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IPMAT 2020 Question Paper IPM Indore Quantitative Ability. Solve questions from IPMAT 2020 Question Paper from IPM Indore and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here: IPM Sample Paper

Question 18 : Consider the following statements:
(i) When 0 < x < 1, then \\frac{1}{1+x}) < 1 - x + x2
(ii) When 0 < x < 1, then \\frac{1}{1+x}) > 1 - x + x2
(iii) When -1 < x < 0, then \\frac{1}{1+x}) < 1 - x + x2
(iv) When -1 < x < 0, then \\frac{1}{1+x}) > 1 - x + x2
Then the correct statements are

  1. (i) and (ii)
  2. (ii) and (iv)
  3. (i) and (iv)
  4. (ii) and (iii)

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Explanatory Answer

We are in essence comparing 2 inequalities \\frac{1}{1 + x}) and 1 - x + x2.
Take the inequality 1 - x + x2 > \\frac{1}{1 + x})
\\frac{(1 + x) (1 - x + x^{2}) - 1}{(1 + x)}) > 0
\\frac{1 + x^{3} - 1}{1 + x}) > 0
\\frac{x^{3}}{1 + x}) > 0
This inequality holds good when x is positive.
Hence option 1 is correct which means option 2 is wrong.
The inequality also holds good when both the numerator and the denominator are negative.
Hence option 4 holds good and option 3 is wrong.
Hence the correct answer is i and iv.

The answer is (i) and (iv)

Choice C is the correct answer.

 

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