Tamil Nadu Board Class 10 Mathematics — Flashcards

A: Step 1: A × B contains all ordered pairs (x, y) where x ∈ A and y ∈ B. Step 2: For each element in A, pair it with each element in B: - 1 pairs with: a, b → (1,a), (1,b) - 2 pairs with: a, b → (2,a),

A: Step 1: Use the formula: n(A × B) = n(A) × n(B) Step 2: Substitute the given values: 20 = 4 × n(B) Step 3: Divide both sides by 4: n(B) = 20 ÷ 4 = 5 Answer: n(B) = 5 Explanation: The total number of o

A: Use A × B when you need the Cartesian product with first coordinates from A and second coordinates from B. Example: If A = {Roll Numbers} and B = {Names}, then: - A × B = {(1, Raj), (2, Priya), ...} -

A: Using Euclid's Division Lemma: a = bq + r, where 0 ≤ r < b Given: a = 34, b = 5 Step 1: Divide 34 by 5 → 34 ÷ 5 = 6 remainder 4 Step 2: Write as 34 = 5(6) + 4 Step 3: Verify: 0 ≤ 4 < 5 ✓ Answer: Quo

A: Using generalized Euclid's Division Lemma: a = bq + r, where 0 ≤ r < |b| Given: a = -12, b = 5 Step 1: We need remainder between 0 and 5 Step 2: -12 = 5(-3) + 3 Step 3: Check: -15 + 3 = -12 ✓ and 0 ≤

A: Euclid's Division Algorithm - Apply division lemma repeatedly until remainder = 0 Step 1: 273 = 119 × 2 + 35 (remainder ≠ 0, continue) Step 2: 119 = 35 × 3 + 14 (remainder ≠ 0, continue) Step 3: 35 =

A: Step 1: Label the equations: (1) 2x - 3y + z = 2, (2) x + y + z = 6, (3) 3x - y + 2z = 11 Step 2: Eliminate z from (1) and (2): From (2): z = 6 - x - y. Substitute into (1): 2x - 3y + (6 - x - y) = 2

A: Step 1: Divide 2x³ - 5x² + 5x - 3 by x³ + x² - x + 2 Step 2: 2x³ - 5x² + 5x - 3 = (x³ + x² - x + 2) × 2 + (-7x² + 7x - 7) Step 3: Remainder = -7(x² - x + 1). Ignore the constant factor, continue with

A: Step 1: Factor the numerator: x² - 16 = (x + 4)(x - 4) Step 2: Factor the denominator: x² + 8x + 16 = (x + 4)² Step 3: Write the expression: [(x + 4)(x - 4)]/[(x + 4)²] Step 4: Cancel common factor (x