# Numerical Computing all previous/ past question papers

– Numerical Computing-Computer Science all subject past paper Numerical Computing –Computer Graphics Course Numerical Computing Project idea – ICT MCQ -Numerical Computing Interview Question –Computer Science all courses -Technology –University Past Paper -Programming language –Question paper –old paper

### Numerical Computing Fall 21 past paper

### Numerical computing final paper

1. Solve the following system using Jacobi method (with 4 digu roues arithmetic, at least). Assume the error tolerance as 0.0001.

15x₁-2X2-6Xj+0x₁ -2x)+12×2-4X3-X4=300

0 -6×1-4×2+19×3-9×4 =0

0x1-X2-9X3+21x₁=0

(Marks 10)

2. Obtain the first and second derivative at x-7 using Stirling formula. Where

Xp= 12

X

5

6

7

8

9

10

f(x)

196

394

686

1090

1624

2306

(Marks-10)

x

3. Use the table in Question no. 2 of values by Newton forward differentiation formula. To compute f (0.25), (0.50), (0.75).

2125 (Marks= 15)

4. Use Question no. lequations, to find X1, X2, X3, and x, values using Gauss

Jordan Elimination Method.

(Marks 10)

5. Compute ff(x) dx based on Trapezoidal rule. 0.6

X

0

0.1

0.2

0.3

0.4

0.5

0.6

f(x)

0

0.0998

0.1987 0.2955 0.38994

0.4794

0.5646

(Marks-05)

### Numerical Computing Mid term paper

Q1:

Find the Error if found then remove that error?

x | F(x) |

2.5 | 24.145 |

2.0 | 22.043 |

2.5 | 20.225 |

2.5 | 18.644 |

2.2 | 17.262 |

3.0 | 16.047 |

Q2:

Find the approximate value of following integral for step, h = 0.25

Over the interval [3,9] where f(x) = x/x+3.

- Composite Bool’s rule
- Composite Weddle’s rule

Q3:

Construct the Newton’s Forward difference interpolating polynomial passing through the points (-1,-3), (1, 5), (3, 17), and (5, 21).

paper 2

Q1:

It is suspected that there is an error in one of the values of f(x) in the following table:

X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

f(x) | 0 | 2 | 20 | 90 | 272 | 605 | 1332 | 2450 | 4160 | 6642 | 10100 |

Construct the differences-table, detect and correct the error.

Q2:

Q3:

The following table represents the time x and the corresponding velocity f(x) of the particle moving with non-uniform velocity.

X | 0.0 | 1.0 | 1.5 | 2.0 |

f(x) | 2.5 | 1.0 | 4.6 | 5.3 |

From this table, using Lagrange’s formula inversely, determine the time when the velocity of the particle becomes 2.75.

## Numerical Computing Sessional 1 question paper

## Numerical Computing Sessional 2 question paper

- Filling the blanks (Score: 2 5=10)

(1) Let ξ=g(ξ)∈[a, b] be a fixed point of the real-valued and continuous function g(x). If g(x) has a continuous derivative in some neighborhood of ξ with ________.

Then the sequence (x_{k}) defined by x_{k+1}=g(x_{k}) converges to ξ as k→∞, provided that x_{0} is sufficiently close to ξ.

(2) Assume that .Let be distinct real numbers and suppose that are real numbers. Then, there exists a unique Lagrange polynomial such that ____________.

(3) Suppose that a real-valued function g(x) has a fixed point ξ in [a, b]. Then, the corresponding expression can be written as________.

(4) Given that 4x^{2}-a=0, where a is positive real number. Then, the iteration for solving this equation by the secant method can be expressed as ____________with x_{0} and x_{1} being the starting values.

(5) During the process of finding the single solution to the equation f(x) =0 in [a_{0}, b_{0}] with f(a_{0})f(b_{0})<0, the first step is to consider the midpoint . If (the given tolerance), then we need to choose the new interval:[a_{1}, b_{1}]=[a_{0}, c_{0}] in the case of _____;or [a_{1}, b_{1}]=[c_{0}, b_{0}] in the case of _____.

**Find solution using Bessel’s formula Score= 10****Find Solution using Newton’s Backward Difference formula Score=10**

x | f(x) |

3.5 | 34.145 |

4.0 | 32.043 |

4.5 | 30.225 |

5.0 | 28.644 |

5.5 | 27.262 |

6.0 | 26.047 |

x = 4.75

## Numerical Computing Final question paper

- MCQ’s (Marks=10)
- How much significant digits in this number 204.020050?
- 5
- 7

- How much significant digits in this number 204.020050?

- 9

- 11
- In which of the following method, we approximate the curve of solution by the tangent in each interval.
- Hermite’s method
- Euler’s method

- Newton’s method

- Lagrange’s method

- When do we apply Lagrange’s interpolation?
- Evenly spaced
- Unevenly spaced

- Both

- None of above
- When Newton’s backward formula is used?
- To interpolate values
- To calculate difference

- To find approximate error

- None of above

- What are the errors in Trapezoidal rule of numerical integration?
- E<Y
- E>Y

- E=Y

- None of above

- Consider the initial value problem; give the condition of the absolute stability for the Euler method. (Marks= 10)

- Suppose that the function values of f(x) are given in the following table.

X | -1 | 1 | 2 |

ln X | -3 | 0 | 4 |

(Marks= 10)

Find the approximate function value at the point by the Lagrange’s interpolation polynomial of degree 2.

- Use the predictor-corrector method to get the approximate solution of the following initial value problem (Marks= 10)

with *h *= 0.1, 0 < *x *< 0.5.

- Consider the function f(x) = cos x−x=0. Approximate a root of f(x) via Newton’s Method. (Marks= 10)

## Numerical Computing Final Paper 2022

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