Which of the following are correct? (Where R is set of real numbers) (A) If x ≤ 8, then -x ≥ -8 (B) If x R, x, ≤ 3, then -3 ≤ x ≤ 3 (C) If x R, x, <-4, then x (D) x=, x, iff x ≥ 0 Choose the correct answer from the options given below: Option 1: (A), (B) and (C) only Option 2: (A), (B), (C) and (D) Option 3: (B), (C) and (D) only Option 4: (A) and (D) only

Answer: (A), (B), (C) and (D). Solution: (A) Multiplying an inequality by -1 reverses it: correct. (B) Standard modulus result, x, ≤ a -a≤ x≤ a: correct. (C), x, ≥ 0 always, so, x, < -4 has no solution: correct. (D), x, = x exactly when x ≥ 0: correct. All four statements hold.

Algebra

Inequalities

Easy

applied

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 $-3 \le x \le 3$

(C) If $x \in R, |x|<-4$ , then $x \in \phi$

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

Choose the correct answer from the options given below:

(A), (B) and (C) only

(A), (B), (C) and (D)

(B), (C) and (D) only

(A) and (D) only

✅ Correct Option: 2

(A) Multiplying an inequality by $-1$ reverses it: correct.

(B) Standard modulus result $|x|\le a \Leftrightarrow -a\le x\le a$ : correct.

(D) $|x| = x$ exactly when $x \ge 0$ : correct.

All four statements hold.

2026: 30 May Shift 1

Match the LIST-I with LIST-II

	LIST-I (Inequality)		LIST-II (Solution Set)
A.	$\vert 3x-5 \vert \geq 4$	I.	$(-\infty,-1] \cup \left[\dfrac{7}{3},\infty\right)$
B.	$\vert 3x \vert \geq \vert 6-3x \vert$	II.	$(-\infty,-4] \cup [2,\infty)$
C.	$\vert x+1 \vert \geq 3$	III.	$[1,\infty)$
D.	$\vert 2-3x \vert \geq 5$	IV.	$\left(-\infty,\dfrac{1}{3}\right] \cup [3,\infty)$

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:

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: 19 May Shift 1

The number that satisfies the inequality $\frac{29}{4} < \frac{x+20}{4} < 8$ is

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:

2025: 15 May Shift 1

The inequality $\frac{5x - 2}{3} - \frac{7x - 3}{5} > \frac{x}{4}$ holds when

Solution

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