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Standard XII

Mathematics

Division and Distribution into Groups of Equal Sizes

An n-digit nu...

Question

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5, and 7. The smallest value of n for which this is possible is

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Solution

The correct option is B 7
Distinct n-digit numbers which can be formed using digits $2, 5, a n d 8 a r e 3^{n}$ . We have to find n so that
$3^{n} \geq 900 o r 3^{n - 2} \geq 100 o r n - 2 \geq 5 o r n \geq 7$
So the least value of n is 7.

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An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5, and 7. The smallest value of n for which this is possible is

The correct option is B 7Distinct n-digit numbers which can be formed using digits 2, 5, and 8 are 3n. We have to find n so that 3n≥900or 3n−2≥100or n−2≥5or n≥7 So the least value of n is 7.

The correct option is B 7
Distinct n-digit numbers which can be formed using digits $2, 5, a n d 8 a r e 3^{n}$ . We have to find n so that
$3^{n} \geq 900 o r 3^{n - 2} \geq 100 o r n - 2 \geq 5 o r n \geq 7$
So the least value of n is 7.