In the given radioactive decay,the number of $\alpha$ and $\beta$ particles emitted are respectively: $_{90}X^{200} \rightarrow _{80}Y^{168}$

In gamma ray emission from a nucleus,

Assertion: ${}^{90}Sr$ from the radioactive fallout of a nuclear bomb ends up in the bones of human beings through the milk consumed by them. It causes impairment of the production of red blood cells.
Reason: The energetic $\beta$-particles emitted in the decay of ${}^{90}Sr$ damage the bone marrow.

${}^{238}U$ has $92$ protons and $238$ nucleons. It decays by emitting an alpha particle and becomes:

$A$ nucleus decays by ${\beta ^ + }$ emission followed by a gamma emission. If the atomic and mass numbers of the parent nucleus are $Z$ and $A$ respectively, the corresponding numbers for the daughter nucleus are respectively.

$A$ radio nuclide $A_1$ with decay constant $\lambda_1$ transforms into a radio nuclide $A_2$ with decay constant $\lambda_2$. If at the initial moment the preparation contained only the radio nuclide $A_1$,then the time interval after which the activity of the radio nuclide $A_2$ reaches its maximum value is: