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

`""^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 =

A

`-84`

B

84

C

81

D

`-81`

Text Solution

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The correct Answer is:
A
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""^20C_10.""^15C_0 + ""^20C_9.""^15C_1 + ""^20C_8.""^15C_2 + …..+""^20C_0.""^15C_10 =

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 :

If ""^(9)C_(3)+""^(9)C_(5)=""^(10)C_(r) then find r.

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

Find the value of ""^(10)C_(5)+2. ""^(10)C_(4)+""^(10)C_(3) .

I : IF ""^(12)C_(r+1) ="" ^(12) C_(3r-5) then r=3 or 4 . II : If ""^(9) C_(3) +""^(9)C_(5) = ""^(10)C_(r) then r=4 or 6.

AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
  1. ""^15C2 + 2.""^15C3 + 3. ""^15C4 + …..+ 14.""^15C15 =

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  2. ""^20C10.""^15C0 + ""^20C9.""^15C1 + ""^20C8.""^15C2 + …..+""^20C0.""^...

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  3. ""^10C1 . ""^9C5 + ""^10C2. ""^9C4 + ""^10C3. ""^9C3 + ""^10C4. ""^9C2...

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

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

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

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

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  8. 1 + ""^2C1x + ""^3C2 + ""^4C3 x^3 + ….. to oo terms can be summed up ...

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

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  10. ""^4C1 + ""^5C2.(1/2) + ""^6C3.(1/2)^2+….. to oo terms :

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

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

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

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

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

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

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

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

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

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  20. If x is numerically so small so that x^2 and higher powers of x can be...

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