IPMAT Indore (MCQ) PYQs

Suppose $\left|\begin{array}{lll}a & a^{2} & a^{3}-1 \\ b & b^{2} & b^{3}-1 \\ c & c^{2} & c^{3}-1\end{array}\right|=0$, where $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ are distinct real numbers. If ${a}=3$, then the value of $abc$ is:

If $A$ is a $3 \times 3$ non-zero matrix such that $A^2 = 0$ then the determinant of $(I + A)^{50} - 50A$ is equal to

Suppose $a, b$ and $c$ are integers such that $a>b>c>0$, and $A=\left[\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right]$. Then the value of the determinant of $A$ is