The major product formed on nitration of N,N-dimethylaniline with conc. H2SO4, HNO3 mixture is 2,4-dinitro-N,N-dimethylaniline. This is because the nitro group is an electron-withdrawing group, which destabilizes the aromatic ring. The methyl groups are electron-donating groups, which stabilize the aromatic ring. Therefore, the nitro group will preferentially attack the position on the ring that is ortho or para to the methyl groups. This is known as the ortho-para directing effect.
The other options are incorrect because they do not have the nitro group in the ortho or para position to the methyl groups. Option A is 3-nitro-N,N-dimethylaniline. This compound is formed when the nitro group attacks the position on the ring that is meta to the methyl groups. Option B is 4-nitro-N,N-dimethylaniline. This compound is also formed when the nitro group attacks the position on the ring that is meta to the methyl groups. Option C is N-methyl-N-nitroaniline. This compound is formed when the nitro group attacks the nitrogen atom.
In conclusion, the major product formed on nitration of N,N-dimethylaniline with conc. H2SO4, HNO3 mixture is 2,4-dinitro-N,N-dimethylaniline.