QJEEM18Maae4c: JEE Main 2018 Mathematics - Class 11 JEEM18Maae4c Solution: n − digit numbers are formed using only three digits 2, 5 and…

In n digit number first place can be filled with any one of 2, 5, 7. So no of ways first digit can be filled = 3

Similarly,
no of ways 2nd digit can be filled = 3 ways
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.
.
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- - - - - - nth - - - - - - - = 3 ways

$$\therefore$$ Total numbers = 3 $$\times$$ 3 $$\times$$ 3 .... n times
= 3ⁿ
$$\therefore$$ According to question, for smallest value of n,

3ⁿ > 900

3⁶ = 729 < 900

3⁷ = 2187 > 900

$$\therefore$$ n = 7