GATE EE 2022 Question Paper (05-Feb-2022) (Shift 2)

Consider a matrix $\mathrm{A}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 4& -2\\ 0& 1& 1\end{array}\right]$

The matrix A satisfies the equation 6A⁻¹ = A² + cA + dI, where c and d are scalars and I is the identity matrix. Then (c + d) is equal to

The network shown below has a resonant frequency of 150 kHz and a bandwidth of 600 Hz. The Q-factor of the network is __________. (round off to nearest integer)

An LTI system is shown in the figure where

$\mathrm{G}(\mathrm{s})=\frac{100}{{\mathrm{s}}^2+0.1s+100}$

The steady state output of the system, to the input r(t), is given as

y(t) = a + b sin(10t + θ). The value of 'a' and 'b' will be

The open loop transfer function of unity gain negative feedback system is given as

$\mathrm{G}(\mathrm{s})=\frac{1}{\mathrm{s}(\mathrm{s}+1)}$

The Nyquist contour in the 𝑠-plane encloses the entire right half plane and a small neighborhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point (−1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to

The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as 𝜁 and ωₙ respectively. The values of 𝜁 and ω n are