1.

The number of increasing function from `f : AtoB` where `A in {a_(1),a_(2),a_(3),a_(4),a_(5),a_(6)}`, `B in {1,2,3,….,9}` such that `a_(i+1) gt a_(i) AA I in N` and `a_(i) ne i` isA. `30`B. `28`C. `24`D. `42`

Answer» Correct Answer - B
`(b)` If `a_(1)` is mapped with `2`, we have `.^(7)C_(5)` ways of mapping rest of the elements.
If `a_(1)` is mapped with `3`, we have `.^(6)C_(5)` ways of mapping rest of the elelments.
If `a_(1)` is mapped with `4`, we have `.^(5)C_(5)` ways of mapping rest of the elements.
Hence total number of increasing function
`=^(7)C_(5)+^(6)C_(5)+^(5)C_(5)=28`


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