37) If m is an odd integer and n is an even integer, which of the following is definitely odd?
a) (2m+n)(m-n)
b) (m + n2 )( m - n2)
c) m2 + mn + n2
d) m+n

• m+n
  even+odd=odd
• 11 years agoHelpfull: Yes(2) No(1)
• ans= b,c & d are odd
  as we know,
  odd*odd=odd ; odd*even=even ; even*even=even;
  odd+odd=even ; odd+even=odd ; even+even=even;
  odd-odd=even ; odd-even=odd ; even-even=even; even-odd=odd.
  now apply it in the given options,
  (a).(2m+n)(m-n) = (even*odd+even)(odd-even) = even*odd = even
  (b).(m+n^2)(m-n^2)= (odd+even*even)(odd-even*even) = odd*odd = odd
  (c). m^2 + mn + n^2= odd*odd +odd*even + even*even = odd+even+even = odd
  (d). m+n = odd + even = odd
  
• 11 years agoHelpfull: Yes(0) No(0)