GATE EE 2021 Question Paper (07-Feb-2021) (Shift 1)

Let f(x) be a real -valued function such that f'(x₀) = 0 for some x₀ ∈ (0, 1), and f${}^{"}$ (x) > 0 for all x ∈ (0, 1). Then f(x) has

A single-phase full-bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across 'ab' as shown. To achieve a modulation index of 0.8, the angle θ expressed in degrees should be ______. (Round off to 2 decimal places.)

(Modulation index is defined as the ratio of the peak of the fundamental component of V${}_{ab}$ to the applied DC value.)

Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is N ${}_L$. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix J as shown below:

≤ft[ {*20c P\\ Q } ] = J≤ft[ {*20c δ \\ V } ] where J = ≤ft[ {*20c H&S\\ M&R } ]

The dimension of the sub-matrix M is

Suppose the circles x² + y² = 1 and (x - 1)² + (y - 1)² = r² intersect each other orthogonally at the point (u, v). Then u + v = ______.

For the closed-loop system shown, the transfer function $\frac{E(s)}{R(s)}$ is