1
GATE ECE 2010
+1
-0.3
The eigen values of a skew-symmetric matrix are
A
always zero
B
always pure imaginary
C
either zero (or) pure imaginary
D
always real
2
GATE ECE 2010
+1
-0.3
If $$\,{e^y} = {x^{1/x}}\,\,$$ then $$y$$ has a
A
maximum at $$x=e$$
B
minimum $$x=e$$
C
maximum at $$x = {e^{ - 1}}$$
D
minimum $$x = {e^{ - 1}}$$
3
GATE ECE 2010
+2
-0.6
If $$\overrightarrow A = xy\,\widehat a{}_x + {x^2}\widehat a{}_y\,\,$$ then $$\,\,\oint {\overrightarrow A .d\overrightarrow r \,\,}$$ over the path shown in the figure is
A
$$0$$
B
$${2 \over {\sqrt 3 }}$$
C
$$1$$
D
$$2\sqrt 3$$
4
GATE ECE 2010
+2
-0.6
A fair coin is tossed independently four times. The probability of the event ''The number of times heads show up is more than the number of times tails show up'' is
A
$$1/16$$
B
$$1/8$$
C
$$1/4$$
D
$$5/16$$
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