1
GATE CE 1998
+1
-0.3
The Taylor's series expansion of sin $$x$$ is ______.
A
$$1 - {{{x^2}} \over {2!}} + {{{x^4}} \over {4!}} - ......$$
B
$$1 + {{{x^2}} \over {4!}} + {{{x^4}} \over {4!}} + ......$$
C
$$x + {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} + ......$$
D
$$x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - ......$$
2
GATE CE 1998
+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 $$(a, b)$$
3
GATE CE 1997
+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 $$x=0$$
4
GATE CE 1997
+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
$$1$$
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
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