Numerical Methods Question and Fill in the Blanks
In which of the following
method, we approximate the curve of solution by the tangent in each interval.
a.
Picard’s method
b.
Euler’s method
c.
Newton’s method
d.
Runge Kutta method
Ans B
The convergence of
which of the following method is sensitive to starting value?
False position


Gauss seidal method


NewtonRaphson method


All of these

Ans – C
NewtonRaphson
method is used to find the root of the equation x2  2 = 0.
If iterations are started from  1, then iterations will be
If iterations are started from  1, then iterations will be
converge to 1


converge to √2


converge to √2
(Ans)


no coverage

Ans – C
Which of the following
statements applies to the bisection method used for finding roots of functions?
Converges within a few iterations


Guaranteed to work for all continuous
functions (Ans)


Is faster than the NewtonRaphson method


Requires that there be no error in
determining the sign of the function

Ans  B
We wish to solve x2 
2 = 0 by Newton Raphson technique. If initial guess is x_{0} = 1.0, subsequent estimate of x (i.e. x_{1}) will be
1.414


1.5 (Ans)


2.0


None of these

Ans  B
Using NewtonRaphson
method, find a root correct to three decimal places of the equation x3  3x  5
= 0
2.275


2.279


2.222


None of these

Ans  B
In the Gauss
elimination method for solving a system of linear algebraic
equations,triangularzation leads to
Diagonal matrix


Lower triangular matrix


Upper triangular matrix


Singular matrix

Ans  B
If Δf(x)
= f(x+h)  f(x), then a constant k, Δk equals
1


0


f(k) f(0)


f(x + k)  f(x)

Ans  B
Double (Repeated) root
of
4x3 8x2 3x + 9 = 0 by Newtonraphson method is
4x3 8x2 3x + 9 = 0 by Newtonraphson method is
1.4


1.5


1.6


1.55

Ans  B
Using Bisection
method, negative root of x3  4x + 9 = 0 correct to three decimal places is
2.506


2.706


 2.406


None of these

Ans  B
Four arbitrary points
(x_{1}, y_{1}),
(x_{2,} y_{2}), (x_{3}, y_{3}),(x_{4}, y_{4}) are given in the x, yplane. Using the
method of least squares, if regressing y upon x gives the fitted line y = ax +
b; and regressing y upon x gives the fitted line y + ax + b; and regressing x
upon y gives the fitted line
x = cy + d, then
x = cy + d, then
Two fitted lines must coincide


Two fitted lines need not coincide


It is possible that ac = 0


A must be 1/c (Ans)
Ans  D

The root of x3  2x 
5 = 0 correct to three decimal places by using NewtonRaphson method is
2.0946


1.0404


1.7321


0.7011

Ans  A
NewtonRaphson method
of solution of numerical equation is not preferred when
Graph of A(B) is vertical


Graph of x(y) is not parallel


The graph of f(x) is nearly horizontalwhere
it crosses the xaxis.


None of these

Ans  C
Following are the
values of a function y(x) : y(1) = 5, y(0), y(1) = 8
dy/dx at x = 0 as per Newton's central difference scheme is
dy/dx at x = 0 as per Newton's central difference scheme is
0


1.5


2.0


3.0

Ans  B
A root of the equation
x3  x  11 = 0 correct to four decimals using bisection method is
2.3737


2.3838


2.3736


None of these

Ans  C
NewtonRaphson method is applicable to the solution of
Both algebraic and transcendental Equations


Both algebraic and transcendental and also
used when the roots are complex


Algebraic equations only


Transcendental equations only

Ans  A
The order of
error s the Simpson's rule for numercal integration with a step size h is
h


h^{2}


h^{3}


h^{4}

Ans  B
In which of the
following methods proper choice of initial value is very important?
Bisection method


False position


NewtonRaphson


Bairsto method

Ans  C
Using NewtonRaphson
method, find a root correct to three decimal places of the equation sin x = 1 
x
0.511


0.500


0.555


None of these

Ans  A
Errors may occur in
performing numerical computation on the computer due to
Rounding errors


Power fluctuation


Operator fatigue


All of these

Ans  A
Match the following:
A. NewtonRaphson 1. Integration
B. Rungekutta 2. Root finding
C. Gaussseidel 3. Ordinary Diferential Equations
D. Simpson's Rule 4. Solution of system of Linear Equations
Codes:
ABCD
A. NewtonRaphson 1. Integration
B. Rungekutta 2. Root finding
C. Gaussseidel 3. Ordinary Diferential Equations
D. Simpson's Rule 4. Solution of system of Linear Equations
Codes:
ABCD
2341


3214


1423


None of these

Ans  A
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