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 _______.
← JEE Main 2022 · 29 Jul · Shift 2
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JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 24
Answer and worked solution
Official answer: 6
Divisible by 55 means the number ends in 5 and is divisible by 11. Every 4-digit number from these digits exceeds 1012; a 5-digit one would have to start with 2 and stay below 23421.
Count. The alternating digit sum must be a multiple of 11: 2365, 3245, 3465, 4235, 6325, 6435. No 5-digit number below 23421 works.
Answer: 6
Topics:Permutations