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Suppose ,m divided by n , then quotient ...

Suppose ,m divided by n , then quotient q and remainder r
`{:("n)m(q"),(" "-), (" "-), (" "r) , (" "):}`
or ` m= nq + r , AA m,n,q, r in 1 and n ne 0 `
If `13^(99)` is divided by 81 , the remainder is

A

13

B

23

C

39

D

55

Text Solution

Verified by Experts

The correct Answer is:
d
` 13^(99) = (12 +1)^(99) + ""^(99)C_(1)(12)^(98) + ""^(99)C_(2) (12)^(97) + …+ `
` ""^(99)C_(97)(12)^(2) + ""^(99)C_(98)(12) + 1`
` = { (12)^(99) + ""^(99)C_(1) (12)^(98) + ""^(99)C_(2) (12)^(97) `
` + …+ ""^(99)C_(97) (12)^(2)} + ""^(99)C_(1) (12) + 1`
` = 8 1 lambda + 99 xx12 + 1 ` , where ` lambda ` is an integer ltbr ` = 81 lambda + 81 xx 14 + 55 `
` therefore ` Remainder = 55 .
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ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Passage Based Questions)
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  4. If (1 + x+ 2x^(2))^(20) = a(0) + a(1) x + a(2) x^(2) + …+ a(40) x^(40)...

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  5. If (1 + x+ 2x^(2))^(20) = a(0) + a(1) x + a(2) x^(2) + …+ a(40) x^(40)...

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  11. Consider the binomial expansion of R = (1 + 2x )^(n) = I = f , where...

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