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The coefficient of x^(53) in the expansi...

The coefficient of `x^(53)` in the expansion of:
`sum_(m=0)^(100)""^(100)C_(m)(x-3)^(100-m)2^m` is:

A

`""^(100)C_(47)`

B

`""^(100)C_(53)`

C

`-""^(100)C_(53)`

D

`-""^(100)C_(54)`

Text Solution

Verified by Experts

The correct Answer is:
C
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MODERN PUBLICATION-BINOMIAL THEOREM-MCQ.s (LEVEL-II)
  1. The digit at unit's place in 2^(9^(100)) is:

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  2. If in the expansion of (1+x)^(m)(1-x)^(n) the coefficients of x and x^...

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  3. The coefficient of x^(53) in the expansion of: sum(m=0)^(100)""^(100...

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  4. The coefficient of x^(4) in the expansion of : (1+x+x^(2)+x^(3))^(n)...

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  5. In the expansion of (1+x+x^(3)+x^(4))^(4), the coefficient of x^(4) is...

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  6. If the sum of the coefficient in the expansion of (alpha^(2)x^(2)-2alp...

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  7. If (3sqrt(3)+5)^(2n+1)=p+f, where p is an integer and f is a proper fr...

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  8. The larger of 99^(50)+100^(50) and 101^(50) is:

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  9. Find the value of x in the expansion of [x+x^(log(10)x)]^(5), if the t...

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  10. Value of 2C(0)+(2^(2))/(2)C(1)+(2^(3))/(3)C(2)+ . . .+(2^(11))/(11)C(1...

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  11. Sum to (n+1) terms of the series: (C(0))/(2)-(C(1))/(3)+(C(2))/(4)-(C(...

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  12. If n is an even integer, then: C(0)^(2)-C(1)^(2)+C(2)^(2)-C(3)^(2)+ ...

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  13. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+ . . .+C(n)x^(n), then the value of ...

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  14. If m,n,r are positive integers such that rltm,n, then: ""^(m)C(r)+""...

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  15. If in the expansion of (2a-(a^(2))/(4))^(9), the sum of middle terms i...

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  16. The term independent of x in the expansion of (1+x)^(n)(1-(1)/(x))^(n)...

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  17. The greatest value of the term independent of x in the expansion of (x...

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  18. If the largest interval to which x belongs so that the greatest term i...

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  19. Let R=(5sqrt(5)+11)^(2n+1) and f=R-[R], where [ ] denotes the greater ...

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  20. If the coefficients of the middle term of (1+x)^(2n+2) is p and the co...

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