A person always prefers to eat parantha and vegetable dish in his meal. How many ways can he makes his platter in a marriage party if there are three types of paranthas, four types of vegetable dish, three types of salads and two types of sauces? a. `3360` b. `4096` c. `3000` d. none of these

A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A while its takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs. 7 and screws B at a profit of Rs. 10 Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit ? Determine the maximum profit.

In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty is a. "^8P_6-2(6!) b. "^8P_6 c. "^8P_5(6!) d. none of these

A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for detts of type B is utmost half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by utmost 600 units . If the company makes profit Rs 12 Rs. 16 per doll respectively on dolls a and B, how many of each should be produced weekly in order to maximise the profit ?

A retired person wants to invest an amount upto Rs 20,000. His broker recommends investing in two types of bonds A and B, bond A yielding 10% return on the amount invested and bond B yielding 15% return on the amount invested. After some consideration he decides to invest atleast Rs 5,000 in bond A and not more than Rs 8,000 in bond B. He also wants to invest atleast as much in bond A as in bond B. How should he invest to maximise his return on investment?