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JEE Main 201815 April

Exam: JEE Main
Year: 2018
Date: 15 April
Subject: Mathematics
Chapter: Permutation and Combination

JEE Main 2018 · 15 April · Mathematics · Permutation and Combination

n -digit numbers are formed using only three digits 2, 5 and 7 ....

n

-digit numbers are formed using only three digits

2, 5

and

7

. The smallest value of

n

for which

900

such distinct numbers can be formed is :

Options

A $9$
B $7$
C $8$
D $6$

Correct answer

B. $7$

Step-by-step solution

$n$ - digit number are formed using only three digits $2, 5$ and $7$ with repetition $= {3}^{n}$ .

Since, ${3}^{6} < 900$ and ${3}^{7} > 900$

So, $n = 7$ .

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