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In the binomial expansion of (1+a)^(m+n)...

In the binomial expansion of `(1+a)^(m+n)` , prove that the coefficient of `a^m a n d\ a^n` are equal.

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RD SHARMA ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the term independent of x in the expansion of: (x-1/x)^(12) .

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  2. Find the term independent of x in the expansion of: \ (2x-1/x)^(10)dot

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  3. In the binomial expansion of (1+a)^(m+n) , prove that the coefficient ...

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  4. Prove that the coefficients of x^n in (1+x)^(2n) is twice the coeffici...

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

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  6. If the coefficients of (r-5)^(t h) and (2r-1)^(t h) terms in the expan...

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  7. The coefficient of three consecutive terms in the expansion of (1+x)^(...

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  8. If the coefficients of a^(r-1),\ a^r and \ a^(r+1) in the binomial exp...

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  9. The coefficients of (r-1)^(t h),\ r t h\ a n d\ (r+1)^(t h) terms in t...

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  10. If the fourth term in the expansion of (a x+1/x)^n \ is \ 5/2,\ then ...

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  11. The sum of the coefficients of first three term in the expansion of (x...

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  12. If x^p occurs in the expansion of (x^2+1//x)^(2n) , prove that its coe...

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  13. The coefficient of x^m in (1+x)^m +(1+m)^(m+1) +...+(1+x)^n ,m≤n is

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  14. If in the expansion of (1-x)^(2n-1) ardenotes the coefficient of x^r t...

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  15. If 3rd, 4th, 5th terms in the expansion of (x+a)^n be 84, 280 and 560,...

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  16. Find the number of terms which are free from radical signs in the e...

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  17. Find the 11th term form the beginning and the 11th term form the end...

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  18. Find the 7th term in the expansion of (3x^2-1/(x^3))^(10)dot

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  19. Find the 5th term from the end in the expansion of (3x-1/(x^2))^(10)do...

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  20. Find the 7th term in the expansion of ((4x)/5+5/(2x))^8dot

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