The decay constant for A is

Therefore, the rate of decay is

Now the decay constant for A is

Therefore, the rate of decay is

Now let us check each option by putting the scenarios in the Decay law. From option (a) to (c) we can see that the initial decay rate of A and B are given. Let us first start by decay rate of A

The initial decay rate of

Putting the value in formula we get

Therefore, putting the value of, we get, .

Hence, option B is true and A is false

In this option we saw that when the value of initial decay was changed to greater value the decay Constant also changed to higher value. Therefore, taking this consideration in mind if the value of initial decay of B is higher than A, then decay constant should also follow but that is not the case as option (c) says , hence, option (c) is false.

Last is the option (d) in which the time for the decay rate of A is and both have same initial decay rate. Therefore the decay constants are

Therefore, the value of decay constant of A is greater than that of B. Hence, Option (d) is correct.