Sample Paper – 2012
Class – XII
Subject – Mathematics

1.  Find the foot of the perpendicular and the perpendicular distance of the point (3,2,1) from the plane 2x-y+z +1=0. Find the image of the point in the plane.

2. From a lot of 30 bulbs which includes 6 defective, a sample of 4 bulbs is drawn at random with replacement. Find the mean and variance of the number of defective bulbs.

3. A furniture firm manufactures chairs and tables each requiring the use of three machines A, B and C . Production of the chair requires 2 hrs on machine A, 1 hr on machine B, and 1 hr on machine C. Each table requires 1 hr on machine A, 1 hr on machine B and 3 hrs on machine C. The profit obtained by selling one chair is Rs. 30 while by selling one table Rs. 60. The total time available per week on machine A is 70 hrs, machine B 40 hrs, and on machine C 90 hrs. How many chairs and tables should be made per week so as to maximize profit? Formulate the problem as LPP and solve it graphically.