Numerical Analysis Past Papers

By: Prof. Fazal Rehman Shamil

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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Prof. Fazal Rehman Shamil
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