PQRSTU is a regular hexagon drawn on the ground. Prashant stands at P and he starts jumping from vertex to vertex beginning from P. From any vertex of the hexagon except S, which is opposite to A, he may jump to any adjacent vertices. When he reaches S, he stops. Let Sn be the number of distinct paths of exactly n jumps ending at S. What is the value of S2k, where k is an integer?
Correct Answer : A
A total of 15 teams participated in a tournament. Each team plays with every other team exactly once. A team gets 3 points for a win, 2 points for a draw and 1 point for a loss. The team which scored the least got 21 points. The scores of all the teams were distinct and at least one match played by winning team was drawn. Which of the following is always true for the winning team?
A shop sells two kinds of rolls- egg roll and mutton roll. Onion, tomato, carrot, chili sauce and tomato sauce are the additional ingredients. You can have any combination of additional ingredients, or have standard rolls without any additional ingredients subject to the following constraints:
(a) You can have tomato sauce if you have an egg roll, but not if you have a mutton roll.
(b) If you have onion or tomato or both you can have chilli sauce, but not otherwise.
How many different rolls can be ordered according to these rules?
Kartik's mother asked him to get the vegetables, milk and butter from the market and gave him the money in the denominator of 1 Rupee, 2 Rupee and 5 Rupee coins. Kartik first goes to the grocery shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins in return receives the same number of 1 Rupee coins. Next he goes to the dairy shop to buy milk and butter and gives all 2 Rupee coins and in return get thirty 5 Rupee coins, which increase the number of five rupee coins by 75% more than the original number. If the number of 1 rupee coins now is 50, the number of 1 rupee and 5 rupee coins originally were: