On dividing a number by 5,we get 3 as the rem | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the number be $n$. According to the problem,when $n$ is divided by $5$,the remainder is $3$. This can be expressed as $n = 5k + 3$,where $k$ i

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Let the number be $n$. According to the problem,when $n$ is divided by $5$,the remainder is $3$. This can be expressed as $n = 5k + 3$,where $k$ is an integer.We need to find the remainder when $n^2$ is divided by $5$.$n^2 = (5k + 3)^2$$n^2 = 25k^2 + 30k + 9$$n^2 = 25k^2 + 30k + 5 + 4$$n^2 = 5(5k^2 + 6k + 1) + 4$Since $5(5k^2 + 6k + 1)$ is divisible by $5$,the remainder when $n^2$ is divided by $5$ is $4$.

On dividing a number by $5$,we get $3$ as the remainder. What will be the remainder when the square of this number is divided by $5$?

Similar Questions

Simplify $\frac{(0.9743)^{3}-(0.0257)^{3}}{(0.9743)^{2}+(0.9743)(0.0257)+(0.0257)^{2}}$

The sum of the digits of a two-digit number is $8$. If the digits are reversed,the number is increased by $54$. Find the number.

For any integral value of $n$,$3^{2n} + 9n + 5$ when divided by $3$ leaves the remainder:

$(13.99)^{2} - (15.02)^{2} + (18.07)^{2} - 36.64 = ?$

Which number should replace both the $$s in $\left(\frac{}{21}\right) \times \left(\frac{*}{189}\right) = 1$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module