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JEE Main2013MathematicsStraight LinesActual

Let ₁ be the angle between two lines 2 x+3 y+c₁=0 and -x+5 y+c₂=0 and ₂ be the angle between two lines 2 x+3 y+c₁=0 and -x+5 y+c₃=0 , where c₁, c₂, c₃ are any real numbers : Statement-1: If c₂ and c₃ are proportional, then ₁= ₂ . Statement-2: ₁= ₂ for all c₂ and c₃ .

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+5 y+c₂=0 and -x+5 y+c₃=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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