What are the functions of $(i)$ methylated guanosine cap,$(ii)$ poly-$A$ tail in a mature $mRNA$?

(N/A) The functions of the modifications in a mature $mRNA$ are as follows:
$(i)$ Methylated guanosine cap: It helps in the binding of $mRNA$ to the smaller ribosomal subunit during the initiation of translation and protects the $mRNA$ from degradation by exonucleases.
$(ii)$ Poly-$A$ tail: It provides stability and longevity to the $mRNA$ molecule. There is a positive correlation between the length of the poly-$A$ tail and the lifespan of the $mRNA$ in the cytoplasm.