1
GATE PI 2005
+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
$${X_{n + 1}} = {{{X_n}f\left( {{X_n}} \right)} \over {{f^1}\left( {{X_n}} \right)}}$$
2
GATE PI 2005
+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 $${q_1} > {q_2}$$
3
GATE PI 2005
+2
-0.6
Two $$8$$ $$mm$$ thick steel plates are placed $$5$$ $$mm$$ apart and welded by a butt joint. Welding is carried out at $$20$$ $$V$$ and speed of $$5$$ $$mm/sec.$$ Heat transfer efficiency is $$0.80.$$ If the heat required to melt steel is $$10$$ $$J/m{m^3}$$ and melting efficiency is $$0.625.$$ The weld current (in Amperes) will be
A
$$100$$
B
$$200$$
C
$$300$$
D
$$400$$
4
GATE PI 2005
+2
-0.6
Match List - I (welding problems) with List - II (Causes) and select the correct answer using the codes given below the lists:
A
$$A - 2,\,B - 1,\,C - 5,\,D - 3$$
B
$$A - 3,\,B - 4,\,C - 2,\,D - 1$$
C
$$A - 2,\,B - 4,\,C - 5,\,D - 3$$
D
$$A - 3,\,B - 1,\,C - 4,\,D - 2$$
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