An $n$-channel MOSFET is connected as shown in the Figure.

Assume $\mathrm{V}_{\mathrm{TH}}=1 \mathrm{~V}, V_{D D}=5 \mathrm{~V}$, and $\mu C_{O x}\left(\frac{W}{L}\right)=2 \mathrm{mAV}^{-2}$ and neglect channel length modulation effects.

The gate voltage ( $V_G$ ) of the n-channel MOSFET (in Volt) is $\_\_\_\_$ . (rounded off to two decimal places)

The identical MOSFETs $M_1$ and $M_2$ in the circuit given below are ideal and biased in the saturation region. $M_1$ and $M_2$ have a transconductance $g_m$ of 5 mS .

The input signals (in Volts) are:

$$ \begin{aligned} & V_1=2.5+0.01 \sin \omega t \\ & V_2=2.5-0.01 \sin \omega t \end{aligned} $$

The output signal $V_3$ (in Volts) is _ .

In the circuit shown below, the transistors $M_1$ and $M_2$ are biased in saturation. Their small signal transconductances are $g_{m1}$ and $g_{m2}$ respectively. Neglect body effect, channel length modulation and intrinsic device capacitances.

Assuming that capacitor $C_i$ is a short circuit for AC analysis, the exact magnitude of small signal voltage gain $\left| \frac{v_{out}}{v_{in}} \right|$ is ______.

An NMOS transistor operating in the linear region has $I_{D}$ of 5 $\mu$A at $V_{DS}$ of 0.1 V. Keeping $V_{GS}$ constant, the $V_{DS}$ is increased to 1.5 V.

Given that $\mu_{n}C_{ox} \frac{W}{L}$ = 50 $\mu$A/$V^2$, the transconductance at the new operating point (in $\mu$A/V, rounded off to two decimal places) is ______.