Home
Class 10
MATHS
Euclid's division lemma states that for ...

Euclid's division lemma states that for positive integers a and b, there exist unique integers q and r such that `a=bq+r`, where r must satisfy.

A

`1 lt r lt b`

B

`0 lt r lt b`

C

`0 le r lt b`

D

`0 lt r le b`

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • NUMBERS AND SEQUENCES

    FULL MARKS|Exercise UNIT EXERCISE|10 Videos

  • NUMBERS AND SEQUENCES

    FULL MARKS|Exercise ADDITIONAL QUESTION SOLVED|25 Videos

  • NUMBERS AND SEQUENCES

    FULL MARKS|Exercise EXERCISE 2.9|7 Videos

  • MENSURATION

    FULL MARKS|Exercise ADDITIONAL QUESTIONS SOLVED (iii)|8 Videos

  • RELATIONS AND FUNCTIONS

    FULL MARKS|Exercise ADDITIONAL QUESTIONS SOLVED (ANSWER THE FOLLOWING QUESTIONS)|26 Videos

Similar Questions

Explore conceptually related problems

If a and b are any two integers then there exists unique integers q and r such that _____ where olerle|b| .

Statement 1: Let A ,B be two square matrices of the same order such that A B=B A ,A^m=O ,n dB^n=O for some positive integers m ,n , then there exists a positive integer r such that (A+B)^r=Odot Statement 2: If A B=B At h e n(A+B)^r can be expanded as binomial expansion.

Knowledge Check

  • Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

    A
    0, 1, 8
    B
    1,4,6
    C
    0,1,3
    D
    1,3,5

  • Using Euclid's division lemma, if the cube of any positive integers is divided by 9 then the possible remainders are ___.

    A
    `0, 1, 8`
    B
    `1, 4, 8`
    C
    `0, 1, 3`
    D
    `1, 3, 5`

    • Similar Questions

    Explore conceptually related problems

    Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 80 , b = 8

    Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 132, b = 11

    Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 125 , b = 5

    Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 13 , b = 3

    Use division algorithm to show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integer

    Show that any positive odd integer is of the form 4q+1 or 4q+3, where q is some integer.

    Home
    Profile