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""^(2n +1)C0^2 -""^(2n+1)C1^2 + ""^(2n+1...

`""^(2n +1)C_0^2 -""^(2n+1)C_1^2 + ""^(2n+1)C_2^2 -…….- ""^(2n+1)C_(2n+1)^2` =

A

0

B

`""^((2n+1))C_n`

C

`-(""^(2n+1)C_n)`

D

`-1/2(""^(2n)C_n)`

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The correct Answer is:
A
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""^((2n + 1))C_0 - ""^((2n+ 1))C_1 + ""^((2n + 1))C_2 - ……+""^((2n + 1))C_(2n) =

""^((2n + 1))C_0 + ""^((2n+ 1))C_1 + ""^((2n + 1))C_2 + ……+""^((2n + 1))C_n =

((1 + ""^nC_1 + ""^nC_2 + ""^nC_3+…….+nC_n)^2)/(1 + ""^(2n)C_1 + ""^(2n)C_2 + ""^(2n)C_3 + ……… + ""^(2n)C_(2n)) =

""^(2n)C_(n+1)+2. ""^(2n)C_(n) + ""^(2n) C_(n-1) =

Prove that (C_(0) +C_(1)+C_(2)+….+C_(n))^(2)=1 +""^(2n)C_(1) +""^(2n)C_(2) +…..+""^(2n)C_(2n)

Prove that (""^(2n)C_(0))^(2)-(""^(2n)C_(1))^(2)+(""^(2n)C_(2))-(""^(2n)C_(3))^(2)+......+(""^(2n)C_(2n))^(2)=(-1)^(n)(""^(2n)C_(n))^2.

Show that ""^(n)C_(0) +""^((n+1))C_(1) +""^((n+2))C_(2) +…+""^((n+k))C_(k) =""^((n+k+1))C_(k)

AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. C0^2 + C1^2 + C2^2 - ………-C15^2 =

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  2. 1/2.""^10C0 -""^10C1 +2.""^10C2 - 2^2.""^10C3+…..+2^9. ""^10C10 =

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  3. ""^(2n +1)C0^2 -""^(2n+1)C1^2 + ""^(2n+1)C2^2 -…….- ""^(2n+1)C(2n+1)^2...

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  4. Prove that following i) 2.C(0)+5.C(1)+8.C(2)+…..+(3n+2)C(n)=(3n+4).2...

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  5. ""^20C0 + ""^20C1 + ""^20C2+…….+""^20C10 =

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  6. C1 + 2. C2 + 3. C3 + …... + n. Cn=

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  7. If ar is the coefficient of x^r in the expansion of (1+x)^n then a1/a0...

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  8. If (1+x)^n = C0 + C1 x+ C2 x^2 + ….....+ Cn x^n, then C0+2. C1 +3. C...

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  9. 1.""^20C1 - 2.""^20C2 + 3.""^20C3 - …..-20.""^20C20 =

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  10. (1+x+x^2 + ……+x^p)^n = a0 + a1x + a2 x^2 + ….+a(np) x^(np) rArr a1 + 2...

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  11. C1 + 4.C2 +7.C3 +…….+(3n-2).Cn=

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

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

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  14. ""^11C0^2 - ""^11C1^2 + ""^11C2^2 - ""^11C3^2 + ……- "^11C11^2 =

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

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

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

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

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

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

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