Assertion (A) : Natural numbers 5, 12 and 13 are Pythagorean triplets as 12² + 5² = 13².

Reason (R) : For any natural number n, (n + 1)² - n² = (n + 1) + n.

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.

According to assertion,

⇒ 12² + 5² = 13²

Solving L.H.S. of the above equation, we get :

⇒ 12² + 5²

⇒ 144 + 25

⇒ 169

⇒ 13 x 13

⇒ 13²

Since, L.H.S. = R.H.S.

So, assertion (A) is true.

According to reason,

⇒ (n + 1)² - n² = (n + 1) + n.

Solving L.H.S. of the above equation, we get :

⇒ (n + 1)² - n²

Using formula; a² - b² = (a - b)(a + b), we get :

= [(n + 1) - n][(n + 1) + n]

= [n + 1 - n][n + 1 + n]

= 1 x [(n + 1) + n]

= (n + 1) + n

Since, L.H.S. = R.H.S.

So, reason (R) is true but it does not explain assertion (A).

Hence, option 2 is the correct option.