VBQs Linear Inequalities Class 11 Mathematics with solutions has been provided below for standard students. We have provided chapter wise VBQ for Class 11 Mathematics with solutions. The following Linear Inequalities Class 11 Mathematics value based questions with answers will come in your exams. Students should understand the concepts and learn the solved cased based VBQs provided below. This will help you to get better marks in class 11 examinations.

**Linear Inequalities VBQs Class 11 Mathematics**

**Question. If f(x) = (3/5) ^{x} + (4/5)^{x} – 1, x ∈ R, then the equation f(x) = 0 has :**

(a) no solution

(b) one solution

(c) two solutions

(d) more than two solutions

## Answer

B

**Question. If A = {x ∈ R : |x| < 2} and B = {x ∈ R : |x – 2| ≥ 3}; then :**

(a) A ∩ B = (–2, –1)

(b) B – A = R – (–2, 5)

(c) A ∪ B = R – (2, 5)

(d) A – B = [–1, 2)

## Answer

B

**Question. The region represented by {z = x + iy ∈ C : |z| – Re(z) ≤ 1} is also given by the inequality:**

(a) y^{2} ≥ 2(x +1)

(b) y^{2} ≤ 2(x +1/2)

(c) y^{2} ≤ x + 1/2

(d) y^{2} ≥ x +1

## Answer

B

**Question. The number of integral values of m for which the quadratic expression, (1 + 2m)x ^{2} – 2(1 + 3m)x + 4(1 + m), x ∈ R, is always positive, is :**

(a) 3

(b) 8

(c) 7

(d) 6

## Answer

A

**Question. All the pairs (x,y) that satisfy the inequality **

** also satisfy the equation:**

(a) 2|sin x| = 3sin y

(b) 2 sin x = sin y

(c) sin x = 2 sin y

(d) sin x = | sin y |

## Answer

D

**Question. Consider the two sets :****A = {m ∈ R : both the roots of x ^{2} – (m + 1)x + m + 4 = 0 are real} and B = [– 3, 5).**

**Which of the following is not true?**

(a) A- B = (-∞, – 3) ∪ (5, ∞)

(b) A ∩ B = {-3}

(c) B – A = (–3, 5)

(d) A ∪ B = R

## Answer

A

**Question. If a, b, c are distinct +ve real numbers and a ^{2} + b^{2} + c^{2} = 1 then ab + bc + ca is**

(a) less than 1

(b) equal to 1

(c) greater than 1

(d) any real no.

## Answer

A

**Question. The number of integral values of m for which the equation (1 + m ^{2})x^{2} – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is :**

(a) 1

(b) 2

(c) infinitely many

(d) 3

## Answer

C

**Question. Let S be the set of all real roots of the equation, 3 ^{x}(3^{x} – 1) + 2 = |3^{x} – 1| + | 3^{x} – 2|. Then S:**

(a) contains exactly two elements.

(b) is a singleton.

(c) is an empty set.

(d) contains at least four elements.

## Answer

B