1
GATE PI 2010
MCQ (Single Correct Answer)
+2
-0.6
During the filling process of a given sand mould cavity by metal through a horizontal runner of circular $$C.S,$$ the frictional head loss of the molten metal in the runner will increase with the
A
Increase in runner diameter
B
Decrease internal surface roughness of the runner
C
Decrease in length of runner
D
Increase in average velocity of molten metal
2
GATE PI 2010
MCQ (Single Correct Answer)
+1
-0.3
The value of $$q$$ for which the following set of linear equations $$2x+3y=0, 6x+qy=0$$ can have non-trivial solution is
A
$$2$$
B
$$7$$
C
$$9$$
D
$$11$$
3
GATE PI 2010
MCQ (Single Correct Answer)
+2
-0.6
The following algorithm computes the integral $$\,J = \int\limits_a^b {f\left( x \right)dx\,\,\,} $$ from the given values $${f_j} = f\left( {{x_j}} \right)$$ at equidistant points $$\,\,{x_0} = a,\,\,{x_1} = {x_0} + h,\,\,$$ $$\,{x_2} = {x_0} + 2h,...\,{x_{2m}} = {x_0} + 2mh = b\,\,$$ compute
$${S_0} = {f_0} + {f_{2m}}$$
$${S_1} = {f_1} + {f_3} + .... + {f_{2m - 1}}$$
$${S_2} = {f_2} + {f_4} + .... + {f_{2m - 2}}$$

$$J = {h \over 3}\left[ {{S_0} + 4\left( {{S_1}} \right) + 2\left( {{S_2}} \right)} \right]$$

The rule of numerical integration, which uses the above algorithm is

A
Rectangle rule
B
Trapezoidal
C
Four $$-$$ point rule
D
Simpson's rule
4
GATE PI 2010
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following differential equations has a solution given by the function $$y = 5\sin \left( {3x + {\pi \over 3}} \right)$$
A
$${{dy} \over {dx}} - {5 \over 3}\cos \left( {3x} \right) = 0$$
B
$${{dy} \over {dx}} + {5 \over 3}\left( {\cos 3x} \right) = 0$$
C
$${{{d^2}y} \over {{d^2}\,x}} + 9y = 0$$
D
$${{{d^2}y} \over {d{x^2}}} - 9y = 0$$
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