If $\left| {\,\begin{array}{*{20}{c}}a&b&{a + b}\\b&c&{b + c}\\{a + b}&{b + c}&0\end{array}\,} \right| = 0$; then $a,b,c$ are in

If the following system of linear equations

$2 x+y+z=5$

$x-y+z=3$

$x+y+a z=b$

has no solution, then :

If $D = \left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{1 + x}&1\\1&1&{1 + y}\end{array}\,} \right|$ for $x \ne 0,y \ne 0$ then $D$ is

For which of the following ordered pairs $(\mu, \delta)$ the system of linear equations  $x+2 y+3 z=1$ ; $3 x+4 y+5 z=\mu$ ; $4 x+4 y+4 z=\delta$ is inconsistent?

The system of equations : $2x\, \cos^2\theta + y\, \sin2\theta – 2\sin\theta = 0$ $x\, \sin2\theta + 2y\, \sin^2\theta = – 2\, \cos\theta$ $x\, \sin\theta – y \cos\theta = 0$ , for all values of $\theta$ , can