Objective Questions 

1.             What type of errors is involved in the reduction of the number of digits?

                a. mistake             b. chopping            c. round-off         d. truncation

2.             In which case the bisection method of finding the roots of f(x) = 0 is applicable?

                a. when f(x) changes signs                                 b. when f(x) retains sign

                c. when f(x) is small                                            d. when f(x) is large

3.             What is the degree of the approximation polynomial corresponding to the trapezoid rule?

                a. linear                 b. quadratic          c. cubic                  d. bi-quadratic

4.        When K th order differences are constant, the tabular function may be approximated by a polynomial of:

                a. degree k-1         b. degree k  c. degree k + 1 d. degree 2k

5.             An error obtained by the difference of true value and approximate value is

                a. an absolute error                                             b. a percentage error

                c. a round- off error                                             d. a relative error

6.             “If f(x) is continuous, for x, between a and b and if f(a) and f(b) have opposite sign, then there exists at least one real root of f(x) = 0 between a and b” this statement is related to which of the following method of solving non-linear equations?

                a. False position                                                   b. Bisection

c. Newton-Raphson                                            d. Iteration

7.             What is the degree of the approximation polynomial to the Trapezoidal rule?

                a.             0              b.             1              c.             2              d.             n

8.             The error involved in the reduction of the number of digits is

                a. mistake             b. round-off          c. chopping  d. truncation

9.             Which of the following is the Descartes’ rule of sign?

a. The number of negative roots of algebraic equation fn(x) = 0 cannot exceed the number of variations in fn(- x)

b. Every equation of even degree has at least two real roots, one positive and other negative

c. Every equation of odd degree has at least one real root, of sign opposite to that of absolute term

d. If a and b are real and fn(a) & fn(b) have opposite signs than $ a least one real root of the equation fn(x) = 0 has between a and b.

10.          What is the value of Ñ3 f(a + 3h)?

                a. 3 f(a + 3h)         b. Ñ3 f(a)                c.3Ñ f(a)                                d. 3Ñ f(a)

11.          What type of error is involved in reduction of the number of digits?

                a.             mistake                 b.             chopping              

c.             round-off              d.             truncation

 

12.          The error involved in the reduction of the number of digits is

                a. mistake             b. round-off          c. chopping           d. truncation

13.          What is the convergence criteria for the Netwon-Raphson method?

                a. f(x) f(x) < [f(x)]2              b. |f(x) f(x)| < [f(x)]2

                c. |f(x) f(x)| > [f(x)]2             d. |f(x) f(x)| < [f(x)]2

14.          Where is linear interpolation adequate for tabulated functions?

                a. for closed tabulated        b. for slowly varying

c. for largely varying           d. both (a) and (b)

15.          What is the degree of the approximating polynomial corresponding to the Simpson’s rule?

                a. linear                  b. quadratic          c. cubic  d. biquadratic

16.          The bisection method for solving equation f(x) = 0 for the roots is based on the theorem

                a. Rolle’s theorem               b. Intermediate value theorem

c. Mean value theorem       d. Taylor’s

 theorem

17.          Which one is the source of error in obtaining numerical solutions to mathematical problems?

                a. The model                                                        b. The data

c. The numerical method                                   d. All of the above

Numerical Methods