GATE Civil 2026 Set 2 | Question: 26

Question

Let $f(x)=\left|\begin{array}{ccc}x^{3} & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^{2} & p^{3}\end{array}\right|$ where $p$ is a constant.

The value of $\dfrac{d^{3}}{d x^{3}} f(x)$ at $x=0$ is

• A. $6 p^{3}$
• B. $p+p^{2}$
• C. $p+p^{3}$
• D. independent of $p$