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ISME-009I
B.Tech. MECIIAlGCAL ENGINEERING
MANUFACTURING)
BTCLEVllBTMEVIIBTELVVBTCSVI/BTECVI
Term-End Examination
December, 2016

BME-009 COMPUTER PROGRAMMING
AND APPLICATIONS
Time 3 hours Maximum Marks: 70
Note: Attempt any· five questions. All questions carry equal marks. Use of scientific calculator is permitted. Assume missing data, if any.

1. Apply Lagrange's formula to find the form of the function, given 7

0 1 2 3 4
3 6 11 18 27

Use Stirling's formula to find y(32.1) for the
following data: 7
20 30 40 50
512 439 346 243

2. Find the sum of the series

........+1/(99)^2

using Euler-Maclaurin summation formula. 7

Apply Simpson's 1/3rd rule to evaluate Integral(dx/(1+x^3) to two decimal places by dividing the range into 4 equal parts. The upper and lower limits are 2 and 0 7

3. Solve the following initial value problem using Runge-Kutta method of order four:

Find y(0.5) taking h=0.5.

Using Taylor series method, obtain the value of y at x if y satisfies the equation y" given that when 1 and O. 7

4. Use the LU decomposition method to solve the following system of equations 7

x1+x2+x3=1
4x1+3x2-x3=6
3x1+5x2+3x3=4

Determine the eigenvalues and the corresponding eigenvectors for the matrix

2 -1 0
A -1 2
0 -1 2

5. Find an approximate value of sqrt(2) using the Newton-Raphson formula. 7

Using Muller's method, find a root of the equation

x^3 which lies between 2 and 3. 7

6. Write a program which calculates multiplication of two matrices. 6

Explain the following with examples: 8

Encapsulation

Virtual functions

7. Write a program which computes the sum of the squares of the first N natural numbers. 5

Explain the following: 9

Scope of Variables

Constructor and Destructor

Dynamic Binding