JEE Advanced 2008 Paper 2Question 1
Consider the lines given by
$L_1: x+3y-5=0$
$L_2: 3x-ky-1=0$
$L_3: 5x+2y-12=0$
Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the $4\times4$ matrix given in the ORS.
Column I:
(A) $L_1,L_2,L_3$ are concurrent, if
(B) One of $L_1,L_2,L_3$ is parallel to at least one of the other two, if
(C) $L_1,L_2,L_3$ form a triangle, if
(D) $L_1,L_2,L_3$ do not form a triangle, if
Column II:
(p) $k=-9$
(q) $k=-\frac{6}{5}$
(r) $k=\frac{5}{6}$
(s) $k=5$
Points and Straight Lines
AnswerA-s, B-p,q, C-r, D-p,q,s
Solution
$L_1,L_3$ meet at $(2,1)$; $L_2$ passes through it iff $k=5$. Slope of $L_2$ is $3/k$: equal to $-\frac13$ for $k=-9$, to $-\frac52$ for $k=-\frac65$ (parallel cases). Triangle forms for other $k$, e.g. $k=\frac56$; no triangle for $k=-9,-\frac65,5$.