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""^20C10.""^15C0 + ""^20C9.""^15C1 + ""^...

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

A

`""^20C_10`

B

`""^25C_10`

C

`""^35C_10`

D

`""^40C_10`

Text Solution

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The correct Answer is:
C
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Explore conceptually related problems

""^15C_2 + 2.""^15C_3 + 3. ""^15C_4 + …..+ 14.""^15C_15 =

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

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

""^10C_1 . ""^9C_5 + ""^10C_2. ""^9C_4 + ""^10C_3. ""^9C_3 + ""^10C_4. ""^9C_2 + ""^10C_5. ""^9C_1 + ""^10C_6 = ""^19C_6 + x then x =

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

1/2.""^10C_0 -""^10C_1 +2.""^10C_2 - 2^2.""^10C_3+…..+2^9. ""^10C_10 =

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 :

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

(""^(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

With usual notations prove that C_1/C_0 + 2. C_2/C_1 + 3.C_3/C_2 + ……+n.(C_n)/(C_(n-1)) = (n(n +1))/(2) Hence prove that (15C_1)/(15C_0) + 2.(15C_2)/(15C_1) + 3. (15C_3)/(15C_2) +……..+ 15. (15C_15)/(15C_14) = 120

AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
  1. If (1+2x +3x^2)^10 = a0 +a1x +a2x^2 + ……+a20x^20 then a2/a1 =

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  2. ""^15C2 + 2.""^15C3 + 3. ""^15C4 + …..+ 14.""^15C15 =

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  3. ""^20C10.""^15C0 + ""^20C9.""^15C1 + ""^20C8.""^15C2 + …..+""^20C0.""^...

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  4. ""^10C1 . ""^9C5 + ""^10C2. ""^9C4 + ""^10C3. ""^9C3 + ""^10C4. ""^9C2...

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  5. sum(r=1)^(10) r. (""^nCr)/(""^nC(r-1)) =

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  6. sum(r = 0)^(n-1) (Cr)/(Cr + C(r+1)) =

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  7. The sum of the coefficients in the binomial expansion of (1/x + 2x)^n ...

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  8. If (1)/((1 - 2x)(1 + 3x)) is to tbe expanded as a power series of x, t...

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  9. 1 + ""^2C1x + ""^3C2 + ""^4C3 x^3 + ….. to oo terms can be summed up ...

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  10. If Sn denotes the sum of first n natural number then S1 + S2x + S3 x^2...

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  11. ""^4C1 + ""^5C2.(1/2) + ""^6C3.(1/2)^2+….. to oo terms :

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  12. If |x| lt 1 , then the coefficient of x^n in expansion of (1+x+x^2 + x...

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  13. If the expansion in powers of x of the function (1)/((1-ax)(1-bx)) is ...

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  14. The coefficient of x^24 in the expansion of (1+x^2)^(12) (1+x^12)(1+x^...

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  15. If 0 lt x lt 1, the first negative term in the expansion of (1+x)^(27/...

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  16. Find the coefficient of x^(10) in the expansion of (1+2x)/((1-2x)^(2))...

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  17. The first negative term in the expansion of (1+x)^(3//4) is

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  18. If T(r +1) is the first negative term in the expansion of (1+x)^(7//2)...

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  19. If x^3, x^4, x^5 …….can be neglected then sqrt(x^2 + 16 ) - sqrt(x^2 +...

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  20. If 'c' is small in comparison with l then ((l)/(l+c))^(1//2) + ((l)/(l...

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