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The coefficient of x^53 in sum(r = 0)^(1...

The coefficient of `x^53` in `sum_(r = 0)^(100) ""^100C_r (x - 3)^(100 - r) .2^r` is

A

`""^100 C_51`

B

`""^100 C_52`

C

`-^100 C_53`

D

`""^100 C_54`

Text Solution

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1A (BINOMIAL THEOREM WITH INTEGRAL INDEX)
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  2. The coefficient of x^4 in the expansion of (1-x+x^2-x^3)^4. Is

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  3. The coefficient of x^53 in sum(r = 0)^(100) ""^100Cr (x - 3)^(100 - r)...

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  4. Which term of (ax+b//x)^14 is independent of x?

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  5. the term independent of x in (x+1//x)^6 is

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  6. If T(r+1) is the term of independent of x in (3x-(5)/(x^3))^8 then r=

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  7. Which term of (sqrt(x//3)+3//2x^2)^10 is independent of x?

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  8. The term independent of x in the expansion of (x^2-(1)/(x))^6 is

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  9. The term independent of x in (ax+(b)/(x))^14 is

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

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  11. The term independent of x in (2x^(1//2)-3x^(-1//3))^20

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  12. The term independent of x in ((sqrtx)/(2)-(2)/(x^2))^10 is

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  13. The term independent of x in the expansion of (sqrtx-(2)/(sqrtx))^18 i...

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  14. The term independent of x in the expansion of (2x^2-(3)/(x^3))^15 is

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  15. The term independent of x in (x^2 -1//3x)^9 is

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  16. Independent term of (sqrtx-2//x)^18 is

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  17. The term independent of x in the expansion of ((2sqrtx)/(5)-(1)/(2xsqr...

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  18. The term independent of x in (x-1//x^2)^(3n) is

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  19. The term independent of x in the expansion of (1+x+2x^3) (3x^2//2-1//3...

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  20. the tern independent of x in (1+x +2x^2)(3x^2//2-1//3x)^9 is

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