1
GATE PI 2016
MCQ (Single Correct Answer)
+1
-0.3
At $$x=0,$$ the function is $$f\left( x \right) = \left| {\sin {{2\pi x} \over L}} \right|\left( { - \infty < x < \infty ,L > 0} \right)$$
A
continuous and differentiable.
B
not continuous and not differentiable.
C
not continuous but differentiable.
D
continuous but not differentiable.
2
GATE PI 2016
MCQ (Single Correct Answer)
+1
-0.3
For the two functions
$$f\left( {x,y} \right) = {x^3} - 3x{y^2}\,\,$$ and $$\,\,g\left( {x,y} \right) = 3{x^2}y - {y^3}\,\,$$

Which one of the following options is correct?

A
$${{\partial f} \over {\partial x}} = {{\partial g} \over {\partial x}}$$
B
$${{\partial f} \over {\partial x}} = - {{\partial g} \over {\partial y}}$$
C
$${{\partial f} \over {\partial y}} = - {{\partial g} \over {\partial x}}$$
D
$${{\partial f} \over {\partial y}} = {{\partial g} \over {\partial x}}$$
3
GATE PI 2015
MCQ (Single Correct Answer)
+1
-0.3
The function $$f\left( x \right) = {x^2} = x + x + x + ....x$$ times, is defined
A
at all real values of $$x$$
B
only at positive integer values of $$x$$
C
only at negative integer values of $$x$$
D
only at rational values of $$x$$
4
GATE PI 2012
MCQ (Single Correct Answer)
+1
-0.3
The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is
A
$$1/6$$
B
$$1/4$$
C
$$1/3$$
D
$$1/2$$
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