The following recursive method is causing an exception because the base case is missing. This method is suppose to display the content of an array backward. For example If the array num contains 1 2 3 4 5 6 then the call print(num, 5) should display: 6 5 4 3 2 1 public static void print(int[] a, int index) {        System.out.println(a[index]);        print(a, index -1); } Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: Index -1 out of bounds for length 5

1. Write a recursive method expFive(n) to compute y=5^n. For instance, if n is 0, y is 1. If n is 3, then y is 125. If n is 4, then y is 625. The recursive method cannot have loops. Then write a testing program to call the recursive method. If you run your program, the results should look like this: > run RecExpTest Enter a number: 3 125 >run RecExpTest Enter a number: 3125 2. For two integers m and n, their GCD(Greatest Common Divisor) can be computed by a recursive function. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Once m is 0, the function returns n. Once n is 0, the function returns m. If neither is 0, the function can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n. Although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. Meaning your code needs to follow the given algorithm. Then…

1. The sorted values array contains 16 integers 5, 7, 10, 13, 13, 20, 21, 25, 30,32, 40, 45, 50, 52, 57, 60. Indicate the sequence of recursive calls that are made tobinaraySearch, given an initial invocation of binarySearch(32, 0, 15).show only the recursive calls. For example, initial invocation is binarySearch(45,0,15)where the target is 45, first is 0 and last is 15.

The following recursive method get Number Equal searches the array x of 'n integers for occurrences of the integer val. It returns the number of integers in x that are equal to val. For example, if x contains the 9 integers 1, 2, 4, 4, 5, 6, 7, 8, and 9, then getNumberEqual(x, 9, 4) returns the value 2 because 4 occurs twice in x. public static int getNumberEqual(int x[], int n, int val) { if (n< 0) ( return 0; } else { if (x[n-1) == val) { return getNumberEqual(x, n-1, val) +1; } else { return getNumber Equal(x, n-1, val); } // end if ) // end if } // end get Number Equal Demonstrate that this method is recursive by listing the criteria of a recursive solution and stating how the method meets each criterion.