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CBSE CLASS XII

Q. 1. Find the distance of (1,-2,0) from the point of intersection of line and plane.

OR

Find the foot of the perpendicular drawn from (1,2,-1) to the plane x+2y-2z=6.

Q. 2. Find the area of the circle which is exterior to the  parabola .

OR

Find the area : Q. 3. A candidate has to reach the examination centre in time. Probability of him going by bus or scooter or by other means of transport are respectively. The probability that he will be late is and respectively, if he travels by bus or scooter. But he reaches in time if he uses any other mode of transport. He reached late at the centre. Find the probability that he traveled by bus.

Q. 4. Evaluate : OR Q. 5. The sum of surface areas of a sphere and a cube is given. Show that sum of their volumes is least when the diameter of sphere is equal to edge of a cube

OR

Show that the ratio of the height and diameter of a half cylinder of maximum volume and given surface area is Q. 6. If A= Find A-1. Using A-1, solve :  2x - 3y + 5z = 11  3x + 2y - 4z = -5  x + y - 2z = -3.

OR Q. 7. A dietician wishes to mix together 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 food is given below :-

 Food Vitamin A Vitamin B Vitamin C X 1 2 3 Y 2 2 1

One Kg of food X costs Rs. 16 and one Kg of food Y costs Rs. 20. Find the least cost of the mixture which will produce the required diet.

OR

A manufactures, two types of products-A and B. The product A require 1hour on machine X ,1hour on machine Y and 4hour on machine Z. The product B require 2 hour on machine X ,1hour on machine Y and 1 hour on machine Z. In a given day machines X,Y and Z works for a maximum of 16, 9 and 24 hour respectively. The profit on product toy A is Rs. 600 and that on product B is Rs. 400. How many each types of products should be made to have maximum profit? Solve the problem graphically.

Paper By Mr. Rajesh Rajput