GATE EE 1995 | GATE EE Year Wise Previous Years Questions

GATE EE 1995

MCQ (Single Correct Answer)

-0.3

A monochromatic plane electromagnetic wave travels in vacuum in the position $$x$$ direction ($$x, y, z$$ system of coordinates). The electric and magnetic fields can be expressed as

$$\eqalign{ & \mathop E\limits^ \to \left( {x,t} \right) = {E_0}\cos \left( {kx - \omega t} \right)\,\,{\widehat a_y} \cr & \mathop H\limits^ \to \left( {x,t} \right) = {H_0}\cos \left( {kx - \omega t} \right){\widehat a_z} \cr} $$

$$\eqalign{ & \mathop E\limits^ \to \left( {x,t} \right) = {E_0}\cos \left( {kx - \omega t} \right)\,\,{\widehat a_y} \cr & \mathop H\limits^ \to \left( {x,t} \right) = - {H_0}\cos \left( {kx - \omega t} \right){\widehat a_z} \cr} $$

GATE EE 1995

MCQ (Single Correct Answer)

-0.3

The Laplace transform of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the final value of $$f(t)$$ is __________.

initially

zero

one

none

GATE EE 1995

MCQ (Single Correct Answer)

-0.3

The inverse of the matrix $$S = \left[ {\matrix{ 1 & { - 1} & 0 \cr 1 & 1 & 1 \cr 0 & 0 & 1 \cr } } \right]$$ is

$$\left[ {\matrix{ 1 & 0 & 1 \cr 0 & 0 & 0 \cr 0 & 1 & 1 \cr } } \right]$$

$$\left[ {\matrix{ 0 & 1 & 1 \cr { - 1} & { - 1} & 1 \cr 1 & 0 & 1 \cr } } \right]$$

$$\left[ {\matrix{ 2 & 2 & { - 2} \cr { - 2} & 2 & { - 2} \cr 0 & 2 & 2 \cr } } \right]$$

$$\left[ {\matrix{ {{1 \over 2}} & {{1 \over 2}} & {{{ - 1} \over 2}} \cr {{{ - 1} \over 2}} & {{1 \over 2}} & {{{ - 1} \over 2}} \cr 0 & 0 & 1 \cr } } \right]$$

GATE EE 1995

Subjective

-0

Given the matrix $$A = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 6} & { - 11} & { - 6} \cr } } \right].\,\,$$ Its eigen values are

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