1
GATE ECE 2014 Set 1
Numerical
+2
-0
The volume under the surface $$z\left( {x,y} \right) = x + y$$ and above the triangle in the $$xy$$ plane defined by $$\left\{ {0 \le y \le x} \right.$$ and $$\,\left. {0 \le x \le 12} \right\}$$ is _________.
2
GATE ECE 2009
MCQ (Single Correct Answer)
+2
-0.6
The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi$$ is given by
A
$$1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
B
$$- 1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
C
$$1 - {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
D
$$- 1 + {{{{\left( {x - \pi } \right)}^2}} \over {3!}} + - - -$$
3
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral of the function $$\,\,g\left( {x,y} \right) = 4{x^3} + 10{y^4}\,\,$$ along the straight line segment from the point $$(0,0)$$ to the point $$(1,2)$$ in the $$xy$$ -plane is
A
$$33$$
B
$$35$$
C
$$40$$
D
$$56$$
4
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
In the Taylor series expansion of $${e^x} + \sin x$$ about the point $$x = \pi ,$$ the coefficient of $${\left( {x = \pi } \right)^2}$$ is
A
$${e^\pi }$$
B
$$0.5$$ $${e^\pi }$$
C
$${e^\pi }$$ $$+1$$
D
$${e^\pi }$$ $$-1$$
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