JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Straight Lines

Consider the lines given by

L_{1} : x + 3 y - 5 = 0 L_{2} : 3 x - k y - 1 = 0 L_{3} : 5 x + 2 y - 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 \times 4

matrix given in the ORS.

Column I	Column II
(A) $L_{1}, L_{2}, L_{3}$ are concurrent, if	(p) $k = - 9$
(B) One of $L_{1}, L_{2}, L_{3}$ is parallel to at least one of the other two, if	(q) $k = - \frac{6}{5}$
(C) $L_{1}, L_{2}, L_{3}$ form a triangle, if	(r) $k = \frac{5}{6}$
(D) $L_{1}, L_{2}, L_{3}$ do not form a triangle, if	(s) $k = 5$

Answer: A → IV, B → I, B → II, C → III, D → I, D → II, D → IV

Solution

Lines

L_{1}

and

L_{3}

intersect at

(2, 1)

. For concurrency,

L_{2}

must pass through

(2, 1)

6 - k - 1 = 0 \Rightarrow k = 5

. For

L_{1} ∥ L_{2}

\frac{1}{3} = \frac{3}{- k} \Rightarrow k = - 9

. For

L_{2} ∥ L_{3}

\frac{3}{5} = \frac{- k}{2} \Rightarrow k = - \frac{6}{5}

. The lines form a triangle when

k \neq = 5, - 9, - \frac{6}{5}

, e.g.,

k = \frac{5}{6}

. They do not form a triangle when

k = 5, - 9, - \frac{6}{5}

JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Match the columns

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JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Straight Lines

Solution

More JEE Advanced questions on Straight Lines