A new long-range Soviet missile exploded last month during its second test flight, the New York Times reported. Quoting Reagan Administration specialists, the newspaper said that the first test of the new version of the SS-18 also ended in failure last April when the missile exploded soon after leaving its silo. The White House had no comment on the report. The newspaper also reported that another Soviet missile, the 10-warhead SS-24, is having problems in the development stage. Earlier this month, another Soviet missile, a submarine-launched SS-N-8, misfired during a test on the Kamchatka Peninsula and reportedly landed near the Sino-Soviet border, more than 1,500 miles off course.