1
GATE CE 2017 Set 2
+2
-0.6
The tangent to the curve represented by $$y=x$$ $$ln$$ $$x$$ is required to have $${45^ \circ }$$ inclination with the $$x-$$axis. The coordinates of the tangent point would be
A
$$(1, 0)$$
B
$$(0,1)$$
C
$$(1,1)$$
D
$$\left( {\sqrt {2,} \sqrt 2 } \right)$$
2
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
$${{{\pi ^3}} \over {64}}$$
3
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
$$\infty$$
4
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
$$2a$$
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Joint Entrance Examination