Numbers and Sequences
Tamil Nadu Board · Class 10 · Mathematics
Flashcards for Numbers and Sequences — Tamil Nadu Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedFind the quotient and remainder when 34 is divided by 5 using Euclid's Division Lemma.
Answer
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…
Find the quotient and remainder when -12 is divided by 5.
Answer
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 ≤…
Use Euclid's Division Algorithm to find HCF of 273 and 119.
Answer
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 =…
Find HCF of 210 and 55, then express it in the form 55x - 325.
Answer
Step 1: Find HCF(210, 55) using Euclid's Algorithm: 210 = 55 × 3 + 45 55 = 45 × 1 + 10 45 = 10 × 4 + 5 10 = 5 × 2 + 0 HCF = 5 Step 2: Express 5 in form 55x - 325: 55x - 325 = 5 55x = 330 x = 6 Answ…
Find the greatest number that divides 445 and 572 leaving remainders 4 and 5 respectively.
Answer
Key Insight: If a number divides 445 leaving remainder 4, then it divides (445 - 4) = 441. Similarly, it divides (572 - 5) = 567. Step 1: Find HCF(441, 567): 567 = 441 × 1 + 126 441 = 126 × 3 + 63 12…
Express 32760 as a product of prime powers (Fundamental Theorem of Arithmetic).
Answer
Use prime factorization: Step 1: Divide by 2 repeatedly 32760 ÷ 2 = 16380 16380 ÷ 2 = 8190 8190 ÷ 2 = 4095 (cannot divide by 2) Step 2: Divide by 3 4095 ÷ 3 = 1365 1365 ÷ 3 = 455 (cannot divide by 3…
Find the remainder when 70004 is divided by 7 using modular arithmetic.
Answer
Use congruence modulo 7: Step 1: Recognize 70000 = 7 × 10000, so 70000 ≡ 0 (mod 7) Step 2: Apply addition property of congruence: 70000 + 4 ≡ 0 + 4 (mod 7) 70004 ≡ 4 (mod 7) Step 3: Since remainder…
Find the least positive value of x such that 78 + x ≡ 3 (mod 5).
Answer
Solve using congruence properties: Step 1: Write the congruence 78 + x ≡ 3 (mod 5) Step 2: Find 78 (mod 5) 78 = 5 × 15 + 3, so 78 ≡ 3 (mod 5) Step 3: Substitute 3 + x ≡ 3 (mod 5) Step 4: Subtract …
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