Inequalities Test 1

Instructions

For the following questions answer them individually

Q 1

Find the smallest integer value of ā€˜nā€™ such that for all m >= n, the value $$m^3 - 16m^2 + 81m - 126$$ is positive.

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789
456
123
0.-
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Q 2

What are the values of ā€˜yā€™ that satisfy the following inequality:
$$15y - \frac{2}{y} > 1$$?

Q 3

What is the sum of the maximum and minimum values of the expression $$\frac{1}{x^2 - 6x + 14}$$?

Q 4

Let x and y be two positive numbers such that $$x + y = 1.$$

Then the minimum value of $$(x+\frac{1}{x})^2+(y+\frac{1}{y})^2$$ is

[CAT 2001]

Q 5

If ā€˜pā€™ is a positive number less than or equal to 6, then what is the maximum possible value of the expression $$(7-p)^3*(p+7)^4$$?

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