Punjab Board Class 11 Mathematics — Flashcards for Quick Revision

A: Solution: (i) NOT a set - The criterion 'most talented' is subjective and varies from person to person. No well-defined rule to decide membership. (ii) IS a set - An even integer is clearly defined as

A: Solution: Step 1: Identify the condition: x is a natural number AND 3 < x ≤ 10. Step 2: Find natural numbers greater than 3 and less than or equal to 10. Step 3: List them: 4, 5, 6, 7, 8, 9, 10. There

A: Solution: Step 1: Analyze the pattern in the set: 1 = 1³, 8 = 2³, 27 = 3³, 64 = 4³, 125 = 5³. Step 2: Recognize that each element is a perfect cube of natural numbers. Step 3: Identify that elements c

A: Since ordered pairs are equal, corresponding elements must be equal. Step 1: Equate first elements: x + 1 = 3 Step 2: Solve for x: x = 3 - 1 = 2 Step 3: Equate second elements: y - 2 = 1 Step 4: Solve

A: Step 1: List all ordered pairs with first element from A and second from B A × B = {(1,4), (1,5), (2,4), (2,5), (3,4), (3,5)} Step 2: Count the elements n(A) = 3 (elements in A) n(B) = 2 (elements in

A: In general, A × B ≠ B × A (they are not equal). Example: Let A = {a, b} and B = {1, 2} A × B = {(a,1), (a,2), (b,1), (b,2)} B × A = {(1,a), (1,b), (2,a), (2,b)} These are different sets because: - In

A: Step 1: Convert minutes to decimal degrees: 40° 20' = 40 + 20/60 = 40 + 1/3 = 121/3 degrees Step 2: Use formula: Radian measure = (π/180) × Degree measure Step 3: Radian measure = (π/180) × (121/3) =

A: Step 1: Use formula: Degree measure = (180/π) × Radian measure Step 2: Degree measure = (180/π) × 6 = (1080 × 7)/22 = 7560/22 = 343 7/11 degrees Step 3: Convert fractional part to minutes: 7/11 × 60 =

A: Step 1: Find revolutions in 1 second: 360 revolutions/minute ÷ 60 seconds = 6 revolutions/second Step 2: Convert revolutions to radians: 1 revolution = 2π radians Step 3: Radians in 1 second = 6 × 2π