Question 1

Find floating point representation, if possible normalized, in the 4-digit mantissa, two digit exponent, if necessary use approximation for each of the following numbers: (i) 27.94 (ii) -0.00943 (iii) -6781014 (iv) 0.0644321 Also, find absolute error, if any, in each case. (b) Convert the decimal in

Accepted Answer

This response comprehensively addresses numerical techniques as applied to floating-point representation, binary conversion, and floating-point arithmetic, aligning with concepts typically covered in BCS-054. It details the process of converting decimal numbers into normalized floating-point format with a specified mantissa and exponent precision, along with calculating associated absolute errors. Furthermore, it demonstrates two distinct methods for converting negative decimal integers to their

Question 2

Solve the system of equations 2x+y+z=3, x+3y+3z=4, x-4y+2z=9 using Gauss elimination method with partial pivoting. Show all the steps. (b) Perform four iterations (rounded to four decimal places) using (i) Jacobi Method and (ii) Gauss-Seidel method, for the following system of equations.

Accepted Answer

This response provides a comprehensive solution to the given system of linear equations using both direct and iterative numerical techniques. Part (a) employs the Gauss elimination method with partial pivoting to find the exact solution, detailing each step of row operations and back substitution. Part (b) demonstrates the application of the Jacobi and Gauss-Seidel iterative methods for the same system, performing four iterations and highlighting the characteristics of each approach. It's import

Question 3

Determine the smallest positive root of the following equation: f(x) = x^3 – 9x^2- x + 9 = 0 to three significant digits using different methods:

Accepted Answer

The problem requires finding the smallest positive root of the equation f(x) = x³ – 9x² – x + 9 = 0 to three significant digits using various numerical methods. First, we identify the function f(x) and its derivative f'(x) where required. We also need to determine an appropriate initial interval or guess for each method.

The given equation can be factored as f(x) = x²(x - 9) - 1(x - 9) = (x² - 1)(x - 9) = (x - 1)(x + 1)(x - 9). The roots are x = 1, x = -1, and x = 9. The smallest positive root

Question 4

Find Lagrange's interpolating polynomial for the following data. Hence obtain the value of f(4). (b) Using the inverse Lagrange's interpolation, find the value of x when y=3 for the following data:

Accepted Answer

Answer available — download the full PDF for complete details.

Question 5

The population of a country for the last 25 years is given in the following table: (Year (x): 1995, 2000, 2005, 2010, 2015; Population in lakhs (y): 678, 1205, 1855, 2745, 3403) (b) Derive the relationship for the operators δ in terms of E.

Accepted Answer

This response addresses the estimation of population using various interpolation formulas and derives the relationship between difference operators. The problem involves analyzing a given population dataset and applying numerical techniques taught in BCS-054 to predict values within and near the given range.

Sub-question (a) focuses on practical application of Newton's forward, Newton's backward, and Stirling's central difference interpolation formulas to estimate population at specific years.

Question 6

Find the values of the first and second derivatives of y = f(x) for x=2.1 from the following table. (Data: x: 2, 2.5, 3, 3.5; y: 8.7, 12.7, 16.8, 20.9)

Accepted Answer

This question requires us to compute the first and second derivatives of a function y = f(x) at a specific point, x=2.1, using a discrete set of data points. We will employ two standard numerical differentiation techniques from the BCS-054 course: the Forward Difference method and Lagrange's Interpolation method. Each method provides an approximation of the derivatives based on the underlying interpolating polynomial of the given data.

We will perform step-by-step calculations for both parts,

Question 7

Compute the value of the integral ∫(from 0 to 8) (4x^4 + 5x^3 + 6x + 5) dx. By taking 8 equal subintervals. Compare the result with the actual value.

Accepted Answer

This response addresses the computation of a definite integral using two common numerical integration techniques: the Trapezoidal Rule and Simpson's 1/3 Rule, as per the BCS-054 'Computer Oriented Numerical Techniques' curriculum. We will integrate the function f(x) = 4x⁴ + 5x³ + 6x + 5 from 0 to 8, using 8 equal subintervals. After computing the approximate values, we will compare them with the analytically derived exact value of the integral.

First, let's calculate the actual value of the int

BCS-054 Solved Assignment — January 2026 / July 2025

Computer Oriented Numerical Techniques | IGNOU Bachelor of Computer Applications (BCA)

BCS-054—January 2026 / July 2025

Computer Oriented Numerical Techniques

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BCS-054 Assignment Questions — January 2026

QQ2. Solve the system of equations 2x+y+z=3, x+3y+3z=4, x-4y+2z=9 using Gauss elimination method with partial pivoting. Show all the steps. (b) Perform four iterations (rounded to four decimal places) using (i) Jacobi Method and (ii) Gauss-Seidel method, for the following system of equations.

QQ3. Determine the smallest positive root of the following equation: f(x) = x^3 – 9x^2- x + 9 = 0 to three significant digits using different methods:

QQ4. Find Lagrange's interpolating polynomial for the following data. Hence obtain the value of f(4). (b) Using the inverse Lagrange's interpolation, find the value of x when y=3 for the following data:

QQ5. The population of a country for the last 25 years is given in the following table: (Year (x): 1995, 2000, 2005, 2010, 2015; Population in lakhs (y): 678, 1205, 1855, 2745, 3403) (b) Derive the relationship for the operators δ in terms of E.

QQ6. Find the values of the first and second derivatives of y = f(x) for x=2.1 from the following table. (Data: x: 2, 2.5, 3, 3.5; y: 8.7, 12.7, 16.8, 20.9)

QQ7. Compute the value of the integral ∫(from 0 to 8) (4x^4 + 5x^3 + 6x + 5) dx. By taking 8 equal subintervals. Compare the result with the actual value.