Inequalities Questions for CAT

Find solution set of $|x-5| ≤ 2$.

Solve the following inequality: $\frac{7 x-5}{8 x+3}>4$

Solve the following inequality: $x+3<\sqrt{x+33}$

What values of $y$ make the inequality $y^3 - 5y^2 + 8y - 4 > 0$ true?

What values of ‘x’ satisfy the inequality: $(|x| - 2)(|x - 2|)(x + 5) > 0$?

A number $z$ lies between 0 and 1. Which of the following is true?

The inequality (n – 4)(n – 16) – 2(n – 5) ≤ 0 is satisfied for how many integers n?

$\frac{\sqrt{x-3}}{x-2}>0$

For all possible integers $n$ satisfying $0.0625 \le 4 + 4^{n} \le 1028$, the number of integer values of $2 + 2^{n+2}$ is

If $a$ is a positive number that is less than or equal to 5, what is the maximum value of the expression $(5 - a)^4 (a + 5)^5$?

Determine the range of $x$ that satisfies: $( \frac{|x|^2 + |x| - 6}{|x| + 5} > 0 )$

Solve: $\frac{x^{4}+x^{2}+1}{x^{2}-4 x-5}>0$

Which of the following statements is incorrect?

How many integer values of $y$ satisfy the inequality $\left| \frac{4 - \left| \frac{y}{7} \right|}{\left| \frac{y}{7} \right| + 2} \right| > \frac{2}{7}$?

If $a, b > 0$ and $ab=1$, then the minimum value of $a+b$ is

If $x>0$, then the minimum value of $x^2+\dfrac{1}{x^2}$ is

What is the product of all integer values of $x$ that satisfy the inequality $|x|^3 - 19|x| + 30 \leq 0$?

What is the number of integral values of $x$ that satisfy: $( \frac{(x - 2)(x - 4)^2 \cdots (x - 20)^{10}}{(x + 2)(x + 4)^2 \cdots (x + 20)^{10}} < 0 )$?

If $n$ is a natural number satisfying $6^{n-1} < 5^{n+2}$, then find the least integer $m$ such that $5^{n+2} < 3^{n+m}$ for each such $n$.

If $x+y=6$ and $x, y > 0$, then the maximum value of $x^3y$ is