$A$ radioactive nucleus emits a beta particle. The parent and daughter nuclei are

If $_a^b X$ emits a positron,then two $\alpha$-particles,two $\beta$-particles,and finally one $\alpha$-particle,it transforms into $_d^c Y$. What is the correct relationship?

After one $\alpha$ and two $\beta$ emissions,what happens to the nucleus?

$A$ free neutron decays spontaneously into:

$A$ radioactive nucleus decays as follows:
$X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4$
If the atomic number and the mass number of $X$ are $72$ and $180$ respectively,then the mass number and atomic number of $X_4$ are:

An $U^{238}$ nucleus is initially at rest. It decays by emitting an $\alpha$-particle with speed $u$. Find the recoil speed of the daughter nucleus.