1
GATE ME 2016 Set 3
MCQ (Single Correct Answer)
+1
-0.3
A real square matrix $$A$$ is called skew-symmetric if
A
$${A^T} = A$$
B
$${A^T} = {A^{ - 1}}$$
C
$${A^T} = - A$$
D
$${A^T} = A + {A^{ - 1}}$$
2
GATE ME 2016 Set 3
Numerical
+2
-0
The number of linear independent eigenvectors of matrix $$A = \left[ {\matrix{ 2 & 1 & 0 \cr 0 & 2 & 0 \cr 0 & 0 & 3 \cr } } \right]$$ is ________.
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3
GATE ME 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
$$\mathop {Lt}\limits_{x \to \infty } \left( {\sqrt {{x^2} + x - 1} - x} \right)$$ is
A
$$0$$
B
$$\infty $$
C
$$1/2$$
D
$$ - \infty $$
4
GATE ME 2016 Set 3
Numerical
+2
-0
The value of the line integral $$\,\,\oint\limits_C {\overrightarrow F .\overrightarrow r ds,\,\,\,} $$ where $$C$$ is a circle of radius $${4 \over {\sqrt \pi }}\,\,$$ units is ________.

Here, $$\,\,\overrightarrow F x,y = y\widehat i + 2x\widehat j\,\,$$ and $$\,\overrightarrow r $$ is the UNIT tangent vector on the curve $$C$$ at an arc length s from a reference point on the curve. $$\widehat i$$ and $$\widehat j$$ are the basis vectors in the $$X-Y$$ Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.

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