CAT Question of the Day Let f( n, k) denote the number of ways in which the set S = {1, 2, 3, 4,… n} can be partitioned into k non-empty subsets. For example, f(3, 2) = 3 since we can partition {1, 2, 3} into 2 subsets in 3 ways: {1, 2}{3}; {1, 3}{2} and {2, 3}{1}.
Similarly f(4, 2) = 7 since there are 7 ways to partition {1, 2, 3, 4} into 2 sets: {1, 2}{3, 4}; {1, 3}{2, 4}; {1, 4}{2, 3}; {1, 2, 3}{4}; {1, 2, 4}{3}; {1, 3, 4}{2}; {1}{2, 3, 4}.
We assume that f(0, 0) = 1.
What is the value of f(7, 4) if f(6, 3) = 90 and f(6, 4) = 65?
| OPTIONS | | |  | 1) | 155 | | | 2) | 5850 | | | 3) | 260 | | | 4) | 350 | | | 5) | 270 |
Tip of the Day RCs that have long passages are usually riddled with facts and figures. In such cases, reading the questions before reading the passage makes much more sense. Last year's Question of the day (02-Apr-11) | In the diagram shown below ABCD is a 20 by 20 square. The points E, F, and G are equally spaced on side BC. The points H, I, J, and K on side DA are placed so that the triangles BKE, EJF, FIG, and GHC are all isosceles. Points L and M are midpoints of the sides AB and CD, respectively. What is the total area of the shaded regions? |  |
| OPTIONS | | | | | 1) | 100 | | | 2) | 200 | | | 3) | 50 | | | 4) | 75 |
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