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

Let $\hat{i}$ and $\hat{j}$ be the unit vectors along x and y axes, respectively and let $A$ be a positive constant. Which one of the following statements is true for the vector fields $\overrightarrow{F_1}=A(\hat{i}y+\hat{j}x)$ and $\overrightarrow{F_2}=A(\hat{i}y\text{–}\hat{j}x)$?

In the circuit below, assume that the long channel NMOS transistor is biased in saturation. The small signal trans-conductance of the transistor is $g_m$ . Neglect body effect, channel length modulation and intrinsic device capacitances. The small signal input impedance $Z_{in}(j\omega )$ is ________

For the closed loop amplifier circuit shown below, the magnitude of open loop low frequency small signal voltage gain is 40. All the transistors are biased in saturation. The current source $I_{SS}$ is ideal. Neglect body effect, channel length modulation and intrinsic device capacitances. The closed loop low frequency small signal voltage gain $\frac{V_{out}}{V_{in}}$ (rounded off to three decimal places) is _________

For the Boolean function
$F(A,B,C,D)=\sum m(0,2,5,7,8,10,12,13,14,15)$,
the essential prime implicants are _________

A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_0}{2}$, when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular time $t=t_k$, the variance of the random variable $n(t_k)$ is