NIFT UG 2019 Question Paper with solutions

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Question : 27 of 150

Marks: +1, -0

When

n

is divided by 5 then remainder is 2 . What is the remainder when

n^{2}

is divided by

5

?

2
3
1
4

Solution:

n=5 q+2

[ ∵

Dividend

=

Divisor

\times

Quotient

+

Remainder

]

On squaring the both sides, we get

n^{2}=25 q^{2}+20 q+4

[ ∵ (a+b)^{2}=a^{2}+2 a b+b^{2}]

i.e.

\;\; n^{2}=5(5 q^{2}+4 q)+4

∴

When

n^{2}

is divided by 5 leaves 4 as remainder.

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