1
GATE PI 2010
+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
2
GATE PI 2007
+2
-0.6
Matching exercise choose the correct one out of the alternatives $$A, B, C, D$$

Group $$-$$ $${\rm I}$$
$$P.$$ $${2^{nd}}$$ order differential equations
$$Q.$$ Non-linear algebraic equations
$$R.$$ Linear algebraic equations
$$S.$$ Numerical integration

Group $$-$$ $${\rm II}$$
$$(1)$$ Runge $$-$$ Kutta method
$$(2)$$ Newton $$-$$ Raphson method
$$(3)$$ Gauss Elimination
$$(4)$$ Simpson's Rule

A
$$P - 3,\,\,Q - 2,\,\,R - 4,\,\,S - 1$$
B
$$P - 2,\,\,Q - 4,\,\,R - 3,\,\,S - 1$$
C
$$P - 1,\,\,Q - 2,\,\,R - 3,\,\,S - 4$$
D
$$P - 1,\,\,Q - 3,\,\,R - 2,\,\,S - 4$$
3
GATE PI 2005
+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
$$0.838$$
GATE PI Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Heat Transfer
Thermodynamics
Casting
Joining of Materials
Metal Forming
Machine Tools and Machining
Metrology
Industrial Engineering
EXAM MAP
Joint Entrance Examination