Within a new class, LX5, write the following methods:

1. Write a method that accepts a parameter int named max and displays the sum of all integers from 1 to max. However, if max < 1 or max > 20000, the method will instead display the message "Invalid input!".

2. Write a method that accepts a Scanner object and an int named size as parameters and requests the user to enter an input that has exactly size characters. The method should keep asking for inputs until the user enters a valid input.

3. Write a method that accepts as parameters a String s and a char c. The method will return the number of times that c appears in s.

4. Write a method that accepts a parameter int named value and returns a String containing the binary equivalent of the number. For example, the number 8 would be converted to "1000" and 9 would be converted to "1001". You can assume value is positive. Hint: use a loop to successively divide value by 2 any remainder will be the binary digit for that power of 2.