Describe test cross. why it is necessary ?

Though the genotypic ratios can be calculated using mathematical probability but it is not possible to know the genotypic composition by looking at the phenotype of dominant trait.

That is for example whether a tall plant from $F_{1}$ or $F_{2}$ has $TT$ or $Tt$ composition cannot be predicted.

Therefore, to solve this problem Mendel devised test cross.

Back cross is a cross of $F_{1}$ progeny back to one of their parents.

A special back cross to the recessive parent is known as test cross.

This method was devised by Mendel to determine whether the dominant phenotype is homozygous or heterozygous.

e.g. In a monohybrid cross, between violet colour flower [$W$] and white colour flower [$w$], the $\mathrm{F}_{1}$. hybrid was a violet colour flower.

If all the $\mathrm{F}_{1}$ - progeny are of violet colour, then the dominant flower is homozygous and if the progenies are in $1: 1$ ratio, then the dominant flower is heterozygous.

In case of double heterozygous i.e. heterozygous violet and axial flower [WwAa] crossed with double recessive i.e. recessive white and terminal flower [wwaa] the ratio will be $1: 1: 1: 1$.