Q63 / 125 · BITSAT 2009 · Mathematics
The digits \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are such that the three digit numbers \(A 88,6 \mathrm{~B} 8,86 \mathrm{C}\) are divisible by 72 then the determinant \(\left|\begin{array}{ccc}\text { A } & 6 & 8 \\ 8 & B & 6 \\ 8 & 8 & C\end{array}\right|\) is divisible by
- Correct answerA72
- B144
- C288
- D216
Solution
\(R_3 \rightarrow 100 R_1+10 R_2+R_3\)
\(\Rightarrow\left|\begin{array}{ccc}
A & 6 & 8 \\
8 & B & 6 \\
8 & 8 & C
\end{array}\right|=\left|\begin{array}{ccc}
A & 6 & 8 \\
8 & B & 6 \\
A 88 & 6 B C & 86 C
\end{array}\right|\)
which is divisible by 72.
Hence, the correct answer is option: 'A'.