Question

Assertion :${\left(\mathrm{666.....}ndigits\right)}^2+\left(\mathrm{888....}ndigits\right)=\left(\mathrm{444....2}ndigits\right)$ Reason: $\left\{\underset{12times}{\underset{}{\mathrm{111...1}}}\right\}$ is a prime number

• 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

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Assertion $:$ ${\left(66\right)}^2+8=4444.$

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$,$ $\left(\mathrm{11...11}\right)$ is not a prime number$.$

Hence Assertion is correct but Reason is wrong$.$