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CAT 1990 Question-4

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Q.) The value of $\frac { (1-{ d }^{ 3 }) }{ (1-d) }$ is
1) >1 if d>-1
2) >3 if d>1
3) >2 if 0 < d < 0.5

Solution: We know that

${ a }^{ 3 }-{ b }^{ 3 }=(a-b)({ a }^{ 2 }+ab+{ b }^{ 2 })$

X = $\frac { (1-{ d }^{ 3 }) }{ (1-d) }$ = $\frac { (1-d)(1+d+{ d }^{ 2 }) }{ (1-d) }$ =$(1+d+{ d }^{ 2 })$ Here , if d>1 , X >3

Hence , Option(2)