**CBSE Previous Year Solved Papers Class 12 Maths Outside 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**

**SECTION – A**

**SECTION – B**

**16. A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall? [4]**

** Solution:** Let AC = 5 m be the ladder and y be the height of the wall at which the ladder touches. Also, let the foot of the ladder be at C whose distance from the wall is x m It is given that

**18. Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.[4]**

** Solution:** The equation of circle in second quadrant which touches the coordinate axis is

**21. Find the coordinates of the point where the line through the points A = (3,4,1) and B = (5,1,6) crosses the XY- plane. [4]**

**22. Two cards are drawn simultaneously (without replacement) from a well-shuffled pack of 52 cards. Find the mean and variance of the number of red cards. [4]**

**SECTION – C**

**24. Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone. [6]**

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

**29. A dietician wishes to mix two types of foods in such a way that the vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 unit/kg of vitamin A and 1 unit /kg of vitamin C while Food II contains 1 unit/kg of vitamin A and 2 unit/kg of vitamin 1 unit/kg of vitamin C. It costs Rs 5 per kg to purchase food I and Rs 7 per kg to purchase Food II. Determine the minimum cost of such a mixture. Formulate the above as a LPP and solve it graphically.[6]**

**SET II**

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

**SECTION – A**

**SECTION – B**

**22. Find the coordinates of the point where the line through the point (3, – 4, – 5) and (2, – 3,1) crosses the plane 2x + y + z = 7. [4]**

**SECTION – C**

**29. Find the length and the foot of the perpendicular from the point P (7,14,5) to the plane 2x + 4y – z = 2. Also find the image of point P in the plane. [6]**

**SET III**

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

**SECTION — A**

**SECTION – B**

**20. Find the coordinates of the point where the line through the points (3, -4,-5) and (2, – 3,1) crosses the plane 3x + 2y + z +14 = 0. [4]**

**SECTION – C**

**29. Using matrices, solve the following system of equations; 3x + 4y + 7z = 4; 2x – y + 3z = – 3; x + 2y – 3z = 8 [6]**