IGNOU MCA 5th SEM SOLVED ASSIGNMENT COMPLETE

Course Code :                                                                MCSE-004
Course Title :                                                                 Numerical and Statistical Computing
Assignment Number :                                                    MCA(5)/E004/Assign/2012
Maximum Marks : 100                                                  Weightage : 25%
Last Dates for Submission :                                          31st October, 2012 (For July 2012 Session
                                                                                       30th April, 2013 (For January 2013 Session)

This assignment has five questions in all and carries 80 marks. The rest of the 20
marks are for viva-voce. Answer all the questions. You may use illustrations and
diagrams to enhance the explanations. Please go through the guidelines regarding
assignments given in the Programme Guide for the format of presentation.

Question 1:

(a) A can solve 90% of the problems given in a book and B can solve 70%.

What is the probability that at least one of them will solve a problem

selected at random?

(b) When a computer uses a number base 2, how many significant decimal

digits are contained in the mantissa of floating numbers?

  

 (c) Evaluate the integral

using (i) composite trapezoidal rule, (ii) composite Simpon‟s rule,

with 2, 4 and 8 equal subintervals.

Question 2: Write the following programme in C language:

(a) Write a programme in C to find a root using bisection method.

Perform the five iterations of the bisection method to obtain the

smallest positive root of the equation f(x) = x3 – 5x +1 = 0,

verify your answer with the programme written by you.

(b) Write a programme in C to find a root using Newton Raphson

Method. Apply Newton-Raphson‟s method to determine a root of

the equation f (x) = cos x – xex= 0, if exists verify your answer

with the programme written by you.

Question 3:

(a) Find the probability of getting between 6 and 9 tails inclusive in

20 tosses of a fair coin by using (i) the binomial distribution,

(ii) the normal approximation to the binomial distribution.

  

(b) Table 2 below shows the respective heights x and y of a sample of

12 fathers and their oldest sons.

(i) Construct a scatter diagram.

(ii) Find the least-squares regression line of y on x.

(iii) Find the least-squares regression line of x and y.

Table 2

Height x of Father (centimetres)	165	160	170	163	173	158	178	168	173	170	175	180
Height y of Son (centimetres)	173	168	173	165	175	168	173	165	180	170	173	178

(c) Find the area under the standard normal curve (a) between z = 0 and z = 1.2, (b) between z = – 0.68 and z = 0, (c) between z = – 0.46 and z = 2.21, (d) between

z = 0.81and z = 1.94. 

 

Question 4: Solve the following equation (if a solution exists) using given method:

(a) Solve the equation:

10x₁ – x₂ + 2x₃ = 4

x₁ + 10x₂ –x₃ = 3

2x₁ + 3x₂ + 20x₃ = 7

using the Gauss elimination method.

(b) Solve the questions:

10x₁ – x₂ + 2x₃ = 4

x₁ + 10x₂ –x₃ = 3

2x₁ + 3x₂ + 20x₃ = 7

using the LU decomposition method.

Question 5: Out of the three method i.e. Secant method, Regula Falsi

method and the Newton Raphson method which method is more

efficient and why? Determine the efficiency or the order of these

three methods?

For Solution Click on below Link:

 MCSE-004