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Show that the sum of the coefficients of `x^(-6)` and `x^(-1)` in `(5x^(2)-(7)/(x^(3)))^(12)` is positive.

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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - 1.1 (Level - 1)
  1. Find the middle term(s) in the expansion of n in N (p^(2)-2q)^(2n-...

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  2. Find the middle term(s) in the expansion of n in N (a^(3)+(2)/(b))...

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  3. Show that the sum of the coefficients of x^(-6) and x^(-1) in (5x^(2)-...

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  4. Show that the sum of the coefficients of x^(25) and x^(-10) of (x^(4) ...

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  5. Find the numerically greatest term of (3+7x)^(15), x=(4)/(5)

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  6. Find the numerically greatest term of (2x-3y)^(12), x=1, y=(5)/(3)

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  7. Find the numerically greatest term of (5x-6y)^(14), x=(2)/(5), y=(1)...

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  8. If the coefficients of x^(9),x^(10),x^(11) in expansion of (1+x)^(n) a...

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  9. If the 2^("nd"),3^("rd")" and "4^("th") terms in the expansion of (a+x...

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  10. If (1+x+2x^(2)+4x^(3))^(10)=a(0)+a(1)x+a(2)x^(2)+….+a(30)x^(30). Fi...

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  11. If (1+x+2x^(2)+4x^(3))^(10)=a(0)+a(1)x+a(2)x^(2)+….+a(30)x^(30). Fi...

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  12. If (1+x+2x^(2)+4x^(3))^(10)=a(0)+a(1)x+a(2)x^(2)+….+a(30)x^(30). Fi...

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  13. If (1+x+2x^(2)+4x^(3))^(10)=a(0)+a(1)x+a(2)x^(2)+….+a(30)x^(30). Fi...

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  14. If (1+x+x^(2))^(n)=b(0)+b(1)x+b(2)x^(2)+….+b(2n)x^(2n) then prove that...

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  15. If (1+x+x^(2))^(n)=b(0)+b(1)x+b(2)x^(2)+….+b(2n)x^(2n) then prove that...

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  16. If (1+x+x^(2))^(n)=b(0)+b(1)x+b(2)x^(2)+….+b(2n)x^(2n) then prove that...

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  17. If (1+x+x^(2))^(n)=b(0)+b(1)x+b(2)x^(2)+….+b(2n)x^(2n) then prove that...

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  18. If (1+x+x^(2))^(n)=b(0)+b(1)x+b(2)x^(2)+….+b(2n)x^(2n) then prove that...

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  19. If (1+x+x^(2))^(n)=b(0)+b(1)x+b(2)x^(2)+….+b(2n)x^(2n) then prove that...

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  20. If (1+x+x^(2))^(n)=b(0)+b(1)x+b(2)x^(2)+….+b(2n)x^(2n) then prove that...

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