Assertion (A): The volume of a cuboid having length, breadth and diagonal as 4 m, 3 m and 13 m is 144 m³.

Reason (R): Length of diagonal of a cuboid is $\sqrt{l^2 + b^2 + h^2}$.

1. Assertion (A) is true, Reason (R) is false.

2. Assertion (A) is false, Reason (R) is true.

3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Given: length, breadth and diagonal of cuboid = 4 m, 3 m and 13 m.

By formula,

Length of diagonal of a cuboid = $\sqrt{l^2 + b^2 + h^2}$

∴ Reason (R) is true.

Substituting the values, we get

$\Rightarrow 13 = \sqrt{3^2 + 4^2 + h^2}\\[1em] \Rightarrow 13^2 = 3^2 + 4^2 + h^2\\[1em] \Rightarrow 169 = 9 + 16 + h^2\\[1em] \Rightarrow 169 = 25 + h^2\\[1em] \Rightarrow h^2 = 169 - 25\\[1em] \Rightarrow h^2 = 144\\[1em] \Rightarrow h = \sqrt{144}\\[1em] \Rightarrow h = 12$

Volume of cuboid = l x b x h

= 3 x 4 x 12

= 144 m³.

∴ Assertion (A) is true.

∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.