question_answer

           

For which of the following ordered pairs \[(\mu ,\delta )\], the system of linear equations

\[x+2y+3z=1\]

\[3x+4y+5z=\mu \]

\[4x+4y+4z=\delta \]

Is inconsistent?

[JEE MAIN Held On 08-01-2020 Morning]

A) \[(4,3)\] 

B) \[(4,\,6)\]

C) \[(3,4)\] 

D) \[(1,0)\]

Correct Answer: A

Solution :

[a] For inconsistent system we need \[\Delta =0\] and at least one of \[\Delta x,\,\,\Delta y\,\Delta z\ne 0\] \[=(-4)-2(4\mu -5\delta )+3(4\mu -4\delta )\ne 0\] \[\Rightarrow -4+4\mu -2\delta \ne 0\] \[\Rightarrow 2\mu \ne \delta +2\] \[\therefore (\mu ,\delta )=(4,3)\] is only possible in given options