Let $$a_{n} = 1 1 1 1 1 1 1..... 1$$, where 1 occurs n number of times. Then,
i. $$a_{741}$$ is not a prime.
ii. $$a_{534}$$ is not a prime.
iii. $$a_{123}$$ is not a prime.
iv. $$a_{77}$$ is not a prime.
Solution
i. $$a_{741}$$ has 741 ones, it will be divisible by 3
ii. $$a_{534}$$ has 534 ones, it will be divisible by 3
iii. $$a_{123}$$ has 123 ones, it will be divisible by 3
iv. $$a_{77}$$ has 77 ones and each pair of 11 ones is divisible by 13.
Therefore, i,ii,iii and iv are not prime.
Ans -(D) All are correct.
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