Answer will be given along with the complete solution tomorrow. So, try to solve it and check your solution with the one we will publish tomorrow.
So, Good Luck with your preparation for GATE.
Is 'V' across 2F is 6.u(t) ?
No. It's not. One simple way you can analyse this from the basic nature of the capacitor. Capacitor is initially said to be containing no charge. So, due to the voltage source, it will charge to its maximum possible value. So, it will be a Increasing curve. U(t) on the other hand is a constant value of 1. So, the voltage across the capacitor can't be 6. u(t).
But, you are partially right. You'll understand why once you see the solution.