Home
Class 12
MATHS
If 6^(83) + 8^(83) is divided by 49 , t...

If ` 6^(83) + 8^(83)` is divided by 49 , the remainder is

A

0

B

14

C

35

D

42

Text Solution

Verified by Experts

The correct Answer is:
c
`6^(83) + 8^(83) = (7-1)^(83) + (7+1)^(83) `
`= 2(7^(83) + ""^(83)C_(2) *7^(81) + ""^(83)C_(4) *7^(79) + ...+ ""^(83)C_(80)7^(3) + ""^(83)C_(82)7)`
` = 2 { 49 m + ""^(83)C_(82) *7}`
where , m is an integer
`= 98m + 2*""^(83)C_(1) *7 = 98m + 2*83 *7`
`= 98m + 2 (77 + 6)*7 = 49 (2m + 22) + 84 `
`= 49 (2m + 22) + 49 + 35 `
` = 49 (2m+ 23) + 35 = 49 n + 35 `
where n is an integer .
Hence , the remainder is 35 .
Promotional Banner

Similar Questions

Explore conceptually related problems

If (25)^(15) is divided by 13 , then the remainder is ………

If the polynomial x^(19) + x^(17) +x^(13) +x^(11) +x^(7) +x^(5) +x^(3) is divided by (x^(2)+1) , then the remainder is

f(x) = 3x^(5) +11 x^(4) +90x^(2) - 19x +53 is divided by x +5 then the remainder is______.

Dividing 5^(99) by 13 , the remainder is …………

When a polynomial 2x ^(3) + 3x ^(2) + ax + b is divided by (x-2) leaves remainder 2, and (x +2) leaves remainder -2. Find a and b.

Dividing 2x^(3) + 6x^(2) + x + 5 by (x+3), the remainder is ……….. .

If the square of any positive integer a is divided by 6, the remainder cannot be

Find the remainder when p (x) = x ^(3) - 6x ^(2) + 14x -3 is divided b y g (x) =1-2x and verify the result by long division.

Find the remainder when f (x) =x ^(4) - 3x ^(2) + 4 is divided by g (x) =x -2 and verify the result by actual division .

If the polynomials ax ^(3) + 3x ^(2) -13 and 2x ^(3) -5x +a arfe divided by (x-2) leave the same remainder, find the value of a.