Examora
|
MCQ & Notes
Back to Home
NCERT Solutions for Class 11 Math Ch-5: Linear Inequalities
NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities covers the algebraic and graphical solution of linear inequalities in one and two variables, and their application in solving systems of inequalities.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: What happens to the direction of an inequality when both sides are multiplied or divided by a negative number?
Answer: When both sides of an inequality are multiplied or divided by the same negative number, the direction (sign) of the inequality reverses; for example, if a < b, then multiplying both sides by −1 gives −a > −b.
Q2: How is a linear inequality in one variable typically represented on a number line?
Answer: A linear inequality in one variable is represented on a number line using an open circle (for strict inequalities like < or >, indicating the boundary point is excluded) or a closed/filled circle (for inequalities like ≤ or ≥, indicating the boundary point is included), along with shading in the direction of the solution set.
Q3: How do you graphically represent a linear inequality in two variables, such as 2x + 3y < 6?
Answer: First, plot the corresponding line 2x + 3y = 6 (using a dashed line for strict inequalities like '<' or '>', and a solid line for '≤' or '≥'). Then, test a point not on the line (commonly the origin) to determine which side of the line satisfies the inequality, and shade that entire region.
Q4: What does the solution region of a system of linear inequalities represent?
Answer: The solution region (or feasible region) of a system of linear inequalities is the common region on the graph that satisfies all the given inequalities simultaneously, typically found by shading the individual regions and identifying their overlapping (intersection) area.
Q5: If x > 5, what can be said about −2x?
Answer: If x > 5, multiplying both sides by −2 (a negative number) reverses the inequality sign, giving −2x < −10.
Read More & Chapter Resources
These short notes are designed for quick revision. Read the main points once, then use the related material below to practise the same chapter. Revising a concept and checking it with questions can make your preparation more focused.