GATE CS question library

The next state table of a $2-$bit saturating up-counter is given below. $\begin{array}{cc|cc} Q_1 & Q_0 & Q_1^+ & Q_0^+ \\ \hline 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 1 \end{array}$ The counter is built as a synchronous sequential circuit using $T$ flip-flops. The …

Consider two hosts $X$ and $Y$, connected by a single direct link of rate $10^6\; \text{bits/sec}$. The distance between the two hosts is $10,000\;\text{km}$ and the propagation speed along the link is $2 \times 10^8 \;\text{m/sec}$. Host $X$ sends a file of $50,000\;\text{bytes}$ as one large message to host $Y$ continuously. Let the …

If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.

If $w, x, y, z$ are Boolean variables, then which one of the following is INCORRECT?

In a file allocation system, which of the following allocation scheme(s) can be used if no external fragmentation is allowed? Contiguous Linked Indexed

Given the following binary number in $32$-bit (single precision) $\text{IEEE-754}$ format : $\large 00111110011011010000000000000000$ The decimal value closest to this floating-point number is :

The maximum number of $\textsf{IPv4}$ router addresses that can be listed in the record route (RR) option field of an $\textsf{IPv4}$ header is______.

An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at $0.05$ bar intervals in this plot. If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following …

The number of roots of $e^{x}+0.5x^{2}-2=0$ in the range $[-5,5]$ is

$X$ is a $30$ digit number starting with the digit $4$ followed by the digit $7$. Then the number $X^3$ will have

There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labeled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

“We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.” The author’s belief that ideology is not as important as literature is revealed by …

There are $3$ red socks, $4$ green socks and $3$ blue socks.You choose $2$ socks. The probability that they are of the same colour is

A test has twenty questions worth $100$ marks in total. There are two types of questions. Multiple choice questions are worth $3$ marks each and essay questions are worth $11$ marks each. How many multiple choice questions does the exam have?

There are five buildings called $V$, $W$, $X$, $Y$ and $Z$ in a row (not necessarily in that order). $V$ is to the West of $W$. $Z$ is to the East of $X$ and the West of $V$. $W$ is to the West of $Y$. Which is the building in the middle?

Saturn is ___________ to be seen on a clear night with the naked eye.

Choose the option with words that are not synonyms.

A message is made up entirely of characters from the set $X=\{P, Q, R, S, T\}$. The table of probabilities for each of the characters is shown below: …

If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .

Consider the following database table named $\text{top\_scorer}$. …