Question of The Day08-06-2020

If the lines 7x - 3y = 5, 2x – 6y = 6 and 5x + Ky = 4 are concurrent, then what is the value of k?

Answer

Correct Answer : a ) 3.875

Explanation :

The lines a₁x + b₁y + c₁ = 0, a₂x + b₂y + c₂ = 0, and a₃x + b₃y + c₃ = 0 will be concurrent to each other if and only if

⇒\(\begin{bmatrix} a1 & b1 & c1 \\ a2 & b2 & c2 \\ a3 & b3 & c3 \end{bmatrix} =0\)

So, lines 7x - 3y = 5, 2x – 6y = 6 and 5x + Ky = 4 are concurrent to each other if

⇒\(\begin{bmatrix} 7 & -3 & -5 \\ 2 & -6 & -6 \\ 5 & k & -4 \end{bmatrix} =0\)

⇒ 7 (24 – (-6k)) – (- 3) (-8 – (- 30)) + (- 5) (2k – (- 30)) = 0

⇒ 168 + 42k – 24 + 90 – 10k – 150 = 0

⇒ 124 + 32k = 0

⇒ k = – 3.875

Hence, (a) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

Read Daily Current Affairs, Banking Awareness, Hindi Current Affairs, Word of the Day, and attempt free mock tests at PendulumEdu and boost your preparation for the actual exam.