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The sum of the coefficients of even powe...

The sum of the coefficients of even powers of x in the expansion of `(1+x+x^2)^15` is

A

`(3^15 +1)/(2)`

B

`(2^15 + 2)/(2)`

C

`(3^15-1)/(2)`

D

none

Text Solution

Verified by Experts

The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1B (BINOMIAL COEFFICIENTS)
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  12. If (1 -x + x^2)^n = a0 +a1x + a2x^2+….+a(2n)x^(2n) then a0 + a2 +a4 +...

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  13. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  14. If (1+2x+x^2)^n= sum(r=0)^(2n) a, x' then ar=

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  15. If (1+2x +3x^2)^10 = a0 +a1x +a2x^2 + ……+a20x^20 then a2/a1 =

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  16. If (1+x -2x^2)^8 =1 -a1x + a2x^2+……+a16x^16, then a2+a4+a6+……+a16 =

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  17. If (1+x+x^2+x^3)^5=sum(k=0)^(15) ak x^k then sum(k=0)^(7) a24=

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  18. If ak is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k...

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  19. If (3 + 7x - 9x^2)^n = a0 +a1x + a2 x^2 + ……+a(2n)x^(2n) prove the a0 ...

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  20. If (1+x+x^2)^n = sum(r=0)^(2n) ar x' then a1-2a2 + 3a3-…..-2na(2n)=….....

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