1
GATE ECE 2009
+2
-0.6
Consider the CMOS circuit shown, where the gate voltage of the n-MOSFET is increased from zero, while the gate voltage of the p-MOSFET is kept constant at 3 V. Assume that, for both transistors, the magnitude of the threshold voltage is 1 V and the product of the transconductance parameter and the $$\left(\frac WL\right)$$ ratio, i.e. the quantity $$\mu C_{ox}\left(\frac WL\right)$$ , is 1 mAV-2.
Estimate the output voltage V0 for VG =1.5 V. [Hints: Use the appropriate current-voltage equation for each MOSFET, based on the answer]
A
$$\left(4-\frac1{\sqrt2}\right)V$$
B
$$\left(4+\frac1{\sqrt2}\right)V$$
C
$$\left(4-\frac{\sqrt3}2\right)V$$
D
$$\left(4+\frac{\sqrt3}2\right)V$$
2
GATE ECE 2009
+2
-0.6
The eigen values of the following matrix $$\left[ {\matrix{ { - 1} & 3 & 5 \cr { - 3} & { - 1} & 6 \cr 0 & 0 & 3 \cr } } \right]$$ are
A
$$3, 3 + 5j, 6 - j$$
B
$$-6 + 5j, 3 + j, 3 - j$$
C
$$3+j, 3-j, 5+j$$
D
$$3, -1+3j, -1-3j$$
3
GATE ECE 2009
+2
-0.6
The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi$$ is given by
A
$$1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
B
$$- 1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
C
$$1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
D
$$- 1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
4
GATE ECE 2009
+2
-0.6
If a vector field$$\overrightarrow V$$ is related to another field $$\overrightarrow A$$ through $$\,\overrightarrow V = \nabla \times \overrightarrow A ,$$ which of the following is true?

Note: $$C$$ and $${S_C}$$ refer to any closed contour and any surface whose boundary is $$C.$$

A
$$\oint\limits_C {\overrightarrow V .\,\overrightarrow {dl} } = \int {\int_{{S_C}} {\overrightarrow A .\,\overrightarrow {ds} } }$$
B
$$\oint\limits_C {\overrightarrow A .\,\overrightarrow {dl} } = \int\limits_{{S_C}} {\int {\overrightarrow \nabla .\,\overrightarrow {ds} } }$$
C
$$\oint\limits_C {\nabla \times \vec V.{\mkern 1mu} \overrightarrow {dl} } = \int\limits_{{S_C}} {\int {\nabla \times \vec A.{\mkern 1mu} \overrightarrow {ds} } }$$
D
$$\oint\limits_C {\nabla \times \vec A.{\mkern 1mu} \overrightarrow {dl} } = \int {\int_{{S_C}} {\vec V.{\mkern 1mu} \overrightarrow {ds} } }$$
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