CBSE Maths Class XII Compartment Paper 2009
SECTION C
Questions number 23 to 29 carry 6 marks each.
Q.23 Show that a cylinder of given volume, open at the top, has minimum total surface area if its height is equal to radius of the base.
Q.24 Evaluate
as the limit of sums.
Q.25 A bag contains 4 red and 4 black balls. Another bag contains 2 red and 6 black balls. One of the bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
Q.26 Find the area of the region enclosed between the two curves ,
(x – 6)2 + y2 = 36 and x2 + y2 = 36.
OR
Using integration find the area of the region bounded by the triangle whose vertices are (1, 3), (2, 5) and (3, 4).
Q.27 Find the length of the perpendicular and the coordinates of the foot of the perpendicular from the point (2, – 1, 5) to the line
Q.28 A housewife wishes to mix two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg of foods is given below :
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Vitamin A |
Vitamin B |
Vitamin C |
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Food X |
1 |
2 |
3 |
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Food Y |
2 |
2 |
1 |
If one kg of food X costs Rs. 6 and one kg of food Y costs Rs. 10, find the least cost of the mixture which will produce the diet. Solve the problem graphically, after making it an L.P.P.
Q.29 Using matrices, solve the following system of equations :
x + y + z = 3
2x – y + z = 2
x – 2y + 3z = 2
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