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JEE Main 201323 AprilOnline
Exam
JEE Main
Year
2013
Date
23 April
Mode
Online
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2013 · 23 April · Online · Mathematics · Straight Lines

Let θ_1 be the angle between two lines 2 x+3 y+ c_1=0 and -x+5...

Let θ1\theta_1 be the angle between two lines 2x+3y+2 x+3 y+ c1=0c_1=0 and −x+5y+c2=0-x+5 y+c_2=0 and θ2\theta_2 be the angle between two lines 2x+3y+c1=02 x+3 y+c_1=0 and −x+5y+-x+5 y+ c3=0c_3=0, where c1,c2,c3c_1, c_2, c_3 are any real numbers : Statement-1: If c2c_2 and c3c_3 are proportional, then θ1=θ2\theta_1=\theta_2. Statement-2: θ1=θ2\theta_1=\theta_2 for all c2c_2 and c3c_3.

Options

  1. AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation of Statement-1.
  2. BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation of Statement-1.
  3. CStatement-1 is false; Statement- 2 is true.
  4. DStatement-1 is true; Statement- 2 is false.

Correct answer

A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation of Statement-1.

Step-by-step solution

Two lines −x+5y+c2=0-x+5 y+c_2=0 and −x+5y+c3-x+5 y+c_3 =0=0 are parallel to each other. Hence statement-1 is true, statement-2 is true and statement-2 is the correct explanation of statement-1.
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