Brahmins taking up other duties

Brahmins have taken on many professions - from being priests, ascetics and scholars to warriors and business people, as is attested for example in Kalhana's Rajatarangini. Brahmins with the qualities of Kshatriyas are known as 'Brahmakshatriyas'. An example is the avatar Parashurama who is considered an avatar of Vishnu. Sage Parashurama was a powerful warrior who had defeated the Haiheya kshatriyas twenty one times, was an expert in the use of weapons, and trained others to fight without weapons. After Sage Parshuram destroyed the Kshatriya race, he was excluded by other Brahmin communities and denied to perform any religious ceremonies for him. At the coast of Arabian sea i.e. the Western Ghats he decided to create a new Brahmin community where he found dead bodies of people came out floating from the sea. He purified them with Agni and brought back to life. Then he taught them all the veda's, weapons, religious knowledge and made the Brahmin known as Chitpavan Konkanastha Brahmins. Chitapavan means Chit + Pavan the Brahmins whose chit/soul was purified, Konkanastha means belong to Konkan region. Chitapavan Konkanastha Brahmin's did not have their own land hence were insulted by other rulers & Brahmins. Hence Sage Parshurama asked the Sea Lord to go back and give some land which he denied. Sage Parshurama got angry and made ready the Brahmastra to destroy the Sea Lord. Sea Lord frightned and asked to forgive him. Sage Parshurama said that as he has made Brahmhaastra on the arrow ready to launch he cannot return the arrow backwards but he will remove the Brahmaastra and wherever the arrow will land till that point sea will leave the Land for his followers Chitpavan Konkanastha Brahmins. The place from where Sage Parshurama released the arrow is there in Konkan area known as Lote Parshuram and has a temple of Sage Parshuram. The Bhumihar Brahmins were established when Parashurama destroyed the Kshatriya race, and he set up in their place the descendants of Brahmins, who, after a time, having mostly abandoned their priestly functions (although some still perform), took to land-owning. Many Brahmins took up the profession of medicine. They are Vaidya Brahmins called Baidya Brahmins of Bengal [gupta, dasgupta and senguptas] are descendants of Dhanavantari, the god of medicine and father of Ayurveda.
The Brahmakhatris caste, descendants of the Khatris, however, are a business caste/community of Punjab and belong to the Kshatriya caste.
Perhaps the word Brahma-kshatriya refers to a person belonging to the heritage of both castes. However, among the Royal Rajput households, Brahmins who became the personal teachers and protectors of the royal princes rose to the status of Rajpurohit and taught the princes everything including martial arts. They would also become the keepers of the Royal lineage and its history. They would also be the protectors of the throne in case the regent was orphaned and a minor.
Kshatriyan Brahmin is a term associated with people of both caste's components.
The Pallavas were an example of Brahmakshatriyas as that is what they called themselves. King Lalitaditya Muktapida of Kashmir ruled all of India and even Central Asia.
King Rudravarma of Champa (Vietnam) of 657 A.D. was the son of a Brahmin father.
King Jayavarma I of Kambuja (Kampuchea) of 781 A.D. was a Brahma-kshatriya.
Hem Chandra Vikramaditya (Hemu), born in a family of Purohits, started the manufacturing of Cannons for the first time in North India with Portugese knowhow and dealt in Gunpowder for supplies to Sher Shah Suri's army. Later he became Prime Minister-cum-Chief of Army of Suris and Emperor of North India in 1556, defeating Akbar's army at Agra and Delhi.
Brahmins with the qualities of a Vaisya or merchant are known as 'Brahmvyasya'. An example of such persons are people of the Ambastha  caste, which exist in places like South India. They perform medical work - that is from ancient times have practised the Ayurveda and have been Vaidyas (or doctors) as have been claimed by these people during the British rule when the Govt. expressed the will to promote cast mobilisation, thence from they started bearing the thread also, but neither the Govt. nor the Hindu oligarchs, none expressed any such sanction .
Many Pallis of South India claim to be Brahmins (while others claim to be Agnikula Kshatriyas.) Kulaman Pallis are nicknamed by outsiders as Kulaman Brahmans. Hemu from Rewari, Haryana was also a Brahmin by birth.