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(1+x)^25 = sum(r = 0)^(25) Cr x^r then ...

`(1+x)^25 = sum_(r = 0)^(25) C_r x^r` then `C_1 - C_3 + C_5 - C_7 + ……-C_25 = `

A

`2^10`

B

`-2^10`

C

`2^12`

D

`-2^12`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. If (1+x -2x^2)^8 =1 -a1x + a2x^2+……+a16x^16, then a2+a4+a6+……+a16 =

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  2. If (1+x-2x^2)^8 = 1 + a1x + a2x^2 + ……+ a16 x^16, then a1 +a3 + a5 + …...

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  3. (1+x)^25 = sum(r = 0)^(25) Cr x^r then C1 - C3 + C5 - C7 + ……-C25 =

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  4. The sum of the coefficients in the expansion of (1+x-3x^2)^(171) is

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  5. If the sum of all the binomial coefficients in (x+y)^n is 512 , then t...

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  6. The coefficient of x^(-n) in (1+x)^n (1+(1)/(x))^n is

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  7. If n is a positive integer then 2^(4n) - 15n - 1 is divisible by

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  8. Smaller of (19^10 + 20^10) and 21^10 is

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  9. 9^11 + 11^9 is divisible by

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  10. Integral part of (8 + 3sqrt7)^n is

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  11. If n = (sqrt2 +1)^6. Then the integer just greater than n is

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  12. 1.C0 + 3.C1+ 3^2.C2+….+3^n.Cn =

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  13. C0 + (C1)/(2) + (C2)/(2^2) + (C3)/(2^3)+…..+(Cn)/(2^n)=

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  14. ""^11C0 + ""^11C1 + ""^11C2 + ……+ ""^11C5 =

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  15. C0^2 + C1^2 + C2^2 - ………-C15^2 =

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  16. 1/2.""^10C0 -""^10C1 +2.""^10C2 - 2^2.""^10C3+…..+2^9. ""^10C10 =

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  17. ""^(2n +1)C0^2 -""^(2n+1)C1^2 + ""^(2n+1)C2^2 -…….- ""^(2n+1)C(2n+1)^2...

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

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  19. ""^20C0 + ""^20C1 + ""^20C2+…….+""^20C10 =

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

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