Which of the following facts are not true ?( Where R is set of real numbers) A., x+y, ≤, x, +, y, x,y R B., x-y, ≥, x, +, y, x,y R C., x+y, ≥, x, +, y, x,y R D., x-y, ≤, x, +, y, x,y R Choose the correct answer from the options given below: Option 1: A and B only Option 2: C and D only Option 3: B and C only Option 4: A and C only

Answer: B and C only. Solution: The triangle inequality gives, x+y, ≤, x, +, y, and, x-y, ≤, x, +, y, so A and D are true. B fails for x=y=1, where 0 ≥ 2 is false, and C fails for x=1, y=-1. So B and C are the untrue statements.

Algebra

Inequalities

Medium

applied

Which of the following facts are not true ?( Where $R$ is set of real numbers)

A. $|x+y| \le |x|+|y|, x,y \in R$

B. $|x-y| \ge |x|+|y|, x,y \in R$

C. $|x+y| \ge |x|+|y|, x,y \in R$

D. $|x-y| \le |x|+|y|, x,y \in R$

Choose the correct answer from the options given below:

A and B only

C and D only

B and C only

A and C only

✅ Correct Option: 3

The triangle inequality gives $|x+y| \le |x|+|y|$ and $|x-y| \le |x|+|y|$ , so A and D are true. B fails for $x=y=1$ , where $0 \ge 2$ is false, and C fails for $x=1$ , $y=-1$ . So B and C are the untrue statements.

2026: 30 May Shift 2

Match List-I with List-II

List-I	List-II
(A) The solution set of the inequation $3x-6\le 0$ is	(I) $(3,\infty)$
(B) The solution set of the inequation $-5x+20<0$ is	(II) $[3,\infty)$
(C) The solution set of the inequation $3x-9\ge 0$ is	(III) $(-\infty,2]$
(D) The solution set of the inequation $8x+11>35$ is	(IV) $(4,\infty)$

Choose the correct answer from the options given below:

2025: 30 May Shift 2

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

2025: 21 May Shift 1

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

2026: 21 May Shift 2

The solution set for the inequality $|5x-3| \le \dfrac{1}{5}$ is:

2025: 19 May Shift 1

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:

2026: 29 May Shift 1

Which of the following are correct? (Where $R$ is set of real numbers)

(A) If $x \le 8$ , then $-x \ge -8$

(B) If $x \in R, |x| \le 3$ , then $-3 \le x \le 3$

(D) $x=|x|$ iff $x \ge 0$

Choose the correct answer from the options given below:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)