Class 11 Math: Linear Inequalities Important Exam Questions
Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 11 Linear Inequalities to help you test your mastery.
Exam-Pattern Questions and Answers
Question 1 (HARD)
This is a descriptive problem. Work out all steps on paper before checking the solution.
Solution Explanation & Steps: Consider the inequation 5(2x - 7) - 3(2x + 3) ≤ 0 ⇒ 10x - 35 - 6x - 9 ≤ 0 ⇒ 4x ≤ 44 ⇒ x ≤ 11 …(i) Consider the inequation, 2x + 19 ≤ 6x + 47 ⇒ 19 - 47 ≤ 6x - 2x ⇒ -28 ≤ 4x ⇒ -7 ≤ x ⇒ x ≥ -7 …(ii) From (i) and (ii), we get Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 8 Solution as -7 ≤ x ≤ 11 Representation on number line SECTION - D Questions 32 to 35 carry 5 marks each.
Question 2 (HARD)
This is a descriptive problem. Work out all steps on paper before checking the solution.
Solution Explanation & Steps: LHS =|x + 1| + |x| As both the terms contain modulus by equating the expression within modulus to zero, We get x = -1, 0 as critical points. These critical points divide the line in three parts as (-∞, -1), [-1, 0), [0, ∞). Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 8 Case I: when -∞ < x < - 1 |x + 1| + |x| > 3 ⇒ -x - 1 - x > 3 ⇒ - 2x > 4 ⇒ x < -2 Case II: when -1 ≤ x < 0 |x + 1| + |x| > 3 ⇒ x + 1 - x > 3 ⇒ 1 > 3 (not possible) Case III: when 0 ≤ x < ∞ |x + 1| + |x| > 3 ⇒ x + 1 + x > 3 ⇒ 2x > 2 ⇒ x > 1 Combining the results of cases, we get x ∈ (-∞, -2) ∪ (1, ∞) SECTION - D Questions 32 to 35 carry 5 marks each.
Question 3 (EASY)
- Option 1: Systematic application of coordinate rules
- Option 2: Advanced integral equations
- Option 3: Infinite boundary coordinates
- Option 4: None of the above
Solution Explanation & Steps: Studying Algebraic solutions of linear inequalities in one variable requires mastering basic coordinate relationships first.
Grading Step-Marking Guidelines
Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.