In 1829, the model of modern policing, the London Metropolitan Police Department, was established. It's main objective was:

a. Criminal apprehension
b. law enforcement
c. Crime prevention
d social order

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http://www.historyhome.co.uk/polspeech/met2.htm

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The main objective of the London Metropolitan Police Department, established in 1829, was c. Crime prevention.

To arrive at this answer, it is necessary to understand the context and purpose of the establishment of the London Metropolitan Police Department. The department was created in response to growing concerns about crime and disorder in the city of London during the early 19th century. The existing system of law enforcement was ineffective, with a lack of coordination and a reliance on unpaid volunteer constables.

The innovative approach of the new police department focused on preventing crime rather than simply reacting to it. The idea was to have a professional, full-time police force that patrolled the streets and maintained order, thus deterring potential criminals and reducing the occurrence of crimes. This emphasis on crime prevention was a departure from the previous approach of relying on the punishment of offenders after crimes had been committed.

Therefore, the main objective of the London Metropolitan Police Department was to prevent crime and maintain public order, which makes option c. Crime prevention the correct answer.