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If (1+x)^(15)=C0+C1x+C2x^2+……..+C(15)x^(...

If `(1+x)^(15)=C_0+C_1x+C_2x^2+……..+C_(15)x^(15)` then `,^15C_0^2-^15C_1^2+^15C_2 ^2 -^15C_3 ^2 +……-^15C_(15) ^2` is equal to

A

0

B

1

C

(-1)

D

none of these

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The correct Answer is:
A
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. Sum of the series 2C0+C1/2 2^2 +C2/3 2^3+………+Cn/(n+1) 2^(n+1)

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  2. The value of nC0. ^nCn +^nC1 . ^nC(n-1)++……..+^nCn . ^nC0

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  3. If (1+x)^(15)=C0+C1x+C2x^2+……..+C(15)x^(15) then ,^15C0^2-^15C1^2+^15C...

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  4. If sn= sum(r=0)^n 1/(^"nCr) and tn=sum(r=0)^n r/("^nCr) then tn/sn is ...

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  5. The fractional part of =(2^(4n))/15 is

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  6. If the fourth term in the expansion of (px+(1/x))^n is independent of ...

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  7. Find the coefficient of x^20 in the expression of (1+x^2)^40(x^2+2+1/x...

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  8. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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  9. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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  10. The greatest integer which divides the number 101^(100)-1 is

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  11. Coefficient of x^(11) in the expansion of (1+3x+2x^2)^6 is equal to

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  12. Show that 101^(50)gt 99^(50)+100^(50)

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  13. The greatest term (numerically) in the expansion of (2+3x)^9 when x=3/...

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  14. If agt0 and coefficients of x^5 and x^(15) in the expansion of (x^2+a/...

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  15. 1/(n!)+1/(2!(n-2)!)+1/(4!(n-4)!)+ …… is equal to

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  16. The coefficients of x^n in (1+x/(1!)+x^2/(2!)+……+x^n/(n!))^2 is

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  17. The sum of the coefficients of all the integral powers of x in the exp...

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  18. The coefficient of x^m in (1+x)^r+ (1+x)^(r+1)+(1+x)^(r+2)+………+(1+x)^n...

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  19. The coefficient of x^ny^n in the expansion of {(1+x)(1+y)(x+y)}^n is

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  20. If log(1-x+x^2)=a1x+a2x^2+a3x^3+……… then a3+a6+a9+……… is equal to

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