1
GATE CE 2013
Numerical
+2
-0
There is no value of $$x$$ that can simultaneously satisfy both the given equations. Therefore, find the 'least squares error' solution to the two equations, i.e., find the value of $$x$$ that minimizes the sum of squares of the errors in the two equations
$$2x=3$$
$$4x=1$$
2
GATE CE 2011
+2
-0.6
The square root of a number $$N$$ is to be obtained by applying the Newton $$-$$ Raphson iteration to the equation $$\,{x^2} - N = 0.\,\,$$ If $$i$$ denotes the iteration index, the correct iterative scheme will be
A
$${x_{i + 1}} = {1 \over 2}\left[ {{x_i} + {N \over {{x_i}}}} \right]$$
B
$${x_{i + 1}} = {1 \over 2}\left[ {x_i^2 - {N \over {x_i^2}}} \right]$$
C
$${x_{i + 1}} = {1 \over 2}\left[ {{x_i} + {{{N^2}} \over {{x_i}}}} \right]$$
D
$${x_{i + 1}} = {1 \over 2}\left[ {{x_i} - {N \over {{x_i}}}} \right]$$
3
GATE CE 2010
+2
-0.6
The table below gives values of a function $$f(x)$$ obtained for values of $$x$$ at intervals of $$0.25$$

The value of the integral of the function between the limits $$0$$ to $$1,$$ using Simpson's rule is

A
$$0.7854$$
B
$$2.3562$$
C
$$3.1416$$
D
$$7.5000$$
4
GATE CE 2009
+2
-0.6
The area under the curve shown between $$x=1$$ and $$x=5$$ is to be evaluated using the trapezoidal rule. The following points on the curve are given

The evaluated area (In m2) will be

A
$$7$$
B
$$8.67$$
C
$$9$$
D
$$18$$
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