If $f(x) = [2 + 7\sin x], 0 < x < π$, then number of points at which the function is discontinuous is

13

f(x) will be discontinuous at the points where

$\sin x = \frac{1}{7},\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7},\frac{6}{7},\frac{7}{7}$

and sin x will be 1/7 for two values of x in the intervals. Hence $\frac{1}{7},\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7},\frac{6}{7}$ will be repeated twice. Total number of pints are 13.