CAT Inequalities & Modulus questions (2017–2025) — actual Quant questions with solutions

For real values of x, the range of the function f(x) = (2x − 3)/(2x² + 4x − 6)

The set of all real values of x for which (x² − |x + 9| + x) > 0, is

Let 3 ≤ x ≤ 6 and [x²] = ([x])², where [x] is the greatest integer not exceeding x. If S represents all feasible values of x, then a possible subset of S is

Vedic Patterns G Strategy | Inequality | EASY | CAT 2025 Slot 1

The number of distinct pairs of integers (x, y) satisfying the inequalities x > y ≥ 3 and x + y < 14 is ____.

In the XY-plane, the area, in sq. units, of the region defined by the inequalities \( y \geq x + 4 \) and \( -4 \leq x^2 + y^2 + 4(x - y) \leq 0 \) is:

All values of x satisfying the inequality 1/(x+5) ≤ 1/(2x−3) are:

If x and y satisfy |x| + x + y = 15 and x + |y| − y = 20, then x − y equals:

The number of distinct real values of x, satisfying the equation max{x, 2} − min{x, 2} = |x + 2| − |x − 2| is:

The number of distinct integer solutions (x, y) of the equation |x + y| + |x − y| = 2 is:

The number of distinct pairs of integers (m, n) satisfying |1+mn| < |m+n| < 5 is

For all possible integers n satisfying 2.25 ≤ 2 + 2ⁿ + 2 ≤ 202, the number of integer values of 3 + 3ⁿ + 1 is

The number of integers n that satisfy the inequalities |n − 60| < |n − 100| < |n − 20| is

If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5, then the maximum possible value of 2x + y equals

If a and b are integers such that 2x² − ax + 2 ＞ 0 and x² − bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a − 6b is

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