A long-channel NMOS transistor is biased in the linear region with V_DS = 50 mV and is used as a resistance. Which one of the following statements is NOT correct?

A voltage V_G is applied across a MOS capacitor with metal gate and p-type silicon substrate at T=300 K. The inversion carrier density (in number of carriers per unit area) for V_G = 0.8 V is $$2\,\, \times \,\,{10^{11}}\,\,\,\,\,\,c{m^{ - 2}}$$ . For $${V_G}\,\, = \,\,1.3\,\,V,$$ the inversion carrier density is $$4\,\,\, \times \,\,\,{10^{11}}\,\,\,\,c{m^{ - 2}}.$$ What is the value of the inversion carrier density for V_G = 1.8 V?

Consider a long-channel NMOS transistor with source and body connected together. Assume that the electron mobility is independent of V_GS and V_DS. Given,
g_m = 0.5$$\mu {\rm A}/V$$ for V_DS = 50 m V and V_GS = 2V,
g_d = $$8\mu {\rm A}/V$$ for V_GS = 2 V and V_DS = 0 V,
Where g_m =$${{\partial {{\rm I}_D}} \over {\partial {V_{GS}}}}\,\,and\,\,{g_d}\,\, = \,{{\partial {{\rm I}_D}} \over {\partial {V_{DS}}}}$$

The threshold voltage (in volts) of the transistor is

The value of $$x$$ for which the matrix $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 9 & 7 & {13} \cr { - 6} & { - 4} & { - 9 + x} \cr } } \right]$$ has zero as an eigen value is __________.