"place a question" is correct and usable in written English.
You can use it when expressing the action of asking someone a question, or the expectation of having a question asked. For example: "The teacher asked us to place a question about the material."
"But I have to place a question mark there.
However, the cost of the drugs is very high, which may place a question mark over their use.
In Maine, with its strong history of ballot initiatives, advocates collected enough signatures to place a question instituting a ranked choice voting system on the November 2016 ballot.
Moreover, their concern was not with how altruism works, but how it evolved in the first place — a question that remains hotly debated today.
It is argued that there appears to be a certain consistency in the problems faced by existing programmes and that these difficulties place a question mark over the longer-term viability of at least some of these schemes.
But now the broadcaster has announced its decision to reduce its cycling activity, in terms that place a question mark against the nature of its involvement.
The Neyroud report also places a question mark over the future of the Bramshill National College of Police Leadership.
Prominent pro-Europeans are planning to lambast Cameron for placing a question mark over Britain's EU membership.
A European court of justice case placed a question mark over whether such an authorisation process meets human rights standards.
His promotion from head of youth development and chief scout to sporting director has placed a question over chief executive Peter Kenyon's role.
The conflict of interest places a question mark over Paul McDowell's future as chief inspector, and Grayling is to address the issue before the sell-off takes place.
