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

A wire of circular cross section with radius $a$ is shown in the figure. The current density is given by $J=k{s}^2$, where $k$ is a constant, $s$ is the radial distance from the axis and $0\le s\le a$. The total current $I$ in the wire is

The measured values from a flow instrument, whose range is between 0 and 2 flow units, are shown in the histogram. The systematic error (bias) and the maximum error (in flow units), respectively are

Consider a discrete-time sequencebr
$x[n]=\{\begin{array}{ll}(0.2{)}^n,& 0\le n\le 7\\ 0,& \text{otherwise}\end{array}$
The region of convergence of $X(z)$, the z-transform of $x[n]$, consists of

In the bridge circuit shown in the figure, under balanced condition, the values of $R$ and $C$ respectively, are

Laplace transform of a signal $x(t)$ is,
$X(s)=\frac{1}{s^2+13s+42}$
Let $u(t)$ be the unit step function. Choose the signal $x(t)$ from the following options if the region of convergence is $-7<\text{Re}\{s\}<-6$.