If 2515 is divided by 13, the reminder is ______. - Mathematics

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If 2515 is divided by 13, the reminder is ______.

Solution

If 2515 is divided by 13, the remainder is 12.

Explanation: Let 2515 = (26– 1)15

= ""^15"C"_0  (26)^15 (-1)^0 + ""^15"C"_1  (26)^14  (-1)^1 + ""^15"C"_2   (26)^13  (-1)^2 + ... + ""^15"C"_15 (-1)^15

= 26^15  - 15(26)^14 + .... - 1 - 13 + 13

= 26^15 - 15 * (26)^14 + ... - 13 + 12

= 13lambda + 12

∴ The remainder = 12.

Concept: Proof of Binomial Therom by Combination
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APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Exercise | Q 33 | Page 146
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