1
GATE ME 2015 Set 1
Numerical
+2
-0
Consider an ant crawling along the curve $$\,{\left( {x - 2} \right)^2} + {y^2} = 4,$$ where $$x$$ and $$y$$ are in meters. The ant starts at the point $$(4, 0)$$ and moves counter $$-$$clockwise with a speed of $$1.57$$ meters per second. The time taken by the ant to reach the point $$(2, 2)$$ is _________ (in seconds).
2
GATE ME 2014 Set 4
+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
$${1 \over 2}{\left( {e - {1 \over e}} \right)^2}$$
3
GATE ME 2012
+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
4
GATE ME 2010
+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
$${e^x}$$
GATE ME Subjects
EXAM MAP
Medical
NEET