The remainder obtained when 12-22-32-42-52- 1002 is divided by 7 is-

The correct option is C 5 ( 1^2+2^2+3^2+4^2+5^2+…100^2 ) =[ n(n+1)(2n+1)]/6 = 338350 or remainders on dividing the terms by 7 1^2/7=1, 2^2/7=4, 3^2/7=2, 4^2 ...

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Quantitative Aptitude

Remainder Theorem

The remainder...

Question

The remainder obtained when $(1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + \dots 100^{2})$ is divided by 7 is:

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Solution

The correct option is C
5

$(1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + \dots 100^{2})$ = $\frac{[n (n + 1) (2 n + 1)]}{6}$ = 338350

or remainders on dividing the terms by 7

$1^{2} / 7 = 1, 2^{2} / 7 = 4, 3^{2} / 7 = 2, 4^{2} / 7 = 2, 5^{2} / 7 = 4, 6^{2} / 7 = 1, 7^{2} / 7 = 0 \Rightarrow (1 + 4 + 2 + 2 + 4 + 1 + 0) / 7 = 0$
so the remainder will be $99^{2} / 7 = 1^{2} / 7 = 1, 100^{2} / 7 = 2^{2} / 7 = 4 \Rightarrow 1 + 4 = 5$

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The remainder obtained when (12+22+32+42+52+…1002) is divided by 7 is:

The correct option is C 5 (12+22+32+42+52+…1002) =[n(n+1)(2n+1)]6 = 338350 or remainders on dividing the terms by 7 12/7=1,22/7=4,32/7=2,42/7=2,52/7=4,62/7=1,72/7=0⇒(1+4+2+2+4+1+0)/7=0 so the remainder will be 992/7=12/7=1,1002/7=22/7=4⇒1+4=5

The remainder obtained when $(1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + \dots 100^{2})$ is divided by 7 is: