1
GATE EE 2009
MCQ (Single Correct Answer)
+2
-0.6
$$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$$. Its line integral over the straight line from (x, y)=(0,2) to (2,0) evaluates to
A
-8
B
4
C
8
D
$$0$$
2
GATE EE 2009
MCQ (Single Correct Answer)
+1
-0.3
The trace and determinant of a $$2 \times 2$$ matrix are shown to be $$-2$$ and $$-35$$ respectively. Its eigen values are
A
$$-30, -5$$
B
$$-37,-1$$
C
$$-7,5$$
D
$$17.5, -2$$
3
GATE EE 2009
MCQ (Single Correct Answer)
+2
-0.6
If $$(x, y)$$ is continuous function defined over $$\left( {x,y} \right) \in \left[ {0,1} \right] \times \left[ {0,1} \right].\,\,\,$$ Given two constants, $$\,x > {y^2}$$ and $$\,y > {x^2},$$ the volume under $$f(x, y)$$ is
A
$$\,\,\int\limits_{y = 0}^{y = 1} {\int\limits_{x = {y^2}}^{x = \sqrt y } {f\left( {x,y} \right)dx\,dy\,\,} } $$
B
$$\int\limits_{y = {x^2}}^{y = 1} {\int\limits_{x = {y^2}}^{x = 1} {f\left( {x,y} \right)dx\,dy\,\,} } $$
C
$$\int\limits_{y = 0}^{y = 1} {\int\limits_{x = 0}^{x = 1} {f\left( {x,y} \right)dx\,dy\,\,} } $$
D
$$\int\limits_{x = 0}^{y = \sqrt x } {\int\limits_{x = 0}^{x = \sqrt y } {f\left( {x,y} \right)dx\,dy\,\,} } $$
4
GATE EE 2009
MCQ (Single Correct Answer)
+2
-0.6
$$F\left( {x,y} \right) = \left( {{x^2} + xy} \right)\,\widehat a{}_x + \left( {{y^2} + xy} \right)\,\widehat a{}_y.\,\,$$ Its line integral over the straight line from $$(x, y)=(0,2)$$ to $$(x,y)=(2,0)$$ evaluates to
A
$$-8$$
B
$$4$$
C
$$8$$
D
$$0$$
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