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If C(0), C(1), C(2), ..., C(n) denote th...

If `C_(0), C_(1), C_(2), ..., C_(n)` denote the binomial
cefficients in the expansion of `(1 + x )^(n)` , then
` a C_(0) + (a + b) C_(1) + (a + 2b) C_(2) + ...+ (a + nb)C_(n) = `.

A

`(2a+nb)2^(n)`

B

`(2a+nb) 2^(n-1)`

C

`(na+2b) 2^(n)`

D

`(na+2b) 2^(n-1)`

Text Solution

Verified by Experts

The correct Answer is:
b
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ML KHANNA-BINOMIAL THEOREM AND MATHEMATICAL INDUCTION -Problem Set (4) (MULTIPLE CHOICE QUESTIONS)
  1. The value of sum(r=1)^(10) r. (""^(n)C(r))/(""^(n)C(r-1) is equal to

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

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

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

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

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  6. 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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  7. 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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  8. 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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  9. The sum of the series .^(20)C(0)-.^(20)C(1)+ .^(20)C(2)-.^(20)C(3)+...

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

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

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

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  13. If (1+x)^(n) = C(0)+C(1)x + C(2) x^(2) +...+C(n)x^(n) then C(0)""^...

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  14. If n is a positive integer and C(k)=""^(n)C(k), then the value of sum(...

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  15. The vaule of sum(r=0)^(n-1) (""^(C(r))/(""^(n)C(r) + ""^(n)C(r +1)) ...

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  16. sum(r=0)^(n) (-1)^(r )" "^(n)C(r ) (1+r x)/(1+n x) equals

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  17. If n gt 3, then abC(0)-(a-1) (b-1) C(1) + (a-2)(b-2) C(2)-(a-3) (b-3) ...

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  18. If C(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value ...

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  19. If n is an odd natural number, then sum(r=0)^(n) ((-1)^(r ))/(""^(n)C(...

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  20. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)) , find the value of sum(...

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