GATE EC 2020 Question Paper (02-Feb-2020) (Shift 2)

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

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

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

X is a random variable with a uniform probability density function in the interval [-2, 10]. For Y = 2X – 6, the conditional probability P(Y ≤ 7 | X ≥ 5) (rounded off to three decimal places) is

Consider the following closed-loop control system



Where $G\left(s\right)=\frac{1}{s\left(s+1\right)}$ and $C\left(s\right)=K\frac{s+1}{s+3}$. If the steady-state error for a unit ramp input is 0.1, then the value of K is