1
GATE CE 2015 Set 1
Numerical
+2
-0
The quadratic equation $${x^2} - 4x + 4 = 0$$ is to be solved numerically, starting with the initial guess $${x_0} = 3.$$ The Newton- Raphson method is applied once to get a new estimate and then the Secant method is applied once using in the initial guess and this new estimate. The estimated value of the root after the application of the Secant method is ________.
2
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
$$2x=3$$
$$4x=1$$
3
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
$${x_{i + 1}} = {1 \over 2}\left[ {{x_i} - {N \over {{x_i}}}} \right]$$
4
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
$$7.5000$$
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Joint Entrance Examination