1
GATE CE 2014 Set 2
+2
-0.6
The expression $$\mathop {Lim}\limits_{a \to 0} \,{{{x^a} - 1} \over a}\,\,$$ is equal to
A
$$\log \,x$$
B
$$0$$
C
$$x$$ $$log$$ $$x$$
D
$$\infty$$
2
GATE CE 2011
+2
-0.6
What is the value of the definite integral? $$\,\,\int\limits_0^a {{{\sqrt x } \over {\sqrt x + \sqrt {a - x} }}dx\,\,}$$?
A
$$0$$
B
$${a \over 2}$$
C
$$a$$
D
$$2a$$
3
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
$$2\int\limits_0^{L/2} {\sqrt {1 + 64{{{h^2}{x^2}} \over {{L^4}}}} dx}$$
4
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 $${{8} \over 3}$$
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
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