A rectangular game board is composed of identical squares arranged in rectangle array of r rows and r+1 columns.The r rows are numbered from 1 through r and the r+1 columns are numbered from 1 through r+1.If r>10,which of the following represents the squares on the board that are neither in the 4th row nor in the 7Th column.
a)r^2-r
2)r^2-1
3)r^2
4)r^2+1
5)r^2+r

• 'r' rows and 'r+1' columns of squares = r(r+1) squares.
  4th row(for that matter any row) has (r+1) squares
  7th column(in fact any column) has r squares
  They have 1 square in common.
  So, number of squares in 4th row or 7th column = (r+1)+r-1 = 2r
  So, remaining squares = r(r+1) - 2r = r^2 - r
  
  i will give an example
  
  now
  
  Given, r > 10
  
  consider r=11 and r+1 = 12
  total squares = r(r+1)=132
  4th row and 7th column = 11+12 = 23
  
  total remaining squares = 109 + 1(common squarea) = 110
  
  (r^2)-r = 110
  (11)^2-11 = 110
  
  so option A suits.
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