The number 916238457 is an example of nine digit number which contains each of the digit 1 to 9 exactly once. It also has the property that the digits 1 to 5 occur in their natural order, while the digits 1 to 6 do not. Number of such numbers are (2024)

Q. Consider all the six digit numbers that can be formed using the digits 1,2,3,4,5 and 6, each digit being used exactly once. Each of such six digit numbers have the property that for each digit, not more than two digits smaller than that digit appear to the right of that digit. Find the number of such six digit numbers having the desired property.

Q. The number of distinct natural numbers up to a maximum of four digits and divisible by 5, which can be formed with the digit 0,1,2,3,4,5,6,7,8,9 each digit not occurring more than once in each number is

Q. All the 7 digit numbers containing each of the digits 1,2,3,4,5,6,7 exactly once, and not divisible by 5 are arranged in the increasing order. Find the (2000)th number in this list.

Q. All the 7−digit numbers containing each of the digits 1,2,3,4,5,6,7 exactly once, and not divisible by 5, are arranged in increasing order. Then which among the following statements is INCORRECT ?

Q. The total number of natural numbers of 6 digits that can be made with digits 1,2,3,4, where all the digits are to appear in the same number at least once, is