GATE CS question library

For the initial state of $000$, the function performed by the arrangement of the $\text{J-K}$ flip-flops in figure is:

If the state machine described in figure should have a stable state, the restriction on the inputs is given by

An $\text{ISAM}$ (indexed sequential) file consists of records of size $64$ bytes each, including key field of size $14$ bytes. An address of a disk block takes $2$ bytes. If the disk block size is $512$ bytes and there are $16K$ records, compute the size of the data and index areas in terms of number blocks. How many levels of $\text{tree}$ do …

$\displaystyle \sum_{1\leq k\leq n} O(n)$, where $O(n)$ stands for order $n$ is:

The less-than relation, $<,$ on real number is

Let $A$ and $B$ be sets with cardinalities $m$ and $n$ respectively. The number of one-one mappings from $A$ to $B$, when $m < n$, is

Let A be a finite set of size n. The number of elements in the power set of $A\times A$ is:

The proposition $p \wedge (\sim p \vee q)$ is:

Let $S$ be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$. Then

Consider a simple connected graph $G$ with $n$ vertices and $n$ edges $(n > 2)$. Then, which of the following statements are true?

Assume that the following jobs are to be executed on a single processor system$$\begin{array}{|c|c|} \hline \textbf{Job Id} & \textbf{CPU Burst Time} \\ \hline \text{p} & 4 \\ \hline \text{q} & 1 \\ \hline \text{r} & 8 \\ \hline \text{s} & 1 \\ \hline \text{t} & 2 \\ \hline \end{array}$$The jobs are assumed to have arrived at time …

Consider a system having $m$ resources of the same type. These resources are shared by $3$ processes $A, B$, and $C$ which have peak demands of $3, 4$, and $6$ respectively. For what value of $m$ deadlock will not occur?

A part of the system software which under all circumstances must reside in the main memory is:

The root directory of a disk should be placed

A simple two-pass assembler does the following in the first pass:

What does the following code do? var a, b: integer; begin a:=a+b; b:=a-b; a:=a-b; end;

The details of an interrupt cycle are shown in figure. Given that an interrupt input arrives every $1$ msec, what is the percentage of the total time that the CPU devotes for the main program execution.

Identify the logic function performed by the circuit shown in figure.

Assume that each character code consists of $8$ bits. The number of characters that can be transmitted per second through an asynchronous serial line at $2400$ baud rate, and with two stop bits is

$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________