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- (Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is:********************Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the above pattern.Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, the pattern generated is as follows: **** *** ** * * ** *** **** Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the preceding pattern.
- 4. The Fibonacci series: 0, 1, 1, 2,3,5,8,13,21... begins with terms 0 and 1 and has the property that each succeeding term is the sum of the two previous terms. Write a program containing a recursive function that computes and displays the nth Fibonacci number, given the value for n.Write a recursive function that returns true if the digits of a positive integer are in increasing order; otherwise, the function returns false. Also, write a program to test your function.Given two integers x snf y, the following recurrsive definition determined the greatest common divisor of x and y, Write gcd(xy). Write a recursive function, gcd, that takes two integers as parameters and returns the greatest commmon divisorof numbers.Also write a program to test your function. Write a recursive function,reverseDigits, that takes an integer as a parameter snd returns the number with the digits reversed. Also write a program to test your application.
- in c++ The Fibonacci number is the one in which each number is the sum of the two precedingnumbers. An example is shown below:0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...Write a recursive function that prints the first fifteen Fibonacci numbers. Your functionmust be recursive. Note that the first three Fibonacci numbers are 0, 1, 1, but after that ,the Fibonacci number is n = n - 1 + n - 2. Note that you will write only a function.Write a recursive function that returns the sum of the digits of an integer.int sumOfDigits(int x);Write a recursive function to compute the following series: m(i) = 1/2 + 2/ 3 + . . . + i/i + 1 Write a test program that prompts the user to enter an integer for i and displays m(i).
- 3. Write a recursion function that prints out message "This is a recursive function" recursively as long as user input n > 0. If n== 0, the message "This is the base case" is printed.A palindrome is any word, phrase, or sentence that reads the same forward and backward. Here are some well-known palindromes:Able was I, ere I saw ElbaA man, a plan, a canal, PanamaDesserts, I stressedKayakWrite a bool function that uses recursion to determine if a string argument is a palindrome. The function should return true if the argument reads the same forward andbackward. Demonstrate the function in a program.1. Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is:********************Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the above pattern. 2. A palindrome is a string that reads the same both forward and backward. For example, the string "madam" is a palindrome. Write a program that uses a recursive function to check whether a string is a palindrome. Your program must contain a value-returning recursive function that returns true if the string is a palindrome and false otherwise. Do not use any global variables; use the appropriate parameter.