Q. A determinant of second order is made with the elements 0, 1. What is the probability that the determinant is positive?
A) $\frac{7}{12}$
B) $\frac{11}{12}$
C) $\frac{3}{16}$
D) $\frac{15}{16}$
Explanation
(c)
Total number of ways =16
The favourable ways are
$\left| \begin{matrix}
1 & 0 \\
0 & 1
\end{matrix} \right|,\ \left| \begin{matrix}
1 & 0 \\
1 & 1
\end{matrix} \right|,\ \left| \begin{matrix}
1 & 1 \\
0 & 1
\end{matrix} \right|$
$\therefore Required\ probability = \frac{3}{16}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.