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1
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
$${{\partial f} \over {\partial y}} = {{\partial g} \over {\partial x}}$$
2
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 $$x$$
3
GATE PI 2012
MCQ (Single Correct Answer)
+1
-0.3
$$\,\mathop {Lim}\limits_{x \to 0} \left( {{{1 - \cos x} \over {{x^2}}}} \right)$$ is
A
$$1/4$$
B
$$1/2$$
C
$$1$$
D
$$2$$
4
GATE PI 2012
MCQ (Single Correct Answer)
+1
-0.3
At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has
A
a maximum value
B
a minimum value
C
a singularity
D
a point of inflection
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Questions Asked from Marks 1
GATE PI 2016 (2) GATE PI 2015 (1) GATE PI 2012 (4) GATE PI 2009 (1) GATE PI 2008 (2) GATE PI 2007 (2) GATE PI 1995 (1)
GATE PI Subjects
Fluid Mechanics
Metrology
Theory of Machines
Engineering Mathematics
Heat Transfer
Machine Tools and Machining
Industrial Engineering
Engineering Mechanics
Strength of Materials
Thermodynamics
Machine Design
Casting
Joining of Materials
Metal Forming