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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) ^100C_m(x-3)^(100-m) 2^m` is equal to

A

`^100C_47`

B

`^100C_53`

C

`-^100C_53`

D

`-^(100)C_(100)`

Text Solution

Verified by Experts

The correct Answer is:
C
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
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  2. Statement-1 : 11^(25) +12^(25) when divided by 23 leaves the remainder...

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

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  4. The coefficient of y in the expansion of (y^2+(c/y))^5 is

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  5. The term independent of x in (x^2-(1/x))^9 is

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  6. The coefficients of x^p and x^q in the expansion of (1+x)^(p+q) are

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  7. If x^m occurs in the expansion of (x+(1/x^2))^(2n) then the coefficien...

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  8. Sum of the series 2C0+C1/2 2^2 +C2/3 2^3+………+Cn/(n+1) 2^(n+1)

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  9. The value of nC0. ^nCn +^nC1 . ^nC(n-1)++……..+^nCn . ^nC0

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  10. If (1+x)^(15)=C0+C1x+C2x^2+……..+C(15)x^(15) then ,^15C0^2-^15C1^2+^15C...

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  11. If sn= sum(r=0)^n 1/(^"nCr) and tn=sum(r=0)^n r/("^nCr) then tn/sn is ...

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  12. The fractional part of =(2^(4n))/15 is

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  13. If the fourth term in the expansion of (px+(1/x))^n is independent of ...

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  14. Find the coefficient of x^20 in the expression of (1+x^2)^40(x^2+2+1/x...

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  15. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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  16. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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  17. The greatest integer which divides the number 101^(100)-1 is

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  18. Coefficient of x^(11) in the expansion of (1+3x+2x^2)^6 is equal to

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  19. Show that 101^(50)gt 99^(50)+100^(50)

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  20. The greatest term (numerically) in the expansion of (2+3x)^9 when x=3/...

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