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if 1( 1! +2! + 3!+.....50!) id divided by 5 what is remainder?

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[Q-5]][[[[ Different from earler]]]]]]
In Loonyville, four people called Doctor, Engineer, Lawyer and
Architect follow the professions of doctor, lawyer, engineer and
architect. However, none of them follow the profession indicated by
their name.
Doctor plays bridge very regularly, as he thinks it as an intellectual
card game. Doctor is allergic to sea food, and does not eat it at all.
Architect nearly died in a car accident two years ago. The architect is
very poor at card games and does not play them at all. The engineer
loves fish and has it twice a week. The engineer is a good driver, and
has never been involved in a car accident. Engineer does not like the
Lawyer’s habit of constantly interrupting others.
What is the profession of Engineer?
Options
o a lawyer
o an architect
o a doctor
o Cannot be determined
for which of the following n is the number (2^74)+(2^2058)+(2^2n) a perfect square..
a. 2010
b. 2011
c. 2012
d. 2100