Relaxing the muscles and mind, trying tai chi and keeping a “mood diary” are among the advice offered to most people.
But concerning responses will prompt a separate alert urging some to visit a GP or make the use of free NHS psychological therapy service.
The Royal Family members have reunited to front the Public Health England’s Every Mind Matters campaign which aims to overhaul how Brits cope with mental health problems.
The online quiz has been launched and has already started conjuring up tailored advice.
It tests respondents to consider their mood, sleep, anxiety, stress and worries over the past two weeks.
The first four questions are based on a sliding scale ranking, with the fifth inviting people to pinpoints the source of their worries – whether it’s based on relationship, money, health and trauma.
If you select the top ranking responses for all questions, the algorithm will say: “Based on your answers, it looks like you’re doing well. These ideas can help you stay on top of your mental health.”
Several ideas ranging from keeping fit to trying a new hobby will appear, with the option to swap this suggestion if it’s “not for you”.
Meanwhile, separate advice based on your response to the fifth question will also be offered.
Health and Social Care Secretary Matt Hancock hailed the dedication and “bravery” of the Royals for supporting the campaign.
He said: “I want to put on record my admiration for the way the Princes and the Duchesses have contributed to changing how society in the UK, and around the world, think about mental health and their own bravery in speaking about it.
“This is one of the most clear examples of them taking that lead and supporting us in a very important project.”
John Newton, from Public Health England, said: “We know that this resource is needed because many people lack the knowledge or confidence to take action on their mental health and many wait too long to do so.
“There are an awful lot of people who fall into the group who could benefit from it.”
For confidential support call the Samaritans in the UK free on 116 123 or visit a local Samaritans branch.