GATE IN 2023 Question Paper (11-Feb-2023) (Shift-1)

In the circuit shown, $\omega =100\pi$ rad/s, $R_1=R_2=2.2\Omega$ and $L=7$ mH. The capacitance $C$ for which $Y_{in}$ is purely real is ________ mF (rounded off to two decimal places).

The R-L circuit with $R=10$ k$\Omega$ and $L=1$ mH is excited by a step current $I_{0}u(t)$. At $t=0^{-}$, there is a current $I_L=I_0/5$ flowing through the inductor. The minimum time taken for the current through the inductor to reach 99% of its final value is ________ $\mu$ s (rounded off to two decimal places).

Consider a standard negative feedback configuration with $G(s)=\frac{1}{(s-2)(s-3)}$ and the controller $C(s)=K_p+\frac{K_I}{s}+K_{D}s$. The root-locus of $G(s)C(s)$ is presented in the figure below. The gain $C(j\omega )=2$ at $\omega =1$ rad/s. The value of $K_D$ is ________ (rounded off to one decimal place).

How many five-digit numbers can be formed using the integers 3, 4, 5 and 6 with exactly one digit appearing twice?

The phase margin of the transfer function $G(s)=\frac{2(1-s)}{(1+s{)}^2}$ is ________ degrees (rounded off to the nearest integer).