Level: Bachelor  Semester –Spring  Year: 2017 
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 Error in numerical Process with its type.  
2.  State the iterative formula for bisection method to solve f(x) = 0  
3.  What are possible solutions to a system of linear equations?  
4.  Define illconditioned system.  
5.  Solve the system of linear equations using the Gauss Jordan method.
2x – 3y = 7 3xy = 5 

6.  State the iterative formula for false position method to solve f(x) = 0  
7.  Define the Initial value problem with an example.  
8.  What is the difference between the bracketing and nonbracketing method?  
9.  Why GaussSeidel method is better than Jacobi’s method?  
10.  Find f’(1) with h = 0.5 for f(x) = exp(x) – sinh(x) using 3points backward difference formula.  
Section “B”
Attempt any six questions 
6×10 

11.  Using Newton’s method, find the root of the equation 3x – 1 = cos(x) such that absolute error at our calculated root should be less than 10^{3}  
12.  Solve the following set of equations by using the Crout algorithm.  
13.  Evaluate the integration by using 2point and 3point Gaussian quadrature formula.  
14.  Growth of bacteria (N) in a LAB after t hrs. is given by
Fit a curve of the form N = ba^{t} and estimate bacteria when t =5 hrs.


15.  Solve the differential equation y^{’’}– y^{’ }+ 2x = 1at x = 0.2 using RK2 method with y(0) = 1 and y^{’}(0) = 1.  
16.  Solve the PDE T_{xx}+ T_{yy}= 2(x+y) over the square domain with sides x = 0 = y ,x = 3 = y and T = 0 on the boundary and mesh length = 1.  
17.  Solve the differential equation by using RK4 method for y(0.5) with y(0) = 2 and h = 0.25  
18. 
Section “C”
Case study The monthly faculty salary in three departments of Pokhara University is given below. Assuming that the salary for a particular category is the same in all the departments, calculate the salary of each category of faculty. Use any suitable method.
Questions: a) Formulate the appropriate system of linear equations to determine the salary of each category of faculty in each month assuming that the salary for a particular category is the same in all the departments. b) Write an algorithm to obtain the salary of each category of faculty using the system obtained from a. c) Determine the salary of each category of faculty using any suitable method.

20 
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