JMO questions STD V / STD VI

1.       You are given that 47658 x 39876 = 1900410408. Without directly multiplying, use the given information to solve the following question:

52.342 x 0.60124

2.       Find the value of 19999 x 299999 using the information 19999 = 20000 – 1 and 299999 = 300000 – 1.

3.       Consider the number 12345.....11121314........566. Find the 500^th digit.

                                                                                                                                  

Find 4 fractions which lie between 2/3 and 3/4  such that they divide the fractions in 5 equal parts.