1
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
2
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
$$0.838$$
3
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
$${X_{n + 1}} = {{{X_n}f\left( {{X_n}} \right)} \over {{f^1}\left( {{X_n}} \right)}}$$
4
GATE PI 2005
MCQ (Single Correct Answer)
+1
-0.3
A well machined steel plate of thickness $$L$$ is kept such that the wall temperature are $${T_h}$$ and $${T_c}$$ as shown in the figure below. A smooth copper plate of the same thickness $$L$$ is now attached to the steel plate without any gap as indicated in the figure below. The temperature at the interface is $${T_i},$$ The temperature of the outer walls are still the same at $${T_h},$$ and $${T_c}.$$ The heat transfer rates are $${q_1}$$ and $${q_2}$$ per unit area in the two cases respectively in the direction shown. Which of the following statements is correct?
A
$${T_h} > {T_i} > {T_c}$$ and $${q_1} < {q_2}$$
B
$${T_h} < {T_i} < {T_c}$$ and $${q_1} = {q_2}$$
C
$${T_h} = \left( {{T_i} + {T_c}} \right)/2$$ and $${q_1} > {q_2}$$
D
$${T_i} < \left( {{T_h} + {T_c}} \right)/2$$ and $${q_1} > {q_2}$$
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