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Class 10MathematicsReal NumbersEuclid’s Division LemmaExpert
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If (a) leaves remainder 14 when divided by 23 and (b) leaves remainder 19 when divided by 23, what is the remainder when (6a+5b) is divided by 23?

Answer and explanation

Correct answer: 18

Step 1: In (6a+5b), the remainder part is (6\times14+5\times19=179). Step 2: (179=23\times7+18), so the remainder is 18. Step 3: In multi-term expressions, handle each term’s remainder separately.

Related tags

Euclids-Division-LemmaLinear-CombinationRemainderEuclid’s Division LemmaEuclid S Division LemmaReal NumbersMathematicsClass 10 Mcq
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10 more MCQs
  1. 1In Euclid’s Division Lemma, if (a) and (b) are positive integers, which condition is correct for the remainder (r)?
  2. 2If (35=6q+r) and (0 \le r < 6), what are the values of (q) and (r)?
  3. 3Which is the standard form of Euclid’s Division Lemma?
  4. 4If a number leaves remainder (0) when divided by (9), in which form can it be written?
  5. 5What possible remainders can occur when an integer is divided by (5)?
  6. 6What is the remainder when (52) is divided by (7)?
  7. 7Which condition is necessary for (b) in Euclid’s Division Lemma?
  8. 8If (a=17) and (b=4), which is the correct Euclidean form (a=bq+r)?
  9. 9How many possible remainders are there when a number is divided by (3)?
  10. 10If a number is odd, what remainder will it leave when divided by (2)?
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