1. (i) (a) True
(b) False
(c) False
(d) True

2. The code will not compile (2 marks), because f is not static.
1 mark for "1 , 1", which is what the code would output if f were made static.

3. Note: Thank you to those who have pointed out that the question is ambiguous, we will take this into account when grading. Full marks will be given for a correct answer to one interpretation of the question.
(a)
public class SimpleAccount extends Account {
    private double balance;
    
    public SimpleAccount(int accountNo, double balance) {
        super(accountNo);
        this.balance = balance;
    }
    
    @Override
    public void deposit(double amount) {
        balance += amount;
    }
    
    @Override
    public boolean withdraw(double amount) {
        if (amount <= balance) {
            balance -= amount;
            return true;
        } else {
            return false;
        }
    }
    
    @Override
    public double getBalance() {
        return balance;
    }
    
    @Override
    public void endOfMonth() {}
}

(b)
public class CheckingAccount extends Account {
    private double balance;
    private double overdraftLimit;
    
    public CheckingAccount(int accountNo, double balance, double overdraftLimit) {
        super(accountNo);
        this.balance = balance;
        this.overdraftLimit = overdraftLimit;
    }

    @Override
    public void deposit(double amount) {
        balance += amount;
    }

    @Override
    public boolean withdraw(double amount) {
        if (balance - amount >= -overdraftLimit) {
            balance -= amount;
            return true;
        } else {
            return false;
        }
    }

    @Override
    public double getBalance() {
        return balance;
    }

    @Override
    public void endOfMonth() {
        balance -= 100;
    }
}

(c)
public class TransactionAccount extends Account {
    private double balance;
    private int transactions;
    
    public TransactionAccount(int accountNo, double balance) {
        super(accountNo);
        this.balance = balance;
        transactions = 0;
    }

    @Override
    public void deposit(double amount) {
        balance += amount;
        transactions++;
        if (transactions > 4) {
            balance -= 50;
        }
    }

    @Override
    public boolean withdraw(double amount) {
        if (amount <= balance) {
            balance -= amount;
            transactions++;
            if (transactions > 4) {
                balance -= 50;
            }
            return true;
        } else {
            return false;
        }
    }

    @Override
    public double getBalance() {
        return balance;
    }

    @Override
    public void endOfMonth() {
        balance *= 1.003;
        transactions = 0;
    }
}

4. (a) 11
(b) It outputs the maximum element of a.

5. 
boolean isLuckyHelper(int p, int k) {
    if (p <= k) {
        return true;
    }
    if (p % (k + 1) == 0) {
        return false;
    }
    return isLuckyHelper(p - p / (k + 1), k + 1);
}

boolean isLucky(int n) {
    return isLuckyHelper(n, 1);
}

An alternative non-recursive solution:

private static boolean isLucky(int n) {
    boolean[] deleted = new boolean[n+1];
    for (int i = 0; i <= n; i++) {
        deleted[i] = false;
    }
    
    for (int step = 2; step <= n; step++) {
        // Delete every "step"th number
        int count = 0;
        
        for (int i = 1; i <= n; i++) {
            // Count step - 1 "false"s, then turn the "step"th false into a true
            if (! deleted[i]) {
                count ++;
                if (count == step) {
                    deleted[i] = true;
                    count = 0;
                }
            }
        }
    }
    
    return ! deleted[n];
}

There are many other possible solutions.