This question tests your understanding of proofs for asymptotic notations.(a) Let f(n) = 5n2 +10000. In order to prove that f(n) 2 O(n2), we need to nd a positiveconstant c > 0 and an integer N 1 such thatf(n) c n2; for every n N: (1)Answer the following questions on the answer sheet.(a1) Will c = 6;N = 100 make the proof correct?(a2) Will c = 6;N = 200 make the proof correct?(a3) Will c = 7;N = 100 make the proof correct?(a4) Will c = 6;N = 50 make the proof correct?(a5) Will c = 5;N = 100 make the proof correct?(b) Let g(n) = 5n2 .. 10000. In order to prove that g(n) 2 (n2), we need to nd a positiveconstant c > 0 and an integer N 1 such thatg(n) c n2; for every n N: (2)Answer the following questions on the answer sheet.(b1) Will c = 4;N = 100 make the proof correct?(b2) Will c = 4;N = 200 make the proof correct?(b3) Will c = 3;N = 100 make the proof correct?(b4) Will c = 4;N = 50 make the proof correct?(b5) Will c = 5;N = 100 make the proof correct?,