1
GATE ECE 2016 Set 3
+2
-0.6
If the vectors $${e_1} = \left( {1,0,2} \right),\,{e_2} = \left( {0,1,0} \right)$$ and $${e_3} = \left( { - 2,0,1} \right)$$ form an orthogonal basis of the three dimensional real space $${R^3},$$ then the vectors $$u = \left( {4,3, - 3} \right) \in {R^3}$$ can be expressed as
A
$$u = - {2 \over 5}{e_1} - 3{e_2} - {{11} \over 5}{e_3}$$
B
$$u = - {2 \over 5}{e_1} - 3{e_2} + {{11} \over 5}{e_3}$$
C
$$u = - {2 \over 5}{e_1} + 3{e_2} + {{11} \over 5}{e_3}$$
D
$$u = - {2 \over 5}{e_1} + 3{e_2} - {{11} \over 5}{e_3}$$
2
GATE ECE 2016 Set 3
+1
-0.3
Consider a $$2 \times 2$$ square matrix $$A = \left[ {\matrix{ \sigma & x \cr \omega & \sigma \cr } } \right]$$
Where $$x$$ is unknown. If the eigenvalues of the matrix $$A$$ are $$\left( {\sigma + j\omega } \right)$$ and $$\left( {\sigma - j\omega } \right)$$, then $$x$$ is equal to
A
$$+ j\omega$$
B
$$- j\omega$$
C
$$+ \omega$$
D
$$- \omega$$
3
GATE ECE 2016 Set 3
Numerical
+2
-0
A triangle in the $$xy-$$plane is bounded by the straight lines $$2x=3y, y=0$$ and $$x=3.$$ The volume above the triangle and under the plane $$x+y+z=6Z$$ is ________.
4
GATE ECE 2016 Set 3
Numerical
+1
-0
The integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}}$$ is equal ________.
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