Home
Class 12
MATHS
Number of four digit positive integers i...

Number of four digit positive integers if the product of their digits is divisible by `3` is.

A

`2700`

B

`5464`

C

`6628`

D

`7704`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Product will be divisible by `3` if atleast one digit is , `0,3,6,9`
Now total four-digit no.`=9xx10^(3)`,
Number of four-digit no. without `0,3,6,9=6^(4)`
Total number of four-digit integers `=9000-1296=7704`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Multiple Correct Answer|2 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Comprehension|8 Videos

  • PARABOLA

    CENGAGE|Exercise Question Bank|9 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE|Exercise Exercise|9 Videos

Similar Questions

Explore conceptually related problems

The number of 4 digit natural numbers such that the product of their digits is 12 is

Among the 8! [permutations of the digits 1, 2, 3..., 8, consider those arrangements which have the following property. If we take any five consecutive positions the product of the digits in these positions is divisible by 5. The number of such arrangements is equal to a. 7! b. 2.(7!) c. ^7C_4 d. none of these

The product of r consecutive positive integers is divisible by

Prove that the product of two consecutive positive integers is divisible by 2.

Count the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digits are repeated?

Count the number of positive integers greater than 7000 and less than 8000 which are divisible by 5, provided that no digits are repeated.

Count the number of positive integers greater than 7000 less than 8000 which are divisible by 5 provided are that no digits are repeated .

The number of distinct natural numbers up to a maximum of four digits and divisible by 5, which can be formed with the digits 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9 each digit not occurring more than once in each number, is a. 1246 b. 952 c. 1106 d. none of these