The target acceptance rate was rumored to be 2% - which roughly corresponded to the percentage of Jewish population in USSR.
I was one of those Jewish applicants in 1973 :)
Exam was conducted in a separate room. When in doubt, the criteria for identifying Jews among all applicants was funny (in retrospect): they tried to guess by the last name. But some names are more "typical" than others, so the criteria was not 100% accurate. They preferred to err on the side of caution, and some perfectly Russian people were put in the same exam room with the Jews. This is my recollection.
Those cases were probably quite common. From wikipedia article about Glenn Gould, the great Canadian pianist:
"The family's surname was changed to Gould informally around 1939 in order to avoid being mistaken for Jewish, given the prevailing anti-Semitism of prewar Toronto and the Gold surname's Jewish association"
I imagine quite small, if any were allowed to. Tests like these usually also have a hidden rubric such that the test taker never quite manages to reach the minimum passing grade. It's unlikely anybody with the education of a high-schooler (even a fairly advanced one) would be able to solve very many of these problems in a typical allotment of time for a test. They're not sophisticated problems, in the sense that relatively basic mathematical principles can be used to solve most (or all) of them, but they're really quite complicated problems for a test. I mean "complicated" in the sense that they require a fair bit of rather tedious busy work to arrive at a solution.
I recall reading elsewhere it was zero, they simply weren't allowed to admit Jewish students and these problems were just to try and cover up the discrimination.
There was a quota, like in the US in the 1930s. In the USSR, about 2% of population was Jews, so university was allowed to admit 2% Jews every year. But because of culture of education and desire to avoid conscription to Red Army[1] and non-uniform population density, it was very difficult for Jews to get admitted in the good universities in Moscow and Leningrad (the two largest cities with most prestigious universities).
1 - The Soviet military was bad for everyone, but Jews tended to get hurt more. Students accepted by a university would not be conscripted and would be listed as reserve officers, having never spent time in uniform
> The Soviet military was bad for everyone, but Jews tended to get hurt more.
I know one Jewish man from the USSR, now deceased, who told me he emigrated from the USSR to avoid conscription; he said that the military at times used Jewish soldiers as cannon fodder: They were sent to the front without arms to draw and consume enemy fire.
If not for this quota, you would have much greater number of "known physicists and mathematicians from USSR with Jewish names" LOL
In some places (Moscow University math dep-t) the target was about 2%, but I heard some technical schools didn't accept anyone (after Natan Scharansky affair. Long story...)