  Based on the nonrelativistic QCD (NRQCD) factorization formalism, we
investigate inclusive productions of two spin-triplet S-wave quarkonia
pp->2J/psi+X, 2Upsilon+X, and J/psi+Upsilon+X at the CERN Large Hadron
Collider. The total production rates integrated over the rapidity (y) and
transverse-momentum (p_T) ranges |y|<2.4 and p_T<50 GGeV are predicted to be
sigma[pp->2J/psi+X] = 22 (35) nb, sigma[pp->2Upsilon+X] = 24 (49) pb, and
sigma[pp->J/psi+Upsilon+X] = 7 (13) pb at the center-of-momentum energy sqrt{s}
= 7 (14) TeV. In order to provide predictions that can be useful in both small-
and large-p_T regions, we do not employ the fragmentation approximation and we
include the spin-triplet S-wave color-singlet and color-octet channels for each
quarkonium final state at leading order in the strong coupling. The p_T
distributions of pp->2J/psi+X and 2Upsilon+X in the low-p_T region are
dominated by the color-singlet contributions. At leading order in the strong
coupling, the color-singlet channel is absent for pp->J/psi+Upsilon+X.
Therefore, the process pp->J/psi+Upsilon+X may provide a useful probe to the
color-octet mechanism of NRQCD.
