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Engineering Maths - Numerical Methods Online Exam Quiz

Important questions about Engineering Maths - Numerical Methods. Engineering Maths - Numerical Methods MCQ questions with answers. Engineering Maths - Numerical Methods exam questions and answers for students and interviews.

1. The convergence of which of the following method is sensitive to starting value?

Options

A : False position

B : Gauss seidal method

C : Newton-Raphson method

D : All of these

3. Which of the following statements applies to the bisection method used for finding roots of functions?

Options

A : Converges within a few iterations

B : Guaranteed to work for all continuous functions

C : Is faster than the Newton-Raphson method

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

4. We wish to solve x 2 - 2 = 0 by Newton Raphson technique. If initial guess is x 0 = 1.0, subsequent estimate of x (i.e. x 1 )  will be

Options

A : 1.414

B : 1.5

C : 2.0

D : None of these

5.  Using Newton-Raphson method, find a root correct to three decimal places of the equation x 3 - 3x - 5 = 0

Options

A : 2.275

B : 2.279

C : 2.222

D : None of these

6. In the Gauss elimination method for solving a system of linear algebraic equations, triangularzation leads to

Options

A : Diagonal matrix

B : Lower triangular matrix

C : Upper triangular matrix

D : Singular matrix

7. If Δf(x) = f(x+h) - f(x), then a constant k, Δk equals

Options

A : 1

B : 0

C : f(k)- f(0)

D : f(x + k) - f(x)

8. Double (Repeated) root of 4x 3 - 8x 2 - 3x + 9 = 0 by Newton-raphson method is

Options

A : 1.4

B : 1.5

C : 1.6

D : 1.55

9. Using Bisection method, negative root of x 3 - 4x + 9 = 0 correct to three decimal places is

Options

A : -2.506

B : -2.706

C : - 2.406

D : None of these

10. Four arbitrary points (x 1 , y 1 ), (x 2, y 2 ), (x 3 , y 3 ),(x 4 , y 4 ) 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

Options

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

11. The root of x 3 - 2x - 5 = 0 correct to three decimal places by using Newton-Raphson method is

Options

A : 2.0946

B : 1.0404

C : 1.7321

D : 0.7011

12. Newton-Raphson method of solution of numerical equation is not preferred when

Options

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

13. 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

Options

A : 0

B : 1.5

C : 2.0

D : 3.0

14. A root of the equation x 3 - x - 11 = 0 correct to four decimals using bisection method is

Options

A : 2.3737

B : 2.3838

C : 2.3736

D : None of these

15. Newton-Raphson method is applicable to the solution of

Options

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

17. In which of the following methods proper choice of initial value is very important?

Options

A : Bisection method

B : False position

C : Newton-Raphson

D : Bairsto method

18. Using Newton-Raphson method, find a root correct to three decimal places of the equation sin x = 1 - x

Options

A : 0.511

B : 0.500

C : 0.555

D : None of these

19. Errors may occur in performing numerical computation on the computer due to

Options

A : Rounding errors

B : Power fluctuation

C : Operator fatigue

D : All of these

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