Calculations :At 12:00 clock both hour and minute hands have an angle of 0 ° Then, minute angle for t minutes past 12\(\theta = {t \times {360 \over 60}} = 6 \times t\)Hour angle for t minutes past 12 \(\theta = { t \times {360 \over {12 \times 60}}} = {t \over 2}\)For Statement 1 :3 hours 20 minutes = 200 minutes. So for t = 200Minute angle \(6 \times t = 6 \times 200 = 1200 \)\(1200 ^\circ = 1200^\circ \mod 360^\circ = 120^\circ\)Hour Angle\({t \over 2} = {200 \over 2} = 100 ^\circ\)So difference = 120 ° - 100 ° = 20 ° For statement 2 : After t minutes hour hand and minute hand are coincidental.Hour angle for t minutes past 4\( {{4 \over 12} \times 360 + {t \over 2}}\)minute hand is coincidental to hour hand means\(6t = {{4 \over 12} \times 360 + {t \over 2}}\)\({11 \over 2} t = 120\)\(t = {240 \over 11} = 21{9 \over 11}\)Hence, statement 1 is false and the statement 2 is true.so, option "4" is correct.