Q1: An uncharged capacitor and a 1 k resistor are connected in series with a switch and a 6 V battery. At the instant the switch is closed, the voltage across the capacitor is

ANS:D - 0 V

Initially, as given in the problem the capacitor is in uncharged condition.at the instant when the switch is closed the voltage across the capacitor is zero because the capacitor only charges when an infinite amount of current flows through it. So, at the time of starting not much amount of current flows through ckt and hence, the voltage across the capacitor is 0
We know;

C = Q/V.
V = Q/C.

And also Q=idt at the starting there is no change in current with respect to time due to that there is no change accumulation.