JEE MAIN - Mathematics (2025 - 24th January Evening Shift - No. 2)
Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability $\mathrm{P}(\mathrm{E})$ is :
$\frac{3}{8}$
$\frac{1}{8}$
$\frac{3}{16}$
$\frac{5}{8}$
Explanation
C-I $\left|\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right| \rightarrow 4$ ways
C-II $\left|\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right| \&\left|\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right| \rightarrow 2$ ways
$$\mathrm{P}=\frac{\text { favourable }}{\text { total }}=\frac{6}{16}=\frac{3}{8}$$
Comments (0)
