Three Questions are Compulsory and last question is optional.


1.(20 marks)
Input a range from user and print all the narcissistic number in that range. 
Hint: A number is called narcissistic if each of its digits raised to the power of
the number of digits 
equals the number.
Example : 153 is a narcissistic number since 1^3 + 5^3 + 3^3
= 1 + 125 + 27 = 153.
1634 = 1^4 + 6^4 + 3^4 + 4^4


2.(30 marks) 
Write a Program to Produce Following Output

                                1
                        1                1
                1                2                1
        1                3                3                1
1                4                6                4                1


3.(50 marks)
The expansion of a steel bridge as it is heated to a final Celsius temperature, T_f, 
from an initial Celsius temperature, T_i, can be approximated using the formula

increase in length = a  * L * (T_f- T_i)

where a is the coefficient of expansion, which for steel is 11.7 E-6, and L is the 
length of the bridge at temperature T_i. Using this formula, write a C program that 
displays a Table of expansion lengths for a steel bridge that is 7365 feet long at zero
degrees Celsius, as the temperature increases to 40 degrees in five-degree increments.


4. (Optional)
Input a positive number m (as double) and find its cube
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 cube root, the estimates are
updated as:
X(n+1) = (2 * X(n))/3 + m/ (3 * (X(n)* 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
cube root thus obtained.