If 27 999 is divided by 7 , then the remainder is, 3, 1, 6, 2

Given, ( 27 ) 999 = 28 - 1 999 7 = 28 λ - 1 7 = 28 λ - 7 + 7 - 1 7 = 7 4 λ - 1 + 6 7 ∴ Remainder = 6

If 27 999 is divided by 7 , then the remainder is

Question: Answered & Verified by Expert

{(27)}^{999}

is divided by

7

, then the remainder is

MathematicsBinomial TheoremJEE MainJEE Main 2017 (08 Apr Online)

Options:

Solution:

1867 Upvotes Verified Answer

The correct answer is:

6

Given, $(27)^{999}$

$= \frac{{(28 - 1)}^{999}}{7}$

$= \frac{28 λ - 1}{7}$

$= \frac{28 λ - 7 + 7 - 1}{7}$

$= \frac{7 (4 λ - 1) + 6}{7}$

$∴$ Remainder $= 6$

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.