Three business entities X Ltd, Y Ltd. and Z Ltd, with 4, 3 and 5 employees respectively, merged into XYZ Ltd in order to jointly raise the capital for setting up a new modern production plant in Jaipur. After two years, on the question of management decisions on the new venture at Jaipur, the employees started adopting differing viewpoints and began to quarrel among themselves. Given the fact that there is no quarrel among the employees of the erstwhile (i.e. former) X Ltd, Y Ltd and Z Ltd, what could be the maximum number of quarrels that can take place within XYZ Ltd?
Correct Answer : C
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?
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?