1
GATE ME 2016 Set 1
Numerical
+2
-0
If $$y = f(x)$$ satiesfies the boundary value problem $$\,\,y''\,\,\, + \,\,\,9y\,\,\, = \,\,\,0,\,\,\,y\left( 0 \right)\,\,\, = \,\,\,0,\,$$ $$\,\,y\left( {{\pi \over 2}} \right) = \sqrt 2 ,\,\,\,$$ then $$\,\,y\left( {{\pi \over 4}} \right)\,\,$$ is _______.
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2
GATE ME 2016 Set 1
Numerical
+2
-0
Solve the equation $$x = 10\,\cos \,\left( x \right)$$ using the Newton-Raphson method. The initial guess is $$x = {\pi \over 4}.$$ The value of the predicted root after the first iteration, up to second decimal, is _____________.
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3
GATE ME 2016 Set 1
Numerical
+2
-0
Gauss-Seidel method is used to solve the following equations (as per the given order). $$${x_1} + 2{x_2} + 3{x_3} = 5$$$ $$$2{x_1} + 3{x_2} + {x_3} = 1$$$ $$$\,3{x_1} + 2{x_2} + {x_3} = 3$$$
Assuming initial guess as $${x_1} = {x_2} = {x_3} = 0,$$ the value of $${x_3}$$ after the first iteration is __________.
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4
GATE ME 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral $$\int\limits_{ - \infty }^\infty {{{\sin x} \over {{x^2} + 2x + 2}}} dx$$
evaluated using contour integration and the residue theorem is
A
$$ - \pi {{\sin \left( 1 \right)} \over e}$$
B
$$ - \pi {{\cos \left( 1 \right)} \over e}$$
C
$${{\sin \left( 1 \right)} \over e}$$
D
$${{\cos \left( 1 \right)} \over e}$$
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