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18 May 2021, 07:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (01:41) correct
40%
(01:30)
wrong
based on 246
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If \(x<\frac{1}{x}\), then which of the following must be true?
I. \(x^3> x^2\)
II.\(x^2> x^3\)
III. \(x > x^2\)
(A) only I
(B) only II
(C) only III
(D) both II and III
(E) none of these
Posted from my mobile device
I. \(x^3> x^2\)
II.\(x^2> x^3\)
III. \(x > x^2\)
(A) only I
(B) only II
(C) only III
(D) both II and III
(E) none of these
Posted from my mobile device
18 May 2021, 08:45
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\(x<\frac{1}{x}.......x-\frac{1}{x}<0........\frac{x^2-1}{x}<0\)
Two cases
1) If x>0, then \(x^2-1<0.....x^2<1........0<x<1\)
2) If x<0, then \(x^2-1>0.....x^2>1........x<-1\)
I. \(x^3> x^2\).......When 0<x<1, this is not true.
II.\(x^2> x^3\).....This is always true in the ranges x<-1 and 0<x<1
III. \(x > x^2\) .......When x<-1, this is not true.
B
Updated on: 19 May 2021, 18:37
Originally posted by LaveenaPanchal on 19 May 2021, 06:01.
Last edited by LaveenaPanchal on 19 May 2021, 18:37, edited 1 time in total.
Last edited by LaveenaPanchal on 19 May 2021, 18:37, edited 1 time in total.
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x < 1/x = x - 1/x < 0
(x^2 - 1)/x <0,
x^2 - 1 <0 or 1/x <0
-1 < x < 1 or X < 0
For a must true option value of x should be -1 < x < 0
I. x^3 > x^2
x^3-x^2>0 = X^2 (x-1)>0 i.e. x>1. Not true
II. x^2>x^3 = x^2 - X^3 >0 = X^2 (1-x) > 0 i.e 1-x >0 i.e. x<1 Not True in all cases.
III. x > x^2 = x - x^2 > 0 = x(1-x)>0
Option 1 X>0 & 1-x >0 i.e. x<1. So 0 < x < 1. True in this case.
Option 2 x<0 & 1-x < 0 i.e x >1 Not true in this case.
Hence answer should be E. None of these.
(x^2 - 1)/x <0,
x^2 - 1 <0 or 1/x <0
-1 < x < 1 or X < 0
For a must true option value of x should be -1 < x < 0
I. x^3 > x^2
x^3-x^2>0 = X^2 (x-1)>0 i.e. x>1. Not true
II. x^2>x^3 = x^2 - X^3 >0 = X^2 (1-x) > 0 i.e 1-x >0 i.e. x<1 Not True in all cases.
III. x > x^2 = x - x^2 > 0 = x(1-x)>0
Option 1 X>0 & 1-x >0 i.e. x<1. So 0 < x < 1. True in this case.
Option 2 x<0 & 1-x < 0 i.e x >1 Not true in this case.
Hence answer should be E. None of these.
