1
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The following four vector fields are given in cartesian coordinate system. The vector field which does not satisfy the property of magnetic flux density is
A
$$y^2{\widehat a}_x\;+\;z^2{\widehat a}_y\;+\;x^2{\widehat a}_z$$
B
$$z^2{\widehat a}_x\;+\;x^2{\widehat a}_y\;+\;y^2{\widehat a}_z$$
C
$$x^2{\widehat a}_x\;+\;y^2{\widehat a}_y\;+\;z^2{\widehat a}_z$$
D
$$y^2z^2{\widehat a}_x\;+\;x^2z^2{\widehat a}_y\;+\;x^2y^2{\widehat a}_z$$
2
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let $$S$$ be the set of points in the complex plane corresponding to the unit circle. $$\left( {i.e.,\,\,S = \left\{ {z:\left| z \right| = 1} \right\}} \right.$$ Consider the function $$f\left( z \right) = z{z^ * }$$ where $${z^ * }$$ denotes the complex conjugate of $$z.$$ The $$f(z)$$ maps $$S$$ to which one of the following in the complex plane?
A
unit circle
B
horizontal axis line segment from origin to $$(1, 0)$$
C
the point $$(1, 0)$$
D
the entire horizontal axis
3
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Let $$X\left( s \right) = {{3s + 5} \over {{s^2} + 10s + 20}}$$ be the Laplace Transform of a signal $$x(t).$$
Then $$\,x\left( {{0^ + }} \right)$$ is
A
$$0$$
B
$$3$$
C
$$5$$
D
$$21$$
4
GATE EE 2014 Set 1
Numerical
+2
-0
A system matrix is given as follows $$$A = \left[ {\matrix{ 0 & 1 & { - 1} \cr { - 6} & { - 11} & 6 \cr { - 6} & { - 11} & 5 \cr } } \right].$$$

The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is ___________.

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