ML Aggarwal Solution Class 10 Chapter 4 Linear Inequations MCQs

 MCQs

Choose the correct answer from the given four options (1 to 5) :

Question 1

If x ∈ { – 3, – 1, 0, 1, 3, 5}, then the solution set of the inequation 3x – 2 ≤ 8 is

(a) { – 3, – 1, 1, 3}

(b) { – 3, – 1, 0, 1, 3}

(c) { – 3, – 2, – 1, 0, 1, 2, 3}

(d) { – 3, – 2, – 1, 0, 1, 2}

Solution:

x ∈ { -3, -1, 0, 1, 3, 5}

3x – 2 ≤ 8

⇒ 3x ≤ 8 + 2

⇒ 3x ≤ 10

⇒ $x \leq \frac{10}{3}$

⇒ $x<3 \frac{1}{3}$

Solution set = { -3, -1, 0, 1, 3}

Ans : (b)

Question 2

If x ∈ W, then the solution set of the inequation 3x + 11 ≥ x + 8 is

(a) { – 2, – 1, 0, 1, 2, …}

(b) { – 1, 0, 1, 2, …}

(c) {0, 1, 2, 3, …}

(d) $\left\{x: x \in R, x \geq-\frac{3}{2}\right\}$

Sol :

x ∈ W

3x + 11 ≥ x + 8

⇒ 3x – x ≥ 8 – 11

⇒2x≥-3

⇒$x \geq \frac{-3}{2}$

⇒$x \geq-1 \frac{1}{2}$

Solution set={0,1,2,3,..}

Ans : (c)

Question 3

If x ∈ W, then the solution set of the inequation 5 – 4x ≤ 2 – 3x is

(a) {…, – 2, – 1, 0, 1, 2, 3}

(b) {1, 2, 3}

(c) {0, 1, 2, 3}

(d) {x : x ∈ R, x ≤ 3}

Sol :

x ∈ W

5 – 4x < 2 – 3x

⇒ 5 – 2 ≤ 3x + 4x

⇒ 3 ≤ x

Solution set = {0, 1, 2, 3,} (c)

Question 4

If x ∈ I, then the solution set of the inequation 1 < 3x + 5 ≤ 11 is

(a) { – 1, 0, 1, 2}

(b) { – 2, – 1, 0, 1}

(c) { – 1, 0, 1}

(d) $\left\{x: x \in R,-\frac{4}{3}<x \leq 2\right\}$

Sol :

x ∈ I

1 < 3x + 5 ≤ 11

⇒ 1 < 3x + 5

⇒ 1 – 5 < 3x

⇒-4<3x

⇒$\frac{-4}{3}<x$

⇒and 3x+5≤11

⇒3x≤11-5

⇒3x≤6

⇒$x \leq \frac{6}{3}$

⇒x≤2

∴$\frac{-4}{3}<x \leq 2$

Solution set={-1,0,1,2}

Question 5

If x ∈ R, the solution set of 6 ≤ – 3 (2x – 4) < 12 is

(a) {x : x ∈ R, 0 < x ≤ 1}

(b) {x : x ∈ R, 0 ≤ x < 1}

(c) {0, 1}

(d) none of these

Sol :

x ∈ R

6 ≤ – 3(2x – 4) < 12

⇒ 6 ≤ – 3(2x – 4)

⇒ 6 ≤ – 6x + 12

⇒ 6 ≤ 12-6

⇒6x≤6

⇒$x \leq \frac{6}{6}$

⇒x≤1...(i)

and -3(2x-4)<12

⇒-6x+12<12

⇒-6<12-12

⇒-6x<0

⇒x<0...(ii)

From (i) and (ii)

∴0<x≤1

Solution set={x : x∈R, 0<x≤1}

Ans : (a)