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Q.

How many zeros are there from 1 to 10000 ?

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Correct choice: A

Explanation:

For solving this problem first we would break the whole range in 5 sections 1) From 1 to 9 Total number of zero in this range = 0 2) From 10 to 99 Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer) 3) From 100 to 999 - three type of numbers are there in this range a) x00 b) x0x c) xx0 (here x represents a non zero number) Total possibilities for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18 for x0x = 9*1*9 = 81, hence total zeros = 81 similarly for xx0 = 81 total zeros in three digit numbers = 18 + 81 +81 = 180 4) From 1000 to 9999 - seven type of numbers are there in this range a)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xx Total possibilities for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27 for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162 for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162 for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162 for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729 for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729 for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729 total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700 thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000) = 2893
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