1.

Let `A_(1),A_(2)….. A_(m)` be non -empty subsets of {1,2,3 …….. 100}, satisfying the following conditions. (1) the numbers `|A_(1)|,|A_(2)|....,|A_(m)|` are disjoint. (2) `A_(1),A_(2) ,….. A_(m)` are pairwise disjoint. (Here|A| denotes the number fo elements in the set A.) Then the maximum possible value of m isA. 13B. 14C. 15D. 16

Answer» Correct Answer - a
The possibility is
`|A_(1)|=1,|A_(2)|, |A_(3)|=3,........,|A_(m)|=m`lt brgt1+2+3+.....+m`ge100` {because all are disjoint}
`Rightarrow(m(m+1))/2 le100`
`Rightarrow mlt14`
`14^("th") set will have the same size as that of one of the previous sets
So, m=13


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