GATE EC 2024 Question Paper (11-Feb-2024) (Shift 1)

Consider the Earth to be a perfect sphere of radius $R$. Then the surface area of the region, enclosed by the $60^{\circ }N$ latitude circle, that contains the north pole in its interior is _______

Consider a unity negative feedback control system with forward path gain $G(s)=\frac{K}{(s+1)(s+2)(s+3)}$ as shown.

The impulse response of the closed-loop system decays faster than $e^{-t}$ if

A satellite attitude control system, as shown below, has a plant with transfer function $G(s)=\frac{1}{s^2}$ cascaded with a compensator $C(s)=\frac{K(s+\alpha )}{s+4}$, where $K$ and $\alpha$ are positive real constants.

In order for the closed-loop system to have poles at $-1\pm j\sqrt{3}$, the value of $a$ must be __________

A uniform plane wave with electric field $\vec{E}(x)=A_y{\hat{a}}_y{e}^{-j\frac{2\pi x}{3}}$ V/m is travelling in the air (relative permittivity, $o_r=1$ and relative permeability, ${\mu }_r=1$) in the +x direction ($A_y$ is a positive constant, ${\hat{a}}_y$ is the unit vector along the y axis). It is incident normally on an ideal electric conductor (conductivity, $\sigma =\infty$) at $x=0$. The position of the first null of the total magnetic field in the air (measured from $x=0$, in metres) is

A 4-bit priority encoder has inputs $D_3,D_2,D_1$, and $D_0$ in descending order of priority. The two-bit output AB is generated as 00, 01, 10, and 11 corresponding to inputs $D_3,D_2,D_1$, and $D_0$, respectively. The Boolean expression of the output bit B is ___________.