1
GATE PI 2005
+1
-0.3
The differential equation $${\left[ {1 + {{\left( {{{d\,y} \over {d\,x}}} \right)}^2}} \right]^3} = {C^2}{\left[ {{{{d^2}\,y} \over {d\,{x^2}}}} \right]^2}$$ is of
A
$${2^{nd}}$$ order and $${3^{rd}}$$ degree
B
$${3^{rd}}$$ order and $${2^{nd}}$$ degree
C
$${2^{nd}}$$ order and $${2^{nd}}$$ degree
D
$${3^{rd}}$$ order and $${3^{rd}}$$ degree
2
GATE PI 2005
+1
-0.3
The function $$w = u + iv = {1 \over 2}\log \left( {{x^2} + {y^2}} \right) + i{\tan ^{ - 1}}\left( {{y \over x}} \right)$$\$ is not analytic at the point.
A
(0, 0)
B
(0, 1)
C
(1, 0)
D
$$(2,\,\alpha )$$
3
GATE PI 2005
+1
-0.3
For solving algebraic and transcendental equation which one of the following is used?
A
Coulomb's theorem
B
Newton - Raphson method
C
Euler's method
D
Stoke's theorem
4
GATE PI 2005
+2
-0.6
The real root of the equation $$x{e^x} = 2$$ is evaluated using Newton $$-$$ Raphson's method. If the first approximation of the value of $$x$$ is $$0.8679,$$ the $${2^{nd}}$$ approximation of the value of $$x$$ correct to three decimal places is
A
$$0.865$$
B
$$0.853$$
C
$$0.849$$
D
$$0.838$$
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