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If the coefficients of x, x^2 and x^3 in...

If the coefficients of x, `x^2` and `x^3` in the binomial expansion of `(1+x)^(2n)` are in A.P., prove that `2n^2-9n+7=0`.

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MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. The coefficients of three consecutive terms in the expansion of (1+a)^...

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  2. If the coefficients of 5th, 6th , and 7th terms in the expansion of (1...

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  3. If the coefficients of x, x^2 and x^3 in the binomial expansion of (1+...

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  4. If three successive coefficients in the expansion of (1+x)^n are 28, 5...

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  5. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

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  6. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

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  7. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

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  8. Show that 9^(n+1) - 8n -9 is divisible by 64, whenever n is a positiv...

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  9. Using Binomial theorem, prove that 6^(n)-5n always leaves remainder 1...

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  10. Evaluate the following : ""^12C0+""^12C1+""^12C2+ ....... +""^12C12.

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  11. Evaluate the following : ""^12C0+""^12C2+""^12C4 +""^12C12.

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  12. Evaluate the following : ""^16C1+""^16C3+""^16C5+ ....... +""^16C15.

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  13. Prove that underset (r=0) overset (n) sum 3^r ""^nCr =4^n.

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  14. Prove that ""^nC0+3""^nC1+5""^nC2+........+(2n+1)""^nCn= (n+1)2^n.

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  15. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0-...

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  16. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : (1+...

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  17. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0-...

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  18. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : C0+...

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  19. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : 2C0...

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  20. If (1+x)^n =C0+C1 x+ C2 x^2 +....... Cnx^n prove the following : 2C0...

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