## Paper 1: Numerical Analysis Past Papers

**University Name – Confidential**

**NOTE:**

*Attempt any five questions. All questions carry equal marks. Mobile phones and other electronic gadgets are not allowed in the examination hall.*

Time Allowed: __3 hours__

Examination: __Final, Fall – 2020__

Total Marks: __70, Passing Marks (35)__

**Q1**. **(a)** Using fixed point iteration, find the root of the following nonlinear equation

** (b)** The function has a root in [1, 2]. Approximate the root correct to three

decimal- places by bisection method.

**Q2. (a) **Using Newton- Rapson’s method to evaluate to four decimal places, the root of the equation

** ** f(x) = Taking .

**(b)** Using the Secant method to find correct to four decimal places, the root between 0.4 and 0.6 of the

equation

**Q3. (a) **Find the root of the following equation by regula falsi method correct to 4 significant figures:

**(b)** Solve the following linear system by Gauss’s elimination method.

**Q4.** (a) Solve the following linear system by Gauss-Jordan elimination method.

**(b)** Find the seond degree Lagrange interpolation polynomial passing through the three point a in the

following table

x | 0 | 1 | 3 |

y | -5 | 1 | 25 |

**Q.5 **Solve the following linear system of equations working to four decimal places:

By using **(a)** Jacobi iterative method **(b)** Gauss Seidel iterative method

**Q6 ** **(a)** Construct only a difference table from the following data

x | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 | 2.2 |

y | 2.0 | 3.5 | -1.7 | 2.3 | 4.2 | 6.5 | 5.7 |

**(b)** Evaluate the integral by using rectangular rule for n = 4 and compare your result with

the exact value.

**Q7.**** (a)** Evaluate the integral, by using Trapezoidal rule for n = 4

**(b)** Using three points Simpson’s rule to estimate the value of.

**Q8.** For the following data

- Using forward difference formula find
- Using backward difference formula find

x | 1 | 2 | 3 | 4 | 5 |

y | 3 | 10 | 29 | 66 | 127 |

## Paper 2: Numerical Analysis Past Papers

**University Name – Confidential**

**NOTE:**

*Attempt any five questions. All questions carry equal marks. Mobile phones and other electronic gadgets are not allowed in the examination hall.*

Time Allowed: __3 hours__

Examination: __Final, Fall – 2019__

Total Marks: __70, Passing Marks (35)__

**Q1**. **(a)** Define the following terms

(i) Error (ii) Absolute error (iii) percentage error

** (b)** Using Newton- Rapson’s method to evaluate the positive root of the equation

**Q2. **Find the positive root of the equation by using

- False position method
**(b)**Secant method

**Q3. (a)** Solve the following linear system by Gauss’s elimination method.

2x – 7y + 4z = 9,

x + 9 y – 6 z = 1,

-3x + 8y + 5 z = 6.

**(b)** Solve the following linear system by Gauss Jordan elimination method.

2x + 2y + 4z = 18,

x + 3 y +2 z = 13,

3x + y + 3 z = 14.

**Q4.** Solve the following linear system of equations working to four decimal places:

x + 0.1y = 1.0

0.1x + y + 0.1z = 2.0

0.1y + 4 z = 3.0.

By using **(a)** Jacobi’s method **(b)** Gauss Seidel method

**Q.5 **Find from the following data at x = 3 by using

** (a)** Forward difference formulas **(b)** Backward difference formulas

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 |

y | 2 | 3 | 10 | 29 | 66 | 127 | 218 |

Q6**(a)** Find the real roots of the equation = 0, using fixed point iteration. Evaluate the following integral

** (b)** Find positive real roots of by using bisection method.

**Q7. (a)** Calculate the integral, using Trapezoidal where step size h = 0.05.

**. (b)** Using Simpson’s Rule to estimate the value of for n = 4.

**Q8**. Use the tabulated data based on Forward differences

x | 0.6 | 0.7 | 1.4 | 0.8 | 1.8 | 0.9 |

y | 0.564642 | 0.644218 | 4.06 | 4.96 | 6.05 | 7.39 |

to estimate , where y(x) = sinx

## Paper 3: Numerical Analysis Past Papers

**University Name – Confidential**

**NOTE:**

*Attempt any five questions. All questions carry equal marks. Mobile phones and other electronic gadgets are not allowed in the examination hall.*

Time Allowed: __3 hours__

Examination: __Final, Fall – 2018__

Total Marks: __70, Passing Marks (35)__

**Q1**. **(a)** Roots of the equation lies between 2 and 3. Using the fixed-point iteration method, find an approximate root correct upto two places of decimal

** (b)** Using **Newton- Rapson’s** method to evaluate to 2 decimal places, the root of the equation ,Taking.

** Q2. (a) ** Applying secant method, find the root correct to 2 dp of the equation (x is in radian measure)

**(b)** Find the root of the following equation by **regula falsi method** correct to 2 significant figures:

**Q3. **Solve the following linear system

by **(a)** **Gauss’s elimination method** **(b)** **Gauss-Jordan** **elimination method**

**Q4.** Carry out the first two iterations; solve the following linear system of equations by using **(a)** **Jacobi’s method (b) Gauss Seidel method**. Taking

** Q.5 **Construct the second degree polynomial passing through the three points in the following table

x | 0 | 1/6 | 1/2 |

y | 0 | 1/2 | 1 |

by using

- Lagrange’s interpolation polynomial formula
- Newton’s interpolation polynomial formula

Q6. **(a)** Construct a difference table from the following data, hence to compute the first order derivative by using Newton’s forward difference formula.

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 |

y | 2 | 3 | 10 | 29 | 66 | 127 | 218 |

**(b)** Roots of the equation lies in the interval [2, 3]. Using bisection method find the approximate root correct to 2 decimal positions only.** **

**
Q7. **Evaluate the integral for n = 4

by using **(a) Trapezoidal rule (b) Simpson’s rule**. Compare your answer with the exact value.

**Q8** Construct a difference table from the following data, also using Newton’s backward difference formula compute

x | 2 | 4 | 6 | 8 | 10 | 12 | 14 |

y | 23 | 93 | 259 | 569 | 1071 | 1813 | 4843 |

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