Class 11 Mathematics Linear Inequalities MCQs

Question. The solution set of inequality 2x/x²-9 ≤ 1/x+2
(a) (-∞, - 2)∪(3, ∞)
(b) (-∞, -3)∪(-2, 3)
(c) (-3, 0]∪(3, ∞)
(d) none of these

Answer :  B
 

Question. The number of integral solutions of x+2 / x²+1 >1/2
(a) 4
(b) 5
(c) 3
(d) none of these

Answer :  C
 

Question. The least integer a, for which
1 log5 (x² + 1) ≤ log5 (ax² + 4x + a) is true for xεR all
(a) 6
(b) 7
(c) 10
(d) 1

Answer :  B
 

Question. Consider the following statements about Linear Inequalities :
(1) Two real numbers or two algebraic expressions related by the symbols <, >, ≤ or ≥ form an inequality.
(2) Equal numbers may be added to (or subtracted from) both sides of an inequality.
(3) Both sides of an inequality can be multiplied  (or divided) by the same positive number.  
Which of the above statements are true ?
(a) only (1)
(b) only (2)
(c) only (3)
(d) all the above

Answer :  D
 

Question. Solutions of the inequalities comprising a system in variable x are represented on number lines as given below, then
(a) x Î(-∞,- 4]∪[3,∞)  
(b) x Î[-3,1]
(c) x Î(-∞,-4)∪(3,∞)
(d) x Î[-4,3]

Answer :  A


Question. x and b are real numbers. If b > 0 and |x| > b, then
(a) x Î(-b,∞)
(b) x Î(-∞,b)
(c) x Î(-b,b)
(d) x Î(-∞,-b)∪(b,∞)

Answer :  D


Question. If x is real number and |x| < 3, then
(a) x ≥ 3
(b) –3 < x < 3
(c) x ≤ -3
(d) -3 ≤ x ≤ 3

Answer :  B
 

Question. The values of x satisfying | x – 4 | + | x – 9 | = 5, is :
(a) x = 4, 9
(b) 4 ≤ x ≤ 9
(c) x ≤ 4 or x ≥ 9
(d) none of these

Answer :  B

Question. The set of real values of x for which log 0.2 x+2/x ≤ 1 is
(a) (-∞, -5/2]∪(0, ∞)
(b) [5/2, ∞)
(c) (-∞, - 2)È[0, ∞)
(d) none of these

Answer :  A

Question. The solution set of the inequality
5 x+2 >(1/25)^1/x is

(a) (-2, 0)
(b) (-2, 2)
(c) (-5, 5)
(d) (0, ∞)

Answer :  D
 

Question. Given that x, y and b are real numbers and x < y , b < 0, then
(a)  x/b < y/b
(b)  x/b ≤ y/b
(c)  x/b > y/b
(d) x/b ≥ y/b

Answer :  C
 

Question. The integral value of x which satisfies the inequality x⁴ - 3x³ - x + 3 < 0 is
(a) 0
(b) 1
(c) 2
(d) 3

Answer :  C
 

Question. Solution of a linear inequality in variable x is represented on number line. Choose the correct answer from the given four options.
(a) x Î(-∞,5)
(b) x Î(-∞,5]
(c) x Î[5,∞)
(d) x Î(5,∞)

Answer :  D
 

Question. The solution set of the inequality 1/x < is
(a) (1, ∞)
(b) (-∞, 1)
(c) (-∞, 0)∪(1, ∞)
(d) none of these

Answer :  C
 

Question. 8x² + 16x - 51 /(2x-3)(x+4) > 3, if x satisfies
(a) x < –4
(b) –3 < x < 3/2
(c) x > 5/2
(d) all the above

Answer :  D
 

Question. The equation
| x + 1|log(x+1) (3+2x - x²) = (x-3) | x | has
(a) unique solution
(b) two solution
(c) no solution
(d) More than two solutions

Answer :  C
 

Question. 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
(a) { 0}
(b) {0, 5/3}
(c) [0, ∞)
(d) none of these

Answer :  B


Question. The equation x +1 - x -1 = 4x -1 has
(a) no solution
(b) one solution
(c) two solution
(d) more than two solutions

Answer :  A
 

Question. The values of x satisfying the inequality | x³ -1| ≥ 1- x belong to
(a) (-∞, -1]
(b) (-∞,-1]∪[0,∞)
(c) [1, ∞)
(d) none of these

Answer :  B 
 

Question. The number of ordered pairs (x, y) satisfying 3^x ×5^y = 75 and 3^y ×5^x = 45 is
(a) 0
(b) 1
(c) 3
(d) none of these

Answer :  B
 

Question. If |x + 3| ≥ 10, then
(a) x Î(-13,7] (b) x Î(-13,7)
(c) x Î(-∞,13]∪[-7,∞)
(d) x Î(-∞, -13]∪[7,∞)

Answer :  D
 

Question. The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then what can you say about breadth?
(a) breadth = 20
(b) breadth ≤ 20
(c) breadth ≥ 20
(d) breadth ≠ 20

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. The solution set of x² - 3x + 4 /x+1 > 1,x ε R is
(a) (3, +∞)
(b) (-1, 1)È(3, +∞)
(c) [-1, 1]È[3, +∞)
(d) none of theses

Answer :  B
 

Question. If k ≠ [0, 8], find the value of x for which the inequality x² k² / k (6 x) ≥ 1 is satisfied.
(a) –1 < x < 1
(b) –1 < x < 2
(c) –2 < x < 1
(d) –3 < x < 1

Answer :  A
 

Question. The integral values of x , which satisfy the equation | x / x -1| + | x | = x2 / x -1 is are
(a) 0
(b) –1
(c) 2
(d) 100

Answer :  (A,C,D)
 

Question. Set of values of x satisfying the inequality x² + 6x - 7 / |x + 4| < is /are
(a) (-∞, - 7)
(b) (-7, - 4)
(c) (–7, –4)∪(-4, 1)
(d) (1, ∞)

Answer :  C