# Numerical Methods || Spring 2015 || Pokhara University

 Level:  Bachelor Semester –Spring Year: 2015 Program: BCIS Full Marks: 100 Course: Numerical Methods Pass Marks: 45 Time:  3hrs.

 Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

Section “A”

Very Short Answer Questions

Attempt all the questions.

10×2

1. Define absolute and relative error.
2. Find the root interval of the equation x2 – 4x -10.
3. State the iterative formula for the false position method to solve f(x)=0.
4. What is the main difference between Gauss elimination and Gauss Jordan method?
5. What is the necessary condition for the solution of a system of linear equations and what are the possible solutions?
6. What are the methods available for interpolations?
7. Write first-order forward difference formula.
8. Numerical integration with a number of interval n=3 and n=6 which one is more accurate and why?
9. Find the normalized regression equation for the transcendental form y=ABx.
10. What are Poisson’s Equations?
Section “B”

Descriptive Answer Questions

Attempt any six questions

6×10

11. Using False Position method, solve the equation xtan(x) = -1 starting with initial guess 2.5 and 3 correct up to 3- decimal places.
12. Solve the following system of linear equations using the Gauss elimination method with partial pivoting.
13. Growth of bacteria (N) in culture after t hrs. is given by

 Time (t) 0 1 2 3 4 N 32 47 65 92 132

Fit a curve of the form N= abt and estimate bacteria when t=5 hrs.

14. Integrate the given integral.

Using the Trapezoidal rule + Simpson’s rule with n=4 and n=6, compare your result and comment on it.

15. Solve the equations y’=  + with x=0.25 and x=0.5 given that y(0)=1

a)      Using Eulers Method (h=0.25)

b)      By using Runge  Kutta method 4th order (h=0.25)

16. Solve the equation T=2  over the square domain with sides x=0=y, x=3=y with T=0 on the boundary, and mesh length=1 using the Gauss-Seidel method.
17. Using Newton’s divided difference formula:

 X 4 5 7 10 11 13 F(x) 48 100 294 900 1210 2028

a)      Evaluate f(8).

b)      Evaluate f(15) of the above-given values in the table.

18.

Section “C”

Case Analysis

Mr. Ram has invested a sum of Rs 20,000 in three types of fixed deposits with an interest rate of 10%, 11%, and 12%. He earns an annual interest of Rs 2,220 from all three types of deposits. If some of the amounts with 11% and 12% interest rates are four times the amount earning 10% interest.

a)      Formulate the appropriate system of linear equations to determine the amount invested in each type.[5]

b)      Compute the amount invested in each type.[7]

c)      Write a program to determine the amount invested in each category of interest.[8]

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