1
GATE PI 2011
+1
-0.3
The eigen values of the following matrix $$\left[ {\matrix{ {10} & { - 4} \cr {18} & { - 12} \cr } } \right]$$ are
A
$$4,9$$
B
$$6,-8$$
C
$$4,8$$
D
$$-6,8$$
2
GATE PI 2011
+2
-0.6
If a matrix $$A = \left[ {\matrix{ 2 & 4 \cr 1 & 3 \cr } } \right]$$ and matrix $$B = \left[ {\matrix{ 4 & 6 \cr 5 & 9 \cr } } \right]$$ the transpose of product of these two matrices i.e., $${\left( {AB} \right)^T}$$ is equal to
A
$$\left[ {\matrix{ {28} & {19} \cr {34} & {47} \cr } } \right]$$
B
$$\left[ {\matrix{ {19} & {34} \cr {47} & {28} \cr } } \right]$$
C
$$\left[ {\matrix{ {48} & {33} \cr {28} & {19} \cr } } \right]$$
D
$$\left[ {\matrix{ {28} & {19} \cr {48} & {33} \cr } } \right]$$
3
GATE PI 2011
+2
-0.6
The line integral $$\int\limits_{{P_1}}^{{P_2}} {\left( {ydx + xdy} \right)}$$ from $${P_1}\left( {{x_1},{y_1}} \right)$$ to $${P_2}\left( {{x_2},{y_2}} \right)$$ along the semi-circle $${P_1}$$ $${P_2}$$ shown in the figure is
A
$${x_2}{y_2} - {x_1}{y_1}$$
B
$$\left( {y_2^2 - y_1^2} \right) + \left( {x_2^2 - x_1^2} \right)$$
C
$$\left( {{x_2} - {x_1}} \right)\left( {{y_2} - {y_1}} \right)$$
D
$${\left( {{y_2} - {y_1}} \right)^2} + {\left( {{x_2} - {x_1}} \right)^2}$$
4
GATE PI 2011
+1
-0.3
If $$A$$ $$(0,4,3),$$ $$B(0,0,0)$$ and $$C(3,0,4)$$ are there points defined in $$x, y, z$$ coordinate system, then which one of the following vectors is perpendicular to both the vectors $$\overrightarrow {AB}$$ and $$\overrightarrow {BC}$$.
A
$$16\widehat i + 9\widehat j - 12\widehat k$$
B
$$16\widehat i - 9\widehat j + 12\widehat k$$
C
$$16\widehat i - 9\widehat j - 12\widehat k$$
D
$$16\widehat i + 9\widehat j + 12\widehat k$$
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