The coach of a cricket team of M.K. Nagar High school buys 3 bats and 6 balls for Rs. 3900. Later he buys one more bat and 2 balls for Rs. 1300.

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman's time in its making while a cricket bat takes 3 hours of machine time and 1 hour of craftman's time. In a day , the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman's time. (i) What number of rackets and bats must be made if the factory is to work at full capacity ? (ii) If the profit on a racket and on a bat is Rs 20 and Rs. 10 respectively, find the maximum profit of the factor when it works at full capacity.

A company produes two types of cricket ball A and B. the production time of one ball of type B is double the type A (Time in units) . The company has a time to produce a maximum 2000 balls per day. The supply of raw material is sufficient for the production of 1500 balls (both A and B) per day. the company wants to make maximum profit by making profit fo Rs 3 from a ball of tye A and Rs. 5 from a ball of type b. Then (i) By defining suitable variables, write the objective function. (ii) Write the constraints. (iii) How many balls should be produced in each type per day in order to get maximum profit ?

Three balls marked with 1, 2 and 3 are placed in an urn. One ball is drawn, its number is noted, then the ball is returned to the urn. This process is repeated and then repeated once more. Each ball is equally likely to be drawn on each occasion. If the sum of the number noted is 6, then the probability that the ball numbered with 2 is drawn at all the three occassion, is

Consider a game where the player tosses a six sided fair die. If the face that comes up is 6, the player wins Rs. 36, otherwise he loses Rs. k^(2) , where k is the face that comes up k = {1, 2, 3, 4, 5}. The expected amount to win at this game in Rs. is