Two radioactive nuclei P and Q in a given sample decay into a stable nucleus R. At time t=0, number of P species are `4N_0` and that of Q are `N_0`. Half-life of P (for conversion to R) is 1 min whereas that of Q is 2min. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be -

(A) `2N_0`
(B) `3N_0`
(C) `(9N_0)/2`
(D) `(5N_0)/2`

Two radioactive nuclei P and Q , in a given sample decay into a stable nucleus R . At time t = 0 , number of P species are 4 N_0 and that of Q are N_0 . Half-life of P (for conversation to R ) is 1mm whereas that of Q is 2 min . Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be :

Two radioactive nuclei P and Q , in a given sample decay into a stable nucleus R . At time t = 0 , number of P species are 4 N_0 and that of Q are N_0 . Half-life of P (for conversation to R ) is 1mm whereas that of Q is 2 min . Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be :

We have two radioactive nuclei A and B . Both convert into a stable nucleus C . Nucleus A converts into C after emitting two two alpha -particles and three beta -particles. Nucleus B converts into C after emitting one. alpha -particle anf five beta -particles. A time t = 0 , nuclei of A are 4N_(0) and that of B are N_(0) . Half-life of A (into the conversion of C ) is 1min and that of B is 2min . Initially number of nuclei of C are zero. What are number of nuclei of C , when number of nuclei of A and B are equal ?

If N_(0) is the number of radioactive nuclei initially present , then the number of nuclei remaining undecayed at the end of nth half life is

Half-life of a radioactive substance A and B are, respectively, 20 min and 40min . Initially, the samples of A and B have equal number of nuclei. After 80 min , the ratio of the ramaining number of A and B nuclei is

Half-life of a radioactive substance A and B are, respectively, 20 min and 40min . Initially, the samples of A and B have equal number of nuclei. After 80 min , the ratio of the ramaining number of A and B nuclei is

If p,q and r are prime numbers such that r=q+2 and q=p+2 , then the number of triples of the form (p,q,r) is