GATE IN 2025 Question Paper (01-Feb-2025) (Shift 2)

Let a continuous-time signal be $x(t)=e^{j9t}+e^{j5t}$, where $j=\sqrt{-1}$ and $t$ is in seconds. The fundamental period of magnitude of $x(t)$, in seconds, is

The minimized expression of the Boolean function Y(P, Q, R) implemented by the multiplexer (MUX) circuit shown in the figure is

The 4-bit signed 2's complement form of $(5{)}_{10}+(5{)}_{10}$ is

An infinite sheet of uniform charge ${\rho }_s=10{\text{ C/m}}^2$ is placed on $z=0$ plane. The medium surrounding the sheet has a relative permittivity of 10. The electric flux density, in ${\text{C/m}}^2$, at a point $P(0,0,5)$, is
Note: $\hat{a}$, $\hat{b}$, and $\hat{c}$ are unit vectors along the $x$, $y$, and $z$ directions, respectively.

For the ideal opamp based circuit shown in the figure, the ratio $\frac{V}{I}$ is