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$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is:

By using the non-zero digits,the number of $5$ digit numbers that can be formed such that each number has the largest digit in its middle place and the digits in the number are distinct is:

How many numbers between $3000$ and $4000$ can be formed using the digits $3, 4, 5, 6, 7, 8$ without repetition,such that the numbers are divisible by $5$?

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If $4 \times ^{15}P_r = 3 \times ^{16}P_{r-1}$,then $r = \dots$

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is allowed),are

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