Question

Let x be the no. Of integers lying between 2999 and 8001 which have at least two digits equal. Then x is equal to

Answer 1

Every 100 from 3001 to 4000 will have 44 integers where digits 0 to 9 repeat except from 3301 to 3400. ( Also 4401 to 4500 and 5501 to 5600 and so on) wherein all 100 integers will have digits 0–9 repeating.

Thus between 3301 and 4000 you will have 44 x 9 plus 100=496 numbers with repeating digits.

Upto 8000 it will be 5x496 = 2480.

Since we're considering 3000 as well,  it will be 2481 numbers.