GATE EC question library

For the solid $S$ shown below, the value of $\underset{S}{\iiint} xdxdydz$ (rounded off to two decimal places) is _______________.

$X\left ( \omega \right )$ is the Fourier transform of $x(t)$ shown below. The value of $\int_{-\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega$ (rounded off to two decimal places) is ____________

The transfer function of a stable discrete-time $\text{LTI}$ system is $H\left ( z \right )=\dfrac{K\left ( z-\alpha \right )}{z+0.5}$, where $K$ and $\alpha$ are real numbers. The value of $\alpha$ (rounded off to one decimal place) with $\mid \alpha \mid > 1$, for which the magnitude response of the system is constant over all frequencies, …

$X$ is a random variable with uniform probability density function in the interval $[-2,\:10]$. For $Y=2X-6$, the conditional probability $P\left ( Y\leq 7\mid X\geq 5 \right )$ (rounded off to three decimal places) is __________.

Consider the following closed loop control system where $G\left ( s \right )=\dfrac{1}{s\left ( s+1 \right )}$ and $C\left ( s \right )=K\dfrac{s+1}{s+3}$. If the steady state error for a unit ramp input is $0.1$, then the value of $K$ is ______________.