1
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 $$x=0$$
2
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
$$1$$
3
GATE CE 1997
MCQ (Single Correct Answer)
+1
-0.3
For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is
A
$$\,{{\partial f} \over {\partial y}} = {{\partial g} \over {\partial x}}$$
B
$${{\partial f} \over {\partial x}} = {{\partial g} \over {\partial y}}$$
C
$$f=g$$
D
$${{{\partial ^2}f} \over {\partial {x^2}}} = {{{\partial ^2}g} \over {\partial {y^2}}}$$
4
GATE CE 1997
MCQ (Single Correct Answer)
+2
-0.6
The differential equation $${{dy} \over {dx}} + py = Q,$$ is a linear equation of first order only if,
A
$$P$$ is a constant but $$Q$$ is a function of $$y$$
B
$$P$$ and $$Q$$ are functions of $$y$$ (or) constants
C
$$P$$ is a function of $$y$$ but $$Q$$ is a constant
D
$$P$$ and $$Q$$ are functions of $$x$$ (or) constants
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