork(); fork(); fork(); The total number of child processes created is

The truth table ${\begin{array}{|c|c|c|}\hline \textbf{X}& \textbf{Y}& \textbf{(X,Y)} \\ \hline 0& 0& 0 \\ \hline 0& 1&0\\ \hline 1& 0& 1 \\ \hline 1& 1& 1 \\ \hline \end{array}}$ represents the Boolean function

The worst case running time to search for an element in a balanced binary search tree with $n2^{n}$ elements is

What will be the output of the following C program segment? char inChar = 'A'; switch ( inChar ) { case 'A' : printf ("Choice A \ n"); case 'B' : case 'C' : printf ("Choice B"); case 'D' : case 'E' : default : printf ("No Choice"); }

Assuming $\textsf{P} \neq \textsf{NP}$, which of the following is TRUE?