1
GATE ECE 2017 Set 2
Numerical
+2
-0
A MOS capacitor is fabricated on p-type Si (silicon) where the metal work function is 4.1 eV and electron affinity of Si is 4.0 eV, Ec - EF = 0.9 eV; where Ec and EF are conduction band minimum and the Fermi energy levels of Si, respectively. Oxide$${\varepsilon _r} = \,\,3.9,\,\,\,{\varepsilon _{0\,\,}}=\,8.85 \times {10^{ - 14}}$$ F/cm, oxide thickness $${t_{ox}} = 0.1\,\mu m$$ and electronic charge q = $$1.6 \times {10^{ - 19}}$$ C. If the measured flat band voltage of the capacitor is –1V, then the magnitude of the fixed charge at the oxide semiconductor interface, in nC/cm2, is __________.
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2
GATE ECE 2017 Set 2
Numerical
+2
-0
The rank of the matrix $$\left[ {\matrix{ 1 & { - 1} & 0 & 0 & 0 \cr 0 & 0 & 1 & { - 1} & 0 \cr 0 & 1 & { - 1} & 0 & 0 \cr { - 1} & 0 & 0 & 0 & 1 \cr 0 & 0 & 0 & 1 & { - 1} \cr } } \right]$$ is __________.
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3
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The values of the integrals $$\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dy} } \right)} dx\,\,$$ and $$\,\,\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dx} } \right)} dy\,\,$$ are
A
same and equal to $$0.5$$
B
same and equal to $$-0.5$$
C
$$0.5$$ and $$-05,$$ respectively
D
$$-0.5$$ and $$-0.5,$$ respectively
4
GATE ECE 2017 Set 2
Numerical
+2
-0
The minimum value of the function $$f\left( x \right) = {1 \over 3}x\left( {{x^2} - 3} \right)\,\,$$ in the interval $$ - 100 \le x \le $$ $$100$$ occurs at $$x=$$ __________.
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