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BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Determinants

BITSAT 2009 · Mathematics · Determinants

The digits ( A, B ) and ( C ) are such that the three digit numbers...

The digits (A,B\mathrm{A}, \mathrm{B}) and (C\mathrm{C}) are such that the three digit numbers (A 88,6  B\mathrm{~B}8,86 C\mathrm{C}) are divisible by 72 then the determinant (\left| A 688B688C\begin{array}{ccc}\text{ A }& 6 & 8 \\ 8 & B & 6 \\ 8 & 8 & C\end{array}\right|) is divisible by

Options

  1. A72
  2. B144
  3. C288
  4. D216

Correct answer

A. 72

Step-by-step solution

R3→100R1+10R2+R3R_3 → 100 R_1+10 R_2+R_3 (\Rightarrow\left|A688B688C\begin{array}{ccc}A & 6 & 8 \\ 8 & B & 6 \\ 8 & 8 & C \end{array}\right|=\left|A688B6A886BC86C\begin{array}{ccc}A & 6 & 8 \\ 8 & B & 6 \\ A 88 & 6 B C & 86 C \end{array}$$\right|) which is divisible by 72.
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