Real Numbers — Flashcards
Telangana Board · Class 10 · Mathematics
28 flashcards for Real Numbers (Telangana Board Class 10 Mathematics) to test yourself on key terms and facts.
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Solve the bees puzzle: A swarm gives remainder 1 when divided by 2, remainder 2 when divided by 3, remainder 3 when divided by 4, and remainder 0 when divided by 5. The number of bees is at most 50. F
Answer
Step 1: The number must be a multiple of 5, so test 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Step 2: It must leave remainder 3 when divided by 4, so check 5, 15, 25, 35, 45. Step 3: It must leave remain…
Write 35 in the form a = bq + r for division by 2, 3, 4, and 5.
Answer
For division by 2: 35 = 2 × 17 + 1 For division by 3: 35 = 3 × 11 + 2 For division by 4: 35 = 4 × 8 + 3 For division by 5: 35 = 5 × 7 + 0 Check: In each case, the remainder is less than the divisor.
Find q and r in 13 = 3q + r.
Answer
Step 1: Divide 13 by 3. Step 2: 3 × 4 = 12, and 13 - 12 = 1. Step 3: So q = 4 and r = 1. Check: 13 = 3 × 4 + 1, and 0 ≤ 1 < 3.
Find the HCF of 60 and 100 using Euclid's algorithm.
Answer
Step 1: 100 = 60 × 1 + 40 Step 2: 60 = 40 × 1 + 20 Step 3: 40 = 20 × 2 + 0 Step 4: The last non-zero remainder is 20. Answer: HCF(60, 100) = 20.
Why does Euclid's algorithm work for finding the HCF?
Answer
It works because the HCF does not change when the larger number is replaced by its remainder. Key idea: HCF(c, d) = HCF(d, r) If c = dq + r, then any common factor of c and d also divides r, and any c…
Find the HCF of 12 and 18 by prime factorisation.
Answer
Step 1: 12 = 2 × 2 × 3 = 2^2 × 3 Step 2: 18 = 2 × 3 × 3 = 2 × 3^2 Step 3: Take the smallest power of each common prime factor. HCF = 2^1 × 3^1 = 6 Answer: 6.
Find the LCM of 12 and 18 by prime factorisation.
Answer
Step 1: 12 = 2^2 × 3 Step 2: 18 = 2 × 3^2 Step 3: Take the greatest power of each prime factor. LCM = 2^2 × 3^2 = 36 Answer: 36.
Use the relation HCF(a,b) × LCM[a,b] = a × b to find the LCM of 60 and 100, given that HCF is 20.
Answer
Step 1: Use HCF(a,b) × LCM[a,b] = a × b Step 2: 20 × LCM = 60 × 100 Step 3: 20 × LCM = 6000 Step 4: LCM = 6000 ÷ 20 = 300 Answer: LCM(60, 100) = 300.
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