All answers with necessary code for separate Java files please:

$1.$ Write a recursive function to find the sum of the first n natural numbers.

Example: For $\backslash ($ n$=5\backslash ),$ the result should be $\backslash (1+2+3+4+5=15\backslash ).$

$2.$ Write a recursive function to count the number of digits in an integer.

Example: Input: $12345-$ Output: $5.$

$3.$ Write a recursive function to check if a given array is sorted in ascending order.

Example: Input: $\backslash ([1,2,3,4]\backslash$rightarrow $\backslash )$ Output: true.

$4.$ Write a recursive function to compute $\backslash ($ a$^\{$b$\}\backslash )($a raised to the power of b$).$

Example: Input: $\backslash ($ a$=2,$ b$=3\backslash$rightarrow $\backslash )$ Output: $8.$

$5.$ Write a recursive function to convert a binary number $($given as a string$)$ to its decimal equivalent.

Example: Input: $"101"\backslash (\backslash$rightarrow $\backslash )$ Output: $5.$

$6.$ Create a base class Shape with a method area$().$ Implement subclasses like Circle and Rectangle to override the area$()$ method.

$7.$ Multiply two matrices entered by the user.

$8.$ Input student marks for $5$ subjects and calculate the total, percentage, and grade using conditions. Work with arrays, loops, and conditions to process multiple inputs.

$9.$ Check if a given string or number reads the same backward as forward. Manipulate strings and numbers, and use loops or recursion.

$10.$ Check if a given number is prime or not.

$11.$ Basic arithmetic calculator: Input two numbers and an operator $\backslash ((+,-,/,*)\backslash ),$ then perform the operation and print the result.

$12.$ Write a program to search for an element in an array.

$13.$ Write a program to find the transpose of the given matrix.

$14.$ Write a program to find the second largest element in a array.

$15.$ Write a program to find if the character is a vowel or a consonant.

$16.$ Write a program to calculate Electricity Bill Calculation.

Write a program to calculate Electricity Bill Calculation.

Input: Units $=250$

Output: Bills: $1050$

$<mtext></mtext><mn>1</mn><mn>0</mn><mn>0</mn>$ units: $1\mathrm{.}5/$unit

$100-200$ units: $2\mathrm{.}5/$unit

$200+$ units: $3\mathrm{.}5/$unit

$17.$ Check if a Year is Both Leap Year and Century Year. Input: $2000,$ Output: Leap and Century year.

$18.$ Write a program to check check Divisibility by $2,3,$ and $5.$

$19.$ Write a program to round the number to the nearest integer using Math.

$20.$ Calculate hypotenuse of right angle triangle, using Math.