For the given numbers $\sqrt{3}, \sqrt{12}, \sqrt{27}, \sqrt{48}…………$

Assertion (A):

To find whether these terms form an A.P. or not. Express each term as the product of a natural number and $\sqrt{3 }$ i.e.,

$\sqrt{3} = 1 \times \sqrt{3}, \sqrt{12} = 2\sqrt{3}, \sqrt{27} = 3\sqrt{3}, \sqrt{48} = 4\sqrt{3}$, etc.

Reason (R): Since, for the given number difference between the consecutive term is same. It is an A.P.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

Given, sequence

$\Rightarrow \sqrt{3}, \sqrt{12}, \sqrt{27}, \sqrt{48}…………\\[1em] \Rightarrow \sqrt{3}, \sqrt{4 \times 3}, \sqrt{9 \times 3}, \sqrt{16 \times 3}…………\\[1em] \Rightarrow \sqrt{3}, \sqrt{4} \times \sqrt{3}, \sqrt{9} \times \sqrt{3}, \sqrt{16} \times \sqrt{3}…………\\[1em] \Rightarrow \sqrt{3}, 2\sqrt{3}, 3\sqrt{3}, 4\sqrt{3}…………$

Difference between first term and second term = $2\sqrt{3} - \sqrt{3} = \sqrt{3}$

Difference between second term and third term = $3\sqrt{3} - 2\sqrt{3} = \sqrt{3}$

So, the first term = $\sqrt{3}$, common difference = $\sqrt{3}$

So, assertion is true.

Since, for the given number difference between the consecutive term is same. Its an A.P., means reason is true and it clearly explain assertion.

Hence, option 3 is the correct option.