GATE EE 2018 Question Paper (10-Feb-2018) (Shift 2)

A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

Consider a non-singular 2×2 square matrix A. If trace (A) = 4 and trace(A²) = 5, the determinant of the matrix A is _________ (up to 1 decimal place).

Let f be a real-valued function of a real variable defined as f(x) = x – [x], where [x] denotes the largest integer less than or equal to x. The value of $\underset{0.25}{\overset{1.25}{\int }}f\left(x\right)dx$ is _______ (up to 2 decimal places).

In the two-port network shown, the h₁₁ parameter $\left(where,h_{11}=\frac{V_1}{I_1}when{V}_2=0\right)$ in ohms is _______ (up to decimal places).

The series impedance matrix of a short three-phase transmission line in phase coordinates is ≤ft[ {*20c z_s&z_m&z_m\\ z_m&z_s&z_m\\ z_m&z_m&z_s } ]. If the positive sequence impedance is (1 + j 10) Ω, and the zero sequence is (4 + j 31) Ω, then the imaginary part of Z${}_m$${}^{\text{­}}$ (in Ω) is _______ (up to 2 decimal places).