NCERT Solutions for class 11 Maths | Chapter 6 - Linear Inequalities

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Questions
1 Solve: |x – 3| < 5
A (2, 8)
B (-2, 8)
C (8, 2)
D (8, -2)

Answer:(-2, 8)
2 If x² = 4 then the value of x is
A -2
B 2
C -2, 2
D None of these

Answer:-2, 2
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3 If (|x| – 1)/(|x| – 2) ≥ 0, x ∈ R, x ± 2 then the interval of x is
A (-∞, -2) ∪ [-1, 1]
B [-1, 1] ∪ (2, ∞)
C (-∞, -2) ∪ (2, ∞)
D (-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

Answer:(-∞, -2) ∪ [-1, 1] ∪ (2, ∞)
4 If x² = -4 then the value of x is
A (-2, 2)
B (-2, ∞)
C (2, ∞)
D No solution

Answer:No solution
5 The interval in which f(x) = (x – 1) × (x – 2) × (x – 3) is negative is
A x > 2
B 2 < x and x < 1
C 2 < x < 1 and x < 3
D 2 < x < 3 and x < 1

Answer:2 < x < 3 and x < 1
6 The solution of the -12 < (4 -3x)/(-5) < 2 is
A 56/3 < x < 14/3
B -56/3 < x < -14/3
C 56/3 < x < -14/3
D -56/3 < x < 14/3

Answer:-56/3 < x < 14/3
7 If x² = -4 then the value of x is
A (-2, 2)
B (-2, ∞)
C (2, ∞)
D No solution

Answer:No solution
8 f(x) = {(x – 1)×(2 – x)}/(x – 3) ≥ 0
A (-∞, 1] ∪ (2, ∞)
B (-∞, 1] ∪ (2, 3)
C (-∞, 1] ∪ (3, ∞)
D None of these

Answer:(-∞, 1] ∪ (2, 3)
9 The solution of |2/(x – 4)| > 1 where x ≠ 4 is
A (2, 6)
B (2, 4) ∪ (4, 6)
C (2, 4) ∪ (4, ∞)
D (-∞, 4) ∪ (4, 6)

Answer:(2, 4) ∪ (4, 6)
10 The graph of the inequations x ≥ 0, y ≥ 0, 3x + 4y ≤ 12 is
A none of these
B interior of a triangle including the points on the sides
C in the 2nd quadrant
D exterior of a triangle

Answer:interior of a triangle including the points on the sides
11 If |x| < 5 then the value of x lies in the interval
A (-∞, -5)
B (∞, 5)
C (-5, ∞)
D (-5, 5)

Answer:(-5, 5)
12 Sum of two rational numbers is ______ number.
A rational
B irrational
C Integer
D Both 1, 2 and 3

Answer:rational
13 The region of the XOY-plane represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10 is
A unbounded
B a polygon
C none of these
D exterior of a triangle

Answer:none of these
14 The solution of the 15 < 3(x – 2)/5 < 0 is
A 27 < x < 2
B 27 < x < -2
C -27 < x < 2
D -27 < x < -2

Answer:27 < x < 2
15 If | x − 1| > 5, then
A x∈(−∞, −4)∪(6, ∞]
B x∈[6, ∞)
C x∈(6, ∞)
D x∈(−∞, −4)∪(6, ∞)

Answer:x∈(−∞, −4)∪(6, ∞)
16 1 ≤ |x – 1| ≤ 3
A [-2, 0]
B [2, 4]
C [-2, 0] ∪ [2, 4]
D None of these

Answer:[-2, 0] ∪ [2, 4]
17 Solve: (x + 1)² + (x² + 3x + 2)² = 0
A x = -1, -2
B x = -1
C x = -2
D None of these

Answer:x = -1
18 If (x + 3)/(x – 2) > 1/2 then x lies in the interval
A (-8, ∞)
B (8, ∞)
C (∞, -8)
D (∞, 8)

Answer:(-8, ∞)
19 If -2 < 2x – 1 < 2 then the value of x lies in the interval
A (1/2, 3/2)
B (-1/2, 3/2)
C (3/2, 1/2)
D (3/2, -1/2)

Answer:(-1/2, 3/2)
20 The solution of the inequality |x – 1| < 2 is
A (1, ∞)
B (-1, 3)
C (1, -3)
D (∞, 1)

Answer:(-1, 3)

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