(b) Perform four iterations (rounded to four decimal places) using

(i) Jacobi Method and

(ii) Gauss-Seidel method for the following system of equations.

With x ⁽⁰⁾ = (0, 0, 0)^T . The exact solution is (3, 2, 1)^T

Which method gives better approximation to the exact solution?

Solve the system of equations

2x + y + 5z = 18

5x + 3y – 2z = 2

x – 6y + 2z = 1

using Gauss elimination method with partial pivoting. Show all the steps

What is a truncation error? How can Taylor's series be used to determine truncation error? Explain with the help of an example.

Find the Maclaurin series for f(x) = e^2x at x=0. Use first four terms of this series to compute the value of the function at any value of x. Also find the bounds of truncation error for such cases.

What is the meaning of the term "Subtractive Cancellation"? Explain with the help of an example. How is subtractive cancellation related to or different from an Unstable Algorithm? Explain with the help of an example.

(a) Use the eight-decimal digit floating point representation as given in your Block 1, Unit 1, Section 1.3.1 page 29 to perform the following operations:

(i) Represent 0.000001235432 and 257890000012 as floating point numbers in normalised form using chopping for first number and rounding for second number.

(ii) What is the absolute and relative error in the representation of the two numbers given above?

(iii) Using the floating point representation, perform an addition of the two numbers given above. What is the error in the resulting number?

(iv) Using the floating point representation, multiply the first number and second number. Convert the result into normalized form in the given format.

(v) Take the first number as 0.00000000000003234 and assume any second number to demonstrate the concept of overflow or underflow for the given representation. (You may assume any second number to demonstrate overflow or underflow).

(vi) What is use of bias in binary floating point representation. Explain the concept of bias with the help of an example for binary floating point numbers.

Trade Union.

Concept of Kinship

Gender and Sex

Concept of Social class

Concept of Subaltern

How is the western notion of secularism different from the Indian?

Discuss the attributional approach to the study of caste in India.

Discuss the contributions of the British administrators in colonial India.

Describe the socio-economic and political status of Tribals in India with suitable examples.

What do you understand by Indology? How did it help the early sociologists?

Create an applet which take a number as input and display whether it is prime number or not. Use appropriate components, layout and formatting in your program.

Write a program in java to store a given paragraph in a text file. Make suitable provisions of exceptions handling in your program.

Write a java program to create two threads and using setName method assign name to them also using setPriority method assign priority to those threads. Make necessary assumptions.

Write java program to find simple interest on a Saving Account. Define appropriate class, constructor and methods in your program. Make necessary assumptions.