# IPMAT Question Paper 2020 | IPM Indore Quants

###### IPMAT Sample Paper | IPMAT Question Paper | Question 18

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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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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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