GATE IN 2024 Question Paper (04-Feb-2024) (Shift 2)

Among the given options, the simplified form of the Boolean function $F=(A+\bar{A}.B)+\bar{A}.(A+\bar{B}).C$ is

Consider the state-space representation of a system
$\dot{x}=Ax+Bu$
where $x$ is the state vector, $u$ is the input, $A$ is the system matrix and $B$ is the input matrix. Choose the matrix $A$ from the following options such that the system has a pole at the origin.

The sinusoidal transfer function corresponding to the polar plot shown in the figure, for $T>0$, is

A matrix $M$ is constructed by stacking three column vectors $v_1,v_2,v_3$ as
$M=[v_1{v}_2{v}_3]$.
Choose the set of vectors from the following options such that $rank(M)=3$.

The capacitance formed between two concentric spherical metal shells having radii $x$ and $y$ with $y>x$ is
Note: $\epsilon$ is the permittivity of the medium between the shells.