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JEE Advanced 2008Paper 2
Exam
JEE Advanced
Year
2008
Paper
Paper 2
Subject
Mathematics
Chapter
Determinants

JEE Advanced 2008 · Paper 2 · Mathematics · Determinants

Consider the lines given by L_1: x+3 y-5=0, L_2: 3 x-k y-1=0, L_3:...

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. 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

Options

  1. A(A) r, (B) p,s, (C) s, (D) p,s
  2. B(A) s, (B) p,q,r, (C) r, (D) p,q
  3. C(A) s, (B) p,q, (C) r, (D) p,q,s
  4. D(A) r, (B) p,q, (C) s, (D) p,q

Correct answer

C. (A) s, (B) p,q, (C) r, (D) p,q,s

Step-by-step solution

(A) Solving equations L1andL3L_1 and L_3, x−36+10=y+12−25=12−15x=2,y=1\begin{aligned}\frac{x}{-36+10}& =\frac{y}{+12-25}=\frac{1}{2-15}\\ x & =2, y=1 \end{aligned}L_1, L_2, L_3areconcurrent,ifpointare concurrent, if point(2,1)liesonlies onL_2.∴6−k−1=0⇒k=5(B)Either. \therefore \quad 6-k-1=0 \Rightarrow k=5 (B) EitherL_1isparalleltois parallel toL_2,or, orL_3isparalleltois parallel toL_2,then, then13=3−k or 35=−k2k=−9 or \quadk=−65\begin{aligned}& \frac{1}{3}=\frac{3}{-k} \text{ or } \frac{3}{5}=\frac{-k}{2}\\ & k=-9 \quad \text{ or } \quadk=-\frac{6}{5} \end{aligned}⇒\Rightarrow \quadk=-9 \text{ or }k=-65(\frac{6}{5} (C) L1,L2,L3formatriangle,iftheyarenotconcurrent,orL_1, L_2, L_3form a triangle, if they are not concurrent, ornot parallel. \therefore \quad k ≠ 5,-9,-65⇒\frac{6}{5} \Rightarrowk=56(\frac{5}{6} (D) L1,L2,L3L_1, L_2, L_3 do not form a triangle, if k=5,-9,-$\frac{6}{5}
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