The small-signal resistance (i.e., $${{d{V_B}} \over {d{I_D}}}$$ ) in $$k\Omega $$ offered by the n-channel MOSFET M shown in the figure below, at bias point of V_B = 2V is (device data for M: device transconductance parameter

k_N = $${\mu _n}{C_{ox}^{'}}$$ (W/L)= 40$$\mu {\rm A}/{V^2},$$ threshold voltage V_TN=1V, and neglect body effect and channel length modulation effects)

The minimum eigenvalue of the following matrix is $$\left[ {\matrix{ 3 & 5 & 2 \cr 5 & {12} & 7 \cr 2 & 7 & 5 \cr } } \right]$$

Let $$A$$ be an $$m\,\, \times \,\,n$$ matrix and $$B$$ an $$n\,\, \times \,\,m$$ matrix. It is given that determinant $$\left( {{{\rm I}_m} + AB} \right) = $$determinant $$\left( {{{\rm I}_n} + BA} \right),$$ where $${{{\rm I}_k}}$$ is the $$k \times k$$ identity matrix. Using the above property, the determinant of the matrix given below is $$\left[ {\matrix{ 2 & 1 & 1 & 1 \cr 1 & 2 & 1 & 1 \cr 1 & 1 & 2 & 1 \cr 1 & 1 & 1 & 2 \cr } } \right]$$

Consider a vector field $$\overrightarrow A \left( {\overrightarrow r } \right).$$ The closed loop line integral $$\oint {\overrightarrow A \bullet \overrightarrow {dl} } $$ can be expressed as