${ }_{92} U^{235}$ undergoes successive disintegrations with the end product of ${ }_{82} Pb^{203}$. The number of $\alpha$ and $\beta$ particles emitted are

$A$ nucleus $_n^mX$ emits one $\alpha$ particle and two $\beta^-$ particles. The resulting nucleus is

In the given nuclear decay process,identify the order in which radioactive radiations are emitted:
${}_{Z}^{A}X \to {}_{Z+1}^{A}Y \to {}_{Z-1}^{A-4}K \to {}_{Z-1}^{A-4}K$

$A$ certain radioactive nuclide of mass number $m_x$ disintegrates,with the emission of an electron and $\gamma$ radiation only,to give a second nuclide of mass number $m_y$. Which one of the following equations correctly relates $m_x$ and $m_y$?

$A$ radioactive nucleus ${}_{Z}^{A}X$ undergoes spontaneous decay in the sequence ${}_{Z}^{A}X \rightarrow {}_{Z-1}B \rightarrow {}_{Z-3}C \rightarrow {}_{Z-2}D$,where $Z$ is the atomic number of element $X$. The possible decay particles in the sequence are:

Actinium $231$,${}^{231}Ac_{89}$,emits in succession two $\beta^-$ particles,four $\alpha$ particles,one $\beta^-$ particle,and one $\alpha$ particle,plus several $\gamma$ rays. What is the resultant isotope?