Assertion :Test cross is the cross between the $F_1$ progeny and either of the parent types. Reason: Back cross is the cross between $F_1$ progeny and the double recessive genotype.

The correct option is D Both Assertion and Reason are incorrect
A test cross is a cross involves the breeding of an individual with a phenotypically recessive individual, in order to determine the zygosity of the former by analyzing proportions of offspring phenotype and not the parent types. Back cross is the crossing of a hybrid with one of its parents or an individual genetically similar to its parent, in order to achieve offspring with a genetic identity which is closer to that of the parent.

So, the correct answer is 'Both Assertion and Reason are incorrect'.