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Find the term independent of x in the ex...

Find the term independent of x in the expansion of `(3/2x^2-1/(3x))^6`.

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To find the term independent of \( x \) in the expansion of \( \left( \frac{3}{2}x^2 - \frac{1}{3x} \right)^6 \), we will follow these steps: ### Step 1: Write the General Term The general term \( T_{r+1} \) in the binomial expansion of \( (a + b)^n \) is given by: \[ T_{r+1} = \binom{n}{r} a^{n-r} b^r \] In our case, \( a = \frac{3}{2}x^2 \), \( b = -\frac{1}{3x} \), and \( n = 6 \). Therefore, the general term becomes: ...
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Knowledge Check

  • The term independent of x in the expansion of (3/2x^2-1/(3x))^6 is

    A
    `5/13`
    B
    `5/12`
    C
    14
    D
    `1/12`
  • The term independent of x in the expansion of (2x+1/(3x))^(6) is

    A
    160/9
    B
    80/9
    C
    160/27
    D
    80/3
  • The term independent of x in the expansion of (2x+(1)/(3x))^(6) is

    A
    `160//9`
    B
    `80//9`
    C
    `160//27`
    D
    `80//3`
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