## CBSE Previous Year Solved  Papers Class 12 Maths Outside Delhi 2013

Time allowed: 3 hours                                                                                          Maximum Marks : 100
General Instructions:

1. All questions are compulsory.
2. Please check that this question paper contains 26 questions.
3. Questions 1-6 in Section A are very short-answer type questions carrying 1 mark each.
4. Questions 7-19 in Section B are long-answer I type questions carrying 4 marks each.
5. Questions 20-26 in Section C are long-answer II type questions carrying 6 marks each.
6. Please write down the serial number of the question before attempting it.

### SET I

SECTION – A

SECTION – B

SECTION – C

27. In a hockey match, both teams A and B scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not. [6]
Solution: Probability of getting a six by the captains of both the teams A and B is
P(A) = 1/6

28.A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 and 17 units of workers (male and female) and capital respectively which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce one unit of B. If A and B are priced at Rs 100 and Rs 120 per unit respectively how should he use his resources to maximize the total revenue ? Form the above as an LPP and solve graphically.
Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate ? [6]
Solution: Let x units of the goods A and y units of goods B be produced to maximize the total revenue. Then the total revenue is Z = 100x + 120y. This is a linear function which is to be maximized. Hence it is the objective function. The constraints are as per the following table:

29. The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to keep the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others using matrix method, find the number of awardees of each category. Apart from these values namely honesty, cooperation and supervision, suggest one more value which the management of the colony must include for awards.[6]

### SET II

Note: Except for the following questions, All the remaining questions have been asked in previous set.

SECTION – A

SECTION – B

SECTION – C

### SET III

Note: Except for the following questions, All the remaining questions have been asked in previous sets.

SECTION – A

SECTION – B