**CBSE HOT Mathematics Questions for Class 12th Board Exam 2013, given here.**

9. How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?

10. Doctor recommended a diet for Ram ( a sick person) that contain at least 35000 units of vitamins, 55 units of minerals and 1800 calories. Two foods M and N are available at a cost of Rs. 6 and Rs. 5 per unit respectively. One unit of food M contains 200 units of vitamins, 1 unit of minerals and 40 calories, whereas 1 unit of food N contains 100 units of vitamins, 2 units of minerals and 40 calories. Find what combination of foods M and N should be used to have least cost, satisfying the requirements. Make it an LPP and solve it graphically.

12. A company sells two different products A and B. The two products are produced in a common production process which has a total capacity of 500 man hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The demand in the market show that the maximum number of units of A that can be sold is 70 and that of B is 125. Profit on each unit of A is Rs. 20 and on B is Rs. 15. How many units of A and B should be produced to maximize the profit? Form an L.P.P. and solve it graphically.