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

`""^20C_0 + ""^20C_1 + ""^20C_2+…….+""^20C_10 = `

A

`[2^19 - 1/2. ""^18C_10]`

B

`[2^19 +1/2.""^20C_10]`

C

`2^19-1/4. ""^18C_10]`

D

`[2^19 - 1/4 . ""^6C_3]`

Text Solution

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The correct Answer is:
B
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Explore conceptually related problems

The sum of the series ""^20C_0 - ""^20C_1 + ""^20C_2 - ""^20C_3 +…….""^20C_10 is

Observe the following statements : Statement - I : 1/2 . ""^10C_0 - ""^10C_1 + 2. ""^10C_2 - 2^2. ""^10C_3 + ……+ 2^9. ""^10C_10 = -1/2 Statement - II : ""^20C_1 - 2(""^20C_2) + 3.(""^20C_3)-…..-20.(""^20C_20) = 0 Then the false statements are :

Prove that (""^20C_1)/(""^20C_0) + 2. (""^20C_2)/(""^20C_1) + 3. (""^20C_3)/(""^20C_2) + …..+20. (""^20C_20)/(""^20C_19) = 210

1.""^20C_1 - 2.""^20C_2 + 3.""^20C_3 - …..-20.""^20C_20 =

""^20C_10.""^15C_0 + ""^20C_9.""^15C_1 + ""^20C_8.""^15C_2 + …..+""^20C_0.""^15C_10 =

(""^(20)C_(1))/(""^(20)C_(0))+2.(""^(20)C_(2))/(""^(20)C_(1))+3.(""^(20)C_(3))/(""^(20)C_(2)) +…20.(""^(20)C_(20))/(""^(20)C_(19)) =210

AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. ""^(2n +1)C0^2 -""^(2n+1)C1^2 + ""^(2n+1)C2^2 -…….- ""^(2n+1)C(2n+1)^2...

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

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  3. ""^20C0 + ""^20C1 + ""^20C2+…….+""^20C10 =

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

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

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

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  7. 1.""^20C1 - 2.""^20C2 + 3.""^20C3 - …..-20.""^20C20 =

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  8. (1+x+x^2 + ……+x^p)^n = a0 + a1x + a2 x^2 + ….+a(np) x^(np) rArr a1 + 2...

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  9. C1 + 4.C2 +7.C3 +…….+(3n-2).Cn=

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

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

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  12. ""^11C0^2 - ""^11C1^2 + ""^11C2^2 - ""^11C3^2 + ……- "^11C11^2 =

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

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

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

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

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

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

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

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

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