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Show that coefficient of a^m and a^n in ...

Show that coefficient of `a^m` and `a^n` in the expansion of `(1+a)^(m+n)` are equal.

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MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. Find the coefficient of x^(8) in the expansion of (x^(2) - (1)/(x)...

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  2. Find a positive value of m for which the coefficient of x^2 in the exp...

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  3. Show that coefficient of a^m and a^n in the expansion of (1+a)^(m+n) a...

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  4. Find 'a' if the coefficients of x^(2) and x^(3) in the expanion of (3 ...

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  5. Find the value of r if the coefficients of (2r+4)th and (r - 2) th ter...

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  6. Find the coefficient of a^(5)b^(7) in (a-2b)^(12).

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  7. Find the coefficient of a^4 in the expansion of the product (1+ 2a)^4 ...

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  8. In the binomial expansion (a+b)^n, the coefficients of fourth and thir...

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  9. In the binomial expansion of (1+x)^34, the coefficients of the (2r-1)t...

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  10. Which term is independent of x in the expansion of (2x^2 +1/x)^12 ? An...

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  11. Write and simplify the term independent x in the expansion of (x^2-2/x...

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  12. Write and simplify the term independent of x in the expansion of (x-1/...

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  13. Find the term independent of x, x ne 0 in the expansion of : (x-1/x)...

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

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  15. Find the term independent of x, x ne 0 in the expansion of : (x^2+3/...

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  16. Find the term independent of x, x ne 0 in the expansion of : (3-x^3/...

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  17. Write and simplify the coefficient of the term independent of x, in th...

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  18. Find the greatest term in (x+y)^n, when x=11, y=4, n = 30.

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  19. Find the greatest term in (1+ 4x)^8, when x=1/3.

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  20. Find a, b and n in the expansion of (a + b)^(n) if the first three ter...

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