CSMA/CD can detect collisions always if below condition is satisfied:

$T.T \geq 2 * P.T$ where T.T is Transmission time and P.T is Propagation time.

If above condition is satisfied CSMA/CD can work always and can not stuck.

So, We know that $T.T = \frac{Data size}{Band width}$ and $P.T = \frac{Distance}{Velocity}$

Therefore, $\frac{Data size}{Band width} \geqslant 2 * \frac{Distance}{Velocity}$

$\frac{Data size}{2\ast 10^{9}} \geqslant 2 * \frac{1000 }{2\ast 10^{8}}$

by solving, Data size $\geqslant$ 10000 bits.

Hence, **Option (A) is correct.**

You can apply same procedure for below questions also by keeping $T.T \geq 2 * P.T$ condition satisfied.

https://gateoverflow.in/3376/gate2008-it-65 Same question as above, asked for 'Frame size' all other things are given.

https://gateoverflow.in/8400/gate2015-3-6 This question is also easily solvable by the same method, here we have to find 'velocity' all other things are given in question.

https://gateoverflow.in/39589/gate2016-2-53 This question also solvable by above formula, here we have to find 'Frame size' all other things are given in question.