Algebra

Inequalities

Medium

common

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 :

(A) and (B) Only

(B) and (C) Only

(D) and (E) Only

(B), (D) and (E) Only

✅ Correct Option: 4

Test the centroid $(5/3, 5/3)$ of the triangle in each inequality.

(A) $5+10/3-18<0$ , fails. (B) $5+10/3>0$ , holds. (C) $10/3+5/3+13>0$ , fails. (D) $10/3-5-12<0$ , holds. (E) $10/3-5+12>0$ , holds.

So (B), (D), (E) only.

2026: 18 May Shift 1

For the inequality $3-2x \geq x-32$ , which of the following are true?

(A) When $x \in N$ (set of natural numbers), the solution set is $\{1,2,3,\dots,11\}$ .

(B) When $x \in I$ (set of integers), the solution set is $\{-\infty,\dots,-3,-2,-1,0,1,2,3,\dots 10,11\}$ .

(D) When $x \in R$ (set of real numbers), the solution set is $(-\infty,\infty)$ .

Choose the correct answer from the options given below:

2026: 19 May Shift 2

Match the LIST-I with LIST-II

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: 21 May Shift 1

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

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: 29 May Shift 2

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

Solution