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The coefficient of a^8b^4c^9d^9 in (a b ...

The coefficient of `a^8b^4c^9d^9` in `(a b c+a b d+a c d d+b c d)^(10)` is `10 !` b. `(10 !)/(8!4!9!9!)` c. `2520` d. none of these

A

`10!`

B

`(10!)/(8!4!9!9!)`

C

`2520`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`a^(10)b^(10)c^(10)d^(10)(1/a+1/b+1/c+1/d)^(10)`
Therefore the required coefficient is equal to the coefficient of
`a^(-2)b^(-6)c^(-1)d^(-1)` in `(1/a+1/b+1/c+1/d)^(10)`, which is given by
`= (10!)/(2!6!1!1!) = (10 xx 9 xx 8 xx 7)/(2) = 2520`
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CENGAGE-BINOMIAL THEOREM-Exercise (Single)
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  2. The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b....

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  3. The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d d+b c d)^(10) is...

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  4. In the expansion of (1+ x + 7/x)^11find the term not containing x.

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  5. The coefficient of x^(7) in the expansion of (1-x-x^(3)+x^(4))^(8) is ...

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  6. Sum of the coefficients of terms of degree 13 in the expansion of(1+x)...

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  7. The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(...

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  8. If coefficient of a^2b^3c^4in(a+b+c)^m(w h e r em in N)i sL(L!=0) , t...

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  9. The coefficient of x^r[0lt=rlt=(n-1)] in lthe expansion of (x+3)^(n-1)...

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  10. If (1+2x+3x^2)^(10)=a0+a1x+a2x^2++a(20)x^(20),t h e na1 equals 10 b. 2...

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  11. If f(x)=1-x^2-x^3++^(15)+x^(16)-x^(17) , then the coefficient of x^2in...

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  12. Let f(x0=a0+a1x+a2x^2++an x^n+ and (f(x))/(1-x)=b0+b1x+b2x^2++bn x^n+ ...

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  13. Statement 1: The coefficient of x^n is (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^...

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  14. In the expansion of (3^(-x//4)+3^(5x//4))^n the sum of binomial coeffi...

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  15. The sum of the coefficients of even power of x in the expansion of (1+...

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  16. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is ...

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  17. If the sum of the coefficients in the expansion of (a+b)^n is 4096, th...

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  18. The value of .^(20)C(10)+.^(20)C(1)+.^(20)C(2)+.^(20)C(3)+.^(20)C(4)+....

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  19. The sum of the series C 20()0-C 20()1+C 20()2-C 20()3+...-...+C 20()(1...

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  20. If (3+x^(2008)+x^(2009))^(2010)=a0+a1x+a2x^2++an x^n , then the value ...

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