Assertion (A) : Factors of the sum of a three-digit number 542 and the numbers obtained by changing the order of the digits cyclically are 1, 11, 111, 5 + 4 + 2.

Reason (R) : The sum of a three-digit number and the two number obtained by changing the digit cyclically is completely divisible by (i)11, (ii) 111 and (iii) sum of the digit.

1. Both A and R are correct, and R is the correct explanation for A.

2. Both A and R are correct, and R is not the correct explanation for A.

3. A is true, but R is false.

4. A is false, but R is true.

Given a three-digit number : 542

The cyclic permutations of the digits are : 542, 425 and 254.

Now we compute the sum of these three numbers : 542 + 425 + 254 = 1221

1221 = 1 x 11 x 111

So, assertion (A) is true.

Let the given a three-digit number : 100p + 10q + r

The cyclic permutations of the digits are: 100p + 10q + r, 100q + 10r + p and 100r + 10p + q

Now we compute the sum of these three numbers: (100p + 10q + r) + (100q + 10r + p) + (100r + 10p + q)

= (100p + 10p + p) + (100q + 10q + q) + (100r + 10r + r)

= 111p + 111q + 111r

= 111(p + q + r)

Factors of 111(p + q + r) = 1 x 111 x (p + q + r)

According to reason (R), 111 and sum of the digits are the factors of the sum of a three - digit number and the two number obtained by changing the digit cyclically, but 11 is not.

So, reason (R) is false.

Hence, option 3 is the correct option.