Answer: Option A. -> 30°
Answer: (a)
Angle traced by the minute hand in 5 minutes = $(360/60 × 5)^o = 30°$

Answer: Option C. -> 155°
Answer: (c)
Angle traced by the hour hand in 12 hrs = 360°
Angle traced by the hour hand in 5 hrs 10 min, i.e., $31/6 hrs = (360/12 × 31/6)^o = 155°$ 

Answer: Option D. -> $\text"197"1°/2$
Answer: (d)
Angle traced by hour hand in$ 125/12 hrs = (360/12 × 125/12)^o = 312 1°/2$
Angle traced by minute hand in 25 min = $(360/60 × 25)^o = 150°$
∴ Reflex angle = $360° - (312 1/2 - 150)^o = 360° - 162 1°/2 = 197  1°/2$

Answer: Option C. -> 130°
Answer: (c)
Angle traced by hour hand in 12 hrs = 360°
Angle traced by it in 11/3 hrs = $(360/12 × 11/3)° = 110°$
Angle traced by minute hand in 60 min = 360°
Angle traced by it in 40 min = $(360/60 × 40)^o$ = 240°
∴ Required angle = $(240 - 110)^o$ = 130°

Answer: Option C. -> 199 $169/209$ min (loss)
Answer: (c)
Therefore, required result = $(720/11 - x) (60 ×24 / 76) min$
Here, x = 76 Therefore, required result = $(720/11 - 76) (60 × 24 /76) min$
= $-116/11 × 360/19 min$
= $- 199 169/206 min$ (loss as sign in negative)

Answer: Option B. -> 185 $25/319$ min (gain)
Answer: (b)
Required result =$ (720/11 - x) (60 × 24 / X)$ min Here, x = 58
Therefore, required result = $(720/11 - 62) (60 × 24 /58)$ min
= $82/11 × 720/29 min = 185 25/319 min $gain (gain as sign is positive)

Answer: Option D. -> 80 $80/341$ min (gain)
Answer: (d)
Required result =$ (720/11 - x) (60 × 24 /x)$ min Here, x = 62
Therefore, required result = $(720/11 - 62) (60 × 24 /62)$ min
= $38/11 × 720/31 $min = 80 $80/341$ min gain (gain as sign is positive)

Answer: Option A. -> 10 $10/143$ min (gain)
Answer: (a)
Required result = $(720/11 - x) (60 × 24 /x) $min Here, x = 65
Therefore, required result = $(720/11 - 65) (60 × 24 / 65)$ min
= $5/11 × 288/13$ min = 10 $10/143$ min gain

Answer: Option B. -> 56 $8/77$ min (gain)
Answer: (b)
Method I
As we know that in a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 min.
To be together again, the minute hand must gain 60 min over the hour hand.
60 min are gained in $(60/55 × 60) min = 65 5/11 min$
But they are together after 63 min.
Therefore, gain in 63 min =$ (65 5/11 - 63) = 2 5/11 min = 27/11 min$
Gain in 24 h = $(27/11 × 60 × 24/63) min = 4320/77 min = 56 8/77 min$
As result is positive, therefore clock gains 56 $8/77$ min.
Method II
In the given question, x = 63 min
According to the formula,
Required result = $(720/11 - x) (60 × 24 /x) min = (720/11 - 63) (60 × 24 /63 ) min$
= $27/11 × 60 × 8 /21 = 56 8/77 $min (gain as sign in positive)

Answer: Option D. -> 2 p.m. on Wednesday
Answer: (d)
Time from 12 p.m. on Monday to 2 p.m.
on the following Monday = 7 days 2 hours = 170 hours.
Therefore, the watch gains $(2 + 4 4/5) min. or 34/5 min.$ in 170 hrs.
now, 34/5 min. are gained in 170 hrs.
2 min. are gained in $(170 × 5/34 × 2) hrs = 50 hrs.$
Therefore, Watch is correct 2 days 2 hrs. after 12 p.m. on Monday
i.e. it will be correct at 2 p.m. on Wednesday