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

A stable real linear time-invariant system with single pole at p, has a transfer function $H\left(s\right)=\frac{s^2+100}{s-p}$ with a dc gain of 5. The smallest positive frequency, in rad/s at unity gain is closest to:

The number of purely real elements in a lower triangular representation of the given 3 × 3 matrix obtained through the given decomposition is _____

≤ft[ {*20c 2&3&3\\ 3&2&1\\ 3&1&7 } ] = ≤ft[ {*20c {a_11}&0&0\\ {a_12}&{a_22}&0\\ {a_13}&{a_23}&{a_33} } ]{≤ft[ {*20c {a_11}&0&0\\ {a_12}&{a_22}&0\\ {a_13}&{a_23}&{a_33} } ]^T}

The figure below shows the per-phase Open Circuit Characteristics (measured in V) and Short Circuit Characteristics (measured in A) of a 14 kVA, 400 V, 50 Hz, 4-pole, 3-phase, delta connected alternator, driven at 1500 rpm. The field current, I${}_f$ is measured in A. Readings taken are marked as respective (x, y) coordinates in the figure. Ratio of the unsaturated and saturated synchronous impedances Z${}_{s(unsat)}$ /Z${}_{s(sat)}$ of the alternator is closest to:

Let aₓ and a${}_y$ be unit vectors along x and y directions, respectively. A vector function is given by

F = aₓ y - a${}_y$ x

The line integral of above function

${\int }_{C}F\cdot dl$

Along the curve C, which follows the parabola y = x² as shown below is ______ (rounded off to 2 decimal places)

A resistor and a capacitor are connected in series to a 10 V dc supply through a switch. The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossing has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).