1
GATE ME 2017 Set 1
+2
-0.6
A parametric curve defined by $$x = \cos \left( {{{\pi u} \over 2}} \right),y = \sin \left( {{{\pi u} \over 2}} \right)\,\,$$ in the range $$0 \le u \le 1$$ is rotated about the $$x-$$axis by $$360$$ degrees. Area of the surface generated is
A
$${\pi \over 2}$$
B
$$\pi$$
C
$${2\pi }$$
D
$${4\pi }$$
2
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 _________.
3
GATE ME 2016 Set 3
+2
-0.6
$$\mathop {Lt}\limits_{x \to \infty } \left( {\sqrt {{x^2} + x - 1} - x} \right)$$ is
A
$$0$$
B
$$\infty$$
C
$$1/2$$
D
$$- \infty$$
4
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 ________.