If $90 \equiv 2 (\mathrm{mod} 4)$ , then

If $90 \equiv 2 (\mathrm{mod} 4)$ , then

Option ( A ) : Given $90\equiv 2\left(\mathrm{mod}4\right)$  by $a\equiv b\left(\mathrm{mod}n\right)$  rule

$4|90-2\Rightarrow 4|88$

To check

$90\equiv 2\left(\mathrm{mod}4\right)$

If $a\equiv b\left(\mathrm{mod}n\right)$  then $ac\equiv bc\left(\mathrm{mod}n\right)$ , C is any integer.

$180\equiv 4\left(\mathrm{mod}4\right)$

$90\times 2\equiv 2\times 2\left(\mathrm{mod}4\right)$

$\therefore$  it is true

Option ( B ): $45\equiv 1\left(\mathrm{mod}4\right)$

So multiply by $4$  for $45\&1$

$45\times 4\equiv 1\times 4\left(\mathrm{mod}4\right)$

$180\equiv 4\left(\mathrm{mod}4\right)$

Hence true.

Option ( C ):  $180\equiv 2\left(\mathrm{mod}4\right)$

So $4$  doesn’t divides $180-2$

$\therefore$ It is false

Option ( D ): $90\equiv 4\left(\mathrm{mod}4\right)$  by $a\equiv b\left(\mathrm{mod}n\right)\Rightarrow n|a-b$

Here $4|90-4\Rightarrow 4$  doesn’t divides $86$

to divisible by $4$  last $2$  digits should be divisible by $4$ .

It is false