IGNOU BCA Computer Oriented Numerical Technique Previous Year Unsolved Papers BCS 054 E-Book

Manish Soni

• Herausgeber: Poorav Publications
• Kategorie: Wissenschaft und neue Technologien
• Serie: IGNOU BCA Unsolved Paper Books Series
• Sprache: Englisch

Seitenzahl: 51

Veröffentlichungsjahr: 2024

Beschreibung

Numerical techniques form an integral part of computer science education, providing students with the tools to solve complex mathematical problems using algorithmic approaches. Understanding these techniques is essential for developing efficient, accurate, and logical problem-solving abilities. In recognition of their importance, the Indira Gandhi National Open University (IGNOU) has included this subject as a core component of the BCA curriculum, ensuring students build a solid foundation in computational mathematics.
"IGNOU BCA Computer Oriented Numerical Technique Previous Year Unsolved Papers BCS 054" has been carefully compiled to help students enhance their preparation through practice with real exam questions. This collection of previous years' unsolved question papers encourages independent thinking, sharpens analytical skills, and reinforces conceptual understanding. By working through these papers, learners can familiarize themselves with the exam format, identify key topics, and assess their readiness—making this book a practical and essential resource for academic success in BCS-054.

Leseprobe

IGNOU BCA Computer Oriented Numerical Technique Previous Year Unsolved Papers BCS 054

Manish Soni

Preface

Numerical techniques form an integral part of computer science education, providing students with the tools to solve complex mathematical problems using algorithmic approaches. Understanding these techniques is essential for developing efficient, accurate, and logical problem-solving abilities. In recognition of their importance, the Indira Gandhi National Open University (IGNOU) has included this subject as a core component of the BCA curriculum, ensuring students build a solid foundation in computational mathematics.

"IGNOU BCA Computer Oriented Numerical Technique Previous Year Unsolved Papers BCS 054" has been carefully compiled to help students enhance their preparation through practice with real exam questions. This collection of previous years' unsolved question papers encourages independent thinking, sharpens analytical skills, and reinforces conceptual understanding. By working through these papers, learners can familiarize themselves with the exam format, identify key topics, and assess their readiness—making this book a practical and essential resource for academic success in BCS-054.

Table of Contents

Preface

Chapter 1: Term-End Examination, December- 2013

Chapter 2: Term-End Examination, December- 2014

Chapter 3: Term-End Examination, June- 2015

Chapter 4: Term-End Examination, December- 2015

Chapter 5: Term-End Examination, June- 2016

Chapter 6: Term-End Examination, December- 2016

Chapter 7: Term-End Examination, June- 2017

Chapter 8: Term-End Examination, December- 2017

Chapter 10: Term-End Examination, June- 2018

Chapter 11: Term-End Examination, December- 2018

Chapter 12: Term-End Examination, June- 2019

Chapter 13: Term-End Examination, December- 2019

Chapter 14: Term-End Examination, June- 2020

Chapter 15: Term-End Examination, February- 2021

Chapter 16: Term-End Examination, June- 2021

Chapter 17: Term-End Examination, December- 2021

Chapter 18: Term-End Examination, June- 2022

Chapter 20: Term-End Examination, December- 2022

Chapter 21: Term-End Examination, June- 2023

BACHELOR OF COMPUTER APPLICATIONS (BCA) (REVISED)

Chapter 1: Term-End Examination, December- 2013

BCS-054: COMPUTER ORIENTED NUMERICAL TECHNIQUES

Time: 3 Hours

Maximum Marks:100

Note: (i) Simple (but not scientific) calculator is allowed during the examination.

(ii) Question No. 1 is compulsory. Attempt any three from the next four questions.

1. (a) Using 8-decimal digit floating-point representation (4 digits for mantissa, 2 digits for exponent, and one each for sign of exponent and mantissa), represent the following numbers in normalized floating-point form:

(i) 89.36

(ii) –0.00004375

(iii) 87604 (use chopping, if required)3

(b) Find the sum of two floating numbers:

(c) Find the product of the two numbers in (b) above.2

(d) What is underflow? Give an example of multiplication in which underflow occurs.3

(e) Write the following system of linear equations in matrix form:

5x – 9y =14

(f) Solve the following system of linear equations using the Gauss elimination method:

3x + 4y =11

(g) Find an interval in which the following equation has a root:

(h) Write the formula used in the Newton-Raphson method for finding the roots of an equation.3

(i) Write the expressions obtained by applying each of the following operators to f(x), for some h:

(i) δ (ii) E (iii) µ3

(j) Write Δ and δ in terms of E.2

(k) State the following two formulas for interpolation:

(i) Newton’s Forward difference formula

(ii) Stirling’s formula3

(l) Construct a difference table for the following data:

2

(m) From the Newton’s Forward difference formula asked in part k(i), derive the formula

for finding the derivative of a function f(x) at   .3

(n) State the Trapezoidal rule for finding the integral (x) dx .3

(o) Define each of the concepts with a suitable example:

(i) Degree and order of a differential equation

(ii) Initial Value Problem4

2.(a) Briefly discuss how zero is represented as a floating-point number for the 8-decimal digit

representation mentioned in Q. No. 1(a).4

(b) For each of the following numbers, find the floating-point representation, if possible normalized, using rounding, if required. The format is 8-decimal digits as mentioned under Q. No. 1(a):

(i) 7854302

(ii) 2/3

Find absolute error, if any, in each case.6

BACHELOR OF COMPUTER APPLICATIONS (BCA) (REVISED)

Chapter 2: Term-End Examination, December- 2014

BCS-054: COMPUTER ORIENTED NUMERICAL TECHNIQUES

Time: 3 Hours

Maximum Marks:100

Note: (i) Simple (but not scientific) calculator is allowed during the examination.

(ii) Question No. 1 is compulsory. Attempt any three from the next four questions.

1.(a) Using 8-decimal digit floating-point representation (4 digits for mantissa, 2 for exponent, and

one each for sign of exponent and mantissa), represent the following numbers in normalized

floating point form (use rounding, if required):

(i) 9561

(ii) -74.794

(iii) -0.007263

(b) What is an overflow? Give an example involving the addition of numbers in which

overflow occurs.3

(d) Find the product of the two numbers given in question no. 1(c) above.2

(e) Write the following system of linear equations in matrix form:

-8x + 6y =13

(f) Solve the following system of linear equations using the Gauss Elimination method:

4x + 3y =1

(g) Find an interval in which the following equation has a root:

(h) Write the formula used in the Regula-Falsi method for finding the roots of an equation.3

(i) Write the expressions obtained by applying each of the operators to f(x), for some h:

(i) Δ (ii) (iii) D3

(j) Write each of V and δ in terms of E.2

(k) State the following two formulas for interpolation:

(i) Newton’s Backward difference formula

(ii) Stirling’s formula3

(l) Construct a difference table for the following data:

2

(m) From Newton’s Backward difference formula in part k(i), derive the formula for finding the derivative of a function f(x) at  x0 .3

(n) State Simpson’s (1/3) rule for finding the value of the integral  (x) dx.3