Class 11 Math: Relations and Functions 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 Relations and Functions to help you test your mastery.
Exam-Pattern Questions and Answers
Question 1 (MEDIUM)
This is a descriptive problem. Work out all steps on paper before checking the solution.
Solution Explanation & Steps: Given, f (x) = 2 4x - ; For Df., f (x) must be a real number. ⇒ 2 4x - must be a real number. ⇒ x2 - 4 ≥ 0 ⇒ (x + 2) (x - 2) ≥ 0 ⇒ Either x ≤ - 2 or x ≥ 2. ⇒ Df = (- ∞, - 2] ∪ [2, ∞). For Rf, let y = 2 4x - ... (i) As square root of a real number is always non-negative, y ≥ 0. On squaring (i), we get y2 = x2 - 4 ⇒ x2 = y2 + 4 but x2 ≥ 0 ∀ x ∈ Df. ⇒ y2 + 4 ≥ 0 ⇒ y2 ≥ - 4, which is true ∀ y ∈ R, Also, y ≥ 0. ⇒ Rf = [0, ∞).
Question 2 (EASY)
- Option 1: Option A
- Option 2: Option B
- Option 3: Option C
- Option 4: Option D
Solution Explanation & Steps: (a) Both A and R are true and R is the correct explanation of A.
Question 3 (MEDIUM)
This is a descriptive problem. Work out all steps on paper before checking the solution.
Solution Explanation & Steps: Given function is f (x) = 29 x- For domain of ‘f ’, 9 - x2 ≥ 0 ⇒ 9 ≥ x2 ⇒ x2 ≤ 9 ⇒ -3 ≤ x ≤ 3 ∴ Domain is {x ∈ R | -3 ≤ x ≤ 3}, i.e. [-3, 3] For range : f (x) = 29 x- 29y x⇒ = - 29 x- is always +ve ⇒ y is always +ve. ⇒ y2 = 9 - x2 ⇒ x2 = 9 - y2 ⇒ x = 29 y- For x to exist 9 - y2 ≥ 0 ⇒ y2 ≤ 9 ⇒ -3 ≤ y ≤ 3 As y ≥ 0 ∴ Range = [0, 3]
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.