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(1+x+x^2 + ……+x^p)^n = a0 + a1x + a2 x^2...

`(1+x+x^2 + ……+x^p)^n = a_0 + a_1x + a_2 x^2 + ….+a_(np) x^(np) rArr a_1 + 2a_2 + 3a_3 + ……+np .a_(np) =`

A

`(np(p+1)^n)/(2)`

B

`(np(p+1)^n)/(4)`

C

`(np(p-1)^n)/(4)`

D

`(np(p-1)^(2n))/(4)`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. If (1+x)^n = C0 + C1 x+ C2 x^2 + ….....+ Cn x^n, then C0+2. C1 +3. C...

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  2. 1.""^20C1 - 2.""^20C2 + 3.""^20C3 - …..-20.""^20C20 =

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  3. (1+x+x^2 + ……+x^p)^n = a0 + a1x + a2 x^2 + ….+a(np) x^(np) rArr a1 + 2...

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  4. C1 + 4.C2 +7.C3 +…….+(3n-2).Cn=

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  5. sum(r=1)^(n) (-1)^(r-1) ""^nCr(a - r) =

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  6. 2.C0 + (2^2)/(2).C1 + (2^3)/(3).C2 + ……+(2^11)/(11).C10 =

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  7. ""^11C0^2 - ""^11C1^2 + ""^11C2^2 - ""^11C3^2 + ……- "^11C11^2 =

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  8. (C0)/(1) + (C2)/(3) + (C4)/(5) + ……+(C16)/(17) =

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  9. (C1)/(2) + (C3)/(4) + …….+(C15)/(16)=

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  10. The coefficient of x^3 in (1-4x)^(1//2) is

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  11. The range of x for which the expansion of (1-3/x)^(-3//4) is valid is

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  12. The range of x of which the expansion of (2-3x^2)^(-11/2)is valid is

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  13. The fifth term of (1 - (2x)/(3))^(3//4) is

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  14. For |x| lt 1, the (r + 1)^(th) term in the expansion of sqrt(1 - x) is

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  15. The general term of (2a - 3b)^(-1//2) is

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  16. In the expansion of (1+x+x^2+x^3+…..oo)^3, coefficient of x^3 is

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  17. In the expansion of (1-2x+3x^2 -4x^3+…."to")^4 coefficient of x^2 is

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  18. The coefficient of x^24 in (1+3x+6x^2 + 10x^3 + ……oo)^(2//3) is

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  19. The coefficient of x^10 in (1-2x + 3x^2)/(1-x) is

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  20. The coefficient of x^9 in the expansion of (1-5x)/(1+x) is

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