JEE MAIN - Mathematics (2022 - 29th July Evening Shift - No. 17)
The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $$2,3,4,5,6$$ (repetition of digits is not allowed) and divisible by 55 is _________.
Answer
6
Explanation
Case-I
When number is 4-digit number $(\overline{a b c d})$ here $d$ is fixed as 5
So, $(a, b, c)$ can be $(6,4,3),(3,4,6),(2,3,6)$, $(6,3,2),(3,2,4)$ or $(4,2,3)$
$\Rightarrow 6$ numbers
Case-II
No number possible
When number is 4-digit number $(\overline{a b c d})$ here $d$ is fixed as 5
So, $(a, b, c)$ can be $(6,4,3),(3,4,6),(2,3,6)$, $(6,3,2),(3,2,4)$ or $(4,2,3)$
$\Rightarrow 6$ numbers
Case-II
No number possible
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