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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