Gujarat Board Class 10 Mathematics — Flashcards

A: Step 1: Divide 32760 by 2 → 16380 Step 2: Divide 16380 by 2 → 8190 Step 3: Divide 8190 by 2 → 4095 Step 4: Divide 4095 by 3 → 1365 Step 5: Divide 1365 by 3 → 455 Step 6: Divide 455 by 5 → 91 Step 7: D

A: Prime factorization: 123456789 = 3² × 3803 × 3607 To verify 3803 is prime: - Check divisibility by primes up to √3803 ≈ 61.7 - Test primes: 2 (odd, so no), 3 (3+8+0+3=14, not divisible), 5 (doesn't e

A: The Fundamental Theorem of Arithmetic: Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, except for the order in which the prime factors oc

A: Step 1: Look at the highest power of x in the polynomial → x² is the highest power Step 2: Degree = 2 Step 3: A polynomial of degree 2 is called a quadratic polynomial Answer: Degree = 2, Type = Quadr

A: Step 1: Check each term in the expression - First term: 5/x = 5x⁻¹ (has negative exponent) - Second term: 3x (positive integer exponent ✓) - Third term: -2 (constant term ✓) Step 2: Polynomials

A: Step 1: Find highest power of variable in each (i) 7y + 4: Highest power is y¹ → Degree = 1 → Linear polynomial (ii) 2x³ - 5x + 1: Highest power is x³ → Degree = 3 → Cubic polynomial (iii) 8: Co

A: Step 1: We have y = 2x + 1 from the first equation. Step 2: Substitute this value of y into the second equation: 3x + (2x + 1) = 11 Step 3: Simplify: 5x + 1 = 11 Step 4: Solve for x: 5x = 10 → x = 2 S

A: Step 1: Observe that the coefficients of y are +3 and -3 (opposites). Step 2: Add both equations to eliminate y: (2x + 3y) + (5x - 3y) = 13 + 8 Step 3: Simplify: 7x = 21 Step 4: Solve for x: x = 3 Ste

A: For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, rewrite: 3x + 4y - 12 = 0 6x + 8y - 24 = 0 Calculate the ratios: a₁/a₂ = 3/6 = 1/2 b₁/b₂ = 4/8 = 1/2 c₁/c₂ = -12/-24 = 1/2 Since a₁/a₂ = b₁/b