MHT CET · Maths · Straight Lines
If the lines \(4 x+3 y-1=0, x-y+5=0\) and \(k x+5 y-3=0\) are concurrent, then \(k=\)
- A 5
- B 6
- C 7
- D 4
Answer & Solution
Correct Answer
(B) 6
Step-by-step Solution
Detailed explanation
For concurrency \(\left|\begin{array}{ccc}4 & 3 & -1 \\ 1 & -1 & 5 \\ k & 5 & -3\end{array}\right|=0\)
\(\Rightarrow 4(3-25)+3(5 k+3)-1(5+k)=0\)
\(\Rightarrow-88+15 k+9-5-k=0\)
\(\Rightarrow-84+14 k=0\)
\(\Rightarrow k=6\)
\(\Rightarrow 4(3-25)+3(5 k+3)-1(5+k)=0\)
\(\Rightarrow-88+15 k+9-5-k=0\)
\(\Rightarrow-84+14 k=0\)
\(\Rightarrow k=6\)
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