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If C(n) is the coefficient of x^(n) in...

If `C_(n)` is the coefficient of `x^(n)` in the expansion of
`(1+x)^(n)` then `C_(1)+2. C_(2)+3. C_(3)+..+n. C_(n) `

A

2 n

B

`n. 2 n `

C

`n. 2^(n+1) `

D

`n. 2^(n-1) `

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The correct Answer is:
D
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HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. If (1+2 x+x^(2))^(n)=sum(r=0)^(2 n) a(r) x^(r), then a(r) =

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  2. If (1+x-2 x^(2))^(6)=1+a(1) x+a(z) x^(2)+l .. .+a(12) x^(12) then a(2...

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  3. If C(n) is the coefficient of x^(n) in the expansion of (1+x)^(n) ...

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  4. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+ . . .+C(n)x^(n), then the value of ...

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  5. The largest term in the expansion of (3+2x)^(50) where x=1/5 is:

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  6. The numerically greatest term of (2 x-3 y)^(12) when x=1 and y=(5...

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  7. The greatest coefficient in the expansion of (1+x)^(24) is

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  8. If A is the sum of the odd terms and B is the sum of even terms in the...

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  9. The number of terms in the expansion (1+x)^(101)(1-x+x^(2))^(100) is

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  10. The number of terms in the expansion of (1+3 x+3 x^(2)+x^(3))^(7) is

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  11. The total number of terms in the expansion of (x+y)^(150)+(x-y)^(150...

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  12. If the coefficient of x^(7) and x^(8) in (2+(x)/(3))^(n) are equal, th...

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  13. If (1+alphax)^(n)=1+8x+24x^(2)+ . . ., then the value of alpha and n i...

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  14. The coefficients of (2 r+4)^(th) and (r-2)^(th) terms in the expansion...

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  15. If the r^(th) term in the expansion of ((x)/(3)-(2)/(x^(2)))^(10) con...

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  16. The coefficient of x^(17) in (x-1)(x-2)(x-3). . . (x-18) is:

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  17. The value of x for which the sixth term in the expansion of [2^(log(...

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  18. If in the expansion of (a+x)^(n),P and Q represent the sum of odd and ...

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  19. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x...

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  20. If the rth term is the middle term in the expansion of (x^(2)-(1)/(2x)...

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