IPMAT Question Paper 2020 | IPM Indore Quants

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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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Video Explanation

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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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