GATE EE 2020 Question Paper (08-Feb-2020) (Shift 1)

Consider a negative unity feedback system with the forward path transfer function $\frac{s^2+s+1}{s^3+2s^2+2s+K}$, where K is a positive real number. The value of K for which the system will have some of its poles on the imaginary axis is ________

Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) h(t) = y(t). Further, if |x(t)| |h(t)| = z(t), which of the following statements is true?

The causal realization of a system transfer function H(s) having poles at (2, -1), (-2, 1) and zeroes at (2, 1), (-2, -1) will be

Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation?

y[n] – ay[n - 1] = b₀x[n] – b₁x[n - 1]

Let aᵣ, a${}_{\text{ϕ},}$ and a${}_z$ be unit vectors along r, ϕ and z directions, respectively in the cylindrical coordinate system. For the electric flux density given by D = (aᵣ 15 + a${}_{\text{ϕ}}$ 2r - a${}_z$ 3rz) Coulomb/m², the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius 3 m and height 5 m oriented along the z-axis with its base at the origin is: