Question 10

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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