m is the smallest positive integer such that for any integer n < m, the quantity n³ – 7n² + 11n – 5 is positive. What is the value of m?(CAT 2001)

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None of these

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Solution

The correct option is D None of these
Option (d)
n=1 is a root of the equation
(n - 1)(n² – 6n + 5) = (n - 1)²(n - 5)
Now, (n - 1)² is always positive.
Now, for n < 5, the expression gives a negative quantity.
Therefore, the least value of n will be 6. Hence m = 7 .

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