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

Suppose ,m divided by n , then quotient q and remainder 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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  2. Consider (1 + x + x^(2))^(n) = sum(r=0)^(n) a(r) x^(r) , where a(0),...

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  3. If ( 1 + x - 2x^(2))^(20) = sum(r=0)^(40) a(r) x^(r) , then find ...

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  4. If ( 1 + x - 2x^(2))^(20) = sum(r=0)^(40) a(r) x^(r) , then find ...

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  5. Find the modulus of the complex number (2 + 3i)/(2 - 3i)

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  6. If a is the remainder when 5^(40) is divided by 11 and b is the rem...

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  7. Suppose ,m divided by n , then quotient q and remainder r or m= n...

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  8. Suppose ,m divided by n , then quotient q and remainder r or m= n...

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

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

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

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  12. If (x + a(1)) (x + a(2)) (x + a(3)) …(x + a(n)) = x^(n) + S(1) x^(n-...

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  13. Find the value of |(1 + i)/(1-i)|

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  14. If (x + a(1)) (x + a(2)) (x + a(3)) …(x + a(n)) = x^(n) + S(1) x^(n-...

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  15. A= (5/2+x/2)^n, B=(1+3x)^m Sum of coefficients of expansion of B is ...

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  16. B= (5/2+x/2)^n , A= (1 + 3x)^m Sum of coefficients of expansion of B ...

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  17. Sum of coefficients of expansion of B is 6561 . The difference of t...

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  18. Let us consider the binomial expansion (1 + x)^(n) = sum(r=0)^(n) a(...

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  19. Let us consider the binomial expansion (1 + x)^(n) = sum(r=0)^(n) a(...

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  20. Let us consider the binomial expansion (1 + x)^(n) = sum(r=0)^(n) a(...

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