1
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
Let $$x$$ and $$y$$ be two vectors in a $$3-$$ dimensional space and $$ < x,y > $$ denote their dot product. Then the determinant det $$\left[ {\matrix{ { < x,x > } & { < x,y > } \cr { < y,x > } & { < y,y > } \cr } } \right] = $$ ______.
A
is zero when $$x$$ and $$y$$ are linearly independent
B
is positive when $$x$$ and $$y$$ are linearly independent
C
is non-zero for all non-zero $$x$$ and $$y$$
D
is zero only when either $$x$$ (or) $$y$$ is zero
2
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
The integral $$\,\,{1 \over {2\pi }}\int\limits_0^{2\Pi } {Sin\left( {t - \tau } \right)\cos \tau \,d\tau \,\,\,} $$ equals
A
$$Sin\,t\cos t$$
B
$$0$$
C
$${1 \over 2}\,\,\cos \,t$$
D
$${1 \over 2}\,\,\sin \,t$$
3
GATE EE 2007
MCQ (Single Correct Answer)
+1
-0.3
Consider the function $$f\left( x \right) = {\left( {{x^2} - 4} \right)^2}$$ where $$x$$ is a real number. Then the function has
A
Only one minimum
B
Only two minima
C
Three minima
D
Three maxima
4
GATE EE 2007
MCQ (Single Correct Answer)
+1
-0.3
Divergence of the vector field $$v\left( {x,y,z} \right) = - \left( {x\,\cos xy + y} \right)\widehat i + \left( {y\,\cos xy} \right)\widehat j + \left[ {\left( {\sin {z^2}} \right) + {x^2} + {y^2}} \right]\widehat k\,\,$$
A
$$2z\,\cos {z^2}$$
B
$$\,\sin \,xy + 2z\,\cos {z^2}$$
C
$$x\,\sin xy - \cos z$$
D
none of these
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