1
GATE ME 2007
MCQ (Single Correct Answer)
+1
-0.3
The partial differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\partial {y^2}}} + {{\partial \phi } \over {\partial x}} + {{\partial \phi } \over {\partial y}} = 0\,\,\,\,$$ has
A
degree $$1$$ and order $$2$$
B
degree $$1$$ and order $$1$$
C
degree $$2$$ and order $$1$$
D
degree $$2$$ and order $$2$$
2
GATE ME 2007
MCQ (Single Correct Answer)
+2
-0.6
If $$\phi (x,y)$$ and $$\psi (x,y)$$ are function with continuous 2nd derivatives then $$\phi (x,y)\, + \,i\psi (x,y)$$ can be expressed as an analytic function of x +iy ($$i = \sqrt { - 1} $$) when
A
$${{\partial \phi } \over {\partial x}} = - {{\partial \psi } \over {\partial x}},\,{{\partial \phi } \over {\partial y}} = {{\partial \psi } \over {\partial y}}$$
B
$${{\partial \phi } \over {\partial y}} = - {{\partial \psi } \over {\partial x}},\,{{\partial \phi } \over {\partial x}} = {{\partial \psi } \over {\partial y}}$$
C
$${{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\partial {y^2}}} = {{{\partial ^2}\psi } \over {\partial {x^2}}} + {{{\partial ^2}\psi } \over {\partial {y^2}}} = 1$$
D
$${{\partial \phi } \over {\partial x}} + {{\partial \phi } \over {\partial y}} = {{\partial \psi } \over {\partial x}} + {{\partial \psi } \over {\partial y}} = 0$$
3
GATE ME 2007
MCQ (Single Correct Answer)
+1
-0.3
If $$F(s)$$ is the Laplace transform of the function $$f(t)$$ then Laplace transform of $$\int\limits_0^t {f\left( x \right)dx} $$ is
A
$${1 \over s}F\left( s \right)$$
B
$${1 \over s}F\left( s \right) - f\left( 0 \right)$$
C
$$s\,F\left( s \right) - f\left( 0 \right)$$
D
$$\int {F\left( s \right)ds} $$
4
GATE ME 2007
MCQ (Single Correct Answer)
+1
-0.3
During inelastic collision of two particles, which one of the following is conserved?
A
Total linear momentum only
B
Total kinetic energy only
C
Both linear momentum and kinetic energy
D
Neither linear momentum nor kinetic energy
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