1
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 ____
2
GATE ECE 2014 Set 3
Numerical
+2
-0
The maximum value of $$f\left( x \right) = 2{x^3} - 9{x^2} + 12x - 3$$
in the interval $$\,0 \le x \le 3$$ is __________.
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 3
MCQ (Single Correct Answer)
+1
-0.3
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is
A
$$0.067$$
B
$$0.073$$
C
$$0.082$$
D
$$0.091$$
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