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JEE Advanced 2007Paper 2
Exam
JEE Advanced
Year
2007
Paper
Paper 2
Subject
Mathematics
Chapter
Straight Lines

JEE Advanced 2007 · Paper 2 · Mathematics · Straight Lines

Lines L_1: y-x=0 and L_2: 2 x+y=0 intersect the line L_3: y+2=0 at...

Lines L1:y−x=0L_1: y-x=0 and L2:2x+y=0L_2: 2 x+y=0 intersect the line L3:y+2=0L_3: y+2=0 at PP and QQ, respectively. The bisector of the acute angle between L1L_1 and L2L_2 intersects L3L_3 at RR. Statement I The ratio PR:RQP R: R Q equals 22:52 \sqrt{2}: \sqrt{5}. Statement II In any triangle, bisector of an angle divides the triangle into two similar triangles.Lines L_1: y-x=0 and L_2: 2 x+y=0 intersect the line L_3: y+2=0 at P and Q , respectively. The bisector of the acuteLines L_1: y-x=0 and L_2: 2 x+y=0 intersect the line L_3: y+2=0 at P and Q , respectively. The bisector of the acute

Options

  1. AStatement I is true, Statement II is true; Statement II is a correct explanation for Statement I
  2. BStatement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
  3. CStatement I is true, Statement II is false
  4. DStatement I is false, Statement II is true

Correct answer

B. Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I

Step-by-step solution

In △OPQ\triangle O P Q Lines L_1: y-x=0 and L_2: 2 x+y=0 intersect the line L_3: y+2=0 at P and Q , respectively. The bisector of the acute
Clearly, PRRQ=OPOQ=225\frac{P R}{R Q}=\frac{O P}{O Q}=\frac{2 \sqrt{2}}{\sqrt{5}}
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