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If (1+x)^(n)= C(0)+C(1).x+C(2). x^(2)+....

If `(1+x)^(n)= C_(0)+C_(1).x+C_(2). x^(2)+.. . C_(n). x^(n)` in the usual notation then `C_(0)^(2)+C_(1)^(2)+C_(2)^(2)+.. .+C_(n)^(2) `=

A

1) `((2 n) !)/(n !) `

B

2) `2 n `

C

3)(2 n) !/(n !)^(2)

D

4)2^(n-1)

Text Solution

Verified by Experts

The correct Answer is:
C
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HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. If (1 +x + x^(2))^(n) = a(0) + a(1) x + a(2) x^(2) + … + a(2n) x^(2n) ...

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  2. If x^(r) occurs in the expansion of (x+(1)/(x))^(n), then is coefficie...

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  3. If (1+x)^(n)= C(0)+C(1).x+C(2). x^(2)+.. . C(n). x^(n) in the usual n...

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  4. nCr+2. nC(r-1)+nC(r-2)=

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  5. If the coefficients of r^(th) and (r+1)^(th) term in the expansion o...

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  6. Sum of the odd binomial coefficients of (1+x)^(50) is

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  7. If (1+x+x^(2))^(n) = a(0)+a(1) x+a(2) x^(2)+.. .+a(2 n) x^(2 n) then ...

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  8. The coefficient of the term independent of x in the expansion of (sqrt...

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  9. If C(0),C(1),C(2), . . . .,C(n) are binomial coefficients of order n,...

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  10. The sum of the coefficients in the expansion of (1+x-3x^(2))^(3148)

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  11. The middle term in the expansion of((x-(1))/(x))^(18) is...

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  12. If the value of C(0)+2C(1)+3C(2)+ . . .+(n+1)C(n)=576, then n is

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  13. The ninth term of the expansion((3x) (-1)/(2x))^(8) is

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  14. The coefficient of x^(5) in (1+x^(2))^(5)(1+x)^(4) is

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  15. If the coefficient of the r^(th) term and the (r+1)^ (th) term is th...

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  16. The co-efficient of x^(-9) in the expansion of ((x^(2))/(2)-(2)/(x)...

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  17. Let (1+x^(2))^(2)(1+x)^(n) = sum(k=0)^(n+4) a(k) x^(k) . If a(1) , a...

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  18. If in the expansion of (1+x)^(m)(1-x)^(n) the coefficients of x and x^...

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  19. The term independent of x in the expansion of (x^(2)-(1)/(x))^(6) ...

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  20. sum(r=0)^(m)( n+r )C(n)=

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