1
GATE CE 2017 Set 1
+1
-0.3
Let $$x$$ be a continuous variable defined over the interval $$\left( { - \infty ,\infty } \right)$$, and $$f\left( x \right) = {e^{ - x - {e^{ - x}}}}.$$
The integral $$g\left( x \right) = \int {f\left( x \right)dx\,\,}$$ is equal to
A
$${e^{e - x}}$$
B
$${e^{ - {e^{ - x}}}}$$
C
$${e^{ - {e^x}}}$$
D
$${e^{ - x}}$$
2
GATE CE 2015 Set 2
+1
-0.3
$$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^{2x}}\,\,$$ is equal to
A
$${e^{ - 2}}$$
B
$$e$$
C
$$1$$
D
$${e^2}$$
3
GATE CE 2015 Set 2
+1
-0.3
Given $$i = \sqrt { - 1} ,$$ the value of the definite integral, $$\,{\rm I} = \int\limits_0^{\pi /2} {{{\cos x + \sin x} \over {\cos x - i\,\sin x}}dx\,\,}$$ is :
A
$$1$$
B
$$-1$$
C
$$i$$
D
$$-i$$
4
GATE CE 2014 Set 1
+1
-0.3
With reference to the conventional Cartesian $$(x,y)$$ coordinate system, the vertices of a triangle have the following coordinates: $$\,\left( {{x_1},{y_1}} \right) = \left( {1,0} \right);\,\,\,\left( {{x_2},{y_2}} \right) = \left( {2,2} \right);\,\,\,$$ and $$\,\left( {{x_3},{y_3}} \right) = \left( {4,3} \right).$$ The area of the triangle is equal to
A
$${3 \over 2}$$
B
$${3 \over 4}$$
C
$${4 \over 5}$$
D
$${5 \over 2}$$
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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