1
GATE ME 2008
+2
-0.6
Let $$\,\,f = {y^x}.$$ What is $$\,\,{{{\partial ^2}f} \over {\partial x\partial y}}\,\,$$ at $$x=2,$$ $$y=1$$?
A
$$0$$
B
$$\ln \,2$$
C
$$1$$
D
$${1 \over {\ln \,2}}$$
2
GATE ME 2007
+2
-0.6
If $$\,\,\,y = x + \sqrt {x + \sqrt {x + \sqrt {x + .....\alpha } } } \,\,\,$$ then $$y(2)=$$ __________.
A
$$4$$ (or) $$1$$
B
$$4$$ only
C
$$1$$ only
D
Undefined
3
GATE ME 2007
+2
-0.6
$$\mathop {Lim}\limits_{x \to 0} {{{e^x} - \left( {1 + x + {{{x^2}} \over 2}} \right)} \over {{x^3}}} =$$
A
$$0$$
B
$${1 \over 6}$$
C
$${1 \over 3}$$
D
$$1$$
4
GATE ME 2005
+2
-0.6
By a change of variables $$x(u, v) = uv,$$ $$\,\,y\left( {u,v} \right) = {v \over u}$$ in a double integral, the integral $$f(x, y)$$ changes to $$\,\,\,f\left( {uv,{\raise0.5ex\hbox{v} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{u}}} \right).\,\,\,$$ Then $$\,\,\phi \left( {u,v} \right)\,\,\,$$ is ________.
A
$${{2v} \over u}$$
B
$$2$$ $$uv$$
C
$${{v^2}}$$
D
$$1$$
GATE ME Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Turbo Machinery
Heat Transfer
Thermodynamics
Production Engineering
Industrial Engineering
General Aptitude
EXAM MAP
Joint Entrance Examination