Solving Inequalities — CAT Previous-Year Questions

The value of x satisfying the inequality $\frac{1}{x+5}$ ≤ $\frac{1}{2x-3}$ are

Any non-zero real numbers x, y such that y ≠ 3 and $\frac{\mathrm{x}}{\mathrm{y}}$ < $\frac{\mathrm{x}+3}{\mathrm{y}-3}$, will satisfy the condition

For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?

If f(x) = x³ – 4x + p, and f(0) and f(1) are of opposite signs, then which of the following is necessarily true?

Given that −1 ≤ v ≤ 1, −2 ≤ u ≤ −0.5 and −2 ≤ z ≤ −0.5 and w = vz/u, then which of the following is necessarily true?

A real number x satisfying $1-\frac{1}{n}<x\le 3+\frac{1}{n},$ for every positive integer n, is best described by:

If x > 5 and y < −1, then which of the following statements is true?

x and y are real numbers satisfying the conditions 2 < x < 3 and –8 < y < –7. Which of the following expressions will have the least value?

If x > 2 and y > – 1, Then which of the following statements is necessarily true?

Which of the following values of x do not satisfy the inequality (x² – 3x + 2 > 0) at all?

What is the value of m which satisfies 3m² – 21m + 30 < 0?