List of top Mathematics Questions on Binary operations asked in BITSAT

The number of values of $r$ satisfying the equation $^{39}C_{3r-1} - ^{39}C_{r^{2}} = ^{39}C_{r^{2}-1} - ^{39}C_{3r} $ is

Let $R$ be the relation on the set $R$ of all real numbers, defined by $aRb$ If $|a - b| \le 1$. Then, $R$ is

$(10101101)_2 = (................)_{10}$