Let $K_a$ denote Kannada, $T_a$ denote Tamil and $T_e$ denote Telegu.
$n(K_a \cup T_a \cup T_e ) = n(K_a) + n(T_a) + n(T_e) - n(K_a \cap T_a ) - n(K_a \cap T_e ) - n(T_e \cap T_a ) + n(K_a \cap T_a \cap T_e )$
$\implies 50 = 24 +24 + n(T_e) - (5+4) - (6+4) - (7+4) + 4$
$\implies 50 = 48 + n(T_e) - 26$
$\implies n(T_e) = 28.$
$\therefore$ Number of people who know Telegu, $n(T_e) =28.$
Number of people who know only Telegu
$= n(T_e) - n(K_a \cap T_e ) - n(T_e \cap T_a ) + n(K_a \cap T_a \cap T_e )$
$= 28 -(6+4) -(7+4) +4$
$= 11$
Correct Option: C.