1
GATE CE 2010
+2
-0.6
A parabolic cable is held between two supports at the same level. The horizontal span between the supports is $$L.$$ The sag at the mid-span is $$h.$$ The equation of the parabola is $$y = 4h{{{x^2}} \over {{L^2}}},\,\,$$ where $$x$$ is the horizontal coordinate and $$y$$ is the vertical coordinate with the origin at the centre of the cable. The expanssion for the total length of the cable is
A
$$\int\limits_0^L {\sqrt {1 + 64{{{h^2}{x^2}} \over {{L^4}}}} dx}$$
B
$$2\int\limits_0^{L/2} {\sqrt {1 + 64{{{h^3}{x^2}} \over {{L^4}}}} dx}$$
C
$$\int\limits_0^{L/2} {\sqrt {1 + 64{{{h^2}{x^2}} \over {{L^4}}}} dx}$$
D
$$2\int\limits_0^{L/2} {\sqrt {1 + 64{{{h^2}{x^2}} \over {{L^4}}}} dx}$$
2
GATE CE 2010
+2
-0.6
Given a function $$f\left( {x,y} \right) = 4{x^2} + 6{y^2} - 8x - 4y + 8,$$ the optimal values of $$f(x,y)$$ is
A
a minimum equal to $${{10} \over 3}$$
B
a maximum equal to $${{10} \over 3}$$
C
a minimum equal to $${{8} \over 3}$$
D
a maximum equal to $${{8} \over 3}$$
3
GATE CE 2004
+2
-0.6
The function $$f\left( x \right) = 2{x^3} - 3{x^2} - 36x + 2\,\,\,$$ has its maxima at
A
$$x=-2$$ only
B
$$x=0$$ only
C
$$x=3$$ only
D
both $$x=-2$$ and $$x=3$$
4
GATE CE 2002
+2
-0.6
Limit of the following sequence as $$n \to \infty$$ $$\,\,\,$$ is $$\,\,\,$$ $${x_n} = {n^{{1 \over n}}}$$
A
$$0$$
B
$$1$$
C
$$\infty$$
D
$$- \infty$$
GATE CE Subjects
Engineering Mechanics
Construction Material and Management
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
General Aptitude
EXAM MAP
Medical
NEET