Roorkee University has to send 10 professors to 5 centers for its entrance examination, 2 to each center. Two of the enters are in Roorkee and the others are outside. Two of the professors prefer to work in Roorkee while three prefer to work outside. In how many ways can this be made if the preferences are to be satisfied?

A library has 5 copies of one books 4 cpies each of two books , 6 copies each of three books and 1 copy each of eight books . In how many ways can all the books be arranged ?

In an assembly of 10 scholars , three are mathematicians and three are physicists , the others are both physicists and mathematicians . There are two rows containing 5 chairs and it is intended that all mathematicians are to be seated in one row and the physicsts in the other , the remaining scholars are to be seated in either row in the vacant positions left .In how many ways can all the scholars be seated ?

Two different books have 3 volumes for each and three other different books have 2 volumes for each . In how many different ways can these 12 volumes be arranged on a shelf , so that the volumes of the same books may remain side by side ?

(Transportaion problem) : There are two factories located one at place P and the other at place Q. From these locations, a certain commodity is to be delivered to each of the three depots situated at A,B and C. The weekly requirements of the depots are respectively 5,5 and 4 units of the commodity while the production capacity of the factories at P and Q are respectively 8 and 6 units. The cost of transportaion per unit is given below: How many units should be transported from each factory to each depot in order that the transportation cost its minimum. What will be the minimum transportation cost?

Kanchan has 10 friends among whom two are married to each other. She wishes to invite five of them for a party. If the married couples refuse to attend separately, then the number of different ways in she can invite five friends is a. ""^8C_5 b. 2xx ""^8C_3 c. ""^10 C_5-2xx ""^8C_4 d. none of these

Three friends invested ₹ 1,20,000, ₹ 1.50,000 and ₹ 1,10,000 respectively to purchase a bus. The first person is a driver and the other two are conductors. They decided to divide 2/5th of the profit among themselves in the ratio of 3 : 2 : 2 according to their work and the remaining in the ratio of their capitals. If they earn ₹29,260 in one month, find share of each of them.

A man has an antique pendulum clock of 1832 which bears the signature of the purchaser. He does not want to replace it in the fond memory of his great-grandparents. It ticks off one second in each side to side swing. It keeps correct time at 20^(@)C . The pendulum shaft is made of steel and its mass can be ignored as compared to the mass of the bob. Linear expansion coefficient of steel is 1.2xx10^(-5@)C^(-1) How many seconds will the clock gain or lose in a day at 10^(@)C ?