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

Let p and q be real numbers such that p² + q² = 1. The eigenvalues of the matrix $\left[\begin{array}{cc}p& q\\ q& -p\end{array}\right]$ are

An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance M between the windings of the transformer is ______ μH.

(Round off to 2 decimal places.)

Consider a continuous-time signal x(t) defined by x(t) = 0 for |t| > 1, and x(t) = 1 - |t| for |t| ≤ 1. Let the Fourier transform of x(t) be defined as $X(\omega )={\int }_{-\infty }^{\infty }x(t)e^{-j\omega t}dt$. The maximum magnitude of X(ω) is _____

Let (-1 - j), (3 - j), (3 + j) and (-1 + j) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise direction, the value of the countour integral ${\oint }_C\frac{dz}{z^2(z-4)}$ is

The state space representation of a first-order system is given as

ẋ = -x + u

y = x

Where, x is the state variable, u is the control input and y is the controlled output. Let u = -K.x be the control law, where K is the controller gain. To place a closed-loop pole at -2, the value of K is ______