MTH603 Final Term Solved Objective Mega File by Syeda

1. to apply Simpson’s 1/3 rule, the number of intervals in the following must be

Answer: (select your correct answer)

2. In integrating by dividing the interval into eight equal parts, width of the interval should be

Answer: (select your correct answer)

1. 125
2. 250

0.500

1. 625
2. ------lies in the category of iterative method.

Answer: (select your correct answer)

Regula falsi method

Muller’s method

4. Regula falsi method lies in the category of -------

Answer: (select your correct answer)

Random method Graphical method

5. It can be verified that for matrix

Answer: (select your correct answer) AA-1=I, I= identity matrix AA-1=D, D= diagonal matrix

AA-1=S, S= symmetric matrix

AA-1=Z, Z= orthogonal matrix

6. Newton’s divided difference interpolation formula is used when the values of the independent variable are

Answer: (select your correct answer)

Constant

7. If f(x) = 5x6 + 6x5 – 7x3 – 9x2 + 4x – 3, then it’s ----- derivative is zero for all x.

Answer: (select your correct answer) 4th

7th

6th 5th

8. to apply Simpson’s 1/3 rule, valid number of intervals are ----

Answer: (select your correct answer)

9. In integrating by dividing into eight equal parts width of the interval should be

Answer: (select your correct answer)

1. 250
2. 500

0.125

1. 625

H=b-1/n….trapezoidal

10. A fourth order ordinary differential equation can be reduced to a system of four ----- order ordinary

Answer: (select your correct answer) First Second

Third

Fourth

11. In Richardson`s extrapolation method, the extrapolation process is repeated until accuracy is achieved, this is called extrapolation to the -----

Answer: (select your correct answer) Limit Function

Arbitrary value of “h”

12. From the following table of values:

X

1. 00
2. 05 1.10 1.15 1.20 1.25 1.30

Y

1. 000
2. 0247 1.048 1.0724 1.095 1.1180 1.1402

Answer: (select your correct answer) Forward difference operator

Backward difference operator

Enter difference operator

7. While deriving Simpson`s 3/8 rule, we approximate f(x) in the form -----

Answer: (select your correct answer) Ax+b

Ax2 + bx +c

13. When we apply Simpson`s 3/8 rule, the number of intervals n must be

Answer: (select your correct answer) Even Odd

Multiple of 3

Multiple of 8

14. Next approximation to the root of the given equation by bisection method can be found if

Answer: (select your correct answer) F(2) =-7, f(3)= -8 F(2) =-7, f(3)= 8 F(2) =7, f(3)= 8

15. if , then

Answer: (select your correct answer) S-1 = ST

ST = S

I = S

16. Lagrange`s interpolation formula is used when the values of the independent variable are

Answer: (select your correct answer)

Constant

17. If there are (n+1) values of y corresponding to (n+1) values of x, then we can represent the function f(x) by a polynomial of degree

Answer: (select your correct answer) n+2 n+1

n

n-1

18. While deriving trapezoidal rule, we approximate f(x) in the form

Answer: (select your correct answer)

Ax+b

Ax2 + bx +c

19. Two segment trapezoidal rule of integration is exact for integrating at most ---- order polynomial.

Answer: (select your correct answer) First Second

Third

Fourth

20. A third order ordinary differential equation can be reduced to a system of ---- first order ordinary

Answer: (select your correct answer)

The first lngrange polynomial with equally spaced nodes produced the formula for

Trapezoidal rule

Newton's method Richardson's method

While employing Trapezoidal and Simpson Rules to evaluate the double integral numerically, by using Trapezoidal and Simpson rule with respect to -------

• variable/variables at time single

The Trapezoidal Rule is an improvement over using rectangles because we have much less "missing" from our calculations. We used ________ to model the curve in trapezoidal Rule

straight lines

curves