1
GATE PI 2005
MCQ (Single Correct Answer)
+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
$$(2,\,\alpha )$$
2
GATE PI 2005
MCQ (Single Correct Answer)
+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
3
GATE PI 2005
MCQ (Single Correct Answer)
+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
$$0.838$$
4
GATE PI 2005
MCQ (Single Correct Answer)
+1
-0.3
Newton $$-$$ Raphson formula to find the roots of an equation $$f(x)=0$$ is given by
A
$${X_{n + 1}} = {X_n} - {{f\left( {{X_n}} \right)} \over {{f^1}\left( {{X_n}} \right)}}$$
B
$${X_{n + 1}} = {X_n} + {{f\left( {{X_n}} \right)} \over {{f^1}\left( {{X_n}} \right)}}$$
C
$${X_{n + 1}} = {{f\left( {{X_n}} \right)} \over {{X_n}{f^1}\left( {{X_n}} \right)}}$$
D
$${X_{n + 1}} = {{{X_n}f\left( {{X_n}} \right)} \over {{f^1}\left( {{X_n}} \right)}}$$
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