If D = 11111+x1111+y for x ≠0; y ≠0. then D is

D = 11111+x1111+yC2→C2→C1 , C3→C3→C1 =1001x010y =xy∴ D is divisible by both x and y

If D = 11111+x1111+y for x ≠0; y ≠0. then D is

D = 11111+x1111+yC2→C2→C1 , C3→C3→C1 =1001x010y =xy∴ D is divisible by both x and y

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If $D = |\begin{matrix} 1 & 1 & 1 \\ 1 & 1 + x & 1 \\ 1 & 1 & 1 + y \end{matrix}|$ for $x \neq 0; y \neq 0$ . then D is

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Divisible by y but not x

Divisible by neither x nor y

Divisible by both x and y

Divisible by x but not y

answer is C.

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Detailed Solution

$\begin{array}{rcl} D & = & |\begin{matrix} 1 & 1 & 1 \\ 1 & 1 + x & 1 \\ 1 & 1 & 1 + y \end{matrix}| \\ C_{2} & \to & C_{2} \to C_{1}, C_{3} \to C_{3} \to C_{1} \\ = & |\begin{matrix} 1 & 0 & 0 \\ 1 & x & 0 \\ 1 & 0 & y \end{matrix}| \\ = & xy \end{array}$