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NDA 2016 Maths · Mathematics · Straight Lines · medium

The points (a,0), (0,b) and (1,1), with a,b≠0, are collinear if

Single correct option

The points (a,0)(a,0), (0,b)(0,b) and (1,1)(1,1), with a,b≠0a,b\ne0, are collinear if
  1. A. a+b=1a+b=1
  2. B. 1a+1b=1\dfrac1a+\dfrac1b=1
  3. C. ab=1ab=1
  4. D. a−b=1a-b=1
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Answer: (B) 1a+1b=1\dfrac1a+\dfrac1b=1

The line through (a,0)(a,0) and (0,b)(0,b) is x/a+y/b=1x/a+y/b=1. It passes through (1,1)(1,1) exactly when 1/a+1/b=11/a+1/b=1. The condition a+b=1a+b=1 is wrong because the reciprocals of the intercepts are involved.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake