GATE CS question library

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 __________

The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ has

Which of the following improper integrals is (are) convergent?

The differential equation $\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0$ is:

Fourier series of the periodic function (period 2π) defined by $$f(x) = \begin{cases} 0, -p < x < 0\\x, 0 < x < p \end{cases} \text{ is }\\ \frac{\pi}{4} + \sum \left [ \frac{1}{\pi n^2} \left(\cos n\pi - 1 \right) \cos nx - \frac{1}{n} \cos n\pi \sin nx \right ]$$ But putting $x = \pi$, we get the sum of the series …

The eigen vector $(s)$ of the matrix $$\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$$ is (are)

Consider the set of integers $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent?

Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree