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In the expansion of (1+x)^(m+n), where m...

In the expansion of `(1+x)^(m+n)`, where m & n are +ve integers, prove that the coefficients of `x^m` and `x^n` are equal.

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PATHFINDER-BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
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  2. Find the coefficient of x in (1-2x^3+3x^5)(1+x+1/x)^10.

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  3. In the expansion of (1+x)^(m+n), where m & n are +ve integers, prove t...

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  4. Determine the term independent of x in the expansion of (3x^2-1/(2x^3)...

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  5. Find the coefficient of x^5 in the expression of (1+x^2)^5(1+x)^4.

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  6. Which term in the expansion of (1+x)^p(1+1/x)^q is independent of x, w...

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  7. Determine the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^n.

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  8. Determine the x-free term in (sqrtx-sqrtc/sqrtx)^10.

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  9. Show that the sum of the coefficients of all odd terms in the expansio...

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  10. Find the fifth term form the end in the expansion of (sqrtx/3+2/5x)^11...

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  11. Show that the middle term in the expansion of (x+1)^(2n) is (1.3.5.......

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  12. The first three terms in the binomial expansion of (x+y)^n are 1,56 an...

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  13. If n be a positive integer, then by using binomial theorem show that 3...

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  14. Find the greatest value of the term independent of x in the expansion ...

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  15. Find the coefficient of x in the expansion (1-x^2+2x^4)(1-1/x)^6.

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  16. If (1+x+x^2)^n=a0+a1x+a2x^2+.......+a(2n)x^(2n), then prove that a0+a2...

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  17. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x...

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  18. If the coefficients of four consecutive terms in the expansion of (1+x...

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  19. The 3rd,4th and fifth terms in the expansion of (x+a)^n are 252, 1512,...

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

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