Title LINEAR INEQUALITIES.pdf ✅

CHAPTER 6 LINER INEQUALITIES Exercise 1: NCERT Based Topic-wise MCQs 6.1, 6.2 &6.3 INTRODUCTION, INEQUALITIES AND ALGEBRAIC SOLUTIONS OF LINER INEQUALITIES IN ONE VARIABLE & THEIR GRAPHICAL REPRESENTATION 1. Which of the following is the solution set of 3x − 7 > 5x − 1∀x ∈ R ? NCERT Page-120/N-92 (a) (−∞, −3) (b) (−∞, −3] (c) (−3, ∞) (d) (−3,3) 2. The solution set of the inequality 4x + 3 < 6x + 7 is NCERT/ Page-120/N-93 (a) [−2, ∞) (b) (−∞, −2) (c) (−2, ∞) (d) None of these 3. The graph of the solution on number line of the inequality 3x − 2 < 2x + 1is NCERT Page-120/N-93 (a) (b) (C) (d) 4. The solution set of the inequality 37 − (3x + 5) ≥ 9x − 8(x − 3) is NCERT/ Page-120/N-92 (a) (−∞, 2) (b) (−∞, −2) (c) (−∞, 2] (d) (−∞, −2] 5. The set of real x satisfying the inequality 5−2x 3 ≤ x 6 − 5 is [a, ∞). The value of ' a ' is NCERT Page-120/N-92 (a) 2 (b) 4 (c) 6 (d) 8 6. The solution set of the inequality 4x + 3 < 6x + 7 is (−a, ∞). The value of ' a ' is NCERT Page-120/N-92 (a) 1 (b) 4
(c) 2 (d) None of these 7. The marks obtained by a student of class XI in first and second terminal examinations are 62 and 48 , respectively. The minimum marks he should get in the annual examination to have an average of at least 60 marks, are NCERT Page-121/N-94 (a) 70 (b) 50 (c) 74 (d) 48 8. The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160cm, then what can you say about breadth? NCERT Page-121/N-94 (a) breadth = 20 (b) breadth ≤ 20 (c) breadth ≥ 20 (d) breadth ≠ 20 9. Ravi obtained 70 and 75 marks in firsttwo unit tests. Then, the minimum marks he should get in the third test to have an average of at least 60 marks, are NCERT Page-121/N-94 (a) 45 (b) 35 (c) 25 (d) None of these 10. The solution set of the inequalities 6 ≤ −3(2x − 4) < 12is NCERT Page-130/N-92 (a) (−∞, 1] (b) (0,1] (c) (0,1] ∪ [1, ∞) (d) [1, ∞) 11. Which of the following is the solution set of linear inequalities 2(x − 1) < x + 5 and 3(x + 2) > 2 − x ? NCERT Page-130/ N-92 (a) a c = b c (b) a c > b c (c) a c < b c (d) None of these 12. The graphical solution of 3x − 6 ≥ 0is (a) (b)
(C) (d) 13. If a < b and c < 0, then NCERT Page-119/N-92 (a) a c = b c (b) a c > b c (c) a c < b c (d) None of these 14. The solution set of the inequality 3(2 − x) ≥ 2(1 − x) is (−∞, a]. The value of ' a ' is (a) 2 NCERT Page-120/N-92 (b) 3 (c) 4 (d) 5] 15. The solutions of the system of inequalities 3x − 7 < 5 + x and 11 − 5x ≤ 1 on the number line is NCERT Page-130/N-93 (a) (b) (C) (d) None of the above 16. The solution set of the inequalities 3x − 7 > 2(x − 6) and 6 − x > 11 − 2x, is NCERT Page-130/N-93 (a) (−5, ∞) (b) [5, ∞) (c) (5, ∞) (d) [−5, ∞) 17. The solution set of 2x−1 3 ≥ ( 3x−2 4 ) − ( 2−x 5 ) is (−∞, a]. The value of ' a ' is (a) 2 NCERT Page-120/N-94 (b) 3 (c) 4 (d) 5 18. If 3x−4 2 ≥ x+1 4 − 1, then x ∈ NCERT Page-120/N-92 (a) [1, ∞) (b) (1, ∞)
(c) (−5,5) (d) [−5,5] 19. If 5−2x 3 ≤ x 6 − 5, then x ∈ NCERT Page-120/N-92 (a) [2, ∞) (b) [−8,8] (c) [4, ∞) (d) [8, ∞) 20. If x satisfies the inequations 2x − 7 < 11 and 3x + 4 < −5, then x lies in the interval (−∞, −m). The value of ' m ' is NCERT Page-130/N-94 (a) 2 (b) 3 (c) 4 (d) 5 21. If 5x + 1 > −24 and 5x − 1 < 24, then x ∈ (−a, a). The value of ' a ' is NCERT Page-130/N-92 (a) 2 (b) 3 (c) 4 (d) 5 22. If −5 ≤ 5−3x 2 ≤ 8, then x ∈ NCERT ∖ Page-130/N-92 (a) [− 11 3 , 5] (b) [−5,5] (c) [− 11 3 , ∞) (d) (−∞, ∞) 23. Solutions of the inequalities comprising a system in variable x are represented on number lines as given below, then NCERT \ Page-130/N-93 (a) x ∈ (−∞, −4] ∪ [3, ∞) (b) x ∈ [−3,1] (c) x ∈ (−∞, −4) ∪ [3, ∞) (d) x ∈ [−4,3] 24. The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160cm, then NCERT Page-121/N-93 (a) breadth > 20cm (b) length < 20cm (c) breadth ≥ 20cm (d) length ≤ 20cm 25. The solution of the inequality −8 ≤ 5x − 3 < 7 is [−a, b). Sum of ' a ' and ' b ' is (a) 1 NCERT Page-130/N-94 (b) 2 (c) 3 (d) 4
26. The inequality 2 x < 3 is true, when x belongs to NCERT/ Page-120/N-93 (a) [ 2 3 , ∞) (b) (−∞, 2 3 ] (c) (−∞, 0) ∪ ( 2 3 , ∞) (d) None of these 27. Solve the following system of linear inequalities : NCERT Page-130/N-92 x + 2 > 11; 2x ≤ 20 (a) (6,9) (b) (10,16) (c) (9,10] (d) [−6,9] 28. Let C 5 = F−32 9 . If Clies between 10 and 20 , then: NCERT Page-131/N-92 (a) 50 < F < 78 (b) 50 < F < 68 (c) 49 < F < 68 (d) 49 < F < 78 29. If x satisfies the inequations 2x − 7 < 11, 3x + 4 < −5, then x lies in the interval (a) (−∞, 3) NCERT Page-130/N-93 (c) (−∞, −3) (b) (−∞, 2) (d) (−∞, ∞) 30. Solve −5 ≤ 5−3x 2 ≤ 8. NCERT Page-130/N-92 (a) − 8 3 ≤ x < 5 (b) − 10 3 < x < 5 (c) − 11 3 ≤ x < 6 (d) − 11 3 ≤ x ≤ 5 31. 3x − 7 > x + 1 NCERT Page-120/N-92 (a) [−4,0) (b) (4, ∞) (c) [−4,4] (d) (2,5] 32. The solution set of (x) 2 + (x + 1) 2 = 25, where (x) is the least integer greater than or equal to x, is (a) (2,4) NCERT Page-120/ N-93 (b) (−5, −4] ∪ (2,3] (c) [−4, −3) ∪ [3,4) (d) None of these 33. 5−2x 3 < x 6 − 5 NCERT Page-120/N-93 (a) (8, ∞) (b) [6,8)