If (x+3)/(2x-1) < 1, then the solution set contains : A. (-∞,1/2) B. (-∞,4) C. (-4,4) D. (4,∞) Choose the correct answer from the options given below: Option 1: A and D only Option 2: A and B only Option 3: B and C only Option 4: C and D only

Answer: A and D only. Solution: (x+3)/(2x-1)-1=(4-x)/(2x-1) 0. Sign analysis gives x 4. The solution set therefore contains (-∞,12) and (4,∞).

Algebra

Inequalities

Medium

applied

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:

A and D only

A and B only

B and C only

C and D only

✅ Correct Option: 1

$\dfrac{x+3}{2x-1}-1=\dfrac{4-x}{2x-1}<0$ , i.e. $\dfrac{x-4}{2x-1}>0$ .

Sign analysis gives $x<\dfrac12$ or $x>4$ .

The solution set therefore contains $(-\infty,\frac12)$ and $(4,\infty)$ .

2025: 3 June Shift 1

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

2026: 21 May Shift 1

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

2026: 22 May Shift 1

Match List-I with List-II

List-I	List-II
Inequalities	Solution set
(A) If $\left\vert 3 - 5x \right\vert < 7$ , then $x \in$	(I) $\left[-\dfrac{5}{2}, \infty\right)$
(B) If $3x - 7 > 5x - 1$ , then $x \in$	(II) $(-\infty, -3)$
(C) If $\dfrac{x}{3} > \dfrac{x}{2} + 1$ , then $x \in$	(III) $\left(-\dfrac{4}{5}, 2\right)$
(D) If $5x + 4 \leq 7x + 9$ , then $x \in$	(IV) $(-\infty, -6)$

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: 27 May Shift 1

If $x, y \in \mathbb{R}$ then match List-I with List-II

Choose the correct answer from the options given below:

2026: 18 May Shift 2

Match the LIST-I with LIST-II

Choose the correct answer from the options given below: