12 NCERT MATH MOST IMPORTANT QUESTIONS

Q1.   A diet is to contain atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of calcium. Two foods f 1 and f 2 are available. A unit of food f 1 contains 1 unit of vitamin A, 2 units of vitamin B and 3 units of calcium and a unit of food f 2 contains 2 units of vitamin A, 2 units of vitamin B and 1 unit of calcium. If one unit of food f 1 costs Rs 16 and one unit of food f 2 costs Rs 20, find the least cost of the mixture which will produce the desired diet. Solution   Problem can be represented as           Minimise z = 16x + 20y           st x + 2y  10           2x + 2y  12 or x + y  16           3x + y  8           x  0, y  0           Corner Poi...

Q1. Find the angle between any two diagonals of a cube. Solution  Let O, one vertex of a cube, be the origin and three edges through O be the Co-ordinate axes. The four diagonals are OP, AA', BB' and CC'. Let 'a' be the length of each edge. Then the co-ordinates of P, A, A' are (a, a, a), (a, 0, 0), (0, a, a).             The direction ratios of OP are a, a, a.             The direction cosines of OP are  .             Similarly, direction cosines of AA' are  .             Let be the angle between the diagonals OP and AA'. Then                                      ...