Tiêu đề Advanced Series 9th Class Maths - Solutions.pdf ✅

Class 9 – Maths | A-9 Real Numbers 1 1. Real Numbers Solutions LEVEL – I 1. Correct option: (B) Step 1: Write the prime factorization of both numbers. a = (2 2 × 3 3 × 5 4 ) b = (2 3 × 3 2 × 5) Step 2: Identify the common prime factors and their minimum powers in both numbers. Common prime factors: 2, 3, and 5 Minimum power of 2 in a and b = 2 2 = 4 Minimum power of 3 in a and b = 3 2 = 9 Minimum power of 5 in a and b = 5 = 5 Step 3: Multiply the common prime factors with their minimum powers to find the HCF. HCF(a, b) = (2 2 × 3 2 × 5) HCF(a, b) = 4 × 9 × 5 = 180 So, the correct answer is (b) 180. 2. Correct option: (C) Step 1: Write the prime factorization of given numbers. a = (2 3 × 3 2 × 5) b = (2 2 × 3 3 × 5 2) c = (2 4 × 3 × 5 3 × 7) Step 2: Identify the common prime factors and their minimum powers in both numbers. Common prime factors: 2, 3, and 5 Minimum power of 2 in a, b and c = 2 2 = 4 Minimum power of 3 in a, b and c = 3 = 3 Minimum power of 5 in a, b and c = 5 = 5 Step 3: Multiply the common prime factors with their minimum powers to find the HCF. HCF(a, b, c) = 4 × 3 × 5 = 60 So, the correct answer is (c) 60. 3. Correct option: (D) To find the LCM (Least Common Multiple) of two numbers, we need to find the highest power of each prime factor that appears in either number and multiply them together. Let's find the LCM of the given numbers: (2 3 × 3 × 5), and (2 4 × 5 × 7), Now, we'll find the highest power of each prime factor that appears in either number: Prime factor 2: The highest power is 2 4 (from the second number). Prime factor 3: The highest power is 3 (from the first number). Prime factor 5: The highest power is 5 (common to both numbers).
Class 9 – Maths | A-9 Real Numbers 2 Prime factor 7: The highest power is 7 (from the second number). Now, we multiply these highest powers together to get the LCM: LCM = 2 4 × 3 × 5 × 7 LCM = 16 × 3 × 5 × 7 LCM = 1680 So, the LCM of (2 3 × 3 × 5) and (2 4 × 5 × 7), is 1680. 4. Correct option: (C) Given information: HCF (Highest Common Factor) = 27 LCM (Least Common Multiple) = 162 One of the numbers = 54 We want to find the other number, denoted as "x." Step 1: Use the relationship between HCF and LCM HCF × LCM = Product of the two numbers Step 2: Substitute the given values into the formula Let's use the information provided: 27 × 162 = 54 × x Step 3: Solve for "x" Now, let's solve for "x": x = (27 × 162) 54 x = 9 Therefore, the other number is 9. 5. Correct option: (C) To find the LCM of two numbers when their product and HCF are given, we can use the formula: LCM = (Product of the two numbers) / HCF Given information: Product of the two numbers = 1600 HCF = 5 Using the formula, we can find the LCM: LCM = 1600 5 LCM = 320 Therefore, the LCM of the two numbers is 320. 6. Correct option: (D) To find the simplest form of the fraction 1095 1168 , we need to find the greatest common divisor (GCD) of the numerator and denominator and then divide both the numerator and denominator by the GCD. Step 1: Find the GCD of 1095 and 1168.