The correct options are
B depends on the total number of identical nuclei present in the sample
D decreases with the life time lived by the nucleus
The decay constant, , represents the average probability per nucleus of decay.
As we know,
−dN/dT=λN
So it will depend upon the total number of identical nuclei present in the sample (N).
Also, it will decreases with the life time lived by the nucleus as no of nuclei present in sample decreases with time.