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

ax³ + bx² + cx + d is a polynomial on real x over real coefficients a, b, c, d wherein a ≠ 0. Which of the following statements is true?

Which of the following is NOT true for all possible non-zero choices of integers m, n; m ≠ n, or all possible non-zero choices of real numbers p, q; p ≠ q, as applicable?

Which of the following statements is true about the two-sided Laplace transform?

Consider a signal $x\left[n\right]={\left(\frac{1}{2}\right)}^{n}1\left[n\right]$, where 1[n] = 0 if n < 0, and 1[n] = 1 if n ≥ 0. The z-transform of x[n - k], k > 0 is $\frac{z^{-k}}{1-\frac{1}{2}{z}^{-1}}$ with region of convergence being

The value of the following complex integral, with C representing the unit circle centered at origin in the counterclockwise sense, is: ${\int }_C\frac{z^2+1}{z^2-2z}dz$