  A detailed investigation of the first order antiferromagnetic insulator (AFI)
to ferromagnetic metal (FMM) transition in $Nd{_{0.5}}Sr{_{0.5}}MnO{_{3}}$ is
carried out by resistivity and magnetization measurements. These studies reveal
several anomalous features of thermomagnetic irreversibility across the first
order transition. We show that these anomalous features can not be explained in
terms of supercooling effect alone and H-T diagram based on isothermal MH or RH
measurement alone do not reflect true nature of the first order transition in
this compound. Our investigations reveal glass-like arrest of kinetics at low
temperature which plays a dominant role in the anomalous thermomagnetic
irreversibility observed in this system. The interplay between kinetic arrest
and supercooling is investigated by following novel paths in the H-T space. It
is shown that coexisting FMM and AFI phases can be tuned in a number of ways at
low temperature. These measurements also show that kinetic arrest temperature
and supercooling temperature are anti-correlated i.e. regions which are
arrested at low temperature have higher supercooling temperature and vice
versa.
