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Prove that the coefficient of x^n in th...

Prove that the coefficient of `x^n` in the expansion of `(1+x)^(2n)` is twice the coefficient of `x^n` in the expansion of `(1+x)^(2n-1)`

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V PUBLICATION-BINOMIAL THEORM-QUESTIONBANK
  1. In the expansion of (1+a)^(m+n), prove that the coefficient of a^m and...

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  2. The coefficients of the (r-1)^(th),r^(th) and (r+1)^(th) terms in the ...

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  3. Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is ...

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  4. Find the positive value of m for which the coefficient of x^2 in the e...

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  5. Find the term independent of x in the expansion of ((3x^2)/2-1/(3x))^6

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  6. If the coefficients of a^(r-1), a^r and a^(r+1) in the expansion of (1...

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  7. Show that the coefficient of the middle term in the expansion of (1+x)...

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  8. Find the coefficient of a^4 in the product (1+2 a)^4 (2-a)^5 using bin...

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  9. Find the r^ (th) term from the end in the expansion of (x+a)^n .

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  10. Find the term independent of x in the following expansion. (root(3)(...

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  11. If the coefficients of (r-5)^( th) and (2 r-1)^ (th) terms in the ex...

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  12. Find a, b and n in the expansion of (a+b)^n if the first three terms o...

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  13. Find a if the coefficients of x^2 and x^3 in the expansion of (3+ax)^9...

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  14. Find the coefficient of x^5 in the product (1+2x)^6(1-x)^7 using binom...

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  15. If a and b are distinct integers prove that a-b is a factor of a^n-b^n...

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  16. Evaluate (sqrt3+sqrt2)^6-(sqrt3-sqrt2)^6

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  17. Find the value of (a^2+sqrt(a^2-1))^4+(a^2-sqrt(a^2-1))^4

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  18. Find an approximation of (0.99)^5 using the first three terms of its e...

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  19. Expand using Binomial theorem (1+x/2-2/x)^4,xne0

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  20. Find the expansion of (3x^2-2ax+3a^2)^3 using Binomial theorem

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