1
GATE CE 2017 Set 2
+2
-0.6
Consider the following definite integral $${\rm I} = \int\limits_0^1 {{{{{\left( {{{\sin }^{ - 1}}x} \right)}^2}} \over {\sqrt {1 - {x^2}} }}dx}$$\$
The value of the integral is
A
$${{{\pi ^3}} \over {24}}$$
B
$${{{\pi ^3}} \over {12}}$$
C
$${{{\pi ^3}} \over {48}}$$
D
$${{{\pi ^3}} \over {64}}$$
2
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
$$\infty$$
3
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
$$2a$$
4
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
$$2\int\limits_0^{L/2} {\sqrt {1 + 64{{{h^2}{x^2}} \over {{L^4}}}} dx}$$
GATE CE Subjects
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude
EXAM MAP
Joint Entrance Examination