GATE IN 2021 Question Paper (06-Feb-2021) (Shift 1)

Consider the row vectors v = (1, 0) and w = (2, 0). The rank of the matrix M = 2v${}^T$ v + 3w${}^T$ w, where the superscript T denotes the transpose, is

Consider the sequence xₙ= 0.5xₙ₋₁ + 1, n = 1, 2, ... ... with x₀ = 0. Then $\underset{n\to \infty }{\lim }{x}_n$

An infinitely long line, with uniform positive charge density, lies along the z-axis. In cylindrical coordinates (r, ϕ, z), at any point $\vec{P}$ not on the z-axis, the direction of the electric field is

The input-output relationship of an LTI system is given below.



For an input x[n] shown below



the peak value of the output when x[n] passes through h is ________

In an ac main, the rms voltage V ${}_{ac}$, rms current I ${}_{ac}$ and power W ${}_{ac}$ are measured as: V ${}_{ac}$ = 100 V ± 1%, I ${}_{ac}$ = 1 A ± 1% and W ${}_{ac}$ = 50 W ± 2% (errors are with respect to readings). The percentage error in calculating the power factor using these readings is