1
GATE CE 2017 Set 2
+1
-0.3
Let $$\,\,W = f\left( {x,y} \right),\,\,$$ where $$x$$ and $$y$$ are functions of $$t.$$ Then, according to the chain rule, $${{dw} \over {dt}}$$ is equal to
A
$${{dw} \over {dx}}{{dx} \over {dt}} + {{dw} \over {dy}}{{dt} \over {dt}}$$
B
$${{\partial w} \over {\partial x}}{{\partial x} \over {\partial t}} + {{\partial w} \over {\partial y}}{{\partial y} \over {\partial t}}$$
C
$${{\partial w} \over {\partial x}}{{dx} \over {dt}} + {{\partial w} \over {\partial y}}{{dy} \over {dt}}$$
D
$${{dw} \over {dx}}{{\partial x} \over {\partial t}} + {{dw} \over {dy}}{{\partial y} \over {\partial t}}$$
2
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
$${e^{ - x}}$$
3
GATE CE 2017 Set 1
Numerical
+1
-0
$$\mathop {Lim}\limits_{x \to 0} \left( {{{\tan x} \over {{x^2} - x}}} \right)$$ is equal to _________.
4
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
$${e^2}$$
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