1
GATE CE 2017 Set 2
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
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
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12