1
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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2
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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3
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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4
GATE ECE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
As $$x$$ varies from $$- 1$$ to $$3,$$ which of the following describes the behavior of the function $$f\left( x \right) = {x^3} - 3{x^2} + 1?$$
A
$$f(x)$$ increases monotonically
B
$$f(x)$$ increases, then decreases and increases again
C
$$f(x)$$ decreases, then increases and decreases again
D
$$f(x)$$ increases and then decreases
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