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Prove that ^nC0 "^(2n)Cn-^nC1 ^(2n-2)Cn ...

Prove that `^nC_0 "^(2n)C_n-^nC_1 ^(2n-2)C_n +^nC_2 ^(2n-4)C_n =2^n`

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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. Find the unit digit in the number 17^(1995)+11^(1995)-7^(1995)

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  2. If ((1+x)/(1-x))^n=1+a1x+a2x^2+…….+arx^r+…….. then prove that a1+a2+a3...

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  3. Prove that ^nC0 "^(2n)Cn-^nC1 ^(2n-2)Cn +^nC2 ^(2n-4)Cn =2^n

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  4. If (1+x)^n=a0+a1x+a2x^2+…….+anx^n then prove that (1+(a/a0))(1+(a2)/(a...

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  5. Prove that the following identity about binomial coefficients ((n),(0)...

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  6. The terms independent of x in (3/2(x^2)-1/(3x))^9 is

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  7. The 10^(th) term in the expansion of (2x^2+1/x)^(12) is

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  8. If the 6th term in the expansion of (1/x^(8//3)+x^2log(10)x)^8 is 5600...

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  9. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is

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  10. The sum of series ,^20C0-^20C1+^20C2-^20C3+.....+ ^20C10 is

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  11. ^8C2+^8C3+^8C4+....^8C7 is equal to

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  12. .^18C15+2(.^18C16)+^17C16+1=^nC3, then n is equal to

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  13. The value of 1^2cdotC1+3^2cdotC3+5^2cdotC5+......, is

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  14. Let [x] denotes the greatest integer less then or equal to x. If x=(sq...

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

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  16. If p=(8+3sqrt7)^n and f=p-[p], where [.] denotes the greatest integer ...

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  17. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is

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  18. If n in N then value of S=sum(r=0)^n(-1)^r((^nCr)/(^(r+2)Cr)) is

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  19. The value of the expression .^47C4 + sum(j = 1)^5.^(52 - j)C3 is equal...

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  20. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+.....oo

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