1
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+1
-0.3
If $$z=xy$$ $$ln(xy),$$ then
A
$$x{{\partial z} \over {\partial x}} + y{{\partial z} \over {\partial y}} = 0$$
B
$$y{{\partial z} \over {\partial x}} = x{{\partial z} \over {\partial y}}$$
C
$$x{{\partial z} \over {\partial x}} = y{{\partial z} \over {\partial y}}$$
D
$$y{{\partial z} \over {\partial x}} + x{{\partial z} \over {\partial y}} = 0$$
2
GATE ECE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
For $$0 \le t < \infty ,$$ the maximum value of the function $$f\left( t \right) = {e^{ - t}} - 2{e^{ - 2t}}\,$$ occurs at
A
$$t = {\log _e}4$$
B
$$t = {\log _e}2$$
C
$$t=0$$
D
$$t = {\log _e}8$$
3
GATE ECE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The value of $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^x}\,\,$$ is
A
$$ln2$$
B
$$1.0$$
C
$$e$$
D
$$\infty $$
4
GATE ECE 2010
MCQ (Single Correct Answer)
+1
-0.3
If $$\,{e^y} = {x^{1/x}}\,\,$$ then $$y$$ has a
A
maximum at $$x=e$$
B
minimum $$x=e$$
C
maximum at $$x = {e^{ - 1}}$$
D
minimum $$x = {e^{ - 1}}$$
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