1
GATE ECE 2014 Set 4
MCQ (Single Correct Answer)
+1
-0.3
The series $$\sum\limits_{n = 0}^\infty {{1 \over {n!}}\,} $$ converges to
A
$$2$$ $$ln$$ $$2$$
B
$${\sqrt 2 }$$
C
$$2$$
D
$$e$$
2
GATE ECE 2014 Set 3
Numerical
+1
-0
The maximum value of the function $$\,f\left( x \right) = \ln \left( {1 + x} \right) - x$$ (where $$x > - 1$$ ) occurs at $$x=$$________.
Your input ____
3
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
$$y{{\partial z} \over {\partial x}} + x{{\partial z} \over {\partial y}} = 0$$
4
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
$$t = {\log _e}8$$
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