(a) Country A has twice the GDP of country B. In the future, the annual growth rates of these two countries are expected to be 1% and 4%, respectively. After how many years will the GDP of country B exceed that of country A?

(b) The sum of $4000 is borrowed from a bank at a rate of 4.8% interest compounded monthly. The loan is repaid in monthly instalments of $x. Show that at the end of n months, the outstanding debt is given by 4000(1.004) n - 250x (1.004n - 1). (i) How many months would it take to repay the loan if x = 100? (ii) What should the monthly repayment be if the debt is to be cleared after 12 months? (iii) Describe briefly what happens to the outstanding debt when x = 16.

12 'one rupee' coins are distributed at random among 5 beggars A, B, C, D and E. Find the probability that: (i) They get 4, 2, 0, 5 and 1 coins respectively. (ii) Each beggar gets at least two coins. (iii) None of them goes empty handed