Properties of Numbers

How many numbers with two or more digits can be formed with the digits 1,2,3,4,5,6,7,8,9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?

If the sum of squares of two numbers is 97, then which one of the following cannot be their product?

The smallest integer n for which 4ⁿ > 17¹⁹ holds, is closest to

In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

The mean of all 4-digit even natural numbers of the form ‘aabb’, where a > 0, is

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?

How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

For a 4-digit number, the sum of its digits in the thousands, hundreds and tensplaces is 14, the sum of its digits in the hundreds, tens and units places is 15, andthe tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is