### Numerical Methods - 20 Multiple Choice Questions and Answers

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# 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?
 A. False position B. Gauss seidal method C. Newton-Raphson method D. All of these
Ans – C

Newton-Raphson method is used to find the root of the equation x2 - 2 = 0.
If iterations are started from - 1, then iterations will be
 A. converge to -1 B. converge to √2 C. converge to    -√2         (Ans) D. no coverage
Ans – C

Which of the following statements applies to the bisection method used for finding roots of functions?
 A. Converges within a few iterations B. Guaranteed to work for all continuous functions   (Ans) C. Is faster than the Newton-Raphson method D. 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 x0 = 1.0, subsequent estimate of x (i.e. x1)  will be
 A. 1.414 B. 1.5   (Ans) C. 2.0 D. None of these

Ans - B

Using Newton-Raphson method, find a root correct to three decimal places of the equation x3 - 3x - 5 = 0
 A. 2.275 B. 2.279 C. 2.222 D. None of these
Ans - B

In the Gauss elimination method for solving a system of linear algebraic equations,triangularzation leads to
 A. Diagonal matrix B. Lower triangular matrix C. Upper triangular matrix D. Singular matrix
Ans - B

If   Δf(x)  =  f(x+h) - f(x), then a constant k, Δk equals
 A. 1 B. 0 C. f(k)- f(0) D. f(x + k) - f(x)
Ans - B

Double (Repeated) root of
4x3- 8x2- 3x + 9 = 0 by Newton-raphson method is
 A. 1.4 B. 1.5 C. 1.6 D. 1.55
Ans - B

Using Bisection method, negative root of x3 - 4x + 9 = 0 correct to three decimal places is
 A. -2.506 B. -2.706 C. - 2.406 D. None of these
Ans - B

Four arbitrary points (x1, y1), (x2, y2), (x3, y3),(x4, y4) are given in the x, y-plane. 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
 A. Two fitted lines must coincide B. Two fitted lines need not coincide C. It is possible that ac = 0 D. A must be 1/c (Ans) Ans - D
The root of x3 - 2x - 5 = 0 correct to three decimal places by using Newton-Raphson method is
 A. 2.0946 B. 1.0404 C. 1.7321 D. 0.7011
Ans - A

Newton-Raphson method of solution of numerical equation is not preferred when
 A. Graph of A(B) is vertical B. Graph of x(y) is not parallel C. The graph of f(x) is nearly horizontal-where it crosses the x-axis. D. 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
 A. 0 B. 1.5 C. 2 D. 3
Ans - B

A root of the equation x3 - x - 11 = 0 correct to four decimals using bisection method is
 A. 2.3737 B. 2.3838 C. 2.3736 D. None of these
Ans - C

Newton-Raphson method is applicable to the solution of
 A. Both algebraic and transcendental Equations B. Both algebraic and transcendental and also used when the roots are complex C. Algebraic equations only D. Transcendental equations only
Ans - A

The order of error s the Simpson's rule for numercal integration with a step size h is
 A. h B. h2 C. h3 D. h4
Ans - B

In which of the following methods proper choice of initial value is very important?
 A. Bisection method B. False position C. Newton-Raphson D. Bairsto method
Ans - C

Using Newton-Raphson method, find a root correct to three decimal places of the equation sin x = 1 - x
 A. 0.511 B. 0.500 C. 0.555 D. None of these
Ans - A

Errors may occur in performing numerical computation on the computer due to
 A. Rounding errors B. Power fluctuation C. Operator fatigue D. All of these
Ans - A

Match the following:

A. Newton-Raphson                     1. Integration
B. Runge-kutta                             2. Root finding
C. Gauss-seidel                            3. Ordinary Diferential Equations
D. Simpson's Rule                        4. Solution of system of Linear Equations

Codes:
ABCD

 A. 2341 B. 3214 C. 1423 D. None of these
Ans - A

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