IGNOU BCS 54 SOLVED ASSIGNMENT 2024 2025

Ques 1.

Explain each of the following concepts, along with at least one suitable example for each: (i) Fixed-point number representation (ii) round-off error (iii) representation of zero as floating point number (iv) significant digits in a decimal number representation (v) normalized representation of a floating point number (vi) overflow

Ques 2.

Explain with suitable example that in computer arithmatics (i.e., numbers represented in computer, with +, -, , / as implemented in a computer) the multiplication operation() may not be distributive over plus (+), i.e.  may not be true for some computer numbers a, b and c

Ques 3.

Find out to how many decimal places the value 22/7 is accurate as an approximation of 3.14159265, where the latter is value of, calculated up to 8 places after decimal?

Ques 4.

Calculate a bound for the truncation error in approximating

 where  and (fact n) denotes factorial of n

Ques 5.

Obtain Approximate the value of (3.7)^-1 using first three terms of Taylor's series expansion.

Ques 6.

Solve the system of equations

using Gauss elimination method with partial pivoting.

Ques 7.

Perform four iterations (rounded to four decimal places) using

(i) Jacobi Method and

(ii) Gauss-Seidel method,

for the following system of equations

. The exact solution is (1, 2, 3)^T. Which method gives better approximation to the exact solution?

Ques 8.

Determine the smallest roots of the following equation:

 to three significant digits using

Ques 9.

Regula-falsi method (ii) Newton Raphson method (iii) Bisection method (iv) Secant method

Ques 10.

Explain what is the role of interpolation in solving numerical problems?

Ques 11.

Express A³f, as a backward difference.

Ques 12.

Express A³fi as a central difference.

Ques 13.

For the following data develop difference table and find forward differences and backward differences

Ques 14.

By decinnial census, the population of a town was given below

Year (x) : 1971 1981 1991 2001 2011

Population (y): 112 132 158 189 226 (in thousands)

(i) Using Stirling's central difference formula, estimate the population for the year 2006

(ii) Using Newton's forward formula, estimate the population for the year 1992.

(iii) Using Newton's backward formula, estimate the population for the year 1980.

Ques 15.

If values of the function 

find the Lagrange's interpolation polynomial of f(x). Also, find f

Ques 16.

Find the values of the first and second derivatives of f(x) at x = 76 from the following table. Use 0(h2 ) forward difference method. Also, find Truncation Error (TE) and actual errors.

Ques 17.

Compute the value of the integral

 by using

Rectangular Rule (ii) Trapezoidal Rule and then (iii) Simpson's 1/3 Rule

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