1
GATE ME 2016 Set 1
Numerical
+2
-0
Consider the function $$f\left( x \right) = 2{x^3} - 3{x^2}\,\,$$ in the domain $$\,\left[ { - 1,2} \right].$$ The global minimum of $$f(x)$$ is _________.
2
GATE ME 2015 Set 1
Numerical
+2
-0
Consider a spatial curve in three -dimensional space given in parametric form by $$\,\,x\left( t \right)\,\, = \,\,\cos t,\,\,\,y\left( t \right)\,\, = \,\,\sin t,\,\,\,z\left( t \right)\,\, = \,\,{2 \over \pi }t,\,\,\,0 \le t \le {\pi \over 2}.$$ The length of the curve is ________.
3
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).
4
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
$${1 \over 2}{\left( {e - {1 \over e}} \right)^2}$$
GATE ME Subjects
EXAM MAP
Medical
NEET