Numerical Methods Previous Year Questions & Detailed Solutions PDF

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and n = 20. Compare the answers and the errors for each of these methods. Problem 26. How would you go about solving the differential equation d2x.

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Numerical Methods Previous Year Questions & Detailed Solutions

By Taylor's series method solution of y'=x. 2. + y. 2. ; y(0) = 1 is. 1) y=l+x – x. 2. 2) y = 1-x+x. 2. 3) y=x+ x. 2. +x. 3. 4) y=l+x+x. 2. +. 4. 3 x3. 19.

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NUMERICAL ANALYSIS PRACTICE PROBLEMS The problems that

Compare the answers and the errors for each of these methods. Problem 26. How would you go about solving the differential equation d2x dt2. = ?x with.

Numerical Methods Previous Year Questions & Detailed Solutions

Numerical Methods. 1. Download Study Materials on www.examsdaily. Previous Year Questions & Detailed Solutions ... By Taylor's series method solution of.

Chapter 10 Numerical Solution Methods for Engineering Analysis

We will learn from this chapter on the use of some of these numerical methods that will not only enable engineers to solve many mathematical problems but they

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Math 371: Numerical Analysis Fall 2015 Solutions to Exam 1 Practice Questions 1 Convert the following base-10 expansions into binary expansions (a) 9:75 Solution 1001:11 (b) 0:1 Solution 2(0:1) = 0+0:2 2(0:2) = 0+0:4 2(0:4) = 0+0:8 2(0:8) = 1+0:6 2(0:6) = 1+0:2 The pattern 0011 will then repeat so the expansion is 0:00011

Numerical Methods

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Previous Year Questions & Detailed Solutions

1. The rate of convergence in the Gauss-Seidal

method is________as fast as in Gauss method

1) thrice 2) half-times

3) twice 4) three by two times

2. In application of Simpsons 1

3rd rule,

theinterval h for closer approximation should be

1) small 2) odd and large

3) large 4) even and small

3. Which of the following is a step by step

method? 1)

2) Picards method

3) Adams Bashforth method

4) Eulers method

4. The interpolation polynomial from the data

x 0 1 3 f(x) 5 4 8

1) x2 2x + 5 2) x2+ 2x +5

3) 2x2 2x + 5 4) 2x2 5x +5

5. The value of the integration ׬

ais approximately equal to 1) h

2[f(a)+3f(a+h)+f(a+2h)]

2) h

3[f(a)+4f(a+h)+f(a+2h)]

3) h

3[f(a)+2f(a+h)+f(a+2h)]

4) h

2[f(a)+4f(a+h)+f(a+2h)]

6. The finite difference approximation for d2y

dx2 at x = x0 is 1) 1 h2 (y(x0-h)-2y(x0)+y(x0+h)] 2) 1 h2 [y(x0-h)+2y(x0)+y(x0+h)] 3) 1 h2 [y(x0-h)-y(x0)+y(x0+h)] 4) 1 h2 [y(x0-h)+y(x0)+y(x0+h)

7. For the following data

X 0 2 4 6

Y -1 3 7 11

the straight line y=mx+c by the method of least square is

1) y=-2x-l 2) y=x-l

3) y=l-2x 4) y=2x-l

8. The velocity v (km/min) of a train which

starts from rest, is given at fixed intervals of time t(min) as follows: t 2 4 6 8 10 12 14 16 18 20 v 10 18 25 29 32 20 11 5 2 0

The approximate distance covered by

Simpson's 1

3 rule is

1) 306.3 2) 309.3

3) 310.3 4) 307.3

9. forward difference which takes the following:

X 0 1 2 3

f(x) 1 2 1 10 then f(4) is

1) 40 2) 41

3) 39 4) 42

10. The first derivative dy

dx at x=0 for the given data

X 0 1 2 3

f(x) 2 1 2 5

Numerical Methods

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1) 2 2) -2

3) -1 4) 1

11. 1

3 rule is of the order

1) h2 2) h3

3) h4 4) 2h3

12. ĮȕȖ3 + px2 + qx+1

= 0, then the equation whose roots are െ1

Ƚ,െ1

Ⱦ,െ1

ɀ is

1) x3 + qx2 px l=0

2) x3+qx3-px+1=0

3) x3-qx2+px-l =0

4) x3- qx2+px+l=0

13. (r+ 1)thiterates, we use the

1) values of the rthiterates

2) values of the (r -1)thiterates

3) values of the (r+ 1)th iterates

4) latest available values

14. If h is the length of the intervals, then the

error in the trapezoidal rule is of order

1) h 2) h2

3) h3 4) h4

15. If E is the translation operator, then the

central difference operator Ɂ is

1) E1/2 + E-1/2 2) E1/2 - E-1/2

3) 1

2 (E1/2 + E-1/2) 4) -1

2 (E1/2 + E-1/2)

16. ǻf(x) = f(x + h)-f(x), E f(x) =f(x + h) and

Ɂf(x)=ቀx+h

2ቁFfቀxെh

2ቁ ǻ׏

1) Ɂ2 2) Ɂ

3) Ɂ1/2 Ͷሻ Ɂ1/2 ൅ Ɂ-1/2

17. Expression for ቀd2y

dx2ቁx=xn backward interpolation 1) 1 h2ቂquotesdbs_dbs2.pdfusesText_3

[PDF] Numerical Methods Previous Year Questions & Detailed Solutions

Numerical Methods

Previous Year Questions & Detailed Solutions

1. The rate of convergence in the Gauss-Seidal

1) thrice 2) half-times

3) twice 4) three by two times

2. In application of Simpsons 1

3rd rule,

1) small 2) odd and large

3) large 4) even and small

3. Which of the following is a step by step

2) Picards method

3) Adams Bashforth method

4) Eulers method

4. The interpolation polynomial from the data

1) x2 2x + 5 2) x2+ 2x +5

3) 2x2 2x + 5 4) 2x2 5x +5

5. The value of the integration ׬

2[f(a)+3f(a+h)+f(a+2h)]

3[f(a)+4f(a+h)+f(a+2h)]

3[f(a)+2f(a+h)+f(a+2h)]

2[f(a)+4f(a+h)+f(a+2h)]

6. The finite difference approximation for d2y

7. For the following data

X 0 2 4 6

Y -1 3 7 11

1) y=-2x-l 2) y=x-l

3) y=l-2x 4) y=2x-l

8. The velocity v (km/min) of a train which

The approximate distance covered by

Simpson's 1

3 rule is

1) 306.3 2) 309.3

3) 310.3 4) 307.3

X 0 1 2 3

1) 40 2) 41

3) 39 4) 42

10. The first derivative dy

X 0 1 2 3

Numerical Methods

1) 2 2) -2

3) -1 4) 1

3 rule is of the order

1) h2 2) h3

3) h4 4) 2h3

12. ĮȕȖ3 + px2 + qx+1

Ƚ,െ1

Ⱦ,െ1

ɀ is

1) x3 + qx2 px l=0

2) x3+qx3-px+1=0

3) x3-qx2+px-l =0

4) x3- qx2+px+l=0

1) values of the rthiterates

2) values of the (r -1)thiterates

3) values of the (r+ 1)th iterates

4) latest available values

14. If h is the length of the intervals, then the

1) h 2) h2

3) h3 4) h4

15. If E is the translation operator, then the

1) E1/2 + E-1/2 2) E1/2 - E-1/2

2 (E1/2 + E-1/2) 4) -1

2 (E1/2 + E-1/2)

16. ǻf(x) = f(x + h)-f(x), E f(x) =f(x + h) and

Ɂf(x)=ቀx+h

2ቁFfቀxെh

2ቁ ǻ׏

1) Ɂ2 2) Ɂ

3) Ɂ1/2 Ͷሻ Ɂ1/2 ൅ Ɂ-1/2

17. Expression for ቀd2y