1
GATE ME 2014 Set 4
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral $$\,\int\limits_0^2 {\int\limits_0^x {{e^{x + y}}\,\,dy} }$$ $$dx$$ is
A
$${1 \over 2}\left( {e - 1} \right)$$
B
$${1 \over 2}{\left( {{e^2} - 1} \right)^2}$$
C
$${1 \over 2}\left( {{e^2} - e} \right)$$
D
$${1 \over 2}{\left( {e - {1 \over e}} \right)^2}$$
2
GATE ME 2012
MCQ (Single Correct Answer)
+2
-0.6
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $$y = 2x\,\,\, - 0.1{x^2}$$ where $$y$$ is the height of the arch in meters. The maximum possible height of the arch is
A
$$8$$ meters
B
$$10$$ meters
C
$$12$$ meters
D
$$14$$ meters
3
GATE ME 2010
MCQ (Single Correct Answer)
+2
-0.6
The infinite series $${\,f\left( x \right) = x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - \,\,}$$ Converges to
A
$$cos (x)$$
B
$$sin (x)$$
C
$$sin$$ $$h(x)$$
D
$${e^x}$$
4
GATE ME 2008
MCQ (Single Correct Answer)
+2
-0.6
Consider the shaded triangular region $$P$$ shown in the figure. What is $$\int\!\!\!\int\limits_p {xy\,dx\,dy\,?}$$
A
$${1 \over 6}$$
B
$${2 \over 9}$$
C
$${7 \over {16}}$$
D
$$1$$
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