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Subjects
Class 10MathematicsReal NumbersEuclid’s Division LemmaHard
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If a number leaves remainder 15 when divided by 16, what is the remainder when its square is divided by 16?

Answer and explanation

Correct answer: 1

Step 1: Let the number be (16q+15). Step 2: The square remainder is obtained from (15^2=225) divided by 16. (225=16\times14+1). Step 3: The square of a remainder (b-1) often gives remainder 1.

Related tags

Euclids-Division-LemmaSquare-RemainderAdvancedEuclid’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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