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

The value of `nC_0. ^nC_n +^nC_1 . ^nC_(n-1)++……..+^nC_n . ^nC_0`

A

`^2nC_(n-2)`

B

`^(2n-1)C_n`

C

`^(2n-1)C_(n-2)`

D

none of these

Text Solution

Verified by Experts

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

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

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

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

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

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

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

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

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

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

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

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

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  16. 1/(n!)+1/(2!(n-2)!)+1/(4!(n-4)!)+ …… is equal to

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

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

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

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

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