Create a base class External_exam with protected member : marks( out of 100)Create a constructor to read the marks.Create another base class Internal_exam with private members: cat1,cat2Create a constructor to read cat1 and  cat2 marks(out of 50).Create a derived class exam from above 2 classes with member function : DA1,DA2,DA3Create a constructor to read DA1,DA2,DA3 marks(out of 10).Create  a member function to calculate the total mark T.T=(0.40*marks)+(0.15*cat1)+ (0.15*cat2)+ DA1,DA2,DA3.Internal marks is (0.15*cat1)+ (0.15*cat2)+ DA1,DA2,DA3External mark is 0.40*marksSample Input78 (marks)34(cat1)28(cat2)9(da1)9(da2)8(da3)Sample OutputInternal:35.30External:31.20Total:66.50

This problem seems to be a task for creating classes in Python. Here is the step-by-step solution:

# Base class External_exam
class External_exam:
    def __init__(self, marks):
        self._marks = marks  # protected member

# Base class Internal_exam
class Internal_exam:
    def __init__(self, cat1, cat2):
        self.__cat1 = cat1  # private member
        self.__cat2 = cat2  # private member

    # getter methods for private members
    def get_cat1(self):
        return self.__cat1

    def get_cat2(self):
        return self.__cat2

# Derived class exam
class Exam(External_exam, Internal_exam):
    def __init__(self, marks, cat1, cat2, da1, da2, da3):
        External_exam.__init__(self, marks)
        Internal_exam.__init__(self, cat1, cat2)
        self.da1 = da1
        self.da2 = da2
        self.da3 = da3

    def calculate_total_mark(self):
        internal = 0.15*self.get_cat1() + 0.15*self.get_cat2() + self.da1 + self.da2 + self.da3
        external = 0.40*self._marks
        total = internal + external
        return internal, external, total

# Sample Input
e = Exam(78, 34, 28, 9, 9, 8)
internal, external, total = e.calculate_total_mark()

# Sample Output
print("Internal: {:.2f}".format(internal))
print("External: {:.2f}".format(external))
print("Total: {:.2f}".format(total))

This code first defines the base classes External_exam and Internal_exam with their respective members and constructors. Then it defines the derived class Exam which inherits from both base classes and adds its own members and methods. The calculate_total_mark method calculates the total mark according to the given formula. The sample input and output demonstrate how to use these classes.

This problem is about creating classes and calculating marks in Python. Here is the step by step solution:

class External_exam:
    def __init__(self, marks):
        self._marks = marks

class Internal_exam:
    def __init__(self, cat1, cat2):
        self.__cat1 = cat1
        self.__cat2 = cat2

    def get_cat1(self):
        return self.__cat1

    def get_cat2(self):
        return self.__cat2

class Exam(External_exam, Internal_exam):
    def __init__(self, marks, cat1, cat2, da1, da2, da3):
        External_exam.__init__(self, marks)
        Internal_exam.__init__(self, cat1, cat2)
        self.da1 = da1
        self.da2 = da2
        self.da3 = da3

    def calculate_total_mark(self):
        internal = (0.15*self.get_cat1()) + (0.15*self.get_cat2()) + self.da1 + self.da2 + self.da3
        external = 0.40*self._marks
        total = internal + external
        return internal, external, total

# Sample Input
e = Exam(78, 34, 28, 9, 9, 8)
internal, external, total = e.calculate_total_mark()

# Sample Output
print("Internal: {:.2f}".format(internal))
print("External: {:.2f}".format(external))
print("Total: {:.2f}".format(total))

In this code, we first create the base classes External_exam and Internal_exam with their respective members and constructors. Then, we create the derived class Exam from these two base classes. In the Exam class, we have a member function calculate_total_mark to calculate the total mark. Finally, we create an instance of the Exam class with the sample input, calculate the total mark, and print the output.