If $x=11,$ then the value of $(x^5-12x^4+12x^3-12x^2+12x-1)$ is:

The given question asks for the value of the algebraic expression:
$x^5-12x^4+12x^3-12x^2+12x-1$
when $x=11$.

To evaluate this expression efficiently without calculating large powers of 11 directly, we can write the coefficients of the terms in relation to $x$.
Since $x=11$, we can express the number 12 as:
$12=x+1$

Now, substitute $12=x+1$ into the expression:
$x^5-(x+1)x^4+(x+1)x^3-(x+1)x^2+(x+1)x-1$

Next, expand each term inside the expression:
$=x^5-(x^5+x^4)+(x^4+x^3)-(x^3+x^2)+(x^2+x)-1$

Remove the parentheses:
$=x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x-1$

Notice that most of the terms cancel out:
- $x^5-x^5=0$
- $-x^4+x^4=0$
- $x^3-x^3=0$
- $-x^2+x^2=0$

After cancellation, the entire expression simplifies to:
$x-1$

Finally, substitute the value of $x=11$:
$11-1=10$

Therefore, the correct answer is 10.