Algebra

Inequalities

Easy

applied

Which of the following are correct?

A. If $|x-5|<2$ , then $x \in (3,7)$

B. If $|x-1|<4$ , then $x \in (-3,5)$

C. If $|x-2|<6$ , then $x \in (4,8)$

D. If $|x-4|<1$ , then $x \in (-3,5)$

Choose the correct answer from the options given below:

A and B only

A, B, and C only

A, B, C, and D

B, C, and D only

✅ Correct Option: 1

The rule $|x-a|<r$ means $x \in (a-r,a+r)$ . A gives $(3,7)$ and B gives $(-3,5)$ , both as stated. C should give $(-4,8)$ , not $(4,8)$ , and D should give $(3,5)$ , not $(-3,5)$ , so both fail.

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: 31 May Shift 2

The solution set $\{x: x \in R, 3x-2 < x+2 \le 2x+6\}$ (Where $R$ is set of real numbers) is :

2025: 26 May Shift 2

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

2024: 16 May Shift 1

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

2025: 30 May Shift 1

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:

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:

Solution

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