**CBSE Previous Year Solved Papers Class 12 Maths Delhi 2012**

**Time allowed: 3 hours Maximum Marks : 100 **

**General Instructions:**

**All questions are compulsory.****Please check that this question paper contains 26 questions.****Questions 1-6 in Section A are very short-answer type questions carrying 1 mark each.****Questions 7-19 in Section B are long-answer I type questions carrying 4 marks each.****Questions 20-26 in Section C are long-answer II type questions carrying 6 marks each.****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. If a line has direction ratios 2, -1, – 2, then what are its direction cosines ?**

**SECTION – B**

**12. How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%? [4]**

**SECTION – C**

**23. Find the equation of the plane determined by the points A (3, -1,2), B (5,2,4) and C (-1, -1,6) and hence find the distance between the plane and the point P (6,5,9). [6]**

**24. Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain “A” grade and 20% of day scholars attain ‘A’ grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an ‘A’ grade, what is the probability that the student is a hostler ? [6]**

**25. A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs 17.50 per package on nuts and Rs 7 per package of bolts. How many packages of each should be produced each day so as to maximize his profits if he operate his machines for at the most 12 I hours a day? Form the above as a linear programming problem and solve it graphically.**

**27. Using the method of integration, find the area of the region bounded by the lines 3x – 2y + 1 = 0. [6]**

**28. Show that the height of a closed right circular cylinder of given surface and maximum volume, is equal to the diameter of its base. [6]**

**29. Using matrices, solve the following system of linear equations:**

** x-y + 2z =7**

** 3x + 4y – 5z = – 5**

** 2x – y + 3z =12**

**SET II**

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

**SECTION – A**

**SECTION – B**

**SECTION -C**

**28. A girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2,3 or 4, she tosses a coin two times and notes the number of heads obtained. If she obtained exactly two heads, what is the probability that she threw 1,2,3 or 4 with the die? [6]**

**29. Using the method of integration, find the area of the region bounded by the following lines 3x – y – 3 = 0, 2x + y -12 = 0, x – 2y -1 = 0.**

**SET III**

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

**SECTION – A**

**SECTION – B**

**SECTION – C**

**28. Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. Two balls are transferred at random from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred balls were both black. [6]**

**29. Using the method of integration, find the area of the region bounded by the following lines 5x – 2y -10 = 0, x + y – 9 = 0, 2x – 5y – 4 = 0. [6]**

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