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

The coefficient of `x^(53)` in the expansion `sum_(m=0)^(100)^(100)C_m(x-3)^(100-m)2^m` is `^100 C_(47)` b. `^100 C_(53)` c. `-^(100)C_(53)` d. none of these

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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DISHA PUBLICATION-BINOMIAL THEOREM -EXERCISE-1 (CONCEPT BUILDER )
  1. If the 6th term in the expansion of [1/x^(8/3)+x^2 log10 x]^8 is 5600...

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  2. The sum of the rational terms in the binomial expansion of (2^((1)/(2)...

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  3. If the 7th tern in the binomial expansion of (3/((84)^(1/3)) +sqrt(3) ...

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  4. The sum of the coefficients in the expansion of (x^(2)- (1)/( 3))^(199...

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

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  6. If the coefficient of x^7in[a x^2-(1/(b x^2))]^(11) equal the coeffici...

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

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  8. The sum of the series (12)/(2!)+(28)/(3!)+ (50)/(4!) + ( 78)/(5!)+"......

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

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  10. The ratio of the coefficient of x^(15) to the term independent of x in...

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  11. (C0)/1+(C2)/3+(C4)/5+(C6)/7+.....=

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  12. Consider the expansion of (1 + x)^(2n+1) If the coefficients of x^(r...

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  13. The value of ""^(50)C(4)+sum(r=1)^(6)""^(56-r)C(3), is

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  14. If x is very small in magnitude compared with a such that ((a)/(a+ ...

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  15. In the expression (x+1) (x+4)(x+9)(x+16)"….."(x+400), the coefficient ...

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  16. (C(1))/(C(0))+(2.C(2))/(C(1))+(3.C(3))/(C(2))+ . . .+(20.C(20))/(C(19)...

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  17. Given positive integers r >1,n >2 and that the coefficient of (3r d)t ...

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  18. The value of sum(r=0)^n sum(s=1)^n .^nC5 .^sCr is

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  19. Find the value of .^n Cr +.^(n-1) Cr + ......+ .^r Cr

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  20. If x^(2)y = 2x - y and |x| lt 1 , then (( y + (y^(3))/(3) + (y^(5))...

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