STATEMENT -1 `:` If a simple pendulum is in a carriage which is accelerating downward and acceleration is greater than acceleration due to gravity , then pendulum turns up side down and oscillates about highest point.
and
STATEMENT -2 `:` The time period of pendulum will be independent of g in above case of pendulum oscillating about highest point.

Answer

To solve the question, we need to analyze both statements provided and determine their validity based on the principles of physics related to oscillations and pendulums.

### Step 1: Analyze Statement 1
**Statement 1:** If a simple pendulum is in a carriage which is accelerating downward and the acceleration is greater than the acceleration due to gravity, then the pendulum turns upside down and oscillates about the highest point.

- When the carriage accelerates downward with an acceleration greater than \( g \) (acceleration due to gravity), the effective gravitational force acting on the pendulum becomes negative. This means that the pendulum will not be able to hang downwards as it normally would. Instead, it will turn upside down and oscillate about the highest point (the position where it is inverted).

**Conclusion for Statement 1:** This statement is **true**.

### Step 2: Analyze Statement 2
**Statement 2:** The time period of the pendulum will be independent of \( g \) in the above case of the pendulum oscillating about the highest point.

- The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g_{\text{effective}}}} \]
where \( g_{\text{effective}} \) is the effective acceleration acting on the pendulum. When the carriage is accelerating downward with an acceleration \( a \) greater than \( g \), the effective acceleration can be expressed as:
\[ g_{\text{effective}} = a - g \]
- Therefore, the time period will depend on both the length \( L \) of the pendulum and the effective gravitational acceleration \( g_{\text{effective}} \). Since \( g_{\text{effective}} \) is influenced by \( g \), the time period is not independent of \( g \).

**Conclusion for Statement 2:** This statement is **false**.

### Final Conclusion
- **Statement 1** is true.
- **Statement 2** is false.