1.A box contains 100 balls of different colours:28 red,17 blue,21 green,10 white, 12 yellow and 12 black.What is the smallest no. 'n' such that any n balls drawn from the box will contain at least 15 balls of the same colour.
2.what is the remainder when ((3^2016)+(5^2016)) is divided by 13?
3.There are three coloured pairs of exactly identical spherical balls.2 are red,2 are blue,and 2 are green.In each same coloured pair ,one ball is lighter and all lighter balls have equal weight,also all heavier balls have equal weight.Identify all lighter bals by using a beam balance only twice.
4.once a king thought to check the wisdom of his ministers.So he took help of his goldsmith.The king ordered to mint 1000 gold coins , each weighing 10gm of pure gold ,and to make 10 bags of it,each containing 100 gold coins. The goldsmith prepared according to the order and used pure gold for it,did not mix any impurites! But he prepared 100 gold coins each weighing 9 gm,and put them in a bag .After finishing the work,he went to the king and handed over all 10 bags.The goldsmith was carrying a beam balance,which can measure from 1 gm to 750 gm.
Then the king told the situation to the ministers and asked to identify the bag carrying the counterfeit coins ,by using the beam balance only once! Help the ministers.
hope it is sufficient.
enjoy solving those :)