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MCQ's on Numerical Methods and Error Analysis, Quizzes of Numerical Methods in Engineering

DBATU MCQs

Typology: Quizzes

2020/2021

Available from 08/05/2021

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MCQ’S on NMME
1. In floating point representation the ‘k’ is stand for _______
a. Intiger
b. Constant
c.
d. Range
2. Round off the given number up to three significant digit 7.893 is ______
a. 7.891
b. 7.91
c. 7.94
d.
3. Round off the following number up to four significant digit 12.46982
is________
a. 12.467
b. 12.469
c.
d. 0.1248*102
4. The Absolute error is given by the formula Er = _________
a.
b. X – X’
c. | X’ – X|
d. None of this
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MCQ’S on NMME

  1. In floating point representation the ‘k’ is stand for _______ a. Intiger b. Constant c. d. Range
  2. Round off the given number up to three significant digit 7.893 is ______ a. 7. b. 7. c. 7. d.
  3. Round off the following number up to four significant digit 12. is________ a. 12. b. 12. c. d. 0.1248*10^2
  4. The Absolute error is given by the formula Er = _________

a. b. X – X’ c. | X’ – X| d. None of this

  1. The relative error i.e. Er is given by the formula __________

a. | true value | | absolute error |

b.

c. | X | | X’ – X |

d. | X’ – X | | X |

  1. Round off the given number 865250 and find Absolute error, Round off up to four significant digit a. b. 86525 & 60 c. 865200 & 90 d. 865288 & 30

  2. The Truncation of the number X = 0.004997 up to three decimal digit is


    a. X = 0. b. c. X = 0. d. X = 0. 
  3. The Newton Raphson Formula is ________ a. Xn-1 = Xn + f’( Xn ) f ( Xn )

b. Xn+1 = Xn + f ( Xn ) f’ ( Xn )

c. Xn = Xn+1 + f ( Xn ) f’( Xn )

d.

  1. The Newton Raphson formula by Taylor’s series expansion is ___ a. Xn+1 = Xn - f ( Xn+1 ) f’( Xn+1 )

b.

c. Both ‘a’ and ‘b’

d. None of the above

  1. In error propogation the Absolute error in Subtraction is given by _ a. | ( X+Y ) – ( X’- Y’ ) | = | Eax + Eay | < | Eax | + | Eay | b. | ( X –Y ) + ( X’ – Y’) | = | Eax – Eay | > | Eax | - | Eay | c. d. None of this
  2. By Newton Raphson Method 3X = COSX+1 correct up to four decimal place is _______ a. 0. b. 0. c. d. 0.
    1. __________ errors are caused by using approximate formula in computation. A. Inherent B. Round off D. Numerical 17.In general the ratio of truncation error to that of round off error is __________. B.1:1 C.1:2 D.1: 18 .A reaction takes place that is expected to yield 171.9g of product, but only yield 154.8g. What is the percentage error for this experiment?

c) 0. d) 0.

24 Find the root of in (2.8,3) using bisection method for one iteration

a) b) 2. c) 2. d) 3.

25 If and are the initial guesses and is a root after first iteration such that f()

f() >0, then the root lies in interval, a) ( b) c) ) d) ,)

26 Bisection method is also known as

a) b) N.R. method c) Both a & b d) None of these

27 Which of the following is bracketing method

a) b) N.R. method c) Both a & b d) None of these

28 In _______ the next guess in the x-intercept of tangent of

a) Bisection method b) c) Chebyshev method d) False position method

29 Which of the following is/are open method?

a) Successive approximation b) Newton- Raphson’s method c) Chebyshev method d)

30 Suppose we want to find a root of the polynomial. Using the Bisection

method and starting boundaries a = 2 and b = 4, what is the third approximation to the root obtained by the algorithm? a) 2. b) 2. c) d) 2.

31 Which method has slow converges?

a) False poison b) Secant c) Newton-Raphson

36 Use the Newton-Raphson method to solve 2 to 4 decimal places.

a) There is no solution since the curve is always increasing. b) c) x = 0. d) Newton-Raphson can’t be use because the tangents to the curve do not cut the axes on the interval 0≤x≤

37 Newton-Raphson method will always converts to a solution for f(x) = 0 on

the interval a ≤ x ≤ b if certain condition are there. Which of the following is not of these confession? a) f is continuous on the interval a ≤ x ≤ b. b) f (a) and f(b) have opposite sign. c) f’(x) does not change sign be the interval a ≤ x ≤ b. d)

38 The function f(x) = + 2 has a root between 0 and 1. Which of the

following condition fail? a) f(0) and f(1) have opposite signs. b) f’(x)≠ 0 on 0 ≤ x ≤ 1. c) d) The tangents at 0 and 1 cut the axes in the interval 0 ≤ x ≤1.

39 The order of convergence of Newton-Raphson iterative algorithm is a) First order b) c) Third order d) None of the above

40 Newton-Raphson method of finding roots of nonlinear equations falls under the category of ________methods. a) b) The graph of f(x) is nearly vertical where it crosses the x-axis. c) Both conditions (A) and (B) above prevail. d) None of the above. Q.41. A system of linear equations said to homogeneous if the constant terms are ---------.

a) one

c) both (a)&(b)

d) None of the above

Q.42.A matrix with only one column is called ---------.

a) A null matrix

b) A row matrix

c) Homogeneous matrix

Q.47.In gauss elimination method , original equations are transformed by using--------.

a) Column operation

b) Mathematical operation

d) None of the above

Q.48.A matrix having m rows and n columns with m≠n is said to be a-------.

a) Square matrix

b) Identity matrix

d) None of the above

Q.49.[a b c] is a -----------.

a) Zero matrix

b) Diagonal matrix

c) Column matrix

Q.50.In the Gauss elimination method for solving a system of linear algebraic equations , triangularization leads to-------.

a) Diagonal matrix

b) Lower triangular matrix

d) Singular matrix