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Find the sum of the coefficients of all the integral powers of `x` in the expansion of `(1+2sqrt(x))^(40)dot`

A

`3^(40) -1`

B

`(1)/(2) (3^(40)-1)`

C

`(1)/(2) (3^(40) +1)`

D

`3^(40)+1`

Text Solution

Verified by Experts

The correct Answer is:
c
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ML KHANNA-BINOMIAL THEOREM AND MATHEMATICAL INDUCTION -Problem Set (4) (MULTIPLE CHOICE QUESTIONS)
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  2. In the expansion of ( 1+ x)^(50), the sum of the coefficient of odd po...

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  3. Find the sum of the coefficients of all the integral powers of x in th...

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  4. The value of ""^(13)C(2) +""^(13)C(3) +""^(13)C(4) +…+""^(13)C(13) is

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  5. The sum of last ten coefficients in the expansion of (1+x)^(19) when ...

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  6. If S=(1)/(2) ""^(10)C(0) -""^(10)C(1) +2""^(10)C(2)-2^(2)" "^(10)C(3)…...

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  7. If (1 + x)^(n) = sum(r=0)^(n) C(r) x^(r),(1 + (C(1))/(C(0))) (1 + (C(...

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  8. Let (1 + x)^(n) = sum(r=0)^(n) C(r) x^(r) and , (C(1))/(C(0)) + 2 (...

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  9. The value of sum(r=1)^(10) r. (""^(n)C(r))/(""^(n)C(r-1) is equal to

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  10. If P(n) denotes the product of the binomial coefficients in the expan...

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  11. If C(0), C(1), C(2), ..., C(n) denote the binomial cefficients in t...

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  12. If C(0), C(1), C(2), …. C(n) denote the coefficients in the expansion ...

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  13. Statement-1: sum(r =0)^(n) (r +1)""^(n)C(r) = (n +2) 2^(n-1) Stat...

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  14. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+…+C(n)x^(n), then C(0)+5C(1)+9C(2)+...

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  15. If (1+x)^(n)= sum(r=0)^(n)C(r )x^(r ) and sum(r =0)^(n) (C(r ))/(r+1)=...

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  16. If (1+x)^(n)=sum(r=0)^(n)*C(r )x^(r ) and sum(r=0)^(n) (-1)^(r ) (C(r ...

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

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  18. The sum to (n+1) terms of the series (C(0))/(2)-(C(1))/(3)+(C(2))/(...

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  19. If C(r ) stands for ""^(n)C(r ), then the sum of first (n+1) terms of...

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  20. The value of the sum of the series 3.""^(n)C(0)-8" "^(n)C(1)+13" "^(n...

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