GATE EE 2009 | GATE EE Year Wise Previous Years Questions

GATE EE 2009

MCQ (Single Correct Answer)

-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

-8

$$0$$

GATE EE 2009

MCQ (Single Correct Answer)

-0.3

The trace and determinant of a $$2 \times 2$$ matrix are shown to be $$-2$$ and $$-35$$ respectively. Its eigen values are

$$-30, -5$$

$$-37,-1$$

$$-7,5$$

$$17.5, -2$$

GATE EE 2009

MCQ (Single Correct Answer)

-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

$$\,\,\int\limits_{y = 0}^{y = 1} {\int\limits_{x = {y^2}}^{x = \sqrt y } {f\left( {x,y} \right)dx\,dy\,\,} } $$

$$\int\limits_{y = {x^2}}^{y = 1} {\int\limits_{x = {y^2}}^{x = 1} {f\left( {x,y} \right)dx\,dy\,\,} } $$

$$\int\limits_{y = 0}^{y = 1} {\int\limits_{x = 0}^{x = 1} {f\left( {x,y} \right)dx\,dy\,\,} } $$

$$\int\limits_{x = 0}^{y = \sqrt x } {\int\limits_{x = 0}^{x = \sqrt y } {f\left( {x,y} \right)dx\,dy\,\,} } $$

GATE EE 2009

MCQ (Single Correct Answer)

-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

$$-8$$

$$4$$

$$8$$

$$0$$

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