Three Questions are Compulsory and last question is optional.


1. (20 marks)
Input a range from user and print all the magic numbers in that range.
A number is magical if repeated adding of its digit gives 1. example 19 is magical
as 1 + 9 = 10, 1 + 0
= 1 hence magical. So is 991 as 9 + 9 + 1 = 19, 1 + 9 = 10, 1 + 0 = 1. However 224
is not.


2. (30 marks)
Write a program to produce the following Output

*        *        *        *        *        *
        *        *        *        *
                *        *
                  *


3.(50 marks)
The outstanding balance on a home loan Rs. 8,00000. Each year a 
payment of Rs 30000 is made which includes both interest and principal
repayment of the car loan. The monthly interest is calculated as (10/12)% of the
outstanding balance of the loan. After the interest is deducted the remaining part 
of the payment is used to payoff the loan. Using this information, write a C program
that produces a table indicating the beginning monthly balance, the interest payment, 
the principal payment, and the remaining loan balance after each payment is made. Your
output should resemble and complete the entries in the following table until the
outstanding loan balance is zero.

4.(Optional)
Input a positive number m (as double) and find its square
root.  Use the Newton-Raphson method for finding
successively better approximations to it.  In this method,
the approximation in the next step (denoted by X(n+1)) is a
function of the approximation in the current step (X(n)),
i.e., X(n+1) = f(X(n)).  For square root, the estimates are
updated as:
X(n+1) = X(n)/2 + m/ (2 * X(n))
Assume that the first term is m, i.e., X(0) = m.

Continue the estimation till the difference between two
successive approximations is less than 0.01. Print the
square root thus obtained.

Finally, compare your value with the value obtained using
the sqrt() function. Print the difference also.