Exam Maths Puzzle Category

how many number have ever decreasing digits (eg.98640 or 732 or 81)? please note that none of the following are ever decreasing numbers 2 or 9 or 12 or 443 or 5298..
a.10!/9
b,2!/1+3!/2..........+9!/8+10!/9
c.2!/2+3!/2..........+9!2+10!/2
d.2^10-11

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Exam Other Question

A farmer has a rose garden. Every day he
either plucks 7 or 6 or 24 or 23 roses. The rose
plants are intelligent and when the farmer plucks
these numbers of roses, the next day 37 or 36 or
9 or 18 new roses bloom in the garden
respectively. On Monday, he counts 189 roses in
the garden. He plucks the roses as per his plan
on consecutive days and the new roses bloom as
per intelligence of the plants mentioned above.
After some days which of the following can be
the number of roses in the garden?
how do we distribute 63 rupees into minimum no. of coins , so that any sum from 1 to 63 is available.