1
GATE CE 1998
MCQ (Single Correct Answer)
+1
-0.3
The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ if
A
$${f_x}\left( {a,\,b} \right) = {f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} < 0$$ at $$(a, b)$$
B
$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} > 0$$ at $$(a, b)$$
C
$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0,$$
$${f_{xx}}$$ and $${f_{yy}} < 0$$ at $$(a, b)$$
D
$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$
$$f_{xy}^2 - {f_{xx}}{f_{yy}} = 0\,\,$$ at $$(a, b)$$
2
GATE CE 1997
MCQ (Single Correct Answer)
+1
-0.3
If $$y = \left| x \right|$$ for $$x < 0$$ and $$y=x$$ for $$x \ge 0$$ then
A
$${{dy} \over {dx}}$$ is discontinuous at $$x=0$$
B
$$y$$ is discontinuous at $$x=0$$
C
$$y$$ is not defined at $$x=0$$
D
Both $$y$$ and $${{dy} \over {dx}}$$ are discontinuous at $$x=0$$
3
GATE CE 1997
MCQ (Single Correct Answer)
+1
-0.3
If $$\varphi \left( x \right) = \int\limits_0^{{x^2}} {\sqrt t \,dt\,}$$ then $${{d\varphi } \over {dx}} = \_\_\_\_\_\_\_.$$
A
$$2\,{x^2}$$
B
$$\sqrt x$$
C
$$0$$
D
$$1$$
4
GATE CE 1995
MCQ (Single Correct Answer)
+1
-0.3
The function $$f\left( x \right) = {x^3} - 6{x^2} + 9x + 25$$ has
A
a maxima at $$x=1$$ and a minima at $$x=3$$
B
a maxima at $$x=3$$ and a minima at $$x=1$$
C
no maxima, but a minima at $$x=3$$
D
a maxima at $$x=1,$$ but no minima
GATE CE Subjects
Engineering Mechanics
Construction Material and Management
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
General Aptitude
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12
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