Hello sir
How to solve this an electric charge of 8.85*10^-13 C is placed at the center of a sphere of radius 1m. The electric flux through the sphere is:
1. 0.2NC ^-1 m²
2. 0.1NC ^-1 m²
3. 0.3NC ^-1 m²
4. 0.01NC ^-1 m²

That isn't correct. If you are going to use that form then you need to integrate over the angle \(\displaystyle \theta\) as it covers the whole surface of the sphere.

The flux through a sphere with a single point charge encolsed in a sphere is
\(\displaystyle \Phi _E = \dfrac{q}{ \epsilon _0 }\)

I can show you this using Gauss' Law but it doesn't seem to me that you know Calculus.