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

Let $z=x+iy$ be a complex variable and $\bar{z}$ be its complex conjugate. The equation$z^2+{\bar{z}}^2=2$ represents a

The pressure drop across a control valve is constant. The control valve with inherentcharacteristic has decreasing sensitivity. If $x$ represents the fraction of maximumstem position of the control valve, then the function $f(x)$ representing the fractionof maximum flow is

A discrete-time sequence is given by $x[n]=[1,2,3,4]$ for $0\le n\le 3$. The zerolag auto-correlation value of $x[n]$ is

Match the following measuring devices with their principle of measurement.

The capacitor shown in the figure has parallel plates, with each plate having an area A. The thickness of the dielectric materials are $d_1$ and $d_2$ and their relative permittivities are ${\epsilon }_1$ and ${\epsilon }_2$, respectively. Assume that the fringing field effects are negligible and ${\epsilon }_0$ is the permittivity of free space.


If $d_1$ is decreased by $\delta d_1$, the resultant capacitance becomes