CUET Mathematics Algebra > Inequalities PYQs

If $\frac{3x - 5}{6} + 8 \geq 4 + \frac{2x}{3}$, then

The solution set of the linear inequation $|4x - 3| \leq \frac{3}{4}$ is:

Solution of the inequality $\frac{2x+3}{4x-5} \geq 0$ is

The solution set of the inequality $\frac{2x+3}{x-1} < 0$ is:

If $\mathbb{Z}$ and $\mathbb{R}$ denote set of integers and set of real numbers respectively, then match List I with List II. | List-I | List-II | |---|---| | (A) $5x - 3 \leq 3x + 1$, $x \in \mathbb{Z}$ | (I) $x \in (-\infty, -3]$ | | (B) $3x + 17 \leq 2(1 - x)$, $x \in \mathbb{R}$ | (II) $x \in (-\infty, -1)$ | | (C) $13x + 17 \leq 2(1 - x)$, $x \in \mathbb{R}$ | (III) $\{......, -4, -3, .......,0,1\}$ | | (D) $\frac{2x + 3}{5} - 2 > \frac{3(x - 2)}{5}$, $x \in \mathbb{Z}$ | (IV) $\{......, -4, -3, -2\}$ | Choose the correct answer from the options given below:

If $\frac{1}{|x| - 3} \leq \frac{1}{2}$, then value of $x$:

If $x, y \in \mathbb{R}$ then match List-I with List-II | List-I | List-II | | --- | --- | | (A) $\vert x\vert < \vert y\vert $ | (I) iff $x^2 > y^2$ | | (B) $\vert x\vert > \vert y\vert $ | (II) iff $x^2 \le y^2$ | | (C) $\vert x\vert \le \vert y\vert $ | (III) iff $x^2 < y^2$ | | (D) $\vert x\vert \ge \vert y\vert $ | (IV) iff $x^2 \ge y^2$ | Choose the correct answer from the options given below:

The solution of $\frac{7x+12}{x-9} < 4$; $ \neq 9$ is:

The solution set of inequality $3x + 5y < 4$ is

The solution set of the inequation $4x + 3y > 5$ is

If $\frac{1}{x^2} - \frac{1}{x} > 0$, then $x$ lies in the interval

If a, b, c are positive real numbers, then the least value of $(a+b+c)(ab+bc+ca)$ is:

The solution set of the inequation $|2x - 3| ≤ 4$ is

Match List-I with List-II | List-I | List-II | | --- | --- | | (Inequality) | (Solution Set) | | --- | --- | | (A) $2x - 3 < x + 2 \le 3x + 5, x \in \mathbb{R}$ | (I) $x \in (-1, \infty)$ | | (B) $\vert 2x + 3\vert < 7, x \in \mathbb{R}$ | (II) $x \in (-\infty, 120]$ | | (C) $\frac{1}{2}\left(\frac{3}{5}x + 4\right) \ge \frac{1}{3}(x - 6), x \in \mathbb{R}$ | (III) $x \in (-5, 2)$ | | (D) $\frac{\vert x + 1\vert }{x + 1} > 0, x \in \mathbb{R} - \{-1\}$ | (IV) $x \in \left[-\frac{3}{2}, 5\right)$ | Choose the correct answer from the options given below:

If, in a pair of consecutive positive integers, both numbers are greater than 5 and their sum is less than 23, then the number of such pairs are:

The solution set of $6 \leq -3(2x - 4) < 12$, $x \in R$ is:

The inequality $\frac{5x - 2}{3} - \frac{7x - 3}{5} > \frac{x}{4}$ holds when

Which of the following inequalities are NOT correct? (A) If $a > 1, b > 1,$ then $\log_b a + \log_a b \leq 2$ (B) For any real number $x, (9^x + 9^{1-x}) \geq 9$ (C) If $a,b,c$ are non-zero real numbers of the same sign, then $\left(\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\right) \leq 3$ (D) If $a,b,c$ are three distinct real numbers, then $(a + b)(b + c)(c + a) \geq 8abc$ Choose the **correct** answer from the options given below:

Which of the following inequalities holds true? (A) $\sqrt{5} + \sqrt{3} > \sqrt{6} + \sqrt{2}$. (B) If $a > b$ and $c < 0$, then $\frac{a}{c} < \frac{b}{c}$. (C) $\frac{1}{x^2} > \frac{1}{x} > 1$, if $0 < x < 1$. (D) If $a$ and $b$ are positive integers and $\frac{a - b}{6.25} = \frac{4}{2.5}$, then $b > a$. Choose the correct answer from the options given below:

If $a > b$ and $c < 0$, then which of the following is NOT correct? (A) $ac < bc$ (B) $a + c < b + c$ (C) $a - c < b - c$ (D) $ac > bc$ Choose the correct answer from the options given below:

If $a, b$ and $c$ are positive real numbers, then Match List-I with List-II | List-I | List-II | |---|---| | (Expression) | (The Least value of the expression) | | (A) $(a + b)(b + c)(c + a)$ | (I) $8abc$ | | (B) $(a + b + c)(ab + bc + ca)$ | (II) $9a^2b^2c^2$ | | (C) $(a^2b + b^2c + c^2a)(ab^2 + bc^2 + ca^2)$ | (III) $9abc$ | | (D) $(a + b)^2(b + c)^2(c + a)^2$ | (IV) $64a^2b^2c^2$ | Choose the correct answer from the options given below:

The solution set of the inequality $|3 x| \geq|6-3 x|$ is :

All points lying inside the triangle formed by the points (5, 0), (-1, 2) and (1, 3) satisfy : (A) $3x + 2y - 18 > 0$ (B) $3x + 2y > 0$ (C) $2x + y + 13 < 0$ (D) $2x - 3y - 12 < 0$ (E) $2x - 3y + 12 > 0$ Choose the **correct** answer from the options given below :

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) The solution set of the inequality $-5x > 3$, $x \in R$, is | (I) $\left[\frac{20}{7}, \infty\right)$ | | (B) The solution set of the inequality is, $\frac{-7x}{4} \leq -5$, $x \in R$ is, | (II) $\left[\frac{4}{7}, \infty\right)$ | | (C) The solution set of the inequality $7x - 4 \geq 0$, $x \in R$ is, | (III) $\left(-\infty, \frac{7}{5}\right)$ | | (D) The solution set of the inequality $9x - 4 < 4x + 3$, $x \in R$ is, | (IV) $\left(-\infty, -\frac{3}{5}\right)$ | Choose the correct answer from the options given below :