GATE EC 2018 Set 1 Q1 — Electronic Devices

Two identical $\text{nMOS}$ transistors $M_{1}$ and $M_{2}$ are connected as shown below. The circuit is used as an amplifier with the input connected between $\text{G and S}$ terminals and the output taken between $D\: \text{and}\: S$ terminals. $V_{bias}$ and $V_{D}$ are so adjusted that both transistors are in saturation. The transconductance of this combination is defined as $g_{m}=\dfrac{\partial i_{D}}{\partial v_{GS}}$ while the output resistance is $r_{o}=\dfrac{\partial v_{DS}}{\partial i_{D}}$, where $i_{D}$ is the current flowing into the drain of $M_{2}$. Let $g_{m1}$, $g_{m2}$ be the transconductances and $r_{o1}$, $r_{o2}$ be the output resistances of transistors $M_{1}$ and $M_{2}$ respectively. Which of the following statements about estimates for and is correct?