Important Questions Regarding Clock

Solution: We know that angle traced by hour hand in 12 hrs. = 360°
From 7 to 1, there are 6 hours.
Angle traced by the hour hand in 6 hours =6*(360/12)=180°
Option B is the correct answer.

Solution: At 4 o’clock the hour hand is at 4 and has an angle of 30°*4=120°
An Hour hand travels 1/2° per minute In 20 minutes it will travel 20 *(1/2°) = 10°. Adding both we get 120° + 10° = 130°
Option D is the correct answer.

Solution: Given: H = 5 and A = 90, since 5 and 6 lies in the first half, a positive sign is considered.
T = 2/11 [H*30±A]
T = 2/11 [5*30+90]
T = 2/11 [240] = 480/11= 43( 7/11)
Option C is the correct answer.

Solution: At 5 ‘o’clock the hour hand is at 5 and hence has made 30° angle.
From 5 to 5.30 its will travel for 30 minutes with a speed of ½ ° Therefore the total distance travelled will be 30 minutes* 1/2 = 15°
The full angle made by the hour hand will be 150°+15° = 165°.
The minute hand at 5 o’clock is at 12, and hence the angle made is zero. In 30 minutes, it will travel a distance of 30 minutes with a speed of 6° per minute. Therefore the total distance travelled will be 30 minutes*6° = 180 °.
The angle between the minute and hour hand is 180 – 165 = 15
Option B is the correct answer.

Solution: The hands of clocks make a straight line of 180° about 22 times in 24 hours. Also, the hands coincide 22 times in 24 hours, the coincidence of the hands also forms a straight line. Hence, the total straight lines are 22+22 = 44.
Option C is the correct answer.