# Linear Inequalities MCQ Questions for Class 11 Math’s Chapter 6 with Answers

## Q1. The solution set of the equation 4{x} = x +[x], where {x} and [x] denote the fractional and integral parts of a real number ‘x’ respectively, is

(i) { 0}
(ii) {0, 5/3}
(iii) [0, ∞)
(iv) none of these

(ii) {0, 5/3}

(i) (-8, ∞)
(ii) (8, ∞)
(iii) (∞, -8)
(iv) (∞, 8)

(i) (-8, ∞)

(i) (-∞, -5)
(ii) (∞, 5)
(iii) (-5, ∞)
(iv) (-5, 5)

(iv) (-5, 5)

## Q4. The number of integral solutions of x+2 / x2+1 >1/2

(i) 4
(ii) 5
(iii) 3
(iv) none of these

(iii) 3

(i) (-5, ∞)
(ii) (5, ∞)
(iii) (∞, -5)
(iv) No solution

(iv) No solution

## Q6. ax + b > 0 is __

(i) double inequality
(iii) numerical inequality
(iv) linear inequality

(iv) linear inequality

## Q7. The solution set of the inequality 1/x < is

(i) (1, ∞)
(ii) (-∞, 1)
(iii) (-∞, 0)∪(1, ∞)
(iv) none of these

(iii) (-∞, 0)∪(1, ∞)

## Q8. The graph of the inequations x ≤ 0 , y ≤ 0, and 2x + y + 6 ≥ 0 is

(i) exterior of a triangle
(ii) a triangular region in the 3rd quadrant
(iv) none of these

(ii) a triangular region in the 3rd quadrant

## Q9. The solution of the -12 < (4 -3x)/(-5) < 2 is

(i) 56/3 < x < 14/3
(ii) -56/3 < x < -14/3
(iii) 56/3 < x < -14/3
(iv) -56/3 < x < 14/3

(iv) -56/3 < x < 14/3

## Q10. The region of the XOY-plane represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10 is

(i) unbounded
(ii) a polygon
(iii) none of these
(iv) exterior of a triangle

(iii) none of these

## Q11. Solve: -1/(|x| – 2) ≥ 1 where x ∈ R, x ≠ ±2

(i) (-2, -1)
(ii) (-2, 2)
(iii) (-2, -1) ∪ (1, 2)
(iv) None of these

(iii) (-2, -1) ∪ (1, 2)

## Q12. Solutions of the inequalities comprising a system in variable x are represented on number lines as given below, then

(i) x Î(-∞,- 4]∪[3,∞)
(ii) x Î[-3,1]
(iii) x Î(-∞,-4)∪(3,∞)
(iv) x Î[-4,3]

(i) x Î(-∞,- 4]∪[3,∞)

## Q13. Given that x, y and b are real numbers and x < y , b < 0, then

(i) x/b < y/b (ii) x/b ≤ y/b (iii) x/b > y/b
(iv) x/b ≥ y/b

(iii) x/b > y/b

(i) (1/2, 3/2)
(ii) (-1/2, 3/2)
(iii) (3/2, 1/2)
(iv) (3/2, -1/2)

(ii) (-1/2, 3/2)

## Q15. The solution of |2/(x – 4)| > 1 where x ≠ 4 is

(i) (2, 6)
(ii) (2, 4) ∪ (4, 6)
(iii) (2, 4) ∪ (4, ∞)
(iv) (-∞, 4) ∪ (4, 6)

(ii) (2, 4) ∪ (4, 6)

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