Algebra

Inequalities

Easy

applied

Which one of the following inequalities are satisfied by $x = 10$ ?

$\frac{2x-5}{4} > 10, x \in \mathbb{R}$

$\frac{5x-2}{4} < 10, x \in \mathbb{R}$

$\frac{2x-5}{4} < 10, x \in \mathbb{R}$

$\frac{2-5x}{4} > 10, x \in \mathbb{R}$

✅ Correct Option: 3

Substitute $x=10$ in each. $\frac{2(10)-5}{4}=3.75$ , which is not greater than 10 but is less than 10, so option 3 holds. $\frac{5(10)-2}{4}=12$ is not less than 10, and $\frac{2-50}{4}=-12$ is not greater than 10.

2025: 22 May Shift 2

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

2026: 25 May Shift 1

If $\dfrac{x+3}{2x-1} < 1$ , then the solution set contains :

A. $(-\infty,1/2)$

B. $(-\infty,4)$

C. $(-4,4)$

D. $(4,\infty)$

Choose the correct answer from the options given below:

2025: 16 May Shift 1

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:

2025: 27 May Shift 1

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:

2026: 22 May Shift 2

Match List-I with List-II

List-I: Inequation	List-II: Solution set
(A) $2(2x+3)-10<6(x-2)$	(I) $x\in(-\infty,3.9)$
(B) $\frac{2x-1}{12}-\frac{x-1}{3}<\frac{3x+1}{4}$	(II) $x\in\left(-\infty,\frac{-1}{2}\right)\cup\left[\frac{1}{2},\infty\right)$
(C) $\frac{x}{2x+1}\ge \frac{1}{4}$	(III) $x\in(0,\infty)$
(D) $\frac{2x-3}{4}+6>2+\frac{4x}{3}$	(IV) $x\in(4,\infty)$

Choose the correct answer from the options given below:

2025: 26 May Shift 2

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

Which one of the following inequalities are satisfied by x=10x = 10x=10?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Which one of the following inequalities are satisfied by $x = 10$ ?