STATEMENT-1 : A block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^\circ$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. STATEMENT-2 : The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

Step 1: Analyze the decrease in mechanical energy for Case 1 (horizontal surface).

On a rough horizontal surface, the block of mass $m$ starts with an initial velocity $v$ and comes to rest. The entire initial kinetic energy is dissipated as heat due to friction, meaning the decrease in mechanical energy is equal to the initial kinetic energy.

$$\Delta ME_1 = \frac{1}{2}mv^2$$

Step 2: Analyze the decrease in mechanical energy for Case 2 (inclined surface).

When the surface is tilted at an angle $\theta = 30^\circ$, the block is projected up the incline with the same initial velocity $v$. It comes to rest at a height $h$.

The final mechanical energy of the block is its potential energy $mgh$. The decrease in mechanical energy is the energy dissipated by friction.

$$\Delta ME_2 = \frac{1}{2}mv^2 - mgh$$

Since $mgh > 0$, the decrease in mechanical energy in this second case is smaller than in the first case.

$$\Delta ME_2 < \Delta ME_1$$

Therefore, Statement-1 is True.

Step 3: Analyze Statement-2.

The coefficient of friction $\mu$ is a property of the two contacting surfaces and depends only on their nature. It is independent of the angle of inclination $\theta$.

Therefore, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is False.