Solution:

Explanation of J-K flip-flop:
A J-K flip-flop is a type of flip-flop that has two inputs namely J (set) and K (reset) and two outputs Q (output) and Q' (complement of output). The output of the flip-flop depends on the inputs and the clock signal. The J-K flip-flop is also called a "universal flip-flop" because it can be used to implement any type of flip-flop.

Explanation of Negative edge-triggered J-K flip-flop:
A negative edge-triggered J-K flip-flop is a flip-flop that changes its state on the falling edge of the clock signal. That is, when the clock signal transitions from high to low.

Given:
Output states required for the next three successive clock pulses are 0, 0, and 1.

To achieve the required output states, the input states to the negative edge-triggered J-K flip-flop can be determined as follows:

For the first clock pulse:
The output state is required to be 0. Therefore, the inputs must be such that the flip-flop is in the reset state. This can be achieved by setting both J and K inputs to 0.

For the second clock pulse:
The output state is required to be 0 again. This means that the flip-flop should remain in the reset state. Therefore, the inputs must be such that the flip-flop continues to be in the reset state. This can be achieved by setting both J and K inputs to 0 again.

For the third clock pulse:
The output state is required to be 1. Therefore, the inputs must be such that the flip-flop changes its state from reset to set. This can be achieved by setting the J input to 1 and the K input to 0.

Hence, the input states required for the next three successive clock pulses are 00, 00, and 10.

Therefore, option A is correct.

However, option B is also correct as it gives the same output states. The input states for option B are as follows:

For the first clock pulse:
The output state is required to be 0. Therefore, the inputs must be such that the flip-flop is in the reset state. This can be achieved by setting both J and K inputs to 0.

For the second clock pulse:
The output state is required to be 0 again. This means that the flip-flop should remain in the reset state. Therefore, the inputs must be such that the flip-flop continues to be in the reset state. This can be achieved by setting the J input to 0 and the K input to 1.

For the third clock pulse:
The output state is required to be 1. Therefore, the inputs must be such that the flip-flop changes its state from reset to set. This can be achieved by setting both J and K inputs to 1.

Hence, the input states required for the next three successive clock pulses are 00, 01, and 11.

Therefore, option B is also correct.