Numerical Analysis 2023 – BSc Computer Science Part 2
Total No. of Questions : 8] [Total No. of Printed Pages : 4
Paper code: 13512
1512
B.Sc. (Computer Science) (Part 2)
Examination, 2023
Paper No. 1.3
NUMERICAL ANALYSIS
Time: Three Hours] [Maximum Marks: 50
Note: Attempt any five questions. All questions carry equal marks.
1. (a) Solve f(a) a positive root of 
by ‘Regula Falsi’ method.
(b) Find the real positive root of 
by Newton – Raphson method.
2. (a) Solve the following system of equations by ‘Gauss Seidel’ method.
(b) Solve the system of equation by ‘Gauss – Jordan’ method.
3. (a) Show that :
(i) ![\mu = \frac{1}{2}\left [ E^{\frac{1}{2}} + E^{-\frac{1}{2}} \right ]](https://s0.wp.com/latex.php?latex=+%5Cmu+%3D+%5Cfrac%7B1%7D%7B2%7D%5Cleft+%5B+E%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D+%2B+E%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D+%5Cright+%5D+&bg=ffffff&fg=000&s=0&c=20201002)
(ii) 
(b) Find the 7th term of the sequence 2, 9, 28, 65, 126, 217.
4. (a) Express 
in factorial polynomials and get their successive forward differences, by taking h=1.
(b) Prove that :
5. (a) From the data given below find the number of students whose weight (By Newton forward difference formula) is between 60 and 70.
| Weight in lbs: | 0-40 | 40-60 | 60-80 | 80-100 | 100-120 |
|---|---|---|---|---|---|
| No. of Students: | 250 | 120 | 100 | 70 | 50 |
(b) Show that :
6. (a) Use Newton’s divided difference formula find the value of f(8) from the following table.
| x: | 4 | 5 | 7 | 10 | 11 | 13 |
|---|---|---|---|---|---|---|
| f(x): | 48 | 100 | 294 | 900 | 1210 | 2028 |
(b) Find the first derivative of the function tabulated below at x = .6.
| x: | .4 | .5 | .6 | .7 | .8 |
|---|---|---|---|---|---|
| f(x): | 1.5836 | 1.7974 | 2.0442 | 2.3275 | 2.6511 |
7. (a) Evaluate :
using Trapezoidal rule with h=.2. Hence obtain an approximate value of π.
(b) Evaluate :
using Simpson’s three eighth’s rule.
8. (a) Using modified Euler method, find y(0.2) given:
(b) Obtain the value of y at x=.1 using Raung -Kutta method for equation:
, given y(0) = 1
……..End……..
Thank You 🙂
