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**Hint:**Before solving this question, we must know about perfect squares and square roots.

PERFECT SQUARE: If we multiply the number $x$ with itself then the result is called Perfect Square.

For example: \[3~\ \ \times \ \ 3\text{ }=\text{ }9\] . Hence, $9$ is a perfect square.

SQUARE ROOT: If we get a number $x$ when we multiply a value $y$ with itself. Then we can say that the value $y$ is the square root of the value of $x$.

For Example, we have $9=3\times 3$, here we can say that $3$ is the square root of $9$

**Complete step-by-step solution:**

From the above results, we can choose the option $\left( d \right)$ as the correct option.

$\text{Example }1.2:-$

In our second example, consider the number ‘$25$’ which has ‘$2$’ digits, hence the value of ‘$n$’ is ‘$2$’

The square of $25$ is ‘$625$’, which is a three-digit number.

Now, substitute the value of ‘$n$’ in the given option to find the correct option.

$\begin{align}

& \left( a \right)\to \\

& \left( b \right)\to \\

& \left( c \right)\to \\

& \left( d \right)\to

\end{align}$$\begin{align}

& 2n+1=2\left( 2 \right)+1=5 \\

& 2n-1=2\left( 2 \right)-1=3 \\

& {{n}^{2}}={{2}^{2}}=4 \\

& 2n=2\left( 2 \right)=4

\end{align}$

Here we got the correct option as $\left( b \right)2n-1$

$\text{Example }1.3:-$

In our third example, consider the number ‘$625$’ which has ‘$3$’ digits, hence the value of ‘$n$’ is ‘$3$’

The square of $625$ is ‘\[\text{390,625}\]’, which is a Six-digit number.

Now, substitute the value of ‘$n$’ in the given option to find the correct option.

$\begin{align}

& \left( a \right)\to \\

& \left( b \right)\to \\

& \left( c \right)\to \\

& \left( d \right)\to

\end{align}$$\begin{align}

& 2n+1=2\left( 3 \right)+1=7 \\

& 2n-1=2\left( 3 \right)-1=5 \\

& {{n}^{2}}={{3}^{2}}=9 \\

& 2n=2\left( 3 \right)=6

\end{align}$

Here we got the correct option as $\left( d \right)2n$

**Note:**From the above observations we can clearly say that for an even digit number the square of the number contains $2n-1$digits and for an odd digit number the square of that number contains $2n$ digits. While coming to the problem it is possible that the correct options are more than two.

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