  We prove Bertini type theorems and give some applications of them. The
applications are in the context of Lefschetz theorem for Nori fundamental group
for normal varieties as well as for geometric formal orbifolds. In another
application, it is shown that certain class of a smooth quasi-projective
variety contains a smooth curve such that irreducible lisse \ell-adic sheaves
on the variety with "ramification bounded by a branch data" remains irreducible
when restricted to the curve.
