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NDA 2017 Maths · Mathematics · Quadratic Equations · medium

The set of real x for which (x-2)/(x+3)>0 is

Single correct option

The set of real xx for which x−2x+3>0\dfrac{x-2}{x+3}>0 is
  1. A. (−∞,−3)∪(2,∞)(-\infty,-3)\cup(2,\infty)
  2. B. (−3,2)(-3,2)
  3. C. (−∞,−3]∪[2,∞)(-\infty,-3]\cup[2,\infty)
  4. D. (2,∞)(2,\infty)
Show answer and solution

Answer: (A) (−∞,−3)∪(2,∞)(-\infty,-3)\cup(2,\infty)

A quotient is positive when numerator and denominator have the same sign: both positive gives x>2x>2; both negative gives x<−3x<-3. The end points are excluded (x=−3x=-3 is undefined and x=2x=2 gives 0). The closed version is the usual slip.
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Original question written in the NDA 2017 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