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has exactly digits when converted to base from the decimal system. What is the minimum possible value of ?
(a)
(b)
(c)
(d)None of these

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Important Questions on Number Systems
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What will be the sum of all natural numbers between which on division by leave remainders respectively?

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Unit digit of which of the following is the same as the units digits of For any positive integer value of ?

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How many Digit numbers are there in the decimal system, which have exactly Digits when expressed in Base , Base , Base ?

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What is the difference between the highest and the least four digit natural numbers that have exactly four digits when expressed in Base and Base .

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If is a natural number, then what is the sum of all the possible distinct remainders when is divided by ?

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If and are natural numbers, then what is the sum of all the possible remainders when is divided by ?

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What is the maximum possible sum of the number of Mondays and Thursdays in two consecutive years?

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In the previous question find the minimum possible sum of the number of Mondays and Thursdays in two consecutive years?
