1
GATE ECE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A voltage VG 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 VG = 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 VG = 1.8 V?
A
$$4.5 \times {10^{11}}\,\,c{m^{ - 2}}$$
B
$$6.0 \times {10^{11}}\,\,c{m^{ - 2}}$$
C
$$7.2 \times {10^{11}}\,\,c{m^{ - 2}}$$
D
$$8.4 \times {10^{11}}\,\,c{m^{ - 2}}$$
2
GATE ECE 2016 Set 2
Numerical
+2
-0
Consider a long-channel NMOS transistor with source and body connected together. Assume that the electron mobility is independent of VGS and VDS. Given,
gm = 0.5$$\mu {\rm A}/V$$ for VDS = 50 m V and VGS = 2V,
gd = $$8\mu {\rm A}/V$$ for VGS = 2 V and VDS = 0 V,
Where gm =$${{\partial {{\rm I}_D}} \over {\partial {V_{GS}}}}\,\,and\,\,{g_d}\,\, = \,{{\partial {{\rm I}_D}} \over {\partial {V_{DS}}}}$$

The threshold voltage (in volts) of the transistor is

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3
GATE ECE 2016 Set 2
Numerical
+1
-0
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 __________.
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4
GATE ECE 2016 Set 2
Numerical
+2
-0
The matrix $$A = \left[ {\matrix{ a & 0 & 3 & 7 \cr 2 & 5 & 1 & 3 \cr 0 & 0 & 2 & 4 \cr 0 & 0 & 0 & b \cr } } \right]$$ has det
$$(A)=100$$ and trace $$(A)=14.$$ The value of $$\left| {a - b} \right|$$ is ___________.
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