Class 11 Mathematics Linear Inequalities MCQs Set 04

Question. The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.
(a) 2
(b) 9
(c) 8
(d) 7
Answer: b

Question. Solution of |3x + 2| < 1 is
(a) [–1, –1/3]
(b) {–1/3,–1}
(c) (–1,–1/3)
(d) None of these
Answer: c

Question. If |x + 3| + x/x + 2 > 1, then x ∈
(a) (–5, –2)
(b) (–1, ∞)
(c) (–5, –2) ∪ (–1, ∞)
(d) None of these
Answer: c

Question. 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
Answer: b

Question. The set of real values of x satisfying |x – 1| ≤ 3 and |x – 1| ≥ 1 is
(a) [2, 4]
(b) (−∞, 2]∪[4, +∞)
(c) [−2, 0]∪[2, 4]
(d) None of these
Answer: c

Question. If a < b and c < 0, then
(a) a/c = b/c
(b) a/c > b/c
(c) a/c < b/c
(d) None of these
Answer: b

Question. A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%?
(a) more than 120 litres but less than 300 litres
(b) more than 140 litres but less than 600 litres
(c) more than 100 litres but less than 280 litres
(d) more than 160 litres but less than 500 litres
Answer: a

Question. The solution set of 2x – 1/3 ≥ (3x – 2/4) – (2 – x/5) is (–∞, a]. The value of ‘a’ is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: a

Question. If x satisfies the inequations 2x – 7 < 11 and 3x + 4 < –5, then x lies in the interval (–∞, –m). The value of ‘m’ is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: b

Question. Ravi obtained 70 and 75 marks in first two unit tests. Then, the minimum marks he should get in the third test to have an average of at least 60 marks, are
(a) 45
(b) 35
(c) 25
(d) None of these
Answer: b

Question. If 3x–4/ ≥ x + 1/4– 1, then x ∈
(a) [1, ∞)
(b) (1, ∞)
(c) (–5, 5)
(d) [–5, 5]
Answer: a

Question. The solution set of the inequality 4x + 3 < 6x + 7 is
(a) [–2, ∞)
(b) (–∞, –2)
(c) (–2, ∞)
(d) None of these
Answer: c

Question. Which of the following is the solution set of linear inequalities 2(x – 1) < x + 5 and 3(x + 2) > 2 – x?
(a) (–∞, –1)
(b) (–1, 1)
(c) (–1, 7)
(d) (1, 7)
Answer: c

Question. A solution of 8% boric is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 L of the 8% solution, of the 2% solution will have to be added is
(a) more than 320 and less than 1000
(b) more than 160 and less than 320
(c) more than 320 and less than 1280
(d) more than 320 and less than 640
Answer: c

Question. If –3x + 17 < –13, then
(a) x ∈ (10, ∞)
(b) x ∈ [10, ∞)
(c) x ∈ (–∞, 10]
(d) x ∈ [–10, 10)
Answer: a

Question. The solution set of the inequality 37 – (3x + 5) ≥ 9x – 8 (x – 3) is
(a) (– ∞, 2)
(b) (– ∞, –2)
(c) (– ∞, 2]
(d) (– ∞, – 2]
Answer: c

Question. A company manufactures cassettes. Its cost and revenue functions are C(x) = 26000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. The number of cassettes must be sold by the company to realise some profit, is
(a) more than 2000
(b) less than 2000
(c) more than 1000
(d) less than 1000
Answer: a

Question. The solution set of the inequalities 3x – 7 > 2(x – 6) and 6 – x > 11 – 2x, is
(a) (–5, ∞)
(b) [5, ∞)
(c) (5, ∞)
(d) [–5, ∞)
Answer: c

Question. The inequality 2/x < 3 is true, when x belongs to 
(a) [2/3,∞)
(b) (–∞,2/3]
(c) (–∞, 0) ∪ (2/3,∞)
(d) None of these
Answer: c

STATEMENT TYPE QUESTIONS

Question. Consider the following statements.
I. Solution set of 24x < 100 is {1, 2, 3, 4}, when x is a natural number.
II. Solution set of 24x < 100 is {…, –3, –2, –1, 0, 1, 2, 3, 4}, when x is an integer.
Choose the correct option.
(a) Only I is false.
(b) Only II is false.
(c) Both are false.
(d) Both are true. 
Answer: d

Question. Consider the following statements.
I. Solution set of the inequality –15 < 3(x−2)/5 ≤ 0 is (–23, 2]
II. Solution set of the inequality 7 ≤ 3x + 11/2 ≤ 11 is [1,11/3]
III. Solution set of the inequality – 5 ≤ 2−3x/4 ≤ 9 is [–1, 1] ∪ [3, 5]
Choose the correct option
(a) Only I and II are true.
(b) Only II and III are true.
(c) Only I and III are true.
(d) All are true.
Answer: a

Question. Consider the following statements.
I. Equal numbers may be added to (or subtracted from)both sides of an inequality.
II. When both sides are multiplied (or divided) by a negative number, then the inequality is reversed.
Choose the correct option.
(a) Only I is true.
(b) Only II is true.
(c) Both I and II are true.
(d) Both I and II are false.
Answer: c

Question. Consider the following statements:
Statement-I : The solution set of the inequality 3(x – 2)/5 ≤ 5(2 – x)/3 is (–∞, 2).
Statement-II : The solution set of the inequality 1/2(13x/5 + 4) ≥ 1/3(x – 6) is (–∞, 120].
Choose the correct option.
(a) Statement I is true
(b) Statement II is true
(c) Both are true
(d) Both are false
Answer: b