Multiple Choice Questions on Inequalities Class 11 OP Malhotra Exe-11G ISC Maths Solutions Ch-11. In this article you would learn to solve all types mcq questions on Inequalities. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-11.

Inequalities Class 11 OP Malhotra Multiple Choice Questions ISC Math Solutions Ch-11

Board	ICSE
Publications	S Chand
Subject	Maths
Class	11th
Chapter-11	Inequalities
Writer	OP Malhotra
Exe-11(G)	Multiple Choice Questions.

Multiple Choice Questions on Inequalities

OP Malhotra ISC Class 11 Maths Solutions

Que-1: The set of all real numbers satisfying the inequality x − 2 < 1 is

(a) (3, ∞)        (b) [3, ∞)           (c) [−3, ∞)            (d) (−∞, 3)

Sol: (d) (−∞, 3)
x − 2 < 1
x < 3
Therefore, x ∈ (−∞, 3).

Que-2: If |x − 2| ≤ 1, then

(a) x ∈ (1, 3]
(b) x ∈ (−1, 3]
(c) x ∈ [1, 3]
(d) x ∈ [−1, 3)

Sol: (c) x ∈ [1, 3]
|x − 2| ≤ 1
−1 ≤ x − 2 ≤ 1
Add 2 on all sides:
1 ≤ x ≤ 3

Que-3: If |x − 3| / (x − 3) > 0, then

(a) x ∈ (−3, ∞)
(b) x ∈ (3, ∞)
(c) x ∈ (2, ∞)
(d) x ∈ (−1, ∞)

Sol: (b) x ∈ (3, ∞)
|x−3|/(x−3) is positive only when x−3 > 0.
∴ x > 3

Que-4: If −3x + 17 < −13, then

(a) x ∈ (10, ∞)
(b) x ∈ [10, ∞)
(c) x ∈ (−∞, 10]
(d) x ∈ [−10, 10)

Sol: (a) x ∈ (10, ∞)
−3x < −30
x > 10

Que-5: If |x + 2| ≤ 9, then

(a) x ∈ (−7, 11)
(b) x ∈ [−11, 7]
(c) x ∈ (−∞, −7) ∪ (1, ∞)
(d) x ∈ (−∞, −7) ∪ (11, ∞)

Sol: (b) x ∈ [−11, 7]
−9 ≤ x + 2 ≤ 9
−11 ≤ x ≤ 7

Que-6: Solve the inequality 3x + 2 > −16, 2x − 3 ≤ 11

(a) (−6, 7)          (b) [−6, 7)           (c) (−6, 7]             (d) [−6, 7]

Sol: (c) (−6, 7]
3x > −18 → x > −6
2x ≤ 14 → x ≤ 7
Common solution: −6 < x ≤ 7

Que-7: The solution of 6x / (4x − 1) < 1/2 is

(a) x < −1/8
(b) −1/8 < x < 1/4
(c) x < −1/8 and x > 1/4
(d) x > 1/8

Sol: (a) x < −1/8
12x < 4x − 1
8x < −1
x < −1/8

Que-8: The solution set of the inequality |x² − 4x| < 5 is

(a) (−1, 5)          (b) (−4, 5)            (c) (−5, 4)            (d) (−1, 4)

Sol: (a) (−1, 5)
|x² − 4x| < 5 ⇒ −5 < x² − 4x < 5
Solving ⇒ −1 < x < 5

Que-9: If |x + 5| ≥ 10, then

(a) x ∈ (−15, 5]
(b) x ∈ (−5, 5]
(c) x ∈ (−∞, −15] ∪ [5, ∞)
(d) x ∈ (−∞, −15) ∪ (5, ∞)

Sol: (c) x ∈ (−∞, −15] ∪ [5, ∞)
|x+5| ≥10 ⇒ x+5 ≥10 or x+5 ≤−10
⇒ x ≥5 or x ≤−15

Que-10: If |x − 3| < 2x + 9, then x lies in

(a) (−∞, −2)        (b) (−2, 0)           (c) (−2, ∞)           (d) (2, ∞)

Sol: (c) (−2, ∞)
|x−3| < 2x+9
⇒ −(2x+9) < x−3 < 2x+9
Solving ⇒ x > −2

Que-11: If 7x − 2 < 4 − 3x and 3x − 1 < 2 + 5x, then x lies in

(a) (3/5, 3/2)
(b) (−3/2, 3/5)
(c) (−3/2, 3/5)
(d) [−3/2, 3/5]

Sol: (b) (−3/2, 3/5)
7x−2 <4−3x
⇒ 10x<6
⇒ x<3/5
3x−1 <2+5x
⇒ −2x<3
⇒ x>−3/2
Intersection ⇒ (−3/2 , 3/5)

Que-12: Number of integral solutions of (x + 2) / (x² + 1) > 1/2 is

(a) 0           (b) 1           (c) 2            (d) 3

Sol: (d) 3
(x+2)/(x²+1) > 1/2
Solving ⇒ −1 < x < 3
Integers ⇒ 0,1,2

Que-13: The region represented by the inequality system x ≥ 0, y ≥ 0, y ≤ 6, x + y ≤ 3 is

(a) unbounded in first quadrant
(b) unbounded in first and second quadrant
(c) bounded in first quadrant
(d) None of these

Sol: (c) bounded in first quadrant
Region lies in first quadrant and limited by lines ⇒ finite area

Que-14: Let C/5 = (F − 32)/9. If C lies between 10 and 20, then

(a) 50 < F < 78
(b) 50 < F < 68
(c) 49 < F < 68
(d) 49 < F < 78

Sol: (b) 50 < F < 68
F = (9C/5)+32
Put limits:
C=10 ⇒ F=50
C=20 ⇒ F=68

Que-15: The solution set of (x + 3)/(x − 2) ≤ 2 is

(a) (−∞, 2) ∪ (7, ∞)
(b) (−∞, 2] ∪ (7, ∞)
(c) (−∞, 2) ∪ [7, ∞)
(d) (−∞, 2] ∪ [7, ∞)

Sol: (c) (−∞, 2) ∪ [7, ∞)
(x+3)/(x−2) ≤2
(x+3)/(x−2) −2 ≤0
(x−7)/(x−2) ≤0
Solution ⇒ (−∞,2) ∪ [7,∞)

Que-16: If x² + 6x − 27 > 0 and −x² + 3x + 4 > 0, then x lies in the interval

(a) (−∞, 3] ∪ (4, ∞)
(b) (3, 4)
(c) (−∞, −3] ∪ (4, ∞)
(d) (−3, 4)

Sol: (b) (3, 4)
−x² + 3x + 4 > 0 ⇒ (x − 4)(x + 1) < 0 ⇒ −1 < x < 4
Common interval = (3, 4)

Que-17: The set of values of x satisfying 2 ≤ |x − 3| < 4 is

(a) −4 ≤ x ≤ 2
(b) (−∞, 1] ∪ [5, ∞)
(c) x ≥ 5 or x < 7
(d) (−1, 1] ∪ [5, 7)

Sol: (d) (−1, 1] ∪ [5, 7)
|x − 3| ≥ 2 ⇒ x ≤ 1 or x ≥ 5
|x − 3| < 4 ⇒ −1 < x < 7
Intersection = (−1,1] ∪ [5,7)

Que-18: A manufacturer has 500 L of a 10% solution of acid. Find the range of 40% acid to be added to it such that the acid content in the resultant mixture will be more than 15% but less than 20%.

(a) More than 250 L and less than 300 L
(b) More than 300 L and less than 400 L
(c) More than 100 L and less than 250 L
(d) More than 250 L and less than 350 L

Sol: (c) More than 100 L and less than 250 L
(50 + 0.4x)/(500 + x) > 0.15
(50 + 0.4x)/(500 + x) < 0.20
Solving ⇒ 100 < x < 250

Que-19: The solution set of the following linear inequalities
x − 2y ≥ 0; 2x − y ≤ 2; x ≥ 0; y ≥ 0 is given by

(a) [1, 2]           (b) null set          (c) x ≥ 1          (d) set of real numbers

Sol: (b) null set
These inequalities do not have any common feasible region.

–: End Inequalities Class 11 OP Malhotra Exe-11G ISC Maths Ch-11 Solutions :–

Return to :- OP Malhotra ISC Class-11 S Chand Publication Maths Solutions
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