A) divisible by neither\[X=a\]nor y
B) divisible by both\[RC{{H}_{2}}X>{{R}_{3}}CX>{{R}_{2}}CHX\]and y
C) divisible by\[RC{{H}_{2}}X>{{R}_{2}}CHX>{{R}_{3}}CX\]but not y
D) divisible by y but not\[{{R}_{3}}CX>{{R}_{2}}CHX>RC{{H}_{2}}X\]
Correct Answer: B
Solution :
\[D=\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \\ \end{matrix} \right|\] On applying\[{{C}_{2}}\to {{C}_{2}}-{{C}_{1}}\]and\[{{C}_{3}}\to {{C}_{3}}-{{C}_{1}}\], \[=\left| \begin{matrix} 1 & 0 & 0 \\ 1 & x & 0 \\ 1 & 0 & y \\ \end{matrix} \right|=xy\] Hence, D is divisible by both\[x\]and y.
You need to login to perform this action.
You will be redirected in
3 sec
