GATE IN 2022 Question Paper (06-Feb-2022) (Shift 2)

The digital circuit shown ______

In the small signal circuit shown, the enhancement mode n-channel MOSFET is biased in saturation with a transconductance g${}_m$. A small signal low-frequency voltage v${}_d$ injected at the supply terminal results in a small signal voltage fluctuation v₀ at the output. If the channel length modulation of the MOSFET is ignored, the small signal gain v₀/v${}_d$ is given by _____

A = a₁a₀and B = b₁b₀ are two 2-bit unsigned binary numbers. If F(a₁, a₀, b₁, b₀) is a Boolean function such that 𝐹 = 1 only when 𝐴 > 𝐵, and 𝐹 = 0 otherwise, then 𝐹 can be minimized to the form ______

The matrix 𝐴 = $\left[\begin{array}{cc}4& 3\\ 9& -2\end{array}\right]$ has eigenvalues −5 and 7. The eigenvector(s) is/are ________

For the complex number $\mathrm{z}=\frac{\mathrm{a}+\mathrm{jb}}{\mathrm{a}-\mathrm{jb}}$ where 𝑎 > 0 and 𝑏 > 0. Which of the following statement(s) is/are true?