Reason
$$\displaystyle \left \{ \underbrace{111...1} _{12\: times}\right \}$$ is a prime number
Assertion
$$\displaystyle \left ( 666.....n\: digits \right )^{2}+\left ( 888....n\: digits \right )=\left ( 444....2n\: digits \right )$$
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C
Assertion is correct but Reason is incorrect
D
Both Assertion and Reason are incorrect
Correct option is C. Assertion is correct but Reason is incorrect
Assertion $$:$$ $$ {(66)}^{2}+8=4444.$$
If it is true for $$2$$ digits then it also true for $$n$$ digits $$.$$
Hence the assertion is correct $$.$$
Reason $$:$$
$$11$$ is divided by $$11.$$ So$$,$$ $$11$$ is not a prime number$$.$$
Similarly $$1111$$ and $$111111$$ is also not a prime number$$.$$
So$$,$$ $$(11...11)$$ is not a prime number$$.$$
Hence Assertion is correct but Reason is wrong$$.$$