JEE MAIN - Chemistry (2018 - 15th April Morning Slot - No. 15)
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 :
6
7
8
9
Explanation
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
.
.
.
.
- - - - - - 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
Similarly,
no of ways 2nd digit can be filled = 3 ways
.
.
.
.
- - - - - - 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
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