# NCERT Class 11-Math's: Chapter –6 Linear Inequalities Part 4

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## Objective Type

### Choose the Correct Answer from the Given Four Options Against Each of the Examples 10 to 13 (M.C.Q.)

**Question 10:**

If then

(A)

(B)

(C)

(D)

**Answer:**

(B) is the correct choice. Since for and .

**Question 11:**

The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is , then

(A)

(B)

(C)

(D)

**Answer:**

(C) is the correct choice. If *x* cm is the breadth, then

**Question 12:**

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

(A)

(B)

(C)

(D)

**Answer:**

(A) Is the correct choice

Common solution of the inequalities is from to and to .

**Question 13:**

If , then

(A)

(B)

(C)

(D)

**Answer:**

(D) is the correct choice, since

**Question 14:**

State whether the following statements are True or False.

(i) If and , then

(ii) If *,* then , and

(iii) If *,* then , and

(iv) If and , then

(v) If *,* then

(vi) Graph of is

(vii) Solution set of is

**Answer:**

(i) True, because the sign of inequality is reversed when we multiply both sides of an inequality by a negative quantity.

(ii) False, product of two numbers is positive if they have the same sign.

(iii) False, product of two numbers is negative if they have opposite signs.

(iv) True (v)

True if .

(vi) False, because for , the line has to be dotted, i.e., the region does not include the points on the line (vii)

False, because does not satisfy the given inequality and it is a point in shaded portion.