NIOS Class 12 Mathematics — Flashcards

A: Step 1: Identify the intersection - find elements common to both sets Step 2: Check each element of A against B: 1(no), 2(no), 3(yes), 4(yes), 5(yes) Step 3: Write the result: A ∩ B = {3, 4, 5} Expla

A: Step 1: Identify the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Step 2: Identify set A = {2, 4, 6, 8, 10} Step 3: Find A' by listing all elements in U that are NOT in A Step 4: A' = {1, 3, 5, 7

A: Step 1: Identify union - collect all elements from both sets Step 2: List elements from A: a, e, i, o, u Step 3: Add elements from B that are NOT already listed: b, c, d Step 4: A ∪ B = {a, b, c, d, e

A: Formula: n(A × B) = n(A) × n(B) Step 1: Identify n(A) = 3 elements Step 2: Identify n(B) = 2 elements Step 3: Apply formula: n(A × B) = 3 × 2 = 6 Verification by listing: A × B = {(1,a), (1,b), (2,a

A: Step 1: Find A × B (first element from A, second from B) A × B = {(2,5), (2,6), (3,5), (3,6), (4,5), (4,6)} Step 2: Find B × A (first element from B, second from A) B × A = {(5,2), (5,3), (5,4), (6,2

A: Step 1: Find B ∪ C (union of B and C) B = {2, 4, 6}, C = {1, 4} B ∪ C = {1, 2, 4, 6} (combine all elements, count 4 only once) Step 2: Find A × (B ∪ C) A × (B ∪ C) = {(1,1), (1,2), (1,4), (1,6), (3,1

A: Step 1: Use the conversion formula 1° = π/180 radians Step 2: 90° = 90 × (π/180) radians Step 3: Simplify = 90π/180 = π/2 radians Answer: π/2 radians

A: Step 1: Use the conversion formula 1 radian = (180/π)° Step 2: 5π/6 radians = (5π/6) × (180/π) degrees Step 3: Cancel π and simplify = (5 × 180)/6 = 900/6 Step 4: = 150° Answer: 150°

A: Formula: θ = ℓ/r (where θ is in radians, ℓ is arc length, r is radius) Step 1: Given ℓ = 14 cm, r = 7 cm Step 2: θ = 14/7 = 2 radians Answer: 2 radians Note: The formula ℓ = rθ is only valid when θ is