GATE ECE 2014 Set 3 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2014 Set 3

Numerical

-0

The slope of the I_D vs. V_GS curve of an n-channel MOSFET in linear region is 10^-3$${\Omega ^{ - 1}}$$ at V_DS = 0.1V. For the same device, neglecting channel length modulation, the slope of the $$\sqrt {{{\rm I}_D}} $$ vs. V _GS curve (in $$\sqrt A /V$$ ) under saturation region is approximately ______.

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GATE ECE 2014 Set 3

MCQ (Single Correct Answer)

-0.3

Which one of the following statements is NOT true for a square matrix $$A$$?

If $$A$$ is upper triangular, the eigenvalues of $$A$$ are the diagonal elements of it

If $$A$$ is real symmetric, the eigenvalues of $$A$$ are always real and positive

If $$A$$ is real , the eigenvalues of $$A$$ and $${A^T}$$ are always the same

If all the principal minors of $$A$$ are positive , all the eigenvalues of $$A$$ are also positive

GATE ECE 2014 Set 3

Numerical

-0

The maximum value of $$f\left( x \right) = 2{x^3} - 9{x^2} + 12x - 3$$
in the interval $$\,0 \le x \le 3$$ is __________.

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GATE ECE 2014 Set 3

MCQ (Single Correct Answer)

-0.3

If $$z=xy$$ $$ln(xy),$$ then

$$x{{\partial z} \over {\partial x}} + y{{\partial z} \over {\partial y}} = 0$$

$$y{{\partial z} \over {\partial x}} = x{{\partial z} \over {\partial y}}$$

$$x{{\partial z} \over {\partial x}} = y{{\partial z} \over {\partial y}}$$

$$y{{\partial z} \over {\partial x}} + x{{\partial z} \over {\partial y}} = 0$$

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