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Let w,x,y and z be four natural numbers such that their sum is 8m+10 where m is natural number. Given m, the following is necessarily true: a) maximum possible value of w^2+x^2+y^2+z^2 is 16m^2+40m+26. Why?

In a class of 50 students, 25 passed in Physics, 27 in Maths, 29 in Chemistry, 33 in Biology and 35 students passed in Geography. What is the maximum number of students who passed in at least 3 subjects?
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