答案選 D.on which to base
句意：這位教授幾乎不可能找到必需的理由,以此來(lái)支持新學(xué)說(shuō).
固定短語(yǔ)：base sth on sth.
原句剖析：The professor could hardly find necessary grounds（ on which to base his arguments） in favour of the new theory.劃線部分為定語(yǔ)從句,正常語(yǔ)序應(yīng)該是which he base his arguments on介詞提前可以得到on which he base his arguments ,大家都知道賓語(yǔ)從句中what to do=what we should do ,類比可得,此句可改成on which to base his arguments 答案：D