Correct option is (B) 29
\(\because\) 2x - 1 is a factor of \((4x^4 -(a – 1) x^3 + ax^2 – 6x – 1)\)
\(\therefore\) \(x=\frac12\) is a zero of \((4x^4 -(a – 1) x^3 + ax^2 – 6x – 1)\)
\(\Rightarrow4(\frac12)^4-(a-1)(\frac12)^3+a(\frac12)^2-6(\frac12)-1=0\)
\(\Rightarrow\frac14-\frac{(a-1)}8+\frac a4-3-1=0\)
\(\Rightarrow\) 2 - (a - 1) + 2a - 32 = 0
\(\Rightarrow\) a - 29 = 0
\(\Rightarrow\) a = 29
