1
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 $$x=0$$
2
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
$$1$$
3
GATE CE 1995
+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
4
GATE CE 1995
+1
-0.3
The function $$f\left( x \right) = \left| {x + 1} \right|$$ on the interval $$\left[ { - 2,0} \right]$$ is __________.
A
continuous and differentiable
B
continuous on the interval but not differentiable at all points
C
Neither continuous nor differentiable
D
Differentiable but not continuous
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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