## CBSE Previous Year Solved  Papers Class 12 Maths Delhi 2014

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

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

SECTION – A

SECTION – B

SECTION – C

23. Two schools P and Q want to award their selected students on the values of Discipline, Politeness and Punctually. The school P wants to award Rs x each, y each and Rs z each for the three respective values to its 3,2 and 1 students with a total award money of Rs 1,000. School Q wants to spend Rs 1,500 to award its 4,1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs 600, using matrices, find the award money for each value. Apart from the above three values, suggest one more value for awards.
Solution: Let the awards for Discipline, Politeness and Punctuality be Rs x, Rs y and Rs z respectively.

28. A dealer in rual area wishes to purchase a number of sewing machines. He has only Rs 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him Rs 360 and a manually operated sewing machine Rs 240. He can sell an electronic sewing machine at a profit of Rs 22 and a manually operated sewing machine at a profit of Rs 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit ? Make it as a LPP and solve it graphically.

29. A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a . spade. [6]

OR
From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution. ,
Solution: Let D be the event of drawing a defective bulb and X denote the variable showing the number of defective bulbs in 4 draws. Then
P(D)=5/15

### SET II

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

SECTION – A

SECTION-B

19. Prove the following using properties of determinants:

SECTION – C

### SET III

Note: Except for the following questions, AH the remaining question have been asked in previous Sets.

SECTION – A

SECTION -B

19. Using properties of determinants, prove the following:

SECTION – C