Get Started
Start Free Mocks
CUETMOCK

Ace Your

CUET Preparation Today

Start Free Mocks
Home Questions FPDRU6TMDA
Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Numbers, Quantification and Numerical Applications

Question:

Match List-I with List-II

List-I (Inequality)

List-II (Solution Set)

(A) $2x-3<x+2≤3x+5,x∈R$

(I) $x ∈ (-1,∞)$

(B) $|2x+3|<7, x∈R$

(II) $x ∈ (-∞, 120]$

(C) $\frac{1}{2}(\frac{3}{5}x+4) ≥\frac{1}{3} (x-6),x∈R$

(III) $x ∈ (-5,2)$

(D) $\frac{|x+1|}{x+1}> 0, x∈R-\{1\}$

(IV) $x∈[-\frac{3}{2},5)$

Choose the correct answer from the options given below:

Options:

(A)-(II), (B)-(I), (C)-(III), (D)-(IV)

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

Correct Answer:

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

Explanation:

The correct answer is Option (4) → (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

List-I (Inequality)

List-II (Solution Set)

(A) $2x-3<x+2≤3x+5,x∈R$

(IV) $x∈[-\frac{3}{2},5)$

(B) $|2x+3|<7, x∈R$

(III) $x ∈ (-5,2)$

(C) $\frac{1}{2}(\frac{3}{5}x+4) ≥\frac{1}{3} (x-6),x∈R$

(II) $x ∈ (-∞, 120]$

(D) $\frac{|x+1|}{x+1}> 0, x∈R-\{1\}$

(I) $x ∈ (-1,∞)$

Given inequalities and solution sets:

(A) 2x − 3 < x + 2 ≤ 3x + 5

Split: 2x − 3 < x + 2 → x < 5

x + 2 ≤ 3x + 5 → −2x ≤ 3 → x ≥ −3/2

Intersection: x ∈ [−3/2, 5] → (A) matches (IV)

(B) |2x + 3| < 7

−7 < 2x + 3 < 7 → −10 < 2x < 4 → −5 < x < 2

(B) matches (III)

(C) 1/2(3/5x + 4) ≥ 1/3(x − 6)

Multiply both sides by 6: 3*(3/5x + 4) ≥ 2*(x − 6) → (9/5)x + 12 ≥ 2x − 12

Bring terms together: 12 + 12 ≥ 2x − (9/5)x → 24 ≥ (10/5 − 9/5)x → 24 ≥ (1/5)x → x ≤ 120

(C) matches (II)

(D) (|x+1|)/(x+1) > 0

Expression positive if x + 1 > 0 → x ∈ (−1, ∞), excluding x = −1

(D) matches (I)

CUET Questions