CAT 2018 Question Paper Shift 2 Solved Paper

Question : 93 of 100

Marks: +1, -0

The smallest integer n such that

n^3

- 11

n^2

+ 32n - 28 > 0 is

Solution:

Given,

n^{3}-11 n^{2}+32 n-28>0

When

n=2, n^{3}-11 n^{2}+32 n-28=0

⇒(n-2)(n^{2}-9 n+14)>28

⇒(n-2)(n-7)(n-2)>28

For

n<2,(n-2)(n-7)(n-2)

is negative.
For $2 For

n>7,(n-2)(n-7)(n-2)

is positive.
When

n=8,(n-2)(n-7)(n-2)=36,

which is greater than

28 .

Least integral value of

n

which satisfies the inequation is 8 .

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