## CBSE Previous Year Solved  Papers  Class 12 Maths Delhi 2011

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 questions have been asked in previous Sets.

SECTION – A

1. State the reason for the relation R in the set {1,2,3} given by R = {(1,2), (2,1)} not to be transitive.

SECTION – B

11. Consider the binary operation * on the set {1, 2, 3, 4, 5} defined by a* b = min. {a, b). Write the operation table of the operation *.

16. Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm ?
Solution: Let r be the radius, h be the height and V be the volume of the sand cone.

Find the points on the curve x2 + y2 2x-3 = 0at which the tangents are parallel to x-axis.
Solution: When the tangent is parallel to x-axis

22. Probabilities of solving a specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem independently, find the probability that
(i) the problem is solved
(ii) exactly one of them solves the problem.
Solution: Given,

SECTION – C

24. Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.
Solution : Let length of rectangle be x and breadth of rectangle be y.

28. A factory makes tennis rackets*,and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hours of machine time and 1 horn1 of craftsman’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. If the profit on aracket and on a bat is Rs 20 and Rs  10 respectively, find the number of tennis rackets and circket bats that the factory must manufacture to earn the maximum profit. Make it as an L.P.P. and solve graphically.
Solution: Let x be the number of tennis rackets and y that of cricket bats produced in one day in the factory.

29. Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male ? Assume  that there are equal number of males and females.

### SET II

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

SECTION – A

SECTION – B

15. Formthe differential equation of the family of parabolas having vertex at the origin and axis along positive y- axis

SECTION – C

23. Bag I contains 3 red and 4 black balls and Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from Bag II.
Solution:

### SET III

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

SECTION – A

SECTION – B

SECTION – C

23. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.
Solution: Let E be the event that the man reports that six occurs in the throwing of a die and let S1 be the event that six occurs and S2 be the event that six does not occur,