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Find the middle terms in the expansion (...

Find the middle terms in the expansion `(3x-(x^3)/6)^7` .

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To find the middle terms in the expansion of \((3x - \frac{x^3}{6})^7\), we will use the Binomial Theorem. Let's go through the solution step by step. ### Step 1: Identify the terms in the binomial expansion The Binomial Theorem states that for any expression of the form \((a + b)^n\), the expansion can be expressed as: \[ \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r \] In our case, we can let: ...
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RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises
  1. Find the coefficients of x^(32) in the expansion of (x^4-1/(x^3))^(15)...

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  2. Find the middle term in the expansion (2/3x^2-3/(2x))^(20) .

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  3. Find the middle terms in the expansion (3x-(x^3)/6)^7 .

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  4. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(6)dot

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  5. The term independent of x in expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)...

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  6. Prove that there is no term involving x^6 in the expansion of (2x^2-3...

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

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  8. Find the coefficient of x^(50) after simplifying and collecting the li...

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  9. Find the coefficient of x^n in the expansion of (1+x)(1-x)^ndot

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  10. If a1,a2, a3, a4 be the coefficient of four consecutive terms in the e...

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  11. Find the number of integral terms in the expansion of (5^(1/2)+7^(1/8)...

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  12. Find the coefficients of x^7 in (a x^2+1/(b x))^(11)a n dx^(-7)in(a x^...

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  13. Find the coefficient of x^5 in the expansion of (1+x)^(21)+(1+x)^(22)+...

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  14. If the middle term in the binomial expansion of (1/x+xsinx^(10)) is eq...

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

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  16. If A be the sum of odd terms and B that of even terms in the expansion...

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  17. Using binomial theorem, expand {(x+y)^5+(x-y)^5}dot and hence find the...

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  18. Using binomial theorem, prove that 2^(3n)-7^n-1 is divisible by 49 , w...

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  19. Using binomial theorem, prove that (101)^(50)> 100^(50)+99^(50)dot

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  20. Expand (x^2+2a)^5 by binomial theorem.

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