1. The problem states we have the cubic polynomial $$f(x) = 2x^3 - 5x^2 + ax - 7$$ and that the value of $f(x)$ at $x=2$ is 11. 2. Substitute $x = 2$ into the polynomial to find $a$: $$f(2) = 2(2)^3 - 5(2)^2 + a(2) - 7 = 11$$ 3. Calculate the powers: $$f(2) = 2(8) - 5(4) + 2a - 7 = 11$$ $$= 16 - 20 + 2a - 7 = 11$$ 4. Simplify the constants: $$16 - 20 - 7 = -11$$ So we have: $$-11 + 2a = 11$$ 5. Solve for $a$: $$2a = 11 + 11 = 22$$ $$a = \frac{22}{2} = 11$$ 6. Check the multiple choice options: A) -1, B) 1, C) 3, D) 5. None of these match $a = 11$. 7. Therefore, the correct value of $a$ that makes $f(2) = 11$ is $a = 11$, which is not listed among the options given. Final answer: $$a = 11$$