Consider an n-channel metal oxide semiconductor field effect transistor (MOSFET) with a gate-to-source voltage of 1.8 V. Assume that $${W \over L} = 4,{\mu _{\rm N}}{C_{ox}} = 70 \times {10^{ - 6}}{\rm A}{V^{ - 2}}$$ , the threshold voltage is 0.3V, and the channel length modulation parameter is 0.09 V^-1, In the saturation region, the drain conductance (in micro siemens) is__________.

Let $${M^4} = {\rm I}$$ (where $${\rm I}$$ denotes the identity matrix) and $$M \ne {\rm I},\,\,{M^2} \ne {\rm I}$$ and $${M^3} \ne {\rm I}$$. Then, for any natural number $$k, $$ $${M^{ - 1}}$$ equals:

A sequence $$x\left[ n \right]$$ is specified as $$$\left[ {\matrix{ {x\left[ n \right]} \cr {x\left[ {n - 1} \right]} \cr } } \right] = {\left[ {\matrix{ 1 & 1 \cr 1 & 0 \cr } } \right]^n}\left[ {\matrix{ 1 \cr 0 \cr } } \right],\,\,for\,\,n \ge 2.$$$
The initial conditions are $$x\left[ 0 \right] = 1,\,\,x\left[ 1 \right] = 1$$ and $$x\left[ n \right] = 0$$ for $$n < 0.$$ The value of $$x\left[ {12} \right]$$ is __________.

The integral $$\,\,{1 \over {2\pi }}\int {\int_D {\left( {x + y + 10} \right)dxdy\,\,} } $$ where $$D$$ denotes the disc: $${x^2} + {y^2} \le 4,$$ evaluates to _________.