If rth term in the expansion of `(2x^2-1/x)^(12)` is without `x` then `r` is equal to a. 7 b. 8 c. 9 d. 10

Explanation

To find the value of \( r \) such that the \( r \)th term in the expansion of \( (2x^2 - \frac{1}{x})^{12} \) is independent of \( x \), we can 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, \( a = 2x^2 \), \( b = -\frac{1}{x} \), and \( n = 12 \). Therefore, the general term becomes:
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