Question

The term independent of \( x \) in the expansion of \( \left( 2x^4 - \frac{1}{x^2} \right)^{12} \) is

• A. 6920
• B. 7920
• C. 7900
• D. 3960

Hint:

Set power of x = 0 to find independent term.

Answer 1

The Correct Option is B

Concept: General term: \[ T_{r+1} = \binom{12}{r}(2x^4)^{12-r}\left(-\frac{1}{x^2}\right)^r \]

Step 1: Power of x.
\[ x^{48-4r-2r} = x^{48-6r} \] For constant term: \[ 48 - 6r = 0 \Rightarrow r=8 \]

Step 2: Compute term.
\[ = \binom{12}{8} (2^4)^4 \] \[ = 495 \cdot 16^4 = 495 \cdot 256 = 7920 \]