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Find the coefficient of a^5b^7in(a-2b)^(...

Find the coefficient of `a^5b^7in(a-2b)^(12)`

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The correct Answer is:
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`T_(r+1)=^(12)C_(r).a^(12-r).(-2b)^(r)`
`=^(12)C_(r).(-2)^(r).a^(12-r).b^(r)`
`"Let " 12-r =5 " and " r=7`
`:.` Coefficient of `a^(5).b^(7)=^(12)C_(7).(-2)^(7)`
`=(121)/(5171)(-128)`
`=(12.11.10.9.8)/(5.4.3.2.1)(-128)`
`=-101376`
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NAGEEN PRAKASHAN-BINOMIAL THEOREM-Exericse 8.2
  1. Find the 4^(t h)term in the expansion of (x-2y)^(12).

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  2. Find the 13^(t h)term in the expansion of (9x-1/(3sqrt(x)))^(18),x!=0

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  3. Find the middle term in the expansion of (3-(x^(3))/(6))^(7)

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  4. Find the middle term in the expansion of :\ (x/3+9y)^(10)

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  5. In the binomial expansion of (1+a)^(m+n) , prove that the coefficient ...

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  6. The coefficient of the (r-1)th, rth and (r+1)th terms in the expansio...

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  7. prove that the coefficient of x^n in the expansion of (1+x)^(2n) is tw...

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  8. Find a positive value of m for which the coefficient of x^2 in the ex...

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  9. Find the coefficient of x^5""in(x+3)^8

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  10. Find the coefficient of a^5b^7in(a-2b)^(12)

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  11. Write the general term in the expansion of (x^2-y)^6dot

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  12. Write the general term in the expansion of (x^2-y x)^(12),x!=0

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  13. Find the 4^(t h)term in the expansion of (x-2y)^(12).

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  14. Find the 13^(t h)term in the expansion of (9x-1/(3sqrt(x)))^(18),x!=0

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  15. Find the middle term in the expansion of (3-(x^(3))/(6))^(7)

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  16. Find the middle term in the expansion of :\ (x/3+9y)^(10)

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  17. In the binomial expansion of (1+a)^(m+n) , prove that the coefficient ...

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  18. The coefficient of the (r-1)th, rth and (r+1)th terms in the expansio...

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  19. prove that the coefficient of x^n in the expansion of (1+x)^(2n) is tw...

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  20. Find a positive value of m for which the coefficient of x^2 in the ex...

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