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Mathematics

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.

Sq & Sq Roots

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Answer

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.

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