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 x^{2 }– 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 firstorder 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=AB^{x}.  
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
Fit a curve of the form N= ab^{t} 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 4^{th} 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 GaussSeidel method.  
17.  Using Newton’s divided difference formula:
a) Evaluate f(8). b) Evaluate f(15) of the abovegiven 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] 
20 
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