  We study quenched SU(N) gauge theories with fermions in the two-index
symmetric, antisymmetric and the adjoint representations. Our main motivation
is to check whether at large number of colours those theories become
non-perturbatively equivalent. We prove the equivalence assuming that the
charge-conjugation symmetry is not broken in pure Yang-Mills theory. We then
carry out a quenched lattice simulation of the quark condensate in the
symmetric, antisymmetric and the adjoint representations for SU(2), SU(3),
SU(4), SU(6) and SU(8). We show that the data support the equivalence and
discuss the size of subleading corrections.
